Mathematical Physics (Chicago Lectures in Physics)

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Summary: An introduction to category theory? For physicists?
Review: Geroch chooses category theory (or the theory of metamathematics) as an exploratory tool that could conceivably provide unified treatment of the various algebraic and topological structures encountered in "fancy" mathematics. This is his masterplan for introducing theoretical physicists to abstract mathematical concepts. While the categorical language is admittedly a bit heavy for (most) physicists, the book itself is clearly written, and Geroch does a fine job of delineating the key topics. That is why I have decided to give this book 4 out of 5, thus betraying my partiality towards mathematical rigor in physics. My personal favorite is Geroch's insightful discussion of dynamical systems and topological spaces. The only objection that may be raised is the layout of the book. The main definitions and theorems are not set apart from the rest, and this makes the text appear denser than it really is.

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Summary: Excellent book for illuminating some of the math in physics
Review: I first read this excellent book about 6 years ago when I was beginning to realize that my undergraduate physics education wasn't going to teach me the math I wanted to know, especially since my main interest in physics was of a more theoretical bent. This book provides an excellent outline of many of the mathematical concepts that are rarely covered (or at least rarely covered well) in most physics curriculums. Running the gamut from category theory to basic group theory to algebraic topology and beyond, this book provides much of the basic mathematical framework that many modern physical theories rely on. Highly recommended.

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Summary: basic topology and geometry for physicists
Review: intended for the physicist; mathematicians can glean very quickly from its contents the power , diversity and wide applicability of their subject, not to mention the lasting impact it will have on the mathematical physics community.

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Summary: One of my favorite books
Review: Robert Geroch's "Mathematical Physics" is a stunningly beautiful exposition of basic mathematics needed for science using the minimal amount of category theory not to be insane from the modern mathematical perspective (he cleverly hints at more category theory in the problems). I would consult this book first on basically any of the subjects that he covers. You will find the most elegant, original and to the point discussions there. There nothing on differential geometry, however.

Rating:
Summary: One of my favorite books
Review: Robert Geroch's "Mathematical Physics" is a stunningly beautiful exposition of basic mathematics needed for science using the minimal amount of category theory not to be insane from the modern mathematical perspective (he cleverly hints at more category theory in the problems). I would consult this book first on basically any of the subjects that he covers. You will find the most elegant, original and to the point discussions there. There nothing on differential geometry, however.

Rating:
Summary: very useful
Review: This is a very nice, compact (no pun intended) book - it's not a mathematics textbook in the usual sense (i.e. a detailed users manual) but an overview of how all the different bits fit together in mathematical physics - a map. It sits beside Choquet-Bruhat et al.'s Analysis, Manifolds and Physics on my shelf.

It's worth pointing out that Robert Geroch is thanked, together with Roger Penrose, in the preface to 'The Large-scale Structure of Spacetime', as inspiration and influence.