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16 of 17 people found the following review helpful
4.0 out of 5 stars A little mathematics goes a long way, September 28, 2008
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This review is from: Special Relativity (Springer Undergraduate Mathematics Series) (Paperback)
This book requires only a working knowledge of linear algebra and multivariate calculus, and a basic understanding of classical mechanics and electromagnetism.

The author begins by providing a simple but general mathematical exposition of relative motion in classical mechanics. The next two chapters review Maxwell's equations and what they imply for the propagation of light. Having set the stage in this way, the axioms of Einstein's theory are introduced and their implications worked out mathematically, leading the reader to a clear understanding of Minkowski four-dimensional space time and the Lorentz transformation. The exposition is accompanied by a number of classic brainteasers in special relativity.

The weak spot (and hence only four stars) is the treatment of the mass-energy equivalence, which does not include a rigorous derivation of Einstein's famous formula E=mc^2, even though such a derivation is no more demanding mathematically or conceptually than the other issues discussed in the book.

In sum, this book should appeal to any mathematically literate non-physicist who wants more than just a superficial introduction of Einstein's special relativity.
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16 of 18 people found the following review helpful
5.0 out of 5 stars Highest Quality Possible, January 19, 2011
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This review is from: Special Relativity (Springer Undergraduate Mathematics Series) (Paperback)
This is a splendid and very carefully prepared book. It gives very clear and concise explanations of the physical content of the special theory of relativity, and it puts those explanations together directly with the simplest correct mathematical descriptions. It makes the subject as simple as possible---but not simpler. The explanation is clear, and the problems are particularly well chosen and insightful. It is a way to establish a true and complete understanding of the subject as quickly as is reasonably possible. In my opinion, it is the best available introduction and the only book that is really "best choice" for a first course in the subject or as the primary text for self-study.

Not everyone has the same taste. Some people would like to study the subject with as much mathematics being forgiven as possible. Those people will want T. M. Helliwell's book "Special Relativity" instead. Most books that try to avoid almost all the mathematics end up avoiding almost everything interesting and sometimes give the wrong impression, at least in some details. Helliwell is distinguished among the "math lite" approaches.

An alternative textbook introduction is A.P. French "Special Relativity," intended for M.I.T. freshmen. Taylor and Wheeler offer "Spacetime Physics," roughly a more "Caltech like" or "Princeton like" approach. Wolfgang Rindler offers "Introduction to Special Relativity." Both French and Taylor/Wheeler are a little bit simpler, yet thorough introductions, and it is likely that most students would want one or the other as a supplementary text, especially if the goal is pure self-study. Taylor/Wheeler is more colorfully phrased. Rindler's book is almost encyclopedically complete, although I find some sections of his writing to be less clear than they really should be---considering that he is a world class scholar writing for one of the world's top technical publishing houses. Because his treatment is so complete, I think most people will want his book as their long-term reference on the subject. In my own opinion, these are all the "good" books on the subject. If you are a college junior or further along, Woodhouse seems the logical place to begin. College freshmen will probably want to start with French or Taylor/Wheeler instead. High school and below will probably make a better start with Helliwell.
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4 of 4 people found the following review helpful
5.0 out of 5 stars Lucid and succinct mathematical introduction, December 19, 2012
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This review is from: Special Relativity (Springer Undergraduate Mathematics Series) (Paperback)
that does not shirk physics motivation. Prof. Woodhouse's goal is to provide a mathematically rigorous understanding of the key conceptual structures underlying special relativity (but eschewing tensors). To this end, he avoids becoming bogged down in detailed discussions of measuring rods and clocks, light signals, tedious calculations using Lorentz transformations, or long-winded analyses of various so-called paradoxes that are standard fare in some other textbooks (indeed, "paradox" is discussed only once in the book: on p.114 where he dispenses with the so-called Twin Paradox in one short paragraph at the end of section 6.5 [Constant Acceleration]). After an introductory chapter [Relativity in Classical Mechanics] to set the stage, he launches, in chapter 2 [Maxwell's Equations] and chapter 3 [The Propagation of Light] into a wonderfully clear, extended exposition of Maxwell's equations and their implications. These two chapters -- excluding the optional final chapter, about 30 pages out of roughly 150 pages -- make the heaviest demands on the reader (at least they did on this reader).

His treatment of Maxwell's equations in chapter 2 is superb. He starts from The Principle of Relativity (p. 21) and three assumptions specific to electromagnetism (pp. 23-24, accessible via Search Inside) and shows, in a step by step fashion with adequate commentary, how to derive Maxwell's Equations, all in a mathematically rigorous but reader friendly style (no difficult steps in the reasoning are omitted). In chapter 3, he draws out key consequences of Maxwell's theory, discussing in detail the all important source-free equations and the prediction of source-free electromagnetic waves. My background in electromagnetism was quite weak, and so I found these two chapters particularly enlightening. If you work your way through those two meaty chapters, the rest should, for the most part, be smooth sailing.

Only in chapter 4 [Einstein's Special Theory of Relativity] does he get into operational definitions of distance and time, the relativity of simultaneity, length contraction, time dilation and using Bondi's k-factor, two-dimensional Lorentz transformations. This discussion is quite short (about 15 pages). Then in chapter 5 [Lorentz Transformations in Four Dimensions], he gets into the heart of the mathematics of Lorentz transformations, making use of matrix theory and matrix-theoretic proofs of some key propositions, covering the main 4-vectors, inner product (invariant line element), causal structure of Minkowski spacetime, invariant operators, and more. Chapter 5 is only about 20 pages excluding an optional section but nonetheless is admirably clear. Chapters 6 [Relative Motion], 7 [Relativistic Collisions] and 8 [Relativistic Electrodynamics] explore standard topics, all written with his characteristic flair for clear, mathematically precise yet enjoyable explanations. There are many definitions and theorems in this book but he is careful to provide physical motivation and caveats to help avoid misunderstanding, and to focus on the main take away points.

For those with the required background in mathematics and physics, his book is an ideal means for achieving a respectably deep understanding of special relativity and for positioning oneself to understand more advanced topics, including general relativity (for which, I recommend his equally lucid and concise General Relativity (Springer Undergraduate Mathematics Series) as the next logical step).

So what are those prerequisites? On the physics side, the main requirement is a sound understanding of standard electromagnetism as taught to undergraduate physics majors (e.g. as treated in Fundamentals of Physics). On the mathematics side, one needs to be comfortable with the basics of linear algebra/matrix theory, vector calculus (e.g. div, curl, grad, divergence theorem aka Gauss's theorem) and not be thrown by rather abstract proofs.

I have many books on special relativity and in my view, Prof. Woodhouse's is, hands down, one of the very best, mathematically oriented introductions.
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Special Relativity (Springer Undergraduate Mathematics Series)
Special Relativity (Springer Undergraduate Mathematics Series) by N. M. J. Woodhouse (Paperback - March 12, 2007)
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