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Mathematics for Physics: A Guided Tour for Graduate Students, by Michael Stone, Paul Goldbart
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An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
- Sales Rank: #956504 in eBooks
- Published on: 2009-07-09
- Released on: 2009-07-09
- Format: Kindle eBook
Review
"The many features that make the book valuable to students and teachers also represent a substantial step toward making modern mathematics a part of the working arsenal of practicing physics. I strongly recommend it to those who feel the need to upgrade their mathematics repertoire."
David Khmelnitskii, Physics Today
About the Author
Michael Stone is a Professor in the Department of Physics at the University of Illinois at Urbana-Champaign. He has worked on quantum field theory, superconductivity, the quantum Hall effect and quantum computing.
Paul Goldbart is a Professor in the Department of Physics at the University of Illinois at Urbana-Champaign, where he directs the Institute for Condensed Matter Theory. His research ranges widely over the field of condensed matter physics, including soft matter, disordered systems, nanoscience and superconductivity.
Most helpful customer reviews
46 of 48 people found the following review helpful.
Great book!
By James
Warning: review based on first half of book.
I used this book for a graduate level Mathematical Physics class where We worked through Chapters 1 through 9. I've skimmed a little through the rest which also looks good. So let me tell you it's strengths and weakness. The book is definitely intended for graduate physics students. Most of the examples are actual physics uses of the math you learned (and there a lot), because of this you probably need a solid undergrad background in physics at least classical mechanics, E&M and Quantum, as well as Calculus, Linear Algebra, Differential Equations (and more math exposure the better!).
Strengths:
1. It goes through a lot of math! In fact because of this it is useful as a reference book as well, the book is 800 pages. Covering a broad range of traditional mathematical physics and more modern methods(e.g. Differential Geometry, Groups, ect.)
2. Lots of real world examples. This I think is probably it's biggest strength, and makes it worth the purchase, at least for me. The starts by explaining the mathematical concept, and then gives you worked out examples from physics. A lot of modern mathematics is extremely abstract, these examples help to get a feel for what the math actually says.
3. The explanations are thorough. For the most part, the book does not gloss over topics. The rigor is what one would expect for a theoretical physics, not as rigorous a pure math course, but more rigorous then what is presented in physics courses.
Weakness:
1. Because the book covers a lot of material and gives so many worked out examples 'simple' steps in derivation are omitted. For the most part this is not a problem. It just means you have to spend more time on each page, perhaps with pencil and paper, but it does make it hard to casually read. (This probably better then the other option where every step is included, the book would have probably been 2000 pages)
2. This is probably a statement about the material in general then about the book. The math is hard. It takes a lot of time and work on the part of the reader to really understand a lot of these concepts.
Overall:
As an aspiring theorist, I have a lot of math and physics books on the shelf(more like shelves). Its hard to say for sure but I see this as a book I can and will return to throughout my graduate school experience for help on understanding the math used in my courses. If your a senior in undergrad physics or somewhere in your graduate program this is a book that will return the investment. If you want a mathematical reference that is relevant to physicist this book is also for you. If you haven't taken that many math courses or don't have a solid physics background you might want to explore other books before diving into this one.
20 of 21 people found the following review helpful.
Not a useful reference
By Scelesti
This was the required text for a graduate course I took in Mathematical Methods for Physicists. We covered material from chapters 1-6, 8, and 17-19 which deal with calculus of variations, function spaces, linear differential operators, ordinary and partial differential equations, Green's functions, special function theory, and topics from complex analysis. The book deals with many other topics, namely group theory and differential topology & calculus on manifolds, but these were not covered in the course I took.
What are the strengths of this book? I suppose it would be useful if you have a *very strong* background in many of these topics already and just want another perspective. The topics covered are broad, and the applications that the authors have chosen to covered may be useful, depending on your area of interest.
What are its weaknesses? Every time I had to reference this book to supplement my notes from class or to help with homework problems, I became frustrated very quickly. Too many steps are omitted in derivations to follow the logic of the authors, and on many occasions they give a partially worked example rather than the mathematical details required to make the concepts clear. I want a book for my reference library that I can pick up, page to the section that deals with the topic I'm interested in (like the book by Kreyzig: Advanced Engineering Mathematics, Textbook and Student Solutions Manual) and read a clear exposition of the mathematics, rather than having to slog through a vague, partially worked example from another area of physics and try to guess what the authors mean. After spending several hours trying to connect one line of a derivation with the next and ultimately failing on several occasions, I started looking elsewhere for textbooks. Let me mention as well that I am a fluid dynamicist by training; I'm certainly no stranger to long and messy derivations.
In short, this book could be useful *supplement* to other applied mathematics texts in your library, but do not expect to be able to pick it up as a reference and obtain useful information in a timely manner.
11 of 15 people found the following review helpful.
Confusing, obscure, and poorly organized. Avoid this one.
By Oliver D. Hanson
I used this text in a graduate math physics class. We covered the first 9 chapters (approximately), with some skipping around. The authors play fast and loose with notation, are excessively sparse, and seem to emphasize overly 'mathematical' excersizes -- often losing sight of this book's purpose: to teach physicists. By the end, I found the only time I was even referencing this book at all was to copy down homework problems. For actual content (and to assemble sufficient supporting material in order to answer those homework questions), I sought out other textbooks which presented topics more straight-forwardly and clearly.
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