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Topics in Contemporary Mathematical Physics [Hardcover]

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Item description for Topics in Contemporary Mathematical Physics by Kai S. Lam...

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry. The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

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Item Specifications...

Studio: World Scientific Publishing Company
Pages   604
Est. Packaging Dimensions:   Length: 1.5" Width: 6.5" Height: 9.75"
Weight:   2.6 lbs.
Binding  Hardcover
Publisher   World Scientific Publishing Company
ISBN  9812384049  
ISBN13  9789812384041  

Availability  0 units.

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Reviews - What do customers think about Topics in Contemporary Mathematical Physics?

Wonderful for a calculational refresher/reference  Sep 8, 2006
(NB. I would give Lam's book 4.5 stars if I could, as there are some minor issues.)

First of all, I bought this book *despite* its being published by World Scientific, a publisher that I consider to have a rather dodgy catalogue. And this book is a pleasant surprise. Having finished a detailed read of it, I expect that I will use it before Nakahara when the rubber has to hit the road.

I bought the book in order to have a single primary calculational reference on the topics it surveys, and worked through the exercises as a refresher and to deal with notation. When I first bought the book, I was incredulous about the author's claim that he used the material in a year-long course for undergraduates, but after working through all but five or so exercises in the last 25 chapters, I find that the vast majority of the exercises can be performed in the book's margins (perhaps by sometimes writing a bit small and using a calculator for numerical matrix manipulations).

That said, they are at a nice level for acquiring basic facility; the emphasis is on calculation, not abstraction and deep understanding. Any exercises the reader has not done elsewhere should be done as they are encountered, and the book needs to be supplemented: either by good lectures or (for the autodidact) more advanced supplements (I would suggest Fulton and Harris for representation theory, and Nakahara for geometry) to provide better insight and foster intuition. Proofs requiring a high degree of abstraction are omitted, which is good for a calculational reference but often leaves motivation and structure more obscure than a Springer "GTM" on the same subject would.

Broadly speaking, one can see the text as comprised from three segments: chapters 1-17, on "the stuff that nearly all practicing physicists will have seen at some point" (though perhaps in different modes of presentation); chapters 18-28, on representation theory; and the remaining chapters, on geometry (with a smattering of topology). The middle section is probably the most demanding, excepting possibly chapters 41-43, which cover characteristic classes and the index theorem. For this there can be no remedy: the subject matter is hard. But Lam makes a gallant effort, including what he can and omitting what he must to keep the book at its level.

Most seniors will be overmatched by its later parts. Though the exercises are generally easy (occasionally some minor subtlety [or an appeal to other sources] is required), the concepts are among the deepest and subtlest mathematics that most physicists (or non-PhD mathematicians) will ever encounter, and Lam is not the place to gain a complete understanding of any of them. On the other hand, the emphasis on calculations, actual coordinates, and (best of all) connections with useful physics make the book very nearly ideal for a student or practitioner who wants to see the rubber hit the road and is prepared to supplement the text.

There are a few misprints, but not many (I have compiled a list of errata and can be reached at schuntsm AT nps DOT edu), and the author's style ensures that most mistakes will be obvious during a careful read. The level of rigor is just right for the intended audience, and the exercises are well-positioned: the book can be read without them, but they are not onerous and can serve to (re)familiarize the reader with the details.

For my stated purposes, I cannot think of a better book. It is concrete and accessible, and includes practical examples from physics. The reader need not be involved with strings to find some benefit from this book.

(I wish there was a complementary book dealing with differential equations, numerical techniques/algorithms and stochastic processes in the same style!)

All in all, this is a wonderful book, well worth the price for the paperback. Don't buy the hardback--just apply some good tape to the covers: they may see a lot of use.
Motivates learning and makes advanced material seem easy  Aug 18, 2006
Though I have yet to finish the book, I am incredibly pleased with it so far. There's no such thing as a perfect book; Lam succeeds by giving us a book that is a good balance between some extremely detailed books for the patient (e.g. Frankel's "Geometry of Physics") and other books that are good, but often move too quickly for first-timers (e.g. Nakahara).

The book does assume that readers are comfortable with a theorem-proof style (though it is extremely casual here) and it assumes a strong linear algebra/abstract vector space background, but those who qualify will find themselves quickly learning about some rather advanced subjects (Lie algebra theory).

Finally, Lam makes sure to interject chapters that illustrate some applications of the math covered up to that point in the book. Chapters like these will keep physics students (like me) plugged in to the book.

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