|Mathematical Physics (Lectures in Physics)||
Mathematics is the language of physics. Thus physicists need some background in mathematics. Within mathematics category theory is a collection of unifying ideas that really gets at the heart of mathematical structures. Mathematical Physics by Robert Geroch provides a good grounding in the basic mathematical structures required in physics from a categorical perspective.
This book consists of 56 short chapters.
Chapers 1 to 24 discuss algebraic categories: groups, vector spaces, associative algebras, Lie algebras and representations. The main ideas of category theory are laid down in these chapters via motivating examples.
Chapters 25 to 42 take on a topological flavour. Topics about topological spaces include continuous mappings,compactness, connectedness, homotopy, homology, topological groups and topological vector spaces.
Chapters 43 to 56 combine algebra and topology by discussing measure spaces, distributions and Hilbert spaces. Topics here include bounded operators, the spectral theorem, not necessarily bounded operators and self-adjoint operators.
Paperback: 358 pages
Publisher: University Of Chicago Press (September 15, 1985)