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Название: Explorations in Mathematical Physics: The Concepts Behind an Elegant Language

Автор: Koks D.

Аннотация:

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_.