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1.

電子ブック
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1. Discrete Mathematics. 1
by Jean Gallier
出版情報: New York, NY : Springer Science+Business Media, LLC, 2011
シリーズ名: Universitext ;
オンライン: http://dx.doi.org/10.1007/978-1-4419-8047-2
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2.

電子ブック
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2. Geometric Methods and Applications : For Computer Science and Engineering
by Jean Gallier
出版情報: New York, NY : Springer Science+Business Media, LLC, 2011
シリーズ名: Texts in Applied Mathematics ; 38
オンライン: http://dx.doi.org/10.1007/978-1-4419-9961-0
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3.

電子ブック
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3. A Guide to the Classification Theorem for Compact Surfaces
by Jean Gallier, Dianna Xu
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Geometry and Computing ; 9
オンライン: http://dx.doi.org/10.1007/978-3-642-34364-3
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目次情報: 続きを見る
The Classification Theorem: Informal Presentation
Surfaces
Simplices, Complexes, and Triangulations
The Fundamental Group, Orientability
Homology Groups
The Classification Theorem for Compact Surfaces
Viewing the Real Projective Plane in R3
Proof of Proposition 5.1
Topological Preliminaries
History of the Classification Theorem
Every Surface Can be Triangulated
Notes
The Classification Theorem: Informal Presentation
Surfaces
Simplices, Complexes, and Triangulations
4.

電子ブック
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4. Differential Geometry and Lie Groups : A Computational Perspective. 1st ed. 2020
by Jean Gallier, Jocelyn Quaintance
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: Geometry and Computing ; 12
オンライン: https://doi.org/10.1007/978-3-030-46040-2
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目次情報: 続きを見る
1. The Matrix Exponential; Some Matrix Lie Groups
2. Adjoint Representations and the Derivative of exp
3. Introduction to Manifolds and Lie Groups
4. Groups and Group Actions
5. The Lorentz Groups ⊛
6. The Structure of O(p,q) and SO(p, q)
7. Manifolds, Tangent Spaces, Cotangent Spaces
8. Construction of Manifolds From Gluing Data ⊛
9. Vector Fields, Integral Curves, Flows
10. Partitions of Unity, Covering Maps ⊛
11. Basic Analysis: Review of Series and Derivatives
12. A Review of Point Set Topology.-13. Riemannian Metrics, Riemannian Manifolds
14. Connections on Manifolds
15. Geodesics on Riemannian Manifolds
16. Curvature in Riemannian Manifolds
17. Isometries, Submersions, Killing Vector Fields
18. Lie Groups, Lie Algebra, Exponential Map
19. The Derivative of exp and Dynkin's Formula ⊛
20. Metrics, Connections, and Curvature of Lie Groups
21. The Log-Euclidean Framework
22. Manifolds Arising from Group Actions
1. The Matrix Exponential; Some Matrix Lie Groups
2. Adjoint Representations and the Derivative of exp
3. Introduction to Manifolds and Lie Groups
5.

電子ブック
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5. Differential Geometry and Lie Groups : A Second Course. 1st ed. 2020
by Jean Gallier, Jocelyn Quaintance
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: Geometry and Computing ; 13
オンライン: https://doi.org/10.1007/978-3-030-46047-1
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目次情報: 続きを見る
1. Tensor Algebras
2. Exterior Tensor Powers and Exterior Algebras
3. Differential Forms
4. Distributions and the Frobenius Theorem
5. Integration on Manifolds
6. Spherical Harmonics and Linear Representations
7. Operators on Riemannian Manifolds
8. Bundles, Metrics on Bundles, Homogeneous Spaces
9. Connections and Curvature in Vector Bundles
10. Clifford Algebras, Clifford Groups, Pin and Spin
1. Tensor Algebras
2. Exterior Tensor Powers and Exterior Algebras
3. Differential Forms