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English | 2018 | ISBN: 9813233915 | 301 pages | True PDF EPUB | 20.69 MB
This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.
Contents:
Mathematical Structures
Abstract Algebra
Vector Algebras
Topological Spaces
Algebraic Topology
Manifolds
Lie Groups
Clifford Groups
Riemannian Manifolds
Fiber Bundles
Categories and Functors
Readership: Students in mathematics and physics who want to explore a level deeper into actual mathematical content.
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