Mathematics for Physics: An Illustrated Handbook by Adam Marsh, ISBN-13: 978-9813233911

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.