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Group Theory: Birdtracks, Lie's, and Exceptional Groups
by Predrag Cvitanović

5.0 out of 5 stars A beautiful work you must have, October 23, 2008
Any practitioner of the famous Bourbaki group would have a brain implosion if they tried to read this book. Their aversion to "practical" and "visual" tools in mathematics as opposed to the rigorous formalisms for which they are justifiably famous is well documented by Benoit Mandelbrot, amongst others. They would not like this work.

This book is, first and foremost, a book about beauty with beautiful ideas and striking visuals. This is deliberately so. As the author states, "if diagrammatic notation is to succeed, it need not only be precise, but also beautiful". Of course one would expect that a book whose subject matter is primarily the many elegant symmetries of nature would end up dealing with beauty, not only at the mathematical but also at the visual level. I can testify to the success of Professor Cvitanović's endeavors on this front. When the book arrived I showed it to my wife, who has some artistic training and a plus-critical eye for visuals, (but who certainly can't tell the difference between a casimir and a casserole). Her response said it all.

To fully appreciate this book you need postgraduate qualifications in a slew of highly technical subjects and I won't pretend that my qualifications are anywhere nearly sufficient for this. But I am mathematically literate enough and have enough formal training, (and enough interest in many of the topics covered), to recognize that this is a beautiful and brilliant work which will give me and other readers years of additional pleasure. I say "additional" because I have been tracking Professor Cvitanović's web book, from which this print originates, for a long time now and the contents of this work are not new to me.

Take note that this is not a textbook or even a standard reference of any sort and it makes no concessions whatsoever to lack of prior knowledge. It is primarily a highly technical research monograph about problem solving. Each chapter launches headfirst into its subject matter without offering any but the most cursory introduction. The reader is expected to understand the nomenclature, the context of the material and be familiar with the mathematics and physics dealt with. But even with this, the amazing clarity of Professor Cvitanović's writing shines through. In contrast to the dense and murky scribblings of many (I might even suggest, most) texts at this level, the writing in this book as well as the flow of logic, the layout and everything else which matters is breathtakingly simple and, may I say, beautiful. The work deserves 10 stars out of 5. (I'm still working on the mathematics of that!)

I only wish that the good professor would see his way clear to publishing in hard cover his other web book, ChaosBook.pdf, which is an equally elegant and valuable work and which aligns much better with material that I am very familiar with. Perhaps one day...

I strongly urge all interested readers to purchase this book in hard cover, even if they have the web book version. This is not only for the considerable value of the book itself, but also as a way of showing appreciation for the remarkable generosity and altruism of the author in making the fruits of years of hard labor available for free.