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A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry Hardcover – 16 Dec 2004

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Product details

  • Hardcover: 618 pages
  • Publisher: Cambridge University Press (16 Dec. 2004)
  • Language: English
  • ISBN-10: 0521829607
  • ISBN-13: 978-0521829601
  • Product Dimensions: 17.4 x 3.3 x 24.7 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 543,130 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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'This is a beautifully crafted book. … Peter Szekeres presents in the most elegant and compelling manner a magnificent overview of how classic areas such as algebra, topology, vector spaces and differential geometry form a consistent and unified language that has enabled us to develop a description of the physical world reaching a truly profound level of comprehension. … Szekeres's style is clear, thorough and immensely readable. His selection of topics concentrates on areas where a fully developed rigorous mathematical exposition is possible. … One cannot help but be slightly awed by the beauty and the capability with which seemingly abstract concepts, often developed in the realms of pure mathematics, turn out to be applicable … I recommend that you get hold of this book for yourself or for your library.' The Times Higher Education Supplement

'The superb layout and an index contribute to the excellent overall impression of this book …'. Zentralblatt MATH

' … the book may serve as an easily accessible introductory text on a wide range of the standard and more basic topics in mathematics and mathematical physics for the beginner, with an emphasis on differential geometry. a nice feature is that a considerable number of examples and exercises is provided, together with numerous suggestions for further reading: there is also an extensive index which will be particularly helpful for beginners in the subject.' General Relativity and Gravitation Journal

Book Description

This book, first published in 2004, provides an introduction to the major mathematical structures used in physics today, presenting the concepts and techniques at a level suitable for advanced undergraduates and beginning graduates. Includes numerous exercises and worked examples, to test the reader's understanding of the various concepts, as well as extending themes covered in the main text.

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The object of mathematical physics is to describe the physical world in purely mathematical terms. Read the first page
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1 of 1 people found the following review helpful By NR on 17 Aug. 2013
Format: Hardcover Verified Purchase
Caveat: I only started reading this a few days ago. So, not having finished it (or even close) please feel free to ignore this 'review', especially the star rating above.

Still, I'm finding I like this book enormously. The explanations are clear and crisp, and the examples are helpful (though maybe not enough). And it's certainly much better than the book I was looking at previously - Mathematics of Classical and Quantum Physics by Byron and Fuller. Also, though I haven't looked at everything yet (or anything like), I'm impressed at how much the book aims to cover (the pace is a little brisk therefore, but that's all right too as it keeps one from getting bored) - just the sort comprehensive coverage at an accessible level I was looking for. Finally, as someone with a maths rather than physics background, I much prefer the author's decidedly 'mathematical' or 'pure' style of exposition to what you find in physics books (he makes a point of highlighting this at the outset, saying this a book on *mathematical* physics, a branch of mathematics, and not on theoretical physics, which is part of physics).

But to tell the truth: I only started writing this in order to complain. *Why is this book so flipping prohibitively expensive?* At the moment I'm reading a PDF version downloaded from the internet on my Kindle. I was impressed enough to decide to buy this on here. But ah, the price! Fifty smackeroonies!! Oh dear oh dear! And not even a second-hand marketplace copy to be had. (I'm not a cheapskate; I'm just poor.)
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4 of 5 people found the following review helpful By Ted Maxwell on 9 Jan. 2009
Format: Hardcover
Many of the other texts on Mathematical Physics are completely inaccesible, containing reams of theorems and proofs of various results, written in an incomprehensible style. This one differs in that, whilst it still contains theorems and proofs, everything is written in an almost conversational tone. All theorems are communicated in a way that makes them particularly relevant to both physics and mathematics research and education. If your pure maths is rusty, or your just out of a physics degree where little pure maths is taught, then this text is perfectly accesible to you, but i do reccomend having a read of A Concise Introduction To Pure Mathematics by Martin Liebeck, and have a go at the problems, this will seriously help aid your understanding. All in all, a wonderful text on mathematical physics.
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Most Helpful Customer Reviews on (beta) 6 reviews
47 of 51 people found the following review helpful
A fast introduction to mathematics in physics 1 Jan. 2006
By Juhani - Published on
Format: Hardcover
The book does not assume prior knowledge of the topics covered. However, the reader will find use of prior knowledge in algebra, in particular group theory, and topology. Compared to texts, such as Arfken Weber, Mathematical Methods for Physics, A Course in Modern Mathematical Physics is different, and emphasis is on proof and theory. The text is reasonably rigorous and build around stating theorems, giving the proofs and lemmas with occasional examples. The style is not the strictest, although making the text more reader friendly, it is easy to get confused with which assumptions have been made, and the direction of the proof. Sometimes only the "if" part is proven.

Students familiar with algebra will notice that the emphasis is on group theory, interestingly the concept of ideals is left mostly untouched. For more on representation theory a good reference is Groups Representations and Physics by H.F. Jones where solutions to some of the exercises can be found, and examples of the use of the fundamental orthogonality theorem applied to characters of represenations.

The first 6 chapters are relatively straight forward, but in chapter 7 Tensors the text becomes much more advanced and difficult. Chapter 10 on topology offers some lighter material but the reader should be careful, these consepts are to re-appear in the discussion of differential geometry, differentiable forms, integration on manifolds and curvature. These are not the most simple subjects and it is clear that they deserve entire courses of their own.

The book has insight and makes many good remarks. However, chapter 15 on Differential Geometry is perhaps too brief considering the importance of understanding this material, which is applied in the chapters thereinafter. The book is suitable for second to third year student in theoretical physics.
15 of 16 people found the following review helpful
A serious, wide spectrum introduction to modern mathematical physics 9 Oct. 2005
By R. C. de Berredo - Published on
Format: Hardcover
This book covers almost every subject one needs to begin a serious graduate study in mathematical and/or theoretical physics. The language is clear, objective and the concepts are presented in a well organized and logical order. This book can be regarded as a solid preparation for further reading such as the works of Reed/Simon, Bratteli/Robinson or Nakahara.
7 of 8 people found the following review helpful
Provides an excellent foundation for advanced studies 10 Feb. 2009
By Gu'an - Published on
Format: Hardcover
I started this book with very little mathematical background (just an electrical engineer's or applied physicist's exposure to mathematics). By the end of this book, I had an advanced exposure to foundational modern mathematics. Now, I am planning to start on "Differential Topology and Quantum Field Theory" by Charles Nash (with other mathematics reference books to complete the proofs in it).

This book also provides a good amount of material showing the application of mathematical structures in physics - Tensors and Exterior algebra in Special relativity and Electromagnetics, Functional Analysis in Quantum mechanics, Differentiable Forms in Thermodynamics (Caratheodory's) and Classical mechanics (Lagrangian, Hamiltonian, Symplectic structures etc), General Relativity etc.
This book is simply outstanding 2 Sept. 2011
By njdj - Published on
Format: Hardcover
For the intended audience (advanced students in theoretical physics) this is by far the best book available on the material it covers. The text is clear, the topics covered are presented in a logical sequence, and the student who works through the book will acquire a good background for understanding more advanced texts. Of course, not every area of mathematics used in theoretical physics is included; that would be impossible in a single book; but it is usable as a reference. In my opinion, however, this is mainly a book to study and work through, rather than a reference book. Exercises in the text help readers to check and solidify their understanding of the material.
The author has obviously taken great care in the preparation of the book. There are very, very few typographical errors. Sadly, it is rare nowadays to find a book which has been as carefully proofread as this one.
If you are a physicist and need to come up to speed on any of the topics covered by this book (one of the other reviews has helpfully listed the table of contents), waste no more time searching, just buy it.
9 of 19 people found the following review helpful
Jumping over the Gap 29 Dec. 2005
By mzg - Published on
Format: Hardcover
Most physicists avoid mathematical formalism, the book attacks this by exposing mathematical structures, the best approach I've ever experience. After reading the first chapter of this books I can assure is a must for everyone lacking mathematical formation undergraduate or graduate.

It surely jumps over this technical gap experienced by most physics opening the gate for advanced books an mathematical thinking with physic intuition.

Unfortunately is very expensive, i hope i could have it some day.
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