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geometric_algebra [2020/03/22 20:07] – [Videos] pbkgeometric_algebra [2020/04/08 18:10] – [Historical] pbk
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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-porteus.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 ====
geometric_algebra.txt · Last modified: 2023/12/30 00:23 by pbk

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