Mathematical Physics (Chicago Lectures in Physics) by Robert Geroch (PDF)

Description

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the “whys” of proofs and of axioms and definitions. This book, based on Geroch’s University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I used this book for a summer course. It covers a wide range of topics through use of category theory. I find this approach very useful. It provides a framework for understanding the various branches of mathematics that he discusses. It’s also easier to remember various theorems since many things are similar from one category to the next.The title though is somewhat misleading. This is very much a math book. He starts with basic definitions in each category and then states various theorems. He does provide proofs for everything. This may not be for everybody but once you get used to it it can be a lot of fun. The actual physics part is very light. There are a few chapter of applications of vector spaces, the Lorenz group, and dynamical systems. But overall it’s pretty much just math.There are exercises after every chapter and the chapters pretty short. This is nice especially since I find myself reading it very slowly as it is kind of dense. It keeps it from getting to tedious.Overall, if your a physics student and want to learn about more advanced math topics (topology, Lie groups, Hilbert spaces) I would give this a try. Just be prepared for a lot of theorems and a lot of proofs.

⭐This book came to my attention because it starts with category theory in the first chapters and then moves to traditional contemporary mathematical physics topics. The author also provides physical examples along the way. The flow of this mathematical text is very smooth (proofs can be omitted from reading) and explanations are very intuitive. The latter seems to be the main goal of this text. It is also structured into 56 chapters so it can be possible to casually read this book in 2 months. One strange thing I noticed though is the avoidance of the manifold terminology: the author only uses the word “manifold” only once and without an explanation what it is about so you may even not notice that.

⭐This book was suggested as a prerequisite for Analysis, Manifolds, and Physics, itself recommended to accompany The Global Approach to Quantum Field Theory by Bryce DeWitt. It serves as an introduction to many of the areas of advanced mathematics needed for theoretical physics, employing categorical language to tie them together.

⭐I purchased it knowing I probably don’t know enough mathematics to understand the book, so I am advancing my understanding of advanced mathematics before I read the book. I purchased the book now to make sure I will have it in the future to read.

⭐Yes, I like it. I felt I had mastered the category of sets and some of groups and vector spaces, but soon after that I bogged down and never took it up again. Sure, I could mostly follow the categorical proofs, but the problems were something else. I’m an amateur. I’ve had no formal math training beyond linear algebra, and that’s probably the reason for my difficulty. In other words, this looks like a good book at the graduate level in physics or applied math, but I wouldn’t recommend it to someone like me or the average physics undergrad.

⭐I found this text to be a clear exposition of the mathematical basis for contemporary theoretical physics. Geroch’s use of category theory provides a nice worked example of the power of that organizing principle. (An aside: I believe Stanislaw Ulam’s mot about an algebraic topologist being someone who likes to draw analogies between analogies refers to category theory.)

⭐There is an old joke about mathematical physics being physics done by mathematicians, and theoretical physics being mathematics done by physicists. Robert Geroch, a physicist and professor of physics, has collected in this medium-sized book a condensed amount of the advanced mathematics that is used in theoretical physics, from category theory to topology to functional analysis.The book is not thought to be a full-featured manual, but an insightful introduction. This target is successfully reached, with precise definitions, lots of examples, relatively few but always well chosen theorems, and lots of exercises to do. The style is quite informal, which makes the reading fun and not tiresome.The only real flaw I could find, is the name “Lebesgue” misspelled “Lebesque” by some typist who clearly knew nothing about integration theory. But this is not enough to deny this book a five stars ranking.

⭐If you want to study all these beautiful modern topics in mathematical physics that lie beyond calculus-level mathematics but you have a finite lifetime, then this is the book for you.Traditionally, mathematical physics was (and still is!) based on calculus-level maths, but nowadays there are many topics in this field that require a higher level of mathematical sophistication.One needs algebra, topology, measure theory, functional analysis, but also smooth manifolds, Riemannian geometry, connections on bundles, distributions & pde, infinite dimensional manifolds and geometric topology. Not all these topics go into this book, but be sure that the first four do!This little book is probable the best introduction to mathematical physics at a higher level, for someone who has already some experience with ‘standard’ mathematical physics (otherwise one may find this approach somewhat unmotivated).An ideal continuation of Geroch’s book is Mme Choquet’s Analysis, Manifolds & Physics.

⭐Fantastic book in explaining introducing algebra and topology to physics audience. I find that Geroch’s explanations are very clear andhelpful in gaining an intuition for the material. He also, manages to not introduce a bunch of mathematics that is never used in physics (yes category theory is used in highly theoretical work). This book should be read by all physics students interested in doing theory, and sometimes get intimidated by pure math texts (like me 😉 ).

⭐Prompt and efficient service from this reliable seller. Item as described, perfect condition. Very pleased with the deal. Thanks a lot.

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