Mathematics for Physics: An Illustrated Handbook

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.