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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)
Language: English
ISBN-10: 0226288625
ISBN-13: 978-0226288628
Thanks for pointing out this one. Geroch is a clever guy. I now have this book on order.
Received the book. Interesting and broad.
I find it a bit curious that he emphasizes categories as a unifying theme, but doesn’t talk about universal objects. Nevertheless his proofs of the uniqueness of free groups and tensor products really boil down to the fact that they are universal objects in the appropriate category.
@DrRocket: I understand your curiosity. I think the book is a great place to get exposed to some category theory and its language, but the book is not really a book on category theory.
I am a strong believer that a little category theory can really help you out.