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geometric_algebra [2020/03/22 16:07]
pbk [Videos]
geometric_algebra [2020/04/23 04:09] (current)
pbk [Articles]
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   * [[https://​s2019.siggraph.org/​presentation/?​id=gensub_345&​sess=sess346|SIGGRAPH 2019]] (2019) - Los Angeles: [[https://​bivector.net/​PROJECTIVE_GEOMETRIC_ALGEBRA.pdf|Course notes for Geometric Algebra for Computer Graphics]] [[https://​arxiv.org/​pdf/​2002.04509|arXiv version]] - //Charles Gunn//.   * [[https://​s2019.siggraph.org/​presentation/?​id=gensub_345&​sess=sess346|SIGGRAPH 2019]] (2019) - Los Angeles: [[https://​bivector.net/​PROJECTIVE_GEOMETRIC_ALGEBRA.pdf|Course notes for Geometric Algebra for Computer Graphics]] [[https://​arxiv.org/​pdf/​2002.04509|arXiv version]] - //Charles Gunn//.
 +
 +  * [[http://​www.cgs-network.org/​cgi20|ENGAGE 2020]] (2020) - Empowering Novel Geometric Algebra for Graphics & Engineering Workshop, CGI 2020, Geneva (Switzerland).
 ==== Book companion ==== ==== Book companion ====
  
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   * [[http://​marctenbosch.com|marctenbosch.com]] - //Marc ten Bosch//.   * [[http://​marctenbosch.com|marctenbosch.com]] - //Marc ten Bosch//.
   * [[http://​www.gary-harper.com|Ripples in Space-Fabric]] - //Gary Harper//.   * [[http://​www.gary-harper.com|Ripples in Space-Fabric]] - //Gary Harper//.
 +  * [[http://​www.martinerikhorn.de|Martin Erik Horn]] - University of Applied Sciences Berlin-Brandenburg.
   * [[https://​sites.google.com/​site/​samsilvaunesp|Samuel da Silva]] - Universidade Estadual Paulista.   * [[https://​sites.google.com/​site/​samsilvaunesp|Samuel da Silva]] - Universidade Estadual Paulista.
   * [[http://​www.siue.edu/​~sstaple|George Stacey Staples]] - Department of Mathematics & Statistics, Southern Illinois University Edwardsville.   * [[http://​www.siue.edu/​~sstaple|George Stacey Staples]] - Department of Mathematics & Statistics, Southern Illinois University Edwardsville.
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   * [[http://​www.math.chalmers.se/​~rosenan|Andreas Rosén]] - Göteborgs Universitet,​ Chalmers Tekniska Högskola.   * [[http://​www.math.chalmers.se/​~rosenan|Andreas Rosén]] - Göteborgs Universitet,​ Chalmers Tekniska Högskola.
   * [[https://​www.zatlovac.eu|Václav Zatloukal]] - Department of Physics, Czech Technical University in Prague.   * [[https://​www.zatlovac.eu|Václav Zatloukal]] - Department of Physics, Czech Technical University in Prague.
 +  * [[http://​www-f1.ijs.si/​~pavsic|Matej Pavsic]] - Department of Theoretical Physics, Jožef Stefan Institute Slovenia.
 +  * [[https://​rastergraphics.wordpress.com|Rumbo Loxodromico]] - //Mauricio López//.
 ==== Other ==== ==== Other ====
   * [[http://​www.williamandlucyclifford.com|William and Lucy Clifford]], A Story of Two Lives   * [[http://​www.williamandlucyclifford.com|William and Lucy Clifford]], A Story of Two Lives
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   * [[https://​www.youtube.com/​playlist?​list=PLpzmRsG7u_gqaTo_vEseQ7U8KFvtiJY4K|Geometric Algebra]] playlist - //​Mathoma//​.   * [[https://​www.youtube.com/​playlist?​list=PLpzmRsG7u_gqaTo_vEseQ7U8KFvtiJY4K|Geometric Algebra]] playlist - //​Mathoma//​.
   * [[https://​www.youtube.com/​playlist?​list=PLQ6JJNfj9jD_H3kUopCXkvvGoZqzYOzsV|Geometric Algebra tutorial]] playlist - //Nick Okamoto//.   * [[https://​www.youtube.com/​playlist?​list=PLQ6JJNfj9jD_H3kUopCXkvvGoZqzYOzsV|Geometric Algebra tutorial]] playlist - //Nick Okamoto//.
 +  * [[https://​www.youtube.com/​watch?​v=-6F74TH1i_g&​list=PL6oNjS6Kc-nQmqvWjRzLYLk1WlMdFudJa|Exterior Algebra aka Grassmann Algebra]] playlist - //​Mathview//​.
   * [[https://​www.youtube.com/​playlist?​list=PLB8F2D70E034E9C29|Intro to differential forms]] playlist - //David Metzler//.   * [[https://​www.youtube.com/​playlist?​list=PLB8F2D70E034E9C29|Intro to differential forms]] playlist - //David Metzler//.
   * [[https://​www.youtube.com/​watch?​v=_AaOFCl2ihc|The Vector Algebra War]] - //​UniAdel//​.   * [[https://​www.youtube.com/​watch?​v=_AaOFCl2ihc|The Vector Algebra War]] - //​UniAdel//​.
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   * [[https://​www.youtube.com/​watch?​v=yG8YKw25f6Y|JMM2018:​ A Brief introduction to Clifford Algebras]] - //Johannes Familton//.   * [[https://​www.youtube.com/​watch?​v=yG8YKw25f6Y|JMM2018:​ A Brief introduction to Clifford Algebras]] - //Johannes Familton//.
   * [[https://​www.youtube.com/​watch?​v=eQjDN0JQ6-s|JuliaCon 2019: Geometric algebra in Julia with Grassmann.jl]] - //Michael Reed//.   * [[https://​www.youtube.com/​watch?​v=eQjDN0JQ6-s|JuliaCon 2019: Geometric algebra in Julia with Grassmann.jl]] - //Michael Reed//.
 +  * [[https://​skillsmatter.com/​skillscasts/​13986-geometric-algebra-in-fsharp|Geometric Algebra in F#]] - //Andrew Willshire//​.
   * [[https://​www.youtube.com/​watch?​v=tX4H_ctggYo|SIGGRAPH 2019: Geometric Algebra for Computer Graphics]] - //Charles Gunn// and //Steven De Keninck//.   * [[https://​www.youtube.com/​watch?​v=tX4H_ctggYo|SIGGRAPH 2019: Geometric Algebra for Computer Graphics]] - //Charles Gunn// and //Steven De Keninck//.
  
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   * [[http://​www.clucalc.info|CLUCalc]] - //Christian Perwass//, Kiel University.   * [[http://​www.clucalc.info|CLUCalc]] - //Christian Perwass//, Kiel University.
   * [[http://​www.cinderella.de/​tiki-index.php|Cinderella]] - The Interactive Geometry Software.   * [[http://​www.cinderella.de/​tiki-index.php|Cinderella]] - The Interactive Geometry Software.
-  * [[http://​www.gaalop.de|Gaalop]] - //Dietmar Hildenbrand//​. ​Geometric Algebra Algorithms Optimizer is a software to optimize geometric algebra files. +  * [[http://​www.gaalop.de|Gaalop]] - Geometric Algebra Algorithms Optimizer is a software to optimize geometric algebra files, //Dietmar Hildenbrand//​
-  * [[https://​sourceforge.net/​projects/​gaalet|Gaalet]] - //Florian Seybold//. Geometric Algebra Algorithms Expression Templates+  * [[https://​sourceforge.net/​projects/​gaalet|Gaalet]] - Geometric Algebra Algorithms Expression Templates, ​//Florian Seybold//​. 
-  * [[https://​sourceforge.net/​projects/​gaigen|Gaigen]] - //Daniel Fontijne//. Geometric Algebra Implementation Generator+  * [[https://​sourceforge.net/​projects/​gaigen|Gaigen]] - Geometric Algebra Implementation Generator, ​//Daniel Fontijne//​. 
-  * [[http://​glucat.sourceforge.net|GluCat]] - //Paul Leopardi//​. ​Library of template classes which model the universal Clifford algebras over the field of real numbers, with arbitrary dimension and arbitrary signature.+  * [[http://​glucat.sourceforge.net|GluCat]] - Library of template classes which model the universal Clifford algebras over the field of real numbers, with arbitrary dimension and arbitrary signature, //Paul Leopardi//.
   * [[https://​users.aalto.fi/​~ppuska/​mirror/​Lounesto/​CLICAL.htm|CLICAL]] - //Pertti Lounesto//, University of Helsinki.   * [[https://​users.aalto.fi/​~ppuska/​mirror/​Lounesto/​CLICAL.htm|CLICAL]] - //Pertti Lounesto//, University of Helsinki.
   * [[http://​versor.mat.ucsb.edu|Versor (libvsr)]] - //Pablo Colapinto//,​ UC Santa Barbara.   * [[http://​versor.mat.ucsb.edu|Versor (libvsr)]] - //Pablo Colapinto//,​ UC Santa Barbara.
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   * [[https://​github.com/​grondilu/​clifford|clifford:​ Geometric Algebra in Perl 6]] - //​grondilu//​.   * [[https://​github.com/​grondilu/​clifford|clifford:​ Geometric Algebra in Perl 6]] - //​grondilu//​.
   * [[https://​github.com/​martinbaker/​multivector|multivector]] - Code to use with FriCAS, //Martin Baker//.   * [[https://​github.com/​martinbaker/​multivector|multivector]] - Code to use with FriCAS, //Martin Baker//.
-  * [[http://​library.wolfram.com/​infocenter/​Conferences/​6951|Symbolic and Numeric Geometric Algebra]] Mathematica notebook ​//Terje Vold//.+  * [[http://​library.wolfram.com/​infocenter/​Conferences/​6951|Symbolic and Numeric Geometric Algebra]] Mathematica notebook//Terje Vold//.
   * [[http://​nklein.com/​software/​geoma|Geoma]] - //Patrick Stein//.   * [[http://​nklein.com/​software/​geoma|Geoma]] - //Patrick Stein//.
   * [[https://​github.com/​andrioni/​GeoAlg.jl|Geometric Algebra for Julia]] - //​Alessandro Andrioni//.   * [[https://​github.com/​andrioni/​GeoAlg.jl|Geometric Algebra for Julia]] - //​Alessandro Andrioni//.
   * [[https://​www.geogebra.org/​m/​qzDtMW2q|Geometric Algebra (Clifford Algebra)]] in GeoGebra - //Jim Smith//.   * [[https://​www.geogebra.org/​m/​qzDtMW2q|Geometric Algebra (Clifford Algebra)]] in GeoGebra - //Jim Smith//.
-  * [[http://​www.cs.uu.nl/​groups/​MG/​gallery/​CGAP|Conformal Geometric Algebra Package]] for the [[http://​www.cgal.org|Computational Geometry Algorithms Library (CGAL)]] ​//Chaïm Zonnenberg//​.+  * [[http://​www.cs.uu.nl/​groups/​MG/​gallery/​CGAP|Conformal Geometric Algebra Package]] for the [[http://​www.cgal.org|Computational Geometry Algorithms Library (CGAL)]]//Chaïm Zonnenberg//​.
   * [[https://​crypto.stanford.edu/​~blynn/​haskell/​ga.html|All Hail Geometric Algebra!]] - GA explorations in Haskell, //Ben Lynn//.   * [[https://​crypto.stanford.edu/​~blynn/​haskell/​ga.html|All Hail Geometric Algebra!]] - GA explorations in Haskell, //Ben Lynn//.
   * [[http://​blog.sigfpe.com/​2006/​08/​geometric-algebra-for-free_30.html|Geometric Algebra for Free!]] in Haskell - //Dan Piponi//.   * [[http://​blog.sigfpe.com/​2006/​08/​geometric-algebra-for-free_30.html|Geometric Algebra for Free!]] in Haskell - //Dan Piponi//.
   * [[http://​clifford-multivector-toolbox.sourceforge.net|Clifford Multivector Toolbox]] for MATLAB - //Steve Sangwine, Eckhard Hitzer//.   * [[http://​clifford-multivector-toolbox.sourceforge.net|Clifford Multivector Toolbox]] for MATLAB - //Steve Sangwine, Eckhard Hitzer//.
   * [[https://​github.com/​ga-explorer/​GMac|GMac]] and [[https://​gmac-guides.netlify.com|GMac Guides]] - Geometric Macro (.NET), //Ahmad Hosny Eid//.   * [[https://​github.com/​ga-explorer/​GMac|GMac]] and [[https://​gmac-guides.netlify.com|GMac Guides]] - Geometric Macro (.NET), //Ahmad Hosny Eid//.
-  * [[https://​github.com/​tingelst/​game|game]] - Geometric Algebra Multivector Estimation, //Lars Tingelstad//​. Framework for estimation of multivectors in geometric algebra ​with focus on the Euclidean and conformal model.+  * [[https://​github.com/​tingelst/​game|game]] - Geometric Algebra Multivector Estimation ​framework ​with focus on the Euclidean and conformal model, //Lars Tingelstad//​.
   * [[https://​github.com/​enkimute/​ganja.js|ganja]] - Geometric Algebra for javascript, //Steven De Keninck//.   * [[https://​github.com/​enkimute/​ganja.js|ganja]] - Geometric Algebra for javascript, //Steven De Keninck//.
   * [[https://​github.com/​jlaragonvera/​Geometric-Algebra|CGAlgebra]] - Mathematica package for the 5D Conformal Geometric Algebra, //Jose L. Aragon//.   * [[https://​github.com/​jlaragonvera/​Geometric-Algebra|CGAlgebra]] - Mathematica package for the 5D Conformal Geometric Algebra, //Jose L. Aragon//.
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   * [[https://​github.com/​reloZid/​algeosharp|AlgeoSharp]] - A class library for using conformal geometric algebra in C#, //​reloZid//​.   * [[https://​github.com/​reloZid/​algeosharp|AlgeoSharp]] - A class library for using conformal geometric algebra in C#, //​reloZid//​.
   * [[https://​github.com/​stephenathel/​gawxm|GAwxM]] - Geometric Algebra using wxMaxima, //Stephen Abbott//.   * [[https://​github.com/​stephenathel/​gawxm|GAwxM]] - Geometric Algebra using wxMaxima, //Stephen Abbott//.
-  * [[https://​github.com/​chakravala/​Grassmann.jl|Grassmann.jl]] - Grassmann-Clifford-Hestenes-Taylor differential geometric algebra of hyper-dual multivector forms Julia package, //Dream Scatter//.+  * [[https://​github.com/​chakravala/​Grassmann.jl|Grassmann.jl]] ​Julia package ​- Grassmann-Clifford-Hestenes-Taylor differential geometric algebra of hyper-dual multivector forms, //Dream Scatter//.
   * [[https://​github.com/​pygae|pygae]] - Pythonic Geometric Algebra Enthusiasts at GitHub.   * [[https://​github.com/​pygae|pygae]] - Pythonic Geometric Algebra Enthusiasts at GitHub.
-  * [[https://​www.jeremyong.com/​klein|Klein]] - An implementation of 3D Projective Geometric Algebra ​//Jeremy Ong//.+  * [[https://​www.jeremyong.com/​klein|Klein]] - An implementation of 3D Projective Geometric Algebra//Jeremy Ong//. 
 +  * [[http://​www.siue.edu/​~sstaple/​index_files/​research.html|CliffMath]] - Clifford algebra computations,​ including zeon, sym-Clifford,​ and idem-Clifford subalgebras,​ //George Stacey Staples//.
 ===== Articles ===== ===== Articles =====
   * [[http://​geocalc.clas.asu.edu/​pdf/​OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes//   * [[http://​geocalc.clas.asu.edu/​pdf/​OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes//
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 Recently suggested scheme of quantum computing uses g-qubit states as circular polarizations from the solution of Maxwell equations in terms of geometric algebra, along with clear definition of a complex plane as bivector in three dimensions. Here all the details of receiving the solution, and its polarization transformations are analyzed. The results can particularly be applied to the problems of quantum computing and quantum cryptography. The suggested formalism replaces conventional quantum mechanics states as objects constructed in complex vector Hilbert space framework by geometrically feasible framework of multivectors. Recently suggested scheme of quantum computing uses g-qubit states as circular polarizations from the solution of Maxwell equations in terms of geometric algebra, along with clear definition of a complex plane as bivector in three dimensions. Here all the details of receiving the solution, and its polarization transformations are analyzed. The results can particularly be applied to the problems of quantum computing and quantum cryptography. The suggested formalism replaces conventional quantum mechanics states as objects constructed in complex vector Hilbert space framework by geometrically feasible framework of multivectors.
  
-  * [[https://​arxiv.org/​ftp/​arxiv/​papers/​1807/1807.08603.pdf|State/​observable interactions using basic geometric algebra solutions of the Maxwell equation]] (2018) - //Alexander Soiguine//+  * [[https://​arxiv.org/​pdf/​1807.08603|State/​observable interactions using basic geometric algebra solutions of the Maxwell equation]] (2018) - //Alexander Soiguine//
 Maxwell equation in geometric algebra formalism with equally weighted basic solutions is subjected to continuously acting Clifford translation. The received states, operators acting on observables,​ are analyzed with different values of the Clifford translation time factor and through the observable measurement results. Maxwell equation in geometric algebra formalism with equally weighted basic solutions is subjected to continuously acting Clifford translation. The received states, operators acting on observables,​ are analyzed with different values of the Clifford translation time factor and through the observable measurement results.
  
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   * [[https://​pastel.archives-ouvertes.fr/​tel-02085820/​document|Algorithmic structure for geometric algebra operators and application to quadric surfaces]] (2018) - //Stephane Breuils//   * [[https://​pastel.archives-ouvertes.fr/​tel-02085820/​document|Algorithmic structure for geometric algebra operators and application to quadric surfaces]] (2018) - //Stephane Breuils//
 Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics problems. The Conformal Geometric Algebra includes circles, spheres, planes and lines as algebraic objects, and intersections between these objects are also algebraic objects. More complex objects such as conics, quadric surfaces can also be expressed and be manipulated using an extension of the conformal Geometric Algebra. However due to the high dimension of their representations in Geometric Algebra, implementations of Geometric Algebra that are currently available do not allow efficient realizations of these objects. In this thesis, we first present a Geometric Algebra implementation dedicated for both low and high dimensions. Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics problems. The Conformal Geometric Algebra includes circles, spheres, planes and lines as algebraic objects, and intersections between these objects are also algebraic objects. More complex objects such as conics, quadric surfaces can also be expressed and be manipulated using an extension of the conformal Geometric Algebra. However due to the high dimension of their representations in Geometric Algebra, implementations of Geometric Algebra that are currently available do not allow efficient realizations of these objects. In this thesis, we first present a Geometric Algebra implementation dedicated for both low and high dimensions.
 +
 +  * [[https://​arxiv.org/​pdf/​1809.09706|Notes on Plucker'​s relations in Geometric Algebra]] (2018) - //Garret Sobczyk//
 +Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up utilizing using many different languages of higher mathematics,​ such as multilinear and tensor algebra, matroid theory, and Lie groups and Lie algebras. Here we explore the basic idea of the Plucker relations in Clifford'​s geometric algebra. We discover that the Plucker Relations can be fully characterized in terms of the geometric product. ​
  
   * [[https://​arxiv.org/​pdf/​1908.08110.pdf|On the Clifford Algebraic Description of the Geometry of a 3D Euclidean Space]] (2019) - //Jaime Vaz, Stephen Mann//   * [[https://​arxiv.org/​pdf/​1908.08110.pdf|On the Clifford Algebraic Description of the Geometry of a 3D Euclidean Space]] (2019) - //Jaime Vaz, Stephen Mann//
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 In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions,​ tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called B-projection functions. Broadly speaking, a B-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras. In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions,​ tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called B-projection functions. Broadly speaking, a B-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras.
  
-   * [[https://​arxiv.org/​pdf/​1901.05873.pdf|Projective geometric algebra: A new framework for doing euclidean geometry]] (2019) - //Charles G. Gunn//+  * [[https://​arxiv.org/​pdf/​1903.02444|Efficient representation and manipulation of quadratic surfaces using Geometric Algebras]] (2019) - //Stéphane Breuils, Vincent Nozick, Laurent Fuchs, Akihiro Sugimoto//​ 
 +Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these frameworks support all the operations required to completely handle these surfaces. Some frameworks do not allow the construction of quadratic surfaces from control points when others do not allow to transform these quadratic surfaces. However , if we consider all the frameworks together, then all the required operations over quadratic are covered. This paper presents a unification of these frameworks that enables to represent any quadratic surfaces either using control points or from the coefficients of its implicit form. The proposed approach also allows to transform any quadratic surfaces and to compute their intersection and to easily extract some geometric properties.  
 + 
 +  ​* [[https://​arxiv.org/​pdf/​1901.05873.pdf|Projective geometric algebra: A new framework for doing euclidean geometry]] (2019) - //Charles G. Gunn//
 A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet operations; compact, polymorphic syntax for euclidean formulas and constructions;​ a single intuitive sandwich form for isometries; native support for automatic differentiation;​ and tight integration of kinematics and rigid body mechanics. Inclusion of vector, quaternion, dual quaternion, and exterior algebras as sub-algebras simplifies the learning curve and transition path for experienced practitioners. On the practical side, it can be efficiently implemented,​ while its rich syntax enhances programming productivity. A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet operations; compact, polymorphic syntax for euclidean formulas and constructions;​ a single intuitive sandwich form for isometries; native support for automatic differentiation;​ and tight integration of kinematics and rigid body mechanics. Inclusion of vector, quaternion, dual quaternion, and exterior algebras as sub-algebras simplifies the learning curve and transition path for experienced practitioners. On the practical side, it can be efficiently implemented,​ while its rich syntax enhances programming productivity.
 +
 +  * [[https://​arxiv.org/​pdf/​1909.02408|A Low-Memory Time-Efficient Implementation of Outermorphisms for Higher-Dimensional Geometric Algebras]] (2019) - //Ahmad Hosny Eid//
 +Many important mathematical formulations in GA can be expressed as outermorphisms such as versor products, linear projection operators, and mapping between related coordinate frames. (...) This work attempts to shed some light on the problem of optimizing software implementations of outermorphisms for practical prototyping applications using geometric algebra. The approach we propose here for implementing outermorphisms requires orders of magnitude less memory compared to other common approaches, while being comparable in time performance,​ especially for high-dimensional geometric algebras.
 +
 +  * [[http://​downloads.hindawi.com/​journals/​cin/​2019/​9374802.pdf|Evaluating a Semi-Autonomous Brain-Computer Interface Based on Conformal Geometric Algebra and Artificial Vision]] (2019) - //Mauricio Ramirez-Moreno,​ David Gutiérrez//​
 +We evaluate a semi-autonomous brain-computer interface (BCI) for manipulation tasks. In such system, the user controls a robotic arm through motor imagery commands. (...) We take a semi-autonomous approach based on a conformal geometric algebra model that solves the inverse kinematics of the robot on the fly, then the user only has to decide on the start of the movement and the final position of the effector (goal-selection approach). Under these conditions, we implemented pick-and-place tasks with a disk as an item and two target areas placed on the table at arbitrary positions.
 +
 +  * [[https://​arxiv.org/​pdf/​1912.11198|Geometric Obstructions on Gravity]] (2019) - //Yuri Martins, Rodney Biezuner//
 +These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author'​s paper. (...) We present obstructions to realize gravity, modeled by the tetradic Einstein-Hilbert-Palatini (EHP) action functional, in a general geometric setting.
 +
 +  * [[https://​vixra.org/​pdf/​1911.0127v1.pdf|Robust Quaternion Estimation with Geometric Algebra]] (2019) - //Mauricio C. Lopez//
 +Robust methods for finding the best rotation aligning two sets of corresponding vectors are formulated in the linear algebra framework, using tools like the SVD for polar decomposition or QR for finding eigenvectors. Those are well established numerical algorithms which on the other hand are iterative and computationally expensive. Recently, closed form solutions has been proposed in the quaternion’s framework, those methods are fast but they have singularities i.e., they completely fail on certain input data. In this paper we propose a robust attitude estimator based on a formulation of the problem in Geometric Algebra. We find the optimal eigen-quaternion in closed form with high accuracy and with competitive performance respect to the fastest methods reported in literature.
 +
 +  * [[https://​arxiv.org/​pdf/​1911.07145|Geometric Manifolds Part I: The Directional Derivative of Scalar, Vector, Multivector,​ and Tensor Fields]] (2020) - //Joseph C. Schindler//
 +This is the first entry in a planned series aiming to establish a modified, and simpler, formalism for studying the geometry of smooth manifolds with a metric, while remaining close to standard textbook treatments in terms of notation and concepts. The key step is extending the tangent space at each point from a vector space to a geometric algebra, which is a linear space incorporating vectors with dot and wedge multiplication,​ and extending the affine connection to a directional derivative acting naturally on fields of multivectors (elements of the geometric algebra). (...) The theory that results from this extension is simpler and more powerful than either differential forms or tensor methods, in a number of ways.
 +
 +  * [[https://​arxiv.org/​pdf/​2002.11313|Computational Aspects of Geometric Algebra Products of Two Homogeneous Multivectors]] (2020) - //Stephane Breuils, Vincent Nozick, Akihiro Sugimoto//
 +Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it does not reflect the practical usage of geometric algebra. Indeed, in applications related to geometry, multivectors are likely to be full homogeneous,​ having their non-zero elements over a single grade. In this paper, we provide a complete computational study on geometric algebra products of two full homogeneous multivectors,​ that is, the outer, inner, and geometric products of two full homogeneous multivectors. We show tight bounds on the number of the arithmetic operations required for these products.
 +
 +  * [[https://​arxiv.org/​pdf/​2001.00656|Two-State Quantum Systems Revisited: A Geometric Algebra Approach]] (2020) - //Pedro Amao, Hernán Castillo//
 +We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions G3. In this description,​ both the quantum states and Hermitian operators are written as elements of G3. By writing the quantum states as elements of the minimal left ideals of this algebra, we compute the energy eigenvalues and eigenvectors for the Hamiltonian of an arbitrary two-state system. The geometric interpretation of the Hermitian operators enables us to introduce an algebraic method to diagonalize these operators in GA. We then use this approach to revisit the problem of a spin-1/2 particle interacting with an external arbitrary constant magnetic field, obtaining the same results as in the conventional theory. However, GA reveals the underlying geometry of these systems, which reduces to the Larmor precession in an arbitrary plane of G3.
 +
 +  * [[https://​arxiv.org/​abs/​2003.07159|Periodic Table of Geometric Numbers]] (2020) - //Garret Sobczyk//
 +Perhaps the most significant,​ if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Elementary Particles in Physics. A comparable achievement in mathematics is the Periodic Table of Geometric Numbers discussed here. In 1878 William Kingdon Clifford discovered the defining rules for what he called geometric algebras. We show how these algebras, and their coordinate isomorphic geometric matrix algebras, fall into a natural periodic table, sidelining the superfluous definitions based upon tensor algebras and quadratic forms.
 +
 +  * [[https://​arxiv.org/​pdf/​2002.05993|Projective Geometric Algebra as a Subalgebra of Conformal Geometric Algebra]] (2020) - //Jaroslav Hrdina, Ales Navrat, Petr Vasik, Dietmar Hildenbrand//​
 +First we introduce briefly the frameworks of CGA and PGA for doing Euclidean geometry and we summarise basic formulas. In the next section, we show that there are actually two naturally related copies of PGA in CGA. After an identification of the two copies, the duality in PGA is obtained in terms of CGA operations. This implies directly the correspondence between flat objects and versors for Euclidean transformations in CGA and the objects and versors in PGA.
 +
 +  * [[https://​arxiv.org/​pdf/​2004.06655|Dimensional scaffolding of electromagnetism using geometric algebra]] (2020) - //Xabier Prado Orbán, Jorge Mira//
 +Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities, the electric field E and the scalar and vector potentials get a geometric interpretation in spacetime diagrams. The geometric vector derivative applied to these magnitudes yields simple expressions leading to concepts like displacement current, continuity and gauge or retarded time, with a clear geometric meaning. As the geometric vector derivative is invertible, we introduce simple Green'​s functions and, with this, it is possible to obtain retarded Liénard-Wiechert potentials propagating naturally at the speed of light. In two dimensions, these magnitudes become more complex, and a magnetic field B appears as a pseudoscalar which was absent in the one-dimensional world. The laws of induction reflect the relations between E and B, and it is possible to arrive to the concepts of capacitor, electric circuit and Poynting vector, explaining the flow of energy. The solutions to the wave equations in this two-dimensional scenario uncover now the propagation of physical effects at the speed of light. (...) Electromagnetic waves propagating entirely at the speed of light can thus be viewed as a consequence of living in a world with an odd number of spatial dimensions. Finally, in the real three-dimensional world the same set of simple multivector differential expressions encode the fundamental laws and concepts of electromagnetism.
  
 ===== Books ===== ===== Books =====
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 | [[https://​archive.org/​details/​geometricalgebra033556mbp|{{:​ga:​geometric_algebra-artin_ip.jpg?​100}}]] ​                                     | **Geometric Algebra (1957)**\\ //Emil Artin//\\ Exposition is centered on the foundations of affine geometry, the geometry of quadratic forms, and the structure of the general linear group. Context is broadened by the inclusion of projective and symplectic geometry and the structure of symplectic and orthogonal groups. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | | [[https://​archive.org/​details/​geometricalgebra033556mbp|{{:​ga:​geometric_algebra-artin_ip.jpg?​100}}]] ​                                     | **Geometric Algebra (1957)**\\ //Emil Artin//\\ Exposition is centered on the foundations of affine geometry, the geometry of quadratic forms, and the structure of the general linear group. Context is broadened by the inclusion of projective and symplectic geometry and the structure of symplectic and orthogonal groups. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |
 | [[https://​archive.org/​details/​cliffordnumberss00ries|{{:​ga:​clifford_numbers_and_spinors-riesz.jpg?​100}}]] ​                                | **Clifford Numbers and Spinors (1958)**\\ //Marcel Riesz//\\ The presentation of the theory of Clifford numbers and spinors given here has grown out of thirteen lectures delivered at the Institute for Fluid Dynamics and Applied Mathematics of the University of Maryland. The work is divided into six chapters which, for the convenience of those readers who are only interested in certain parts of the material treated, are largely independent of each other. This arrangement has, of course, certain disadvantages such as repetitions and over-lappings. ​                                                                                                                                                                                                                                                                                                                                                                                                                                      | | [[https://​archive.org/​details/​cliffordnumberss00ries|{{:​ga:​clifford_numbers_and_spinors-riesz.jpg?​100}}]] ​                                | **Clifford Numbers and Spinors (1958)**\\ //Marcel Riesz//\\ The presentation of the theory of Clifford numbers and spinors given here has grown out of thirteen lectures delivered at the Institute for Fluid Dynamics and Applied Mathematics of the University of Maryland. The work is divided into six chapters which, for the convenience of those readers who are only interested in certain parts of the material treated, are largely independent of each other. This arrangement has, of course, certain disadvantages such as repetitions and over-lappings. ​                                                                                                                                                                                                                                                                                                                                                                                                                                      |
-| [[https://​archive.org/​details/​ElementaryDifferentialGeometry|{{:​ga:​elementary_differential_geometry-oneill.jpg?​100}}]] ​                   | **Elementary Differential Geometry (1966)**\\ //Barrett O'​Neill//​\\ The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives,​ Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates,​ and integration and orientation. ​ |+| [[https://​archive.org/​details/​ElementaryDifferentialGeometry|{{:​ga:​elementary_differential_geometry-oneill.jpg?​100}}]] | **Elementary Differential Geometry (1966)**\\ //Barrett O'​Neill//​\\ The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives,​ Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates,​ and integration and orientation.  | 
 +| [[https://​www.cambridge.org/​core/​books/​topological-geometry/​AAEBEBC695CF4A98242A74EA2C59E212|{{:​ga:​topological_geometry-porteous.jpg?​100}}]] | **Topological Geometry, 2nd Edition (1981)**\\ //Ian R. Porteous//​\\ The earlier chapters of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford'​s geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological spaces and of continuous and differentiable maps that leads up to the definitions of smooth manifolds and their tangent spaces and of Lie groups and Lie algebras. The calculus is presented as far as possible in basis free form to emphasize its geometrical flavor and its linear algebra content. In this second edition Dr. Porteous has taken the opportunity to add a chapter on triality which extends earlier work on the Spin groups in the chapter on Clifford algebras. The details include a number of important transitive group actions and a description of one of the exceptional Lie groups, the group G2.  |
  
 ==== Modern ==== ==== Modern ====
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-| [[https://​www.amazon.com/​Space-Time-Algebra-David-Hestenes/​dp/​3319184121|{{:​ga:​space-time_algebra-hestenes.jpg?​650}}]] ​                                                                                 | **Space-Time Algebra, 2nd Ed (2015)**\\ //David Hestenes//​\\ This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions,​ tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | +| [[https://​www.amazon.com/​Space-Time-Algebra-David-Hestenes/​dp/​3319184121|{{:​ga:​space-time_algebra-hestenes.jpg?​650}}]] | **Space-Time Algebra, 2nd Ed (2015)**\\ //David Hestenes//​\\ This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions,​ tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | 
-| [[https://​www.amazon.com/​Foundations-Classical-Mechanics-Fundamental-Theories/​dp/​0792355148|{{:​ga:​new_foundations_for_classical_mechanics-hestenes.jpg?​100}}]] ​                                         | **New Foundations for Classical Mechanics, 2nd Ed (1999)**\\ //David Hestenes//​\\ This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. ​                                                                                                                                                                                                                                                                                | +| [[https://​www.amazon.com/​Foundations-Classical-Mechanics-Fundamental-Theories/​dp/​0792355148|{{:​ga:​new_foundations_for_classical_mechanics-hestenes.jpg?​100}}]] | **New Foundations for Classical Mechanics, 2nd Ed (1999)**\\ //David Hestenes//​\\ This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. ​                                                                                                                                                                                                                                                                                | 
-| [[https://​www.amazon.com/​Clifford-Algebra-Geometric-Calculus-Mathematics/​dp/​9027725616|{{:​ga:​clifford_algebra_to_geometric_calculus-hestenes_sobczyk.jpg?​100}}]] ​                                       | **Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (1984)**\\ //David Hestenes, Garret Sobczyk//\\ Matrix algebra has been called "the arithmetic of higher mathematics"​ [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated,​ and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called '​Clifford Algebra',​ though we prefer the name '​Geometric Algebm'​ suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications,​ so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably,​ so they provide several different mathematical representations for individual geometrical or physical ideas. ​                                                           | +| [[https://​www.amazon.com/​Clifford-Algebra-Geometric-Calculus-Mathematics/​dp/​9027725616|{{:​ga:​clifford_algebra_to_geometric_calculus-hestenes_sobczyk.jpg?​100}}]] | **Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (1984)**\\ //David Hestenes, Garret Sobczyk//\\ Matrix algebra has been called "the arithmetic of higher mathematics"​ [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated,​ and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called '​Clifford Algebra',​ though we prefer the name '​Geometric Algebm'​ suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications,​ so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably,​ so they provide several different mathematical representations for individual geometrical or physical ideas. ​                                                           | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Physicists-Chris-Doran/​dp/​0521480221|{{:​ga:​geometric_algebra_for_physicists-doran_lasenby.jpg?​100}}]] ​                                                       | **Geometric Algebra for Physicists (2003)**\\ //Chris Doran, Anthony Lasenby//\\ This book is a complete guide to the current state of geometric algebra with early chapters providing a self-contained introduction. Topics range from new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors, the structure of the Lie groups, non-Euclidean geometry, quantum entanglement,​ and gauge theories. Applications such as black holes and cosmic strings are also explored. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | +| [[https://​www.amazon.com/​Geometric-Algebra-Physicists-Chris-Doran/​dp/​0521480221|{{:​ga:​geometric_algebra_for_physicists-doran_lasenby.jpg?​100}}]] | **Geometric Algebra for Physicists (2003)**\\ //Chris Doran, Anthony Lasenby//\\ This book is a complete guide to the current state of geometric algebra with early chapters providing a self-contained introduction. Topics range from new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors, the structure of the Lie groups, non-Euclidean geometry, quantum entanglement,​ and gauge theories. Applications such as black holes and cosmic strings are also explored. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Dover-Books-Mathematics/​dp/​0486801551|{{:​ga:​geometric_algebra-artin.jpg?​100}}]] ​                                                                             | **Geometric Algebra (1957)**\\ //Emil Artin//\\ This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication,​ noting that "​mathematicians will find on many pages ample evidence of the author'​s ability to penetrate a subject and to present material in a particularly elegant manner." ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Geometric-Algebra-Dover-Books-Mathematics/​dp/​0486801551|{{:​ga:​geometric_algebra-artin.jpg?​100}}]] | **Geometric Algebra (1957)**\\ //Emil Artin//\\ This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication,​ noting that "​mathematicians will find on many pages ample evidence of the author'​s ability to penetrate a subject and to present material in a particularly elegant manner." ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​History-Vector-Analysis-Evolution-Mathematics/​dp/​0486679101|{{:​ga:​a_history_of_vector_analysis-crowe.jpg?​100}}]] ​                                                              ​| **A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1967)**\\ //Michael J. Crowe//\\ On October 16, 1843, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics,​ physics and engineering. Yet the Gibbs-Heaviside system won acceptance only after decades of debate and controversy in the latter half of the nineteenth century concerning which of the competing systems offered the greatest advantages for mathematical pedagogy and practice. ​                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​History-Vector-Analysis-Evolution-Mathematics/​dp/​0486679101|{{:​ga:​a_history_of_vector_analysis-crowe.jpg?​100}}]] | **A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1967)**\\ //Michael J. Crowe//\\ On October 16, 1843, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics,​ physics and engineering. Yet the Gibbs-Heaviside system won acceptance only after decades of debate and controversy in the latter half of the nineteenth century concerning which of the competing systems offered the greatest advantages for mathematical pedagogy and practice. ​                                                                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Theory-Spinors-Dover-Books-Mathematics/​dp/​0486640701|{{:​ga:​the_theory_of_spinors-cartan.jpg?​100}}]] ​                                                                           | **The Theory of Spinors (1981)**\\ //Elie Cartan//\\ The French mathematician Elie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections,​ and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | +| [[https://​www.amazon.com/​Theory-Spinors-Dover-Books-Mathematics/​dp/​0486640701|{{:​ga:​the_theory_of_spinors-cartan.jpg?​100}}]] | **The Theory of Spinors (1981)**\\ //Elie Cartan//\\ The French mathematician Elie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections,​ and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | 
-| [[https://​www.amazon.com/​Past-Future-Gra%C3%9Fmanns-Bicentennial-Conference/​dp/​3034604041|{{:​ga:​hermann_grassmann_from_past_to_future.jpg?​100}}]] ​                                                      ​| **From Past to Future: Graßmann'​s Work in Context: Graßmann Bicentennial Conference, September 2009 (2011)**\\ //​Birkhauser//​\\ On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877),​ an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann'​s hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | +| [[https://​www.amazon.com/​Past-Future-Gra%C3%9Fmanns-Bicentennial-Conference/​dp/​3034604041|{{:​ga:​hermann_grassmann_from_past_to_future.jpg?​100}}]] | **From Past to Future: Graßmann'​s Work in Context: Graßmann Bicentennial Conference, September 2009 (2011)**\\ //​Birkhauser//​\\ On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877),​ an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann'​s hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 
-| [[https://​www.amazon.com/​Grassmann-Algebra-Foundations-Exploring-Mathematica/​dp/​1479197637|{{:​ga:​grassmann_algebra_volume_1_foundations-browne.jpg?​100}}]] ​                                             | **Grassmann Algebra Volume 1: Foundations (2012)**\\ //John Browne//\\ Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, ... multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors,​ which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors:​ for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. ​ | +| [[https://​www.amazon.com/​Grassmann-Algebra-Foundations-Exploring-Mathematica/​dp/​1479197637|{{:​ga:​grassmann_algebra_volume_1_foundations-browne.jpg?​100}}]] | **Grassmann Algebra Volume 1: Foundations (2012)**\\ //John Browne//\\ Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, ... multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors,​ which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors:​ for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. ​ | 
-| [[https://​www.amazon.com/​Linear-Geometric-Algebra-Alan-Macdonald/​dp/​1453854932|{{:​ga:​linear_and_geometric_algebra-macdonald.jpg?​100}}]] ​                                                                ​| **Linear and Geometric Algebra (2011)**\\ //Alan Macdonald//​\\ This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics.Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more.Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields.The book can be used for self study by those comfortable with the theorem/​proof style of a mathematics text.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | +| [[https://​www.amazon.com/​Linear-Geometric-Algebra-Alan-Macdonald/​dp/​1453854932|{{:​ga:​linear_and_geometric_algebra-macdonald.jpg?​100}}]] | **Linear and Geometric Algebra (2011)**\\ //Alan Macdonald//​\\ This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics.Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more.Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields.The book can be used for self study by those comfortable with the theorem/​proof style of a mathematics text.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | 
-| [[https://​www.amazon.com/​Vector-Geometric-Calculus-Alan-Macdonald/​dp/​1480132454|{{:​ga:​vector_and_geometric_calculus-macdonald.jpg?​100}}]] ​                                                              ​| **Vector and Geometric Calculus (2012)**\\ //Alan Macdonald//​\\ This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. The book is a sequel to the text Linear and Geometric Algebra by the same author. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | +| [[https://​www.amazon.com/​Vector-Geometric-Calculus-Alan-Macdonald/​dp/​1480132454|{{:​ga:​vector_and_geometric_calculus-macdonald.jpg?​100}}]] | **Vector and Geometric Calculus (2012)**\\ //Alan Macdonald//​\\ This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. The book is a sequel to the text Linear and Geometric Algebra by the same author. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 
-| [[https://​www.amazon.com/​Understanding-Geometric-Algebra-Hamilton-Grassmann/​dp/​1482259508|{{:​ga:​understanding_geometric_algebra-kanatani.jpg?​100}}]] ​                                                   | **Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics (2015)**\\ //Kenichi Kanatani//​\\ Introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer graphics and computer vision. Unlike similar texts, this book first gives separate descriptions of the various algebras and then explains how they are combined to define the field of geometric algebra. It starts with 3D Euclidean geometry along with discussions as to how the descriptions of geometry could be altered if using a non-orthogonal (oblique) coordinate system. The text focuses on Hamilton’s quaternion algebra, Grassmann’s outer product algebra, and Clifford algebra that underlies the mathematical structure of geometric algebra. It also presents points and lines in 3D as objects in 4D in the projective geometry framework; explores conformal geometry in 5D, which is the main ingredient of geometric algebra; and delves into the mathematical analysis of camera imaging geometry involving circles and spheres. ​                                                                                                                                                                          | +| [[https://​www.amazon.com/​Understanding-Geometric-Algebra-Hamilton-Grassmann/​dp/​1482259508|{{:​ga:​understanding_geometric_algebra-kanatani.jpg?​100}}]] | **Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics (2015)**\\ //Kenichi Kanatani//​\\ Introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer graphics and computer vision. Unlike similar texts, this book first gives separate descriptions of the various algebras and then explains how they are combined to define the field of geometric algebra. It starts with 3D Euclidean geometry along with discussions as to how the descriptions of geometry could be altered if using a non-orthogonal (oblique) coordinate system. The text focuses on Hamilton’s quaternion algebra, Grassmann’s outer product algebra, and Clifford algebra that underlies the mathematical structure of geometric algebra. It also presents points and lines in 3D as objects in 4D in the projective geometry framework; explores conformal geometry in 5D, which is the main ingredient of geometric algebra; and delves into the mathematical analysis of camera imaging geometry involving circles and spheres. ​                                                                                                                                                                          | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Computer-Science-Revised/​dp/​0123749425|{{:​ga:​geometric_algebra_for_computer_science-dorst.jpg?​100}}]] ​                                                       | **Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (2007)**\\ //Leo Dorst, ​ Daniel Fontijne, Stephen Mann//\\ Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates,​ however, which can make many geometric programming tasks very specific and complex―often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations,​ it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective,​ and performance-enhancing way to represent the geometry of 3D objects in computer programs. ​                                                                                                                                                                                                                                                                                                                                                                                                                                            | +| [[https://​www.amazon.com/​Geometric-Algebra-Computer-Science-Revised/​dp/​0123749425|{{:​ga:​geometric_algebra_for_computer_science-dorst.jpg?​100}}]] | **Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (2007)**\\ //Leo Dorst, ​ Daniel Fontijne, Stephen Mann//\\ Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates,​ however, which can make many geometric programming tasks very specific and complex―often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations,​ it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective,​ and performance-enhancing way to represent the geometry of 3D objects in computer programs. ​                                                                                                                                                                                                                                                                                                                                                                                                                                            | 
-| [[https://​www.amazon.com/​New-Foundations-Mathematics-Geometric-Concept/​dp/​0817683844|{{:​ga:​new_foundations_in_mathematics-sobczyk.jpg?​100}}]] ​                                                          ​| **New Foundations in Mathematics:​ The Geometric Concept of Number (2013)**\\ //Garret Sobczyk//\\ The first book of its kind, New Foundations in Mathematics:​ The Geometric Concept of Number ​uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics,​ physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. ​                                                                                                                                                                                                                                                                                                                                                                                                           | +| [[https://​www.amazon.com/​New-Foundations-Mathematics-Geometric-Concept/​dp/​0817683844|{{:​ga:​new_foundations_in_mathematics-sobczyk.jpg?​100}}]] | **New Foundations in Mathematics:​ The Geometric Concept of Number (2013)**\\ //Garret Sobczyk//\\ The first book of its kind uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics,​ physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. ​                                                                                                                                                                                                                                                                                                                                                                                                           ​
-| [[https://​www.amazon.com/​Clifford-Algebra-Computational-Tool-Physicists/​dp/​0195098242|{{:​ga:​clifford_algebra_a_computational_tool_for_physicists-snygg.jpg?​100}}]] ​                                     | **Clifford Algebra: A Computational Tool for Physicists (1997)**\\ //John Snygg//\\ Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac'​s equation for the electron at the other. Clifford algebras have also become a virtual necessity in some areas of physics, and their usefulness is expanding in other areas, such as algebraic manipulations involving Dirac matrices in quantum thermodynamics;​ Kaluza-Klein theories and dimensional renormalization theories; and the formation of superstring theories. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | +| [[https://​www.amazon.com/​Clifford-Algebras-Classical-Cambridge-Mathematics/​dp/​0521551773|{{:​ga:​clifford_algebras_and_the_classical_groups-porteous.jpg?​100}}]] | **Clifford Algebras and the Classical Groups (1995)**\\ //Ian R. Porteous//​\\ This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author includes an exhaustive treatment of all the generalizations of the classical groups, as well as an excellent exposition of the classification of the conjugation anti-involution of the Clifford algebras and their complexifications. Toward the end of the book, the author introduces ideas from the theory of Lie groups and Lie algebras. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | 
-| [[https://​www.amazon.com/​Approach-Differential-Geometry-Cliffords-Geometric/​dp/​0817682821|{{:​ga:​a_new_approach_to_differential_geometry_using_clifford_geometric_algebra-snygg.jpg?​100}}]] ​             | **A New Approach to Differential Geometry using Clifford'​s Geometric Algebra (2012)**\\ //John Snygg//\\ Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford'​s Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | +| [[https://​www.amazon.com/​Clifford-Algebras-Analysis-Advanced-Mathematics/​dp/​0849384818|{{:​ga:​clifford_algebras_in_analysis-ryan.jpg?​100}}]] | **Clifford Algebras in Analysis and Related Topics (1995)**\\ //John Ryan//\\ Contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much more.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ​
-| [[https://​www.amazon.com/​Clifford-Algebras-Spinors-Mathematical-Society/​dp/​0521005515|{{:​ga:​clifford_algebras_and_spinors-lounesto.jpg?​100}}]] ​                                                         | **Clifford Algebras and Spinors, 2nd Ed (2001)**\\ //Pertti Lounesto//​\\ The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy'​s integral formula is generalized to higher dimensions. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                          | +| [[https://​www.amazon.com/​Clifford-Algebra-Computational-Tool-Physicists/​dp/​0195098242|{{:​ga:​clifford_algebra_a_computational_tool_for_physicists-snygg.jpg?​100}}]] | **Clifford Algebra: A Computational Tool for Physicists (1997)**\\ //John Snygg//\\ Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac'​s equation for the electron at the other. Clifford algebras have also become a virtual necessity in some areas of physics, and their usefulness is expanding in other areas, such as algebraic manipulations involving Dirac matrices in quantum thermodynamics;​ Kaluza-Klein theories and dimensional renormalization theories; and the formation of superstring theories. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | 
-| [[https://​www.amazon.com/​Mathematics-Computer-Graphics-Undergraduate-Science/​dp/​1447162897|{{:​ga:​mathematics_for_computer_graphics-vince.jpg?​100}}]] ​                                                   | **Mathematics for Computer Graphics, 4th Ed (2014)**\\ //John Vince//\\ Explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications,​ each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | +| [[https://​www.amazon.com/​Approach-Differential-Geometry-Cliffords-Geometric/​dp/​0817682821|{{:​ga:​a_new_approach_to_differential_geometry_using_clifford_geometric_algebra-snygg.jpg?​100}}]] | **A New Approach to Differential Geometry using Clifford'​s Geometric Algebra (2012)**\\ //John Snygg//\\ Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford'​s Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Algebraic-Computer-Animation/​dp/​1848823789|{{:​ga:​geometric_algebra_an_algebraic_system_for_computer_games_and_animation-vince.jpg?​100}}]] ​                   | **Geometric Algebra: An Algebraic System for Computer Games and Animation (2009)**\\ //John Vince//\\ Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations,​ tabulations,​ and easy-to-follow algebraic proofs. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Clifford-Algebras-Spinors-Mathematical-Society/​dp/​0521005515|{{:​ga:​clifford_algebras_and_spinors-lounesto.jpg?​100}}]] | **Clifford Algebras and Spinors, 2nd Ed (2001)**\\ //Pertti Lounesto//​\\ The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy'​s integral formula is generalized to higher dimensions. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 
-| [[https://​www.amazon.com/​Differential-Forms-Electromagnetics-Ismo-Lindell/​dp/​0471648019|{{:​ga:​differential_forms_in_electromagnetics-lindell.jpg?​100}}]] ​                                               | **Differential Forms in Electromagnetics (2004)**\\ //Ismo V. Lindell//\\ An introduction to multivectors,​ dyadics, and differential forms for electrical engineers. While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. ​ (...) Lindell simplifies the notation and adds memory aids in order to ease the reader'​s leap from Gibbsian analysis to differential forms, and provides the algebraic tools corresponding to the dyadics of Gibbsian analysis that have long been missing from the formalism. He introduces the reader to basic EM theory and wave equations for the electromagnetic two-forms, discusses the derivation of useful identities, and explains novel ways of treating problems in general linear (bi-anisotropic) media. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Mathematics-Computer-Graphics-Undergraduate-Science/​dp/​1447162897|{{:​ga:​mathematics_for_computer_graphics-vince.jpg?​100}}]] | **Mathematics for Computer Graphics, 4th Ed (2014)**\\ //John Vince//\\ Explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications,​ each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | 
-| [[https://​www.amazon.com/​Understanding-Geometric-Algebra-Electromagnetic-Theory/​dp/​0470941634|{{:​ga:​understanding_geometric_algebra_for_electromagnetic_theory-arthur.jpg?​100}}]] ​                      ​| **Understanding Geometric Algebra for Electromagnetic Theory (2011)**\\ //John W. Arthur//\\ This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. ​                                                                                                                                                                                                                                                                                                                                                 | +| [[https://​www.amazon.com/​Geometric-Algebra-Algebraic-Computer-Animation/​dp/​1848823789|{{:​ga:​geometric_algebra_an_algebraic_system_for_computer_games_and_animation-vince.jpg?​100}}]] | **Geometric Algebra: An Algebraic System for Computer Games and Animation (2009)**\\ //John Vince//\\ Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations,​ tabulations,​ and easy-to-follow algebraic proofs. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Geometric-Applications-Engineering-Geometry-Computing/​dp/​354089067X|{{:​ga:​geometric_algebra_with_applications_in_engineering-perwass.jpg?​100}}]] ​                              ​| **Geometric Algebra with Applications in Engineering (2008)**\\ //Christian Perwass//\\ The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations,​ the representation of geometric constraints,​ and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations,​ a generalized camera model, and pose estimation. ​                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Differential-Forms-Electromagnetics-Ismo-Lindell/​dp/​0471648019|{{:​ga:​differential_forms_in_electromagnetics-lindell.jpg?​100}}]] | **Differential Forms in Electromagnetics (2004)**\\ //Ismo V. Lindell//\\ An introduction to multivectors,​ dyadics, and differential forms for electrical engineers. While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. ​ (...) Lindell simplifies the notation and adds memory aids in order to ease the reader'​s leap from Gibbsian analysis to differential forms, and provides the algebraic tools corresponding to the dyadics of Gibbsian analysis that have long been missing from the formalism. He introduces the reader to basic EM theory and wave equations for the electromagnetic two-forms, discusses the derivation of useful identities, and explains novel ways of treating problems in general linear (bi-anisotropic) media. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Foundations-Geometric-Algebra-Computing-Geometry/​dp/​3642317936|{{:​ga:​foundations_of_geometric_algebra_computing.jpg?​100}}]] ​                                                   | **Foundations of Geometric Algebra Computing (2013)**\\ //Dietmar Hildenbrand//​\\ The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation,​ and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Understanding-Geometric-Algebra-Electromagnetic-Theory/​dp/​0470941634|{{:​ga:​understanding_geometric_algebra_for_electromagnetic_theory-arthur.jpg?​100}}]] | **Understanding Geometric Algebra for Electromagnetic Theory (2011)**\\ //John W. Arthur//\\ This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. ​                                                                                                                                                                                                                                                                                                                                                 | 
-| [[https://​www.amazon.com/​Classical-Geometric-Algebra-Graduate-Mathematics/​dp/​0821820192|{{:​ga:​classical_groups_and_geometric_algebra-grove.jpg?​100}}]] ​                                                 | **Classical Groups and Geometric Algebra (2001)**\\ //Larry C. Grove//​\\ ​ The classical groups have proved to be important in a wide variety of venues, ranging from physics to geometry and far beyond. In recent years, they have played a prominent role in the classification of the finite simple groups. This text provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | +| [[https://​www.amazon.com/​Geometric-Applications-Engineering-Geometry-Computing/​dp/​354089067X|{{:​ga:​geometric_algebra_with_applications_in_engineering-perwass.jpg?​100}}]] | **Geometric Algebra with Applications in Engineering (2008)**\\ //Christian Perwass//\\ The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations,​ the representation of geometric constraints,​ and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations,​ a generalized camera model, and pose estimation. ​                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Clifford-Geometric-Applications-Mathematics-Engineering/​dp/​0817638687|{{:​ga:​clifford_geometric_algebras-baylis.jpg?​100}}]] ​                                                    ​| **Clifford (Geometric) Algebras with Applications in Physics, Mathematics,​ and Engineering (1999)**\\ //William Baylis//\\ The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas­ sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating,​ and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "​geometric algebra"​ was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability,​ and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others. ​                                                                                                                                                                                                                                                                                                                                         | +| [[https://​www.amazon.com/​Foundations-Geometric-Algebra-Computing-Geometry/​dp/​3642317936|{{:​ga:​foundations_of_geometric_algebra_computing.jpg?​100}}]] | **Foundations of Geometric Algebra Computing (2013)**\\ //Dietmar Hildenbrand//​\\ The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation,​ and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Guide-Geometric-Algebra-Practice-Dorst/​dp/​0857298100|{{:​ga:​guide_to_geometric_algebra_in_practice-dorst_lasenby.jpg?​100}}]] ​                                                   | **Guide to Geometric Algebra in Practice (2011)**\\ //Leo Dorst, Joan Lasenby//\\ This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering,​ and the relationships between them. The topics covered range from powerful new theoretical developments,​ to successful applications,​ and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics;​ discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry. ​                                                                                                                                                                                                                                                                                                                  | +| [[https://​www.amazon.com/​Classical-Geometric-Algebra-Graduate-Mathematics/​dp/​0821820192|{{:​ga:​classical_groups_and_geometric_algebra-grove.jpg?​100}}]] | **Classical Groups and Geometric Algebra (2001)**\\ //Larry C. Grove//​\\ ​ The classical groups have proved to be important in a wide variety of venues, ranging from physics to geometry and far beyond. In recent years, they have played a prominent role in the classification of the finite simple groups. This text provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | 
-| [[https://​www.amazon.com/​Quaternions-Clifford-Algebras-Relativistic-Physics/​dp/​3764377909|{{:​ga:​quaternions_clifford_algebras_and_relativistic_physics-girard.jpg?​100}}]] ​                              ​| **Quaternions,​ Clifford Algebras and Relativistic Physics (2007)**\\ //Patrick R. Girard//\\ The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions,​ with applications mainly in special relativity, classical electromagnetism,​ and general relativity. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | +| [[https://​www.amazon.com/​Clifford-Geometric-Applications-Mathematics-Engineering/​dp/​0817638687|{{:​ga:​clifford_geometric_algebras-baylis.jpg?​100}}]] | **Clifford (Geometric) Algebras with Applications in Physics, Mathematics,​ and Engineering (1999)**\\ //William Baylis//\\ The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas­ sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating,​ and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "​geometric algebra"​ was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability,​ and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others. ​                                                                                                                                                                                                                                                                                                                                         | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Applications-Physics-Sabbata/​dp/​1584887729|{{:​ga:​geometric_algebra_and_applications_to_physics-sabbata.jpg?​100}}]] ​                                          ​| **Geometric Algebra and Applications to Physics (2006)**\\ //Venzo de Sabbata, Bidyut Kumar Datta//\\ Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors,​ and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | +| [[https://​www.amazon.com/​Guide-Geometric-Algebra-Practice-Dorst/​dp/​0857298100|{{:​ga:​guide_to_geometric_algebra_in_practice-dorst_lasenby.jpg?​100}}]] | **Guide to Geometric Algebra in Practice (2011)**\\ //Leo Dorst, Joan Lasenby//\\ This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering,​ and the relationships between them. The topics covered range from powerful new theoretical developments,​ to successful applications,​ and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics;​ discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry. ​                                                                                                                                                                                                                                                                                                                  | 
-| [[https://​www.amazon.com/​Geometric-Computing-Clifford-Algebras-Gerald/​dp/​3540411984|{{:​ga:​geometric_computing_with_clifford_algebras-sommer.jpg?​100}}]] ​                                                ​| **Geometric Computing with Clifford Algebras (2001)**\\ //Gerald Sommer//\\ This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "​mother algebra"​ in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition,​ computer vision, and robotics. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Quaternions-Clifford-Algebras-Relativistic-Physics/​dp/​3764377909|{{:​ga:​quaternions_clifford_algebras_and_relativistic_physics-girard.jpg?​100}}]] | **Quaternions,​ Clifford Algebras and Relativistic Physics (2007)**\\ //Patrick R. Girard//\\ The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions,​ with applications mainly in special relativity, classical electromagnetism,​ and general relativity. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | 
-| [[https://​www.amazon.com/​Lectures-Clifford-Geometric-Algebras-Applications/​dp/​0817632573|{{:​ga:​lectures_on_clifford_geometric_algebras_and_applications-ablamowicz_sobczyk.jpg?​100}}]] ​                 | **Lectures on Clifford (Geometric) Algebras and Applications (2004)**\\ //Rafal Ablamowicz, Garret Sobczyk//\\ The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird'​s-eye view of the discipline is presented by six of the world'​s leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics,​ physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | +| [[https://​www.amazon.com/​Geometric-Algebra-Applications-Physics-Sabbata/​dp/​1584887729|{{:​ga:​geometric_algebra_and_applications_to_physics-sabbata.jpg?​100}}]] | **Geometric Algebra and Applications to Physics (2006)**\\ //Venzo de Sabbata, Bidyut Kumar Datta//\\ Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors, multivectors,​ and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Applications-Science-Engineering/​dp/​0817641998|{{:​ga:​geometric_algebra_with_applications_in_science_and_engineering-bayro_sobczyk.jpg?​100}}]] ​               | **Geometric Algebra with Applications in Science and Engineering (2001)**\\ //Eduardo Bayro-Corrochano,​ Garret Sobczyk//\\ The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics,​ physics, computer science, and engineer­ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar­ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math­ematics and physics. ​                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Geometric-Computing-Clifford-Algebras-Gerald/​dp/​3540411984|{{:​ga:​geometric_computing_with_clifford_algebras-sommer.jpg?​100}}]] | **Geometric Computing with Clifford Algebras (2001)**\\ //Gerald Sommer//\\ This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "​mother algebra"​ in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition,​ computer vision, and robotics. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Geometries-Application-Kinematics/​dp/​3658076178|{{:​ga:​clifford_algebras_geometric_modelling_and_chain_geometries-klawitter.jpg?​100}}]] ​                      ​| **Clifford Algebras: Geometric Modelling and Chain Geometries with Application in Kinematics (2015)**\\ //Daniel Klawitter//​\\ After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | +| [[https://​www.amazon.com/​Lectures-Clifford-Geometric-Algebras-Applications/​dp/​0817632573|{{:​ga:​lectures_on_clifford_geometric_algebras_and_applications-ablamowicz_sobczyk.jpg?​100}}]] | **Lectures on Clifford (Geometric) Algebras and Applications (2004)**\\ //Rafal Ablamowicz, Garret Sobczyk//\\ The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird'​s-eye view of the discipline is presented by six of the world'​s leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics,​ physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 
-| [[https://​www.amazon.com/​Application-Geometric-Algebra-Electromagnetic-Scattering/​dp/​9811000883|{{:​ga:​application_of_geometric_algebra_to_electromagnetic_scattering-seagar.jpg?​100}}]] ​                ​| **Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique (2016)**\\ //Andrew Seagar//\\ This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green'​s functions, double integrals, vector calculus and the combined field integral equation (CFIE). ​ Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. ​                                                                                                                                                                                                                                                                                                                                                                   | +| [[https://​www.amazon.com/​Geometric-Algebra-Applications-Science-Engineering/​dp/​0817641998|{{:​ga:​geometric_algebra_with_applications_in_science_and_engineering-bayro_sobczyk.jpg?​100}}]] | **Geometric Algebra with Applications in Science and Engineering (2001)**\\ //Eduardo Bayro-Corrochano,​ Garret Sobczyk//\\ The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics,​ physics, computer science, and engineer­ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar­ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math­ematics and physics. ​                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Geometric-Algebra-Computing-Engineering-Computer/​dp/​1849961077|{{:​ga:​geometric_algebra_computing-bayro_scheuermann.jpg?​100}}]] ​                                                ​| **Geometric Algebra Computing: in Engineering and Computer Science (2010)**\\ //Eduardo Bayro-Corrochano,​ Gerik Scheuermann//​\\ This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | +| [[https://​www.amazon.com/​Clifford-Algebras-Geometries-Application-Kinematics/​dp/​3658076178|{{:​ga:​clifford_algebras_geometric_modelling_and_chain_geometries-klawitter.jpg?​100}}]] | **Clifford Algebras: Geometric Modelling and Chain Geometries with Application in Kinematics (2015)**\\ //Daniel Klawitter//​\\ After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 
-| [[https://​www.amazon.com/​Handbook-Geometric-Computing-Applications-Neuralcomputing/​dp/​3540205950|{{:​ga:​handbook_of_geometric_computing-bayro.jpg?​100}}]] ​                                               | **Handbook of Geometric Computing: Applications in Pattern Recognition,​ Computer Vision, Neuralcomputing,​ and Robotics (2005)**\\ //Eduardo Bayro-Corrochano//​\\ Many computer scientists, engineers, applied mathematicians,​ and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience,​ neural networks, image processing, pattern recognition,​ computer vision, uncertainty in geometric computations,​ conformal computational geometry, computer graphics and visualization,​ medical imagery, geometry and robotics, and reaching and motion planning. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Application-Geometric-Algebra-Electromagnetic-Scattering/​dp/​9811000883|{{:​ga:​application_of_geometric_algebra_to_electromagnetic_scattering-seagar.jpg?​100}}]] | **Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique (2016)**\\ //Andrew Seagar//\\ This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green'​s functions, double integrals, vector calculus and the combined field integral equation (CFIE). ​ Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. ​                                                                                                                                                                                                                                                                                                                                                                   | 
-| [[https://​www.amazon.com/​Applications-Geometric-Algebra-Computer-Engineering/​dp/​1461266068|{{:​ga:​applications_of_geometric_algebra_in_computer_science_and_engineering-dorst_doran_lasenby.jpg?​100}}]] ​ | **Applications of Geometric Algebra in Computer Science and Engineering (2002)**\\ //Leo Dorst, Chris Doran, Joan Lasenby//\\ Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering,​ physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |+| [[https://​www.amazon.com/​Geometric-Algebra-Computing-Engineering-Computer/​dp/​1849961077|{{:​ga:​geometric_algebra_computing-bayro_scheuermann.jpg?​100}}]] | **Geometric Algebra Computing: in Engineering and Computer Science (2010)**\\ //Eduardo Bayro-Corrochano,​ Gerik Scheuermann//​\\ This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 
 +| [[https://​www.amazon.com/​Handbook-Geometric-Computing-Applications-Neuralcomputing/​dp/​3540205950|{{:​ga:​handbook_of_geometric_computing-bayro.jpg?​100}}]] | **Handbook of Geometric Computing: Applications in Pattern Recognition,​ Computer Vision, Neuralcomputing,​ and Robotics (2005)**\\ //Eduardo Bayro-Corrochano//​\\ Many computer scientists, engineers, applied mathematicians,​ and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience,​ neural networks, image processing, pattern recognition,​ computer vision, uncertainty in geometric computations,​ conformal computational geometry, computer graphics and visualization,​ medical imagery, geometry and robotics, and reaching and motion planning. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 
 +| [[https://​www.amazon.com/​Applications-Geometric-Algebra-Computer-Engineering/​dp/​1461266068|{{:​ga:​applications_of_geometric_algebra_in_computer_science_and_engineering-dorst_doran_lasenby.jpg?​100}}]] | **Applications of Geometric Algebra in Computer Science and Engineering (2002)**\\ //Leo Dorst, Chris Doran, Joan Lasenby//\\ Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering,​ physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
 | [[https://​www.amazon.com/​Operator-Calculus-Graphs-Applications-Computer/​dp/​1848168764|{{:​ga:​operator_calculus_on_graphs-schott.jpg?​100}}]] ​                                                             | **Operator Calculus On Graphs: Theory and Applications in Computer Science (2012)**\\ //Rene Schott, G. Stacey Staples//\\ This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications,​ neural networks, electrical circuits, transportation,​ and the world wide web.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | | [[https://​www.amazon.com/​Operator-Calculus-Graphs-Applications-Computer/​dp/​1848168764|{{:​ga:​operator_calculus_on_graphs-schott.jpg?​100}}]] ​                                                             | **Operator Calculus On Graphs: Theory and Applications in Computer Science (2012)**\\ //Rene Schott, G. Stacey Staples//\\ This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications,​ neural networks, electrical circuits, transportation,​ and the world wide web.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
-| [[https://​www.amazon.com/​Multivectors-Clifford-Algebra-Electrodynamics-Jancewicz/​dp/​9971502909|{{:​ga:​multivectors_and_clifford_algebra_in_electrodynamics-jancewicz.jpg?​100}}]] ​                        ​| **Multivectors And Clifford Algebra In Electrodynamics (1989)**\\ //Bernard Jancewicz//​\\ Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space. Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. ​                                                                                                                                                                                                                                                                                                                                            | +| [[https://​www.amazon.com/​Multivectors-Clifford-Algebra-Electrodynamics-Jancewicz/​dp/​9971502909|{{:​ga:​multivectors_and_clifford_algebra_in_electrodynamics-jancewicz.jpg?​100}}]] | **Multivectors And Clifford Algebra In Electrodynamics (1989)**\\ //Bernard Jancewicz//​\\ Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space. Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. ​                                                                                                                                                                                                                                                                                                                                            | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Applications-Mathematical-Physics/​dp/​0817641823|{{:​ga:​clifford_algebras_and_their_applications_in_mathematical_physics_vol1-ablamowicz.jpg?​100}}]] ​          ​| **Clifford Algebras and Their Applications in Mathematical Physics, Vol.1: Algebra and Physics (2000)**\\ //Rafal Ablamowicz, Bertfried Fauser//\\ The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. ​                                                                                                                                                                                                                                                                                                                                                                                                                               | +| [[https://​www.amazon.com/​Clifford-Algebras-Applications-Mathematical-Physics/​dp/​0817641823|{{:​ga:​clifford_algebras_and_their_applications_in_mathematical_physics_vol1-ablamowicz.jpg?​100}}]] | **Clifford Algebras and Their Applications in Mathematical Physics, Vol.1: Algebra and Physics (2000)**\\ //Rafal Ablamowicz, Bertfried Fauser//\\ The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. ​                                                                                                                                                                                                                                                                                                                                                                                                                               | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Applications-Mathematical-Physics/​dp/​0817641831|{{:​ga:​clifford_algebras_and_their_applications_in_mathematical_physics_vol2-ablamowicz.jpg?​100}}]] ​          ​| **Clifford Algebras and Their Applications in Mathematical Physics, Vol. 2: Clifford Analysis (2000)**\\ //John Ryan, Wolfgang Sproessig//​\\ The second part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. from applications such as complex-distance potential theory, supersymmetry,​ and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications,​ to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and hypermonogenic functions and their derivatives,​ quaternionic Beltrami equations, Fourier theory under Mobius transformations,​ Cauchy-Reimann operators, and Cauchy type integrals. ​                                                                                                                                                                                                                                                                                                                                                                                                         | +| [[https://​www.amazon.com/​Clifford-Algebras-Applications-Mathematical-Physics/​dp/​0817641831|{{:​ga:​clifford_algebras_and_their_applications_in_mathematical_physics_vol2-ablamowicz.jpg?​100}}]] | **Clifford Algebras and Their Applications in Mathematical Physics, Vol. 2: Clifford Analysis (2000)**\\ //John Ryan, Wolfgang Sproessig//​\\ The second part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. from applications such as complex-distance potential theory, supersymmetry,​ and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications,​ to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and hypermonogenic functions and their derivatives,​ quaternionic Beltrami equations, Fourier theory under Mobius transformations,​ Cauchy-Reimann operators, and Cauchy type integrals. ​                                                                                                                                                                                                                                                                                                                                                                                                         | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Spinor-Structures-Applications/​dp/​9048145252|{{:​ga:​clifford_algebras_and_spinor_structures-ablamowicz.jpg?​100}}]] ​                                           | **Clifford Algebras and Spinor Structures (1995)**\\ //Rafal Ablamowicz, Pertti Lounesto//​\\ This volume is dedicated to the memory of Albert Crumeyrolle,​ who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle'​s own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle'​s research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | +| [[https://​www.amazon.com/​Clifford-Algebras-Spinor-Structures-Applications/​dp/​9048145252|{{:​ga:​clifford_algebras_and_spinor_structures-ablamowicz.jpg?​100}}]] | **Clifford Algebras and Spinor Structures (1995)**\\ //Rafal Ablamowicz, Pertti Lounesto//​\\ This volume is dedicated to the memory of Albert Crumeyrolle,​ who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle'​s own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle'​s research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | 
-| [[https://​www.amazon.com/​Quaternionic-Clifford-Calculus-Physicists-Engineers/​dp/​0471962007|{{:​ga:​quaternionic_and_clifford_calculus_for_physicists_and_engineers-gurlebeck.jpg?​100}}]] ​                 | **Quaternionic and Clifford Calculus for Physicists and Engineers (1998)**\\ //Klaus Gürlebeck, Wolfgang Sprössig//​\\ Quarternionic calculus covers a branch of mathematics which uses computational techniques to help solve problems from a wide variety of physical systems which are mathematically modelled in 3, 4 or more dimensions. Examples of the application areas include thermodynamics,​ hydrodynamics,​ geophysics and structural mechanics. Focusing on the Clifford algebra approach the authors have drawn together the research into quarternionic calculus to provide the non-expert or research student with an accessible introduction to the subject. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | +| [[https://​www.amazon.com/​Quaternionic-Clifford-Calculus-Physicists-Engineers/​dp/​0471962007|{{:​ga:​quaternionic_and_clifford_calculus_for_physicists_and_engineers-gurlebeck.jpg?​100}}]] | **Quaternionic and Clifford Calculus for Physicists and Engineers (1998)**\\ //Klaus Gürlebeck, Wolfgang Sprössig//​\\ Quarternionic calculus covers a branch of mathematics which uses computational techniques to help solve problems from a wide variety of physical systems which are mathematically modelled in 3, 4 or more dimensions. Examples of the application areas include thermodynamics,​ hydrodynamics,​ geophysics and structural mechanics. Focusing on the Clifford algebra approach the authors have drawn together the research into quarternionic calculus to provide the non-expert or research student with an accessible introduction to the subject. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Numeric-Symbolic-Computations/​dp/​1461581591|{{:​ga:​clifford_algebras_with_numeric_and_symbolic_computations-ablamowicz.jpg?​100}}]] ​                           | **Clifford Algebras with Numeric and Symbolic Computations (1996)**\\ //Rafal Ablamowicz, Joseph Parra, Pertti Lounesto//​\\ This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations,​ projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | +| [[https://​www.amazon.com/​Clifford-Algebras-Numeric-Symbolic-Computations/​dp/​1461581591|{{:​ga:​clifford_algebras_with_numeric_and_symbolic_computations-ablamowicz.jpg?​100}}]] | **Clifford Algebras with Numeric and Symbolic Computations (1996)**\\ //Rafal Ablamowicz, Joseph Parra, Pertti Lounesto//​\\ This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations,​ projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 
-| [[https://​www.amazon.com/​Quadratic-Mappings-Clifford-Algebras-Helmstetter/​dp/​3764386053|{{:​ga:​quadratic_mappings_and_clifford_algebras-helmstetter.jpg?​100}}]] ​                                         | **Quadratic Mappings and Clifford Algebras (2008)**\\ //Jacques Helmstetter,​ Artibano Micali//\\ After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Quadratic-Mappings-Clifford-Algebras-Helmstetter/​dp/​3764386053|{{:​ga:​quadratic_mappings_and_clifford_algebras-helmstetter.jpg?​100}}]] | **Quadratic Mappings and Clifford Algebras (2008)**\\ //Jacques Helmstetter,​ Artibano Micali//\\ After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Algebraic-Theory-Spinors-Clifford-Algebras/​dp/​3540570632|{{:​ga:​the_algebraic_theory_of_spinors_and_clifford_algebras-chevalley.jpg?​100}}]] ​                                    ​| **The Algebraic Theory of Spinors and Clifford Algebras (1997)**\\ //Claude Chevalley, Pierre Cartier, Catherine Chevalley//​\\ This volume is Vol. 2 of a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of spinors. Since its appearance in 1954, "The Algebraic Theory of Spinors"​ has been a very sought after reference. It presents the whole story of one subject in a concise and especially clear manner. The reprint of the book is supplemented by a series of lectures on Clifford Algebras given by the author in Japan at about the same time. Also included is a postface by J. P. Bourguignon describing the many uses of spinors in differential geometry developed by mathematical physicists from the 1970s to the present day. After its appearance the book was reviewed at length by Jean Dieudonné. His insightful criticism of the book is also made available to the reader in this volume. ​                                                                                                                                                                                                                                                                                                                                               | +| [[https://​www.amazon.com/​Algebraic-Theory-Spinors-Clifford-Algebras/​dp/​3540570632|{{:​ga:​the_algebraic_theory_of_spinors_and_clifford_algebras-chevalley.jpg?​100}}]] | **The Algebraic Theory of Spinors and Clifford Algebras (1997)**\\ //Claude Chevalley, Pierre Cartier, Catherine Chevalley//​\\ This volume is Vol. 2 of a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of spinors. Since its appearance in 1954, "The Algebraic Theory of Spinors"​ has been a very sought after reference. It presents the whole story of one subject in a concise and especially clear manner. The reprint of the book is supplemented by a series of lectures on Clifford Algebras given by the author in Japan at about the same time. Also included is a postface by J. P. Bourguignon describing the many uses of spinors in differential geometry developed by mathematical physicists from the 1970s to the present day. After its appearance the book was reviewed at length by Jean Dieudonné. His insightful criticism of the book is also made available to the reader in this volume. ​                                                                                                                                                                                                                                                                                                                                               | 
-| [[https://​www.amazon.com/​Faces-Maxwell-Dirac-Einstein-Equations/​dp/​3319276360|{{:​ga:​the_many_faces_of_maxwell_dirac_and_einstein_equations-rodrigues.jpg?​100}}]] ​                                       | **The Many Faces of Maxwell, Dirac and Einstein Equations: A Clifford Bundle Approach (2016)**\\ //Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira//​\\ This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | +| [[https://​www.amazon.com/​Faces-Maxwell-Dirac-Einstein-Equations/​dp/​3319276360|{{:​ga:​the_many_faces_of_maxwell_dirac_and_einstein_equations-rodrigues.jpg?​100}}]] | **The Many Faces of Maxwell, Dirac and Einstein Equations: A Clifford Bundle Approach (2016)**\\ //Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira//​\\ This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 
-| [[https://​www.amazon.com/​Clifford-Ergebnisse-Mathematik-Grenzgebiete-Mathematics/​dp/​364236215X|{{:​ga:​clifford_algebras_and_lie_theory-meinrenken.jpg?​100}}]] ​                                           | **Clifford Algebras and Lie Theory (2013)**\\ //Eckhard Meinrenken//​\\ This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation,​ culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré-Birkhoff-Witt theorem. This is followed by discussions of Weil algebras, Chern-Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations,​ and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. ​                                                                                                                    | +| [[https://​www.amazon.com/​Clifford-Ergebnisse-Mathematik-Grenzgebiete-Mathematics/​dp/​364236215X|{{:​ga:​clifford_algebras_and_lie_theory-meinrenken.jpg?​100}}]] | **Clifford Algebras and Lie Theory (2013)**\\ //Eckhard Meinrenken//​\\ This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation,​ culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré-Birkhoff-Witt theorem. This is followed by discussions of Weil algebras, Chern-Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations,​ and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. ​                                                                                                                    | 
-| [[https://​www.amazon.com/​Introduction-Clifford-Algebras-Spinors/​dp/​0198782926|{{:​ga:​an_introduction_to_clifford_algebras_and_spinors-vaz.jpg?​100}}]] ​                                                   | **An Introduction to Clifford Algebras and Spinors (2016)**\\ // Jayme Vaz, Roldao da Rocha//\\ This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. ​                                                                                                                                                                                                                                                                                                                                                                       | +| [[https://​www.amazon.com/​Introduction-Clifford-Algebras-Spinors/​dp/​0198782926|{{:​ga:​an_introduction_to_clifford_algebras_and_spinors-vaz.jpg?​100}}]] | **An Introduction to Clifford Algebras and Spinors (2016)**\\ // Jayme Vaz, Roldao da Rocha//\\ This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. ​                                                                                                                                                                                                                                                                                                                                                                       | 
-| [[https://​www.amazon.com/​Modern-Trends-Hypercomplex-Analysis-Mathematics/​dp/​3319425285|{{:​ga:​modern_trends_in_hypercomplex_analysis-birkhauser.jpg?​100}}]] ​                                                   | **Modern Trends in Hypercomplex Analysis (2016)**\\ //  Swanhild Bernstein, Uwe Kähler, Irene Sabadini, Franciscus Sommen (Editors)//​\\ This book contains a selection of papers presented at the session "​Quaternionic and Clifford Analysis"​ at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications. ​                                                                                                                                                                                                                                                                                                                                                                       | +| [[https://​www.amazon.com/​Modern-Trends-Hypercomplex-Analysis-Mathematics/​dp/​3319425285|{{:​ga:​modern_trends_in_hypercomplex_analysis-birkhauser.jpg?​100}}]] | **Modern Trends in Hypercomplex Analysis (2016)**\\ //  Swanhild Bernstein, Uwe Kähler, Irene Sabadini, Franciscus Sommen (Editors)//​\\ This book contains a selection of papers presented at the session "​Quaternionic and Clifford Analysis"​ at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications. ​                                                                                                                                                                                                                                                                                                                                                                       | 
-| [[https://​www.amazon.com/​Clifford-Algebras-Introduction-Mathematical-Society/​dp/​1107096383|{{:​ga:​clifford_algebras_an_introduction-garling.jpg?​100}}]] ​                                                 | **Clifford Algebras: An Introduction (2011)**\\ //D. J. H. Garling//\\ Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics,​ as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell'​s equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts. ​                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Clifford-Algebras-Introduction-Mathematical-Society/​dp/​1107096383|{{:​ga:​clifford_algebras_an_introduction-garling.jpg?​100}}]] | **Clifford Algebras: An Introduction (2011)**\\ //D. J. H. Garling//\\ Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics,​ as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell'​s equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts. ​                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Standard-Quantum-Physics-Clifford-Algebra/​dp/​9814719862|{{:​ga:​standard_model_of_quantum_physics_in_clifford_algebra-daviau.jpg?​100}}]] ​                                        ​| **The Standard Model of Quantum Physics in Clifford Algebra (2015)**\\ //Claude Daviau, Jacques Bertrand//​\\ We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl*_3, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | +| [[https://​www.amazon.com/​Standard-Quantum-Physics-Clifford-Algebra/​dp/​9814719862|{{:​ga:​standard_model_of_quantum_physics_in_clifford_algebra-daviau.jpg?​100}}]] | **The Standard Model of Quantum Physics in Clifford Algebra (2015)**\\ //Claude Daviau, Jacques Bertrand//​\\ We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl*_3, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 
-| [[https://​www.amazon.com/​lunification-mathematiques-algebresgeometriques-algebrique-informatique/​dp/​2746238381|{{:​ga:​lunification_des_mathematiques-parrochia.jpg?​100}}]] ​                              ​| **L'​unification des mathématiques:​ algèbres géométriques,​ géométrie algébrique et philosophie de Langlands (2012)**\\ //Daniel Parrochia, Artibano Micali, Pierre Anglès//\\ La pensée mathématique offre un panorama impressionnant de recherches dans les multiples directions dessinées par les réorganisations successives que la matière a connues. Cet ouvrage porte un éclairage philosophique et historique sur certains développements qui donne un sens aux transformations subies par la pensée mathématique au cours du temps pour actualiser le portrait déjà ancien de "​l'​unité des mathématiques"​. Deux mouvements symétriques d'​unification se sont produits en mathématiques. Le premier est l'​aboutissement du long chemin qui, depuis les Grecs, a tendu à résoudre l'​opposition de la géométrie et de l'​arithmétique,​ puis de la géométrie et de l'​algèbre. Le second mode d'​unification date de la fin des années 1960. Via la géométrie algébrique,​ il tend à reconstruire l'​ensemble des mathématiques sur la base des correspondances de Langlands, lesquelles résorbent intégralement l'​opposition de l'​algèbre et de l'​analyse,​ et constituent un fabuleux dictionnaire pour la physique de demain. ​                                                                                                                                                      | +| [[https://​www.amazon.com/​lunification-mathematiques-algebresgeometriques-algebrique-informatique/​dp/​2746238381|{{:​ga:​lunification_des_mathematiques-parrochia.jpg?​100}}]] | **L'​unification des mathématiques:​ algèbres géométriques,​ géométrie algébrique et philosophie de Langlands (2012)**\\ //Daniel Parrochia, Artibano Micali, Pierre Anglès//\\ La pensée mathématique offre un panorama impressionnant de recherches dans les multiples directions dessinées par les réorganisations successives que la matière a connues. Cet ouvrage porte un éclairage philosophique et historique sur certains développements qui donne un sens aux transformations subies par la pensée mathématique au cours du temps pour actualiser le portrait déjà ancien de "​l'​unité des mathématiques"​. Deux mouvements symétriques d'​unification se sont produits en mathématiques. Le premier est l'​aboutissement du long chemin qui, depuis les Grecs, a tendu à résoudre l'​opposition de la géométrie et de l'​arithmétique,​ puis de la géométrie et de l'​algèbre. Le second mode d'​unification date de la fin des années 1960. Via la géométrie algébrique,​ il tend à reconstruire l'​ensemble des mathématiques sur la base des correspondances de Langlands, lesquelles résorbent intégralement l'​opposition de l'​algèbre et de l'​analyse,​ et constituent un fabuleux dictionnaire pour la physique de demain. ​                                                                                                                                                      | 
-| [[http://​www.lulu.com/​shop/​sergei-winitzki/​linear-algebra-via-exterior-products/​paperback/​product-6214034.html|{{:​ga:​linear_algebra_via_exterior_products-winitzki.jpg?​100}}]] ​                         | ** Linear Algebra via Exterior Products (2010)**\\ //Sergei Winitzki//​\\ This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative,​ "​wedge"​) product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations,​ this text derives the standard properties of determinants,​ the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |+| [[http://​www.lulu.com/​shop/​sergei-winitzki/​linear-algebra-via-exterior-products/​paperback/​product-6214034.html|{{:​ga:​linear_algebra_via_exterior_products-winitzki.jpg?​100}}]] | ** Linear Algebra via Exterior Products (2010)**\\ //Sergei Winitzki//​\\ This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative,​ "​wedge"​) product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations,​ this text derives the standard properties of determinants,​ the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
 | [[https://​www.amazon.com/​Road-Reality-Complete-Guide-Universe/​dp/​0679776311|{{:​ga:​the_road_to_reality-penrose.jpg?​100}}]] ​                                                                              | **The Road to Reality: A Complete Guide to the Laws of the Universe (2004)**\\ //Roger Penrose//\\ Roger Penrose presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | | [[https://​www.amazon.com/​Road-Reality-Complete-Guide-Universe/​dp/​0679776311|{{:​ga:​the_road_to_reality-penrose.jpg?​100}}]] ​                                                                              | **The Road to Reality: A Complete Guide to the Laws of the Universe (2004)**\\ //Roger Penrose//\\ Roger Penrose presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
-| [[https://​www.amazon.com/​How-Schrodingers-Cat-Escaped-Box/​dp/​9814635197|{{:​ga:​how_schrodinger_cat_escaped_the_box-rowlands.jpg?​100}}]] ​                                                                 | **How Schrodinger'​s Cat Escaped the Box (2015)**\\ //Peter Rowlands//​\\ This book attempts to explain the core of physics, the origin of everything and anything. It explains why physics at the most fundamental level, and especially quantum mechanics, has moved away from naive realism towards abstraction,​ and how this means that we can begin to answer some of the most fundamental questions which trouble us all, about space, time, matter, etc. It provides an original approach based on symmetry which will be of interest to professionals as well as lay people. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | +| [[https://​www.amazon.com/​How-Schrodingers-Cat-Escaped-Box/​dp/​9814635197|{{:​ga:​how_schrodinger_cat_escaped_the_box-rowlands.jpg?​100}}]] | **How Schrodinger'​s Cat Escaped the Box (2015)**\\ //Peter Rowlands//​\\ This book attempts to explain the core of physics, the origin of everything and anything. It explains why physics at the most fundamental level, and especially quantum mechanics, has moved away from naive realism towards abstraction,​ and how this means that we can begin to answer some of the most fundamental questions which trouble us all, about space, time, matter, etc. It provides an original approach based on symmetry which will be of interest to professionals as well as lay people. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | 
-| [[https://​www.amazon.com/​Foundations-Game-Engine-Development-Mathematics/​dp/​0985811749|{{:​ga:​foundations_of_game_engine_development-lengyel.jpg?​100}}]] ​                                                ​| **Foundations of Game Engine Development,​ Volume 1: Mathematics (2016)**\\ //Eric Lengyel//\\ The goal of this project is to create a new textbook that provides a detailed introduction to the mathematics used by modern game engine programmers. (...) One example of an important topic missing from the existing literature is Grassmann algebra. Ever since I began giving conference presentations on this topic in 2012, I have been frequently asked whether there is a book that provides a thorough and intuitive discussion of Grassmann algebra (or the related topic of geometric algebra) in the context of game development and computer graphics. I don't believe that there is, and I'd like to take the opportunity to fill this void.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | +| [[https://​www.amazon.com/​Foundations-Game-Engine-Development-Mathematics/​dp/​0985811749|{{:​ga:​foundations_of_game_engine_development-lengyel.jpg?​100}}]] | **Foundations of Game Engine Development,​ Volume 1: Mathematics (2016)**\\ //Eric Lengyel//\\ The goal of this project is to create a new textbook that provides a detailed introduction to the mathematics used by modern game engine programmers. (...) One example of an important topic missing from the existing literature is Grassmann algebra. Ever since I began giving conference presentations on this topic in 2012, I have been frequently asked whether there is a book that provides a thorough and intuitive discussion of Grassmann algebra (or the related topic of geometric algebra) in the context of game development and computer graphics. I don't believe that there is, and I'd like to take the opportunity to fill this void.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | 
-| [[https://​www.amazon.com/​Foundations-Game-Engine-Development-Rendering/​dp/​0985811757|{{:​ga:​foundations_of_game_engine_development2-lengyel.jpg?​100}}]] ​                                                ​| **Foundations of Game Engine Development,​ Volume 2: Rendering (2019)**\\ //Eric Lengyel//\\ This second volume in the Foundations of Game Engine Development series explores the vast subject of real-time rendering in modern game engines. The book provides a detailed introduction to color science, world structure, projections,​ shaders, lighting, shadows, fog, and visibility methods. This is followed by extensive discussions of a variety of advanced rendering techniques that include volumetric effects, atmospheric shadowing, ambient occlusion, motion blur, and isosurface extraction. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | +| [[https://​www.amazon.com/​Foundations-Game-Engine-Development-Rendering/​dp/​0985811757|{{:​ga:​foundations_of_game_engine_development2-lengyel.jpg?​100}}]] | **Foundations of Game Engine Development,​ Volume 2: Rendering (2019)**\\ //Eric Lengyel//\\ This second volume in the Foundations of Game Engine Development series explores the vast subject of real-time rendering in modern game engines. The book provides a detailed introduction to color science, world structure, projections,​ shaders, lighting, shadows, fog, and visibility methods. This is followed by extensive discussions of a variety of advanced rendering techniques that include volumetric effects, atmospheric shadowing, ambient occlusion, motion blur, and isosurface extraction. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 
-| [[https://​www.amazon.com/​Invariant-Algebras-Geometric-Reasoning-Hongbo/​dp/​9812708081|{{:​ga:​invariant_algebras_and_geometric_reasoning-li.jpg?​100}}]] ​                                                   | **Invariant Algebras And Geometric Reasoning (2008)**\\ //Hongbo Li//\\ The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics among them, Grassmann-Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author and his collaborators'​ most recent, original development of Grassmann-Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras Cayley bracket algebra, conformal geometric algebra, and null bracket algebra for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. ​                                                                                                                                                                                                                                                                                                                                                                                                                                             | +| [[https://​www.amazon.com/​Invariant-Algebras-Geometric-Reasoning-Hongbo/​dp/​9812708081|{{:​ga:​invariant_algebras_and_geometric_reasoning-li.jpg?​100}}]] | **Invariant Algebras And Geometric Reasoning (2008)**\\ //Hongbo Li//\\ The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics among them, Grassmann-Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author and his collaborators'​ most recent, original development of Grassmann-Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras Cayley bracket algebra, conformal geometric algebra, and null bracket algebra for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. ​                                                                                                                                                                                                                                                                                                                                                                                                                                             | 
-| [[https://​www.amazon.com/​Code-Generation-Geometric-Algebra-Abstractions/​dp/​3330804653|{{:​ga:​code_generation_for_geometric_algebra-eid.jpg?​100}}]] ​                                                      ​| **Code Generation for Geometric Algebra: Combining Geometric, Algebraic, and Software Abstractions for Scientific Computations (2016)**\\ //Ahmad Hosny Eid//\\ Geometry is an essential part of almost every solution to problems in computer science and engineering. The process of manually creating geometry-enabled software for representing and processing geometric data is tedious and error-prone. The use of automatic code generators for such process is more suitable, especially for low-dimensional geometric problems. Such problems can be commonly found in computer graphics, computer vision, robotics, and many other fields of application. A mathematical algebraic system with special characteristics must be used as the base of the code transformations required for final code generation. Geometric Algebra (GA) is one of the most suitable algebraic systems for such task. This work describes the design and use of one such GA-based prototype code generation system: GMac.                                                                                                                                                                                                                                                                                                                                                                   | +| [[https://​www.amazon.com/​Code-Generation-Geometric-Algebra-Abstractions/​dp/​3330804653|{{:​ga:​code_generation_for_geometric_algebra-eid.jpg?​100}}]] | **Code Generation for Geometric Algebra: Combining Geometric, Algebraic, and Software Abstractions for Scientific Computations (2016)**\\ //Ahmad Hosny Eid//\\ Geometry is an essential part of almost every solution to problems in computer science and engineering. The process of manually creating geometry-enabled software for representing and processing geometric data is tedious and error-prone. The use of automatic code generators for such process is more suitable, especially for low-dimensional geometric problems. Such problems can be commonly found in computer graphics, computer vision, robotics, and many other fields of application. A mathematical algebraic system with special characteristics must be used as the base of the code transformations required for final code generation. Geometric Algebra (GA) is one of the most suitable algebraic systems for such task. This work describes the design and use of one such GA-based prototype code generation system: GMac.                                                                                                                                                                                                                                                                                                                                                                   | 
-| [[http://​www.xtec.cat/​~rgonzal1/​treatise2.htm|{{:​ga:​treatise_of_plane_geometry_through_geometric_algebra-gonzalez-calvet.jpg?​100}}]] ​                                                                   | **Treatise of Plane Geometry through Geometric Algebra (2007)**\\ //Ramon González Calvet//\\ The Clifford-Grassman Geometric Algebra is applied to solve geometric equations, which are like the algebraic equations but containing geometric (vector) unknowns instead of real quantities. The unique way to solve these kind of equations is by using an associative algebra of vectors, the Clifford-Grassmann Geometric Algebra. Using the CGGA we have the freedom of transposition and isolation of any geometric unknown in a geometric equation. Then the typical problems and theorems of geometry, which have been hardly proved till now by means of synthetic methods, are more easily solved through the CGGA. On the other hand, the formulas obtained from the CGGA can immediately be written in Cartesian coordinates,​ giving a very useful service for programming computer applications,​ as in the case of the notable points of a triangle. ​                                                                                                                                                                                                                                                                                                                                                                                                                   | +| [[http://​www.xtec.cat/​~rgonzal1/​treatise2.htm|{{:​ga:​treatise_of_plane_geometry_through_geometric_algebra-gonzalez-calvet.jpg?​100}}]] | **Treatise of Plane Geometry through Geometric Algebra (2007)**\\ //Ramon González Calvet//\\ The Clifford-Grassman Geometric Algebra is applied to solve geometric equations, which are like the algebraic equations but containing geometric (vector) unknowns instead of real quantities. The unique way to solve these kind of equations is by using an associative algebra of vectors, the Clifford-Grassmann Geometric Algebra. Using the CGGA we have the freedom of transposition and isolation of any geometric unknown in a geometric equation. Then the typical problems and theorems of geometry, which have been hardly proved till now by means of synthetic methods, are more easily solved through the CGGA. On the other hand, the formulas obtained from the CGGA can immediately be written in Cartesian coordinates,​ giving a very useful service for programming computer applications,​ as in the case of the notable points of a triangle. ​                                                                                                                                                                                                                                                                                                                                                                                                                   | 
-| [[https://​www.amazon.com/​Modern-Mathematics-Applications-Computer-Graphics/​dp/​9814449326|{{:​ga:​modern_mathematics_and_applications_in_computer_graphics_and_vision-guo.jpg?​100}}]] ​                     | **Modern Mathematics and Applications in Computer Graphics and Vision (2014)**\\ //Hongyu Guo//\\ Presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts: Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |+| [[https://​www.amazon.com/​Modern-Mathematics-Applications-Computer-Graphics/​dp/​9814449326|{{:​ga:​modern_mathematics_and_applications_in_computer_graphics_and_vision-guo.jpg?​100}}]] | **Modern Mathematics and Applications in Computer Graphics and Vision (2014)**\\ //Hongyu Guo//\\ Presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts: Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |
 | [[http://​www.morikita.co.jp/​books/​book/​2745|{{:​ga:​geometric_algebra-kanaya.jpg?​100}}]] ​                                                                                                                 | **幾何学と代数系 Geometric Algebra (2014)**\\ //金谷 健一//\\ アメリカの物理学者ヘステネスを中心に提唱された「幾何学的代数」(geometric algebra) は,幾何学に古典的な代数系を対応させる手法であり,現在,物理学や工学のさまざまな分野で関心が寄せられている.本書は,この幾何学的代数の和書初となる入門書である.まず,背景をなすハミルトン代数,グラスマン代数,クリフォード代数を初歩からていねいに解説しているため,初学者でも自然に幾何学的代数の考え方を学ぶことができる.また,現代数学とのつながりも随所に見せることで,より深い理解が得られるようになっている. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | | [[http://​www.morikita.co.jp/​books/​book/​2745|{{:​ga:​geometric_algebra-kanaya.jpg?​100}}]] ​                                                                                                                 | **幾何学と代数系 Geometric Algebra (2014)**\\ //金谷 健一//\\ アメリカの物理学者ヘステネスを中心に提唱された「幾何学的代数」(geometric algebra) は,幾何学に古典的な代数系を対応させる手法であり,現在,物理学や工学のさまざまな分野で関心が寄せられている.本書は,この幾何学的代数の和書初となる入門書である.まず,背景をなすハミルトン代数,グラスマン代数,クリフォード代数を初歩からていねいに解説しているため,初学者でも自然に幾何学的代数の考え方を学ぶことができる.また,現代数学とのつながりも随所に見せることで,より深い理解が得られるようになっている. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
-| [[https://​www.amazon.com/​Exterior-Algebras-Elementary-Tribute-Grassmanns/​dp/​1785482378|{{:​ga:​exterior_algebras-pavan.jpg?​100}}]] ​                                                                       | **Exterior Algebras: Elementary Tribute to Grassmann'​s Ideas (2017)**\\ //Vincent Pavan//\\ Provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann'​s algebras. Then, it shows how the latter can be used to treat a few basic, though significant,​ questions of linear algebra, such as co-linearity,​ determinant calculus, linear systems analyzing, volumes computations,​ invariant endomorphism considerations,​ skew-symmetric operator studies and decompositions,​ and Hodge conjugation,​ amongst others. Presents a self-contained guide that does not require any specific algebraic background. Includes numerous examples and direct applications that are suited for beginners. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | +| [[https://​www.amazon.com/​Exterior-Algebras-Elementary-Tribute-Grassmanns/​dp/​1785482378|{{:​ga:​exterior_algebras-pavan.jpg?​100}}]] | **Exterior Algebras: Elementary Tribute to Grassmann'​s Ideas (2017)**\\ //Vincent Pavan//\\ Provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann'​s algebras. Then, it shows how the latter can be used to treat a few basic, though significant,​ questions of linear algebra, such as co-linearity,​ determinant calculus, linear systems analyzing, volumes computations,​ invariant endomorphism considerations,​ skew-symmetric operator studies and decompositions,​ and Hodge conjugation,​ amongst others. Presents a self-contained guide that does not require any specific algebraic background. Includes numerous examples and direct applications that are suited for beginners. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 
-| [[https://​www.amazon.com/​dp/​331990664X|{{:​ga:​a_geometric_algebra_invitation-lavor_xambo.jpg?​100}}]] ​                                                                                                    ​| **A Geometric Algebra Invitation to Space-Time Physics, Robotics and Molecular Geometry (2018)**\\ //Carlile Lavor, Sebastià Xambó-Descamps//​\\ This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | +| [[https://​www.amazon.com/​dp/​331990664X|{{:​ga:​a_geometric_algebra_invitation-lavor_xambo.jpg?​100}}]] | **A Geometric Algebra Invitation to Space-Time Physics, Robotics and Molecular Geometry (2018)**\\ //Carlile Lavor, Sebastià Xambó-Descamps//​\\ This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 
-| [[https://​www.amazon.com/​dp/​3319748289|{{:​ga:​geometric-algebra-applications_vol_i-bayro.jpg?​100}}]] ​                                                                                                    ​| **Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing (2018)**\\ //Eduardo Bayro-Corrochano//​\\ The goal is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​dp/​3319748289|{{:​ga:​geometric-algebra-applications_vol_i-bayro.jpg?​100}}]] | **Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing (2018)**\\ //Eduardo Bayro-Corrochano//​\\ The goal is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​dp/​1498748384|{{:​ga:​introduction_to_geometric_algebra_computing-hildenbrand.jpg?​100}}]] ​                                                                                       | **Introduction to Geometric Algebra Computing (Computer Vision) (2018)**\\ //Dietmar Hildenbrand//​\\ This book is intended to give a rapid introduction to computing with Geometric Algebra and its power for geometric modeling. From the geometric objects point of view, it focuses on the most basic ones, namely points, lines and circles. This algebra is called Compass Ruler Algebra, since it is comparable to working with a compass and ruler. The book explores how to compute with these geometric objects, and their geometric operations and transformations,​ in a very intuitive way. The book follows a top-down approach, and while it focuses on 2D, it is also easily expandable to 3D computations. Algebra in engineering applications such as computer graphics, computer vision and robotics are also covered. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​dp/​1498748384|{{:​ga:​introduction_to_geometric_algebra_computing-hildenbrand.jpg?​100}}]] | **Introduction to Geometric Algebra Computing (Computer Vision) (2018)**\\ //Dietmar Hildenbrand//​\\ This book is intended to give a rapid introduction to computing with Geometric Algebra and its power for geometric modeling. From the geometric objects point of view, it focuses on the most basic ones, namely points, lines and circles. This algebra is called Compass Ruler Algebra, since it is comparable to working with a compass and ruler. The book explores how to compute with these geometric objects, and their geometric operations and transformations,​ in a very intuitive way. The book follows a top-down approach, and while it focuses on 2D, it is also easily expandable to 3D computations. Algebra in engineering applications such as computer graphics, computer vision and robotics are also covered. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​dp/​3319946366|{{:​ga:​imaginary_mathematics_for_computer_science-vince.jpg?​100}}]] ​                                                                                       | **Imaginary Mathematics for Computer Science (2018)**\\ //John Vince//\\ The imaginary unit //i// has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately,​ Rene Descartes referred to it as "​imaginary",​ and the use of the term "​complex number"​ compounded the unnecessary mystery associated with this amazing object. Today, //i// has found its way into virtually every branch of mathematics,​ and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamilton'​s quaternions,​ Cayley'​s octonions, to Grassmann'​s geometric algebra. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​dp/​3319946366|{{:​ga:​imaginary_mathematics_for_computer_science-vince.jpg?​100}}]] | **Imaginary Mathematics for Computer Science (2018)**\\ //John Vince//\\ The imaginary unit //i// has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately,​ Rene Descartes referred to it as "​imaginary",​ and the use of the term "​complex number"​ compounded the unnecessary mystery associated with this amazing object. Today, //i// has found its way into virtually every branch of mathematics,​ and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamilton'​s quaternions,​ Cayley'​s octonions, to Grassmann'​s geometric algebra. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​dp/​1498738915|{{:​ga:​handbook_of_geometric_constraint_systems_principles-crc.jpg?​100}}]] ​                                                                                       | **Handbook of Geometric Constraint Systems Principles (2018)**\\ //Meera Sitharam, Audrey St. John, Jessica Sidman//\\ Entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​dp/​1498738915|{{:​ga:​handbook_of_geometric_constraint_systems_principles-crc.jpg?​100}}]] | **Handbook of Geometric Constraint Systems Principles (2018)**\\ //Meera Sitharam, Audrey St. John, Jessica Sidman//\\ Entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​dp/​0815378688|{{:​ga:​neural_networks_for_robotics-crc.jpg?​100}}]] ​                                                                                       | **Neural Networks for Robotics: An Engineering Perspective (2018)**\\ //Nancy Arana-Daniel,​ Alma Y. Alanis, Carlos Lopez-Franco//​\\ The book offers an insight on artificial neural networks for giving a robot a high level of autonomous tasks, such as navigation, cost mapping, object recognition,​ intelligent control of ground and aerial robots, and clustering, with real-time implementations. The reader will learn various methodologies that can be used to solve each stage on autonomous navigation for robots, from object recognition,​ clustering of obstacles, cost mapping of environments,​ path planning, and vision to low level control. These methodologies include real-life scenarios to implement a wide range of artificial neural network architectures. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​dp/​0815378688|{{:​ga:​neural_networks_for_robotics-crc.jpg?​100}}]] | **Neural Networks for Robotics: An Engineering Perspective (2018)**\\ //Nancy Arana-Daniel,​ Alma Y. Alanis, Carlos Lopez-Franco//​\\ The book offers an insight on artificial neural networks for giving a robot a high level of autonomous tasks, such as navigation, cost mapping, object recognition,​ intelligent control of ground and aerial robots, and clustering, with real-time implementations. The reader will learn various methodologies that can be used to solve each stage on autonomous navigation for robots, from object recognition,​ clustering of obstacles, cost mapping of environments,​ path planning, and vision to low level control. These methodologies include real-life scenarios to implement a wide range of artificial neural network architectures. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Introduction-Theoretical-Kinematics-mathematics-movement/​dp/​0978518039|{{:​ga:​introduction_to_theoretical_kinematics-mccarthy.jpg?​100}}]] ​                                                                                       | **Introduction to Theoretical Kinematics: The mathematics of movement (2018)**\\ //J. Michael McCarthy//​\\ An introduction to the mathematics used to model the articulated movement of mechanisms, machines, robots, and human and animal skeletons. Its concise and readable format emphasizes the similarity of the mathematics for planar, spherical and spatial movement. A modern approach introduces Lie groups and algebras and uses the theory of multivectors and Clifford algebras to clarify the construction of screws and dual quaternions. The pursuit of a unified presentation has led to a format in which planar, spherical, and spatial mechanisms are all studied in each chapter. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Introduction-Theoretical-Kinematics-mathematics-movement/​dp/​0978518039|{{:​ga:​introduction_to_theoretical_kinematics-mccarthy.jpg?​100}}]] | **Introduction to Theoretical Kinematics: The mathematics of movement (2018)**\\ //J. Michael McCarthy//​\\ An introduction to the mathematics used to model the articulated movement of mechanisms, machines, robots, and human and animal skeletons. Its concise and readable format emphasizes the similarity of the mathematics for planar, spherical and spatial movement. A modern approach introduces Lie groups and algebras and uses the theory of multivectors and Clifford algebras to clarify the construction of screws and dual quaternions. The pursuit of a unified presentation has led to a format in which planar, spherical, and spatial mechanisms are all studied in each chapter. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Real-Spinorial-Groups-Mathematical-SpringerBriefs/​dp/​3030004031|{{:​ga:​real_spinorial_groups-xambo.jpg?​100}}]] ​                                                                                       | **Real Spinorial Groups: A Short Mathematical Introduction (2018)**\\ //Sebastià Xambó-Descamps//​\\ This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry and how they relate to the group of isometries of that geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions),​ it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Real-Spinorial-Groups-Mathematical-SpringerBriefs/​dp/​3030004031|{{:​ga:​real_spinorial_groups-xambo.jpg?​100}}]] | **Real Spinorial Groups: A Short Mathematical Introduction (2018)**\\ //Sebastià Xambó-Descamps//​\\ This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry and how they relate to the group of isometries of that geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions),​ it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Topics-Clifford-Analysis-Wolfgang-Mathematics/​dp/​3030238539|{{:​ga:​topics_in_clifford_analysis-bernstein.jpg?​100}}]] ​                                                                                       | **Topics in Clifford Analysis: Special Volume in Honor of Wolfgang Sprößig (2019)**\\ // Swanhild Bernstein (Editor)//​\\ Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig'​s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Topics-Clifford-Analysis-Wolfgang-Mathematics/​dp/​3030238539|{{:​ga:​topics_in_clifford_analysis-bernstein.jpg?​100}}]] | **Topics in Clifford Analysis: Special Volume in Honor of Wolfgang Sprößig (2019)**\\ // Swanhild Bernstein (Editor)//​\\ Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig'​s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Geometric-Multivector-Analysis-Birkh%C3%A4user-Lehrb%C3%BCcher/​dp/​3030314103|{{:​ga:​geometric_multivector_analysis-rosen.jpg?​100}}]] ​                                                                                       | **Geometric Multivector Analysis: From Grassmann to Dirac (2019)**\\ // Andreas Rosén//\\ Presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of Marcel Riesz and Lars Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. Also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | +| [[https://​www.amazon.com/​Geometric-Multivector-Analysis-Birkh%C3%A4user-Lehrb%C3%BCcher/​dp/​3030314103|{{:​ga:​geometric_multivector_analysis-rosen.jpg?​100}}]] | **Geometric Multivector Analysis: From Grassmann to Dirac (2019)**\\ // Andreas Rosén//\\ Presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of Marcel Riesz and Lars Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. Also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
-| [[https://​www.amazon.com/​Advanced-Calculus-Fundamentals-Carlos-Polanco/​dp/​9811415072|{{:​ga:​advanced_calculus-polanco.jpg?​100}}]] ​                                                                                       | **Advanced Calculus - Fundamentals of Mathematics (2019)**\\ // Carlos Polanco//\\ Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations.This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms.Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |+| [[https://​www.amazon.com/​Advanced-Calculus-Fundamentals-Carlos-Polanco/​dp/​9811415072|{{:​ga:​advanced_calculus-polanco.jpg?​100}}]] | **Advanced Calculus - Fundamentals of Mathematics (2019)**\\ // Carlos Polanco//\\ Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations.This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms.Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter.                                                                                                                                                                                                                                                                                                                                                                                                                                                                               | 
 +| [[https://​www.amazon.com/​Geometric-Multiplication-Vectors-Introduction-Mathematics/​dp/​3030017559|{{:​ga:​geometric_multiplication_of_vectors-josipovic.jpg?​100}}]] | **Geometric Multiplication of Vectors: An Introduction to Geometric Algebra in Physics (2019)**\\ // Miroslav Josipović//​\\ Enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism,​ to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. The universality,​ the clear geometric interpretation,​ the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth. ​                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 
 +| [[https://​www.amazon.com/​Clifford-Algebras-Zeons-Geometry-Combinatorics/​dp/​9811202575|{{:​ga:​clifford_algebras_and_zeons-staples.jpg?​100}}]] | **Clifford Algebras And Zeons: Geometry to Combinatorics and Beyond (2020)**\\ // George Stacey Staples//\\ Clifford algebras have many well-known applications in physics, engineering,​ and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world. As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics.                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
  
geometric_algebra.1584907669.txt.gz · Last modified: 2020/03/22 16:07 by pbk