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Explorations in Mathematical Physics: The Concepts Behind an Elegant Language |  | Author: Don Koks
Publisher: Springer
List Price: $79.95
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Rating:  3 reviews
Sales Rank: 651021
Media: Hardcover
Edition: 1
Pages: 544
Number Of Items: 1
Shipping Weight (lbs): 2
Dimensions (in): 9.3 x 6.4 x 1.2
ISBN: 0387309438
Dewey Decimal Number: 530
EAN: 9780387309439
ASIN: 0387309438
Publication Date: September 15, 2006
Availability: Usually ships in 1-2 business days
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| Editorial Reviews:
Product Description
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
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| Customer Reviews:
 The book I turn to for clarity on mathematical physics February 1, 2010
Bookster
1 out of 1 found this review helpful
I own about a dozen textbooks on different subjects in mathematics covering topics like Fourier analysis, mathematical statistics and mathematical physics. I also have textbooks on quantum mechanics and solid state physics that use a lot of that math. This all came about through graduate school studies and my current job. Having studied much of this material in school and on the job, I thought I understood the basics of it all. Yet when I started reading this book I discovered some eye-opening insights and had several aha-of-course! moments that kept me reading on.
As Dr. Koks explains, the book is more a narrative than a textbook. Thus, there are no problem sets, no useless end-of-chapter summaries, no extraneous color-coded exercise boxes. Instead, Dr. Koks gets straight to the point of explaining the whys of several mathematical phenomena in conversational, common-sense prose. For example, Dr. Koks discusses the familiar exponential function and its relation to radioactive decay by drawing a parallel to a group of persons each flipping a coin; this analogy intuitively shows, in a manner equations can't, why radioactive decay follows exponential behavior. Another example I found useful was his point about the relationship between the reciprocal lattice and a vector cobasis. I've worked with reciprocal lattices but never realized that point before. And his explanation of how a probability density evolves from a histogram is superb, invoking nothing more than first-semester calculus. Yet I've never seen a comparable explanation in any of the statistical books I've read.
The above examples are from the first few chapers of the book, which I've read. The latter chapters cover aspects of tensors, special and general relativity, field theory, and cosmology. Having embarked on self-study of these subjects out of academic curiosity, I know I'll be turning to this book for clarification on a lot of these subjects. But even though I've noted that the book is not a textbook per se, the number of equations is still on par with any mathematics textbook, and I wouldn't recommend this book for the mathematically faint of heart. Yet the equations aren't there to intimidate but instead are used to make the author's points. With a bit of effort they can be readily understood.
If you're studying mathematical physics (say, using Hassani), quantum mechanics, special or general relativity, or just love a clear exposition on the subtleties of many of the mathematical concepts underlying physics, you will want this book for its lucid discussions that are usually missing from mainstream textbooks. The book is accessible to advanced undergraduates, and as a working professional with an engineering Ph.D. I glean all sorts of insights from it. I highly recommend _Explorations in Mathematical Physics_.
UNIQUE AND MONUMENTAL February 14, 2009
Cantilli Giacomo
8 out of 8 found this review helpful
If you aim at reaching the summit of a mountain so that you can seize the whole at glance, then you must read this precious and (relatively) small book.
Most textbooks exhibit kilometers of formulas, but are unable to tell you the essence (i.e. the concepts). This is obvious, because the mathematical language (like all the languages) is not semantic!
In Explorations, instead, a formula is never a starting point; it is the formalization of a line of reasoning. The absence of specific arguments doesn't matter; on the contrary, it's to your advantage. In this way, in fact, you can't lose yourself in details and may concentrate on the project of the author, who can give you very much. I am hinting at the conceptual foundations of Physics in splendid symbiosis with their modern mathematical counterparts.
I don't see any restriction on the reading public. The book is for anyone loves (first of all) knowledge and (then) Physics. Besides, in my opinion, it is the ideal guide (in the use of ordinary textbooks) for truly concerned undergraduate and graduate students. After all, Differential Calculus and an introductory course in Linear Algebra are the only requirements, even though the book ranges (in clear and polish style) over the entire realm of Physics.
I am not saying that Explorations is an easy book. On the other hand you can't combine simplicity with a profound thought, unless you admit that the simplicity of the form is always related to the complexity of the content. From this point of view Don Koks treats a difficult matter with the greatest simplicity one could possibly imagine.
In all sincerity, only the reading of section 2.10 (dealing with Commutators and the Indeterminacy Principle) has been somewhere laborious to me. Besides, I think (but I could be wrong) that section 8.10 (dealing with Exterior Calculus and the Theorems of Stokes and Gauss in Higher Dimensions) could have been written with greater clarity.
As an ex-professor I want to send a message to the students: if you do your best to assimilate this superfine pedagogical work, your course of study will be handy and pleasant.
 Delivers on its promise May 20, 2007
S. Shuman (South Africa)
30 out of 31 found this review helpful
As an advanced undergraduate physics student, I found this book to be one of the few physics books which focusses on bridging the gap between physical understanding and the mathematics. I found the book a bit too orientated towards diff forms and relativity. To round it off a bit more, I would have liked to see some of the more difficult concepts from electromagnetics included e.g explanations behind quadrupole tensors, stress-energy tensor, helmoltz decomposition and TE,TM,TEM waves.
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