Georgia Tehch’s Pedrag Cvitanovic’ and friends write physics and maths books under the nome de guerre of The cyclist team. These books are interesting in many ways. First of all, they are comprehensive and of excellent quality, although, fortunately, these are not extremely rare in the field. What is not so common is the dose of humour and engaging wittiness distilled in their pages. And, besides, they’re being written over a span of many years in a totally public manner: you can view and download them in PDF of Postscript and are frequently updated. As they explain in their webbook rationale, they don’t even plan to ever publish them:
The relevant parts of a good text will be printed and perused, no less than a good electronic preprint. A bad text should be junked anyway. If a student in Buenos Aires or Salamanca reads a chapter and is wiser for it, that is all it takes to make us happy. The webbook has done something to further little piece of wisdom that we know and love.
Relax by reading Classics Illustrated, diagrammatic, Predragian vision of field theory. The exposition assumes no prior knowledge of anything (other than Taylor expansion of an exponential, taking derivatives, and inate knack for doodling). The techniques covered apply to QFT, Stat Mech and stochastic processes.
Next comes the Group Theory Book, which, under the subtitle of Birdtracks, Lie’s and Exceptional Groups and spanning almost 300 pages, will tell you all you’ll ever need about Lie Groups and Algebras. This nice PDF presentation makes for a good summary of its contents, or, as Pedrag says, of “most of the Webbook at a cyclist pace, in 50 overheads” (see also here for more short intros). In case you’re wondering, birdtracks are to Lie Groups what Feynman’s diagrams to QFT, and then more. As you can see, Pedrag loves diagrams and pictures, in a way that reminds me of Penrose’s fondness for geometrical descriptions (actually, birdtracks have many a point in common with Penrose’s diagrammatic tensor notation, who even wrote a letter claiming his precedence on it). And, again, don’t miss the book’s site for lots of additional goodies.
Finally, there’s the Chaos Book, probably my favourite. Again, the authors introduce it far better than i would:
Quite a few excellent mathematics monographs on nonlinear dynamics and ergodic theories have been published in last three decades. On the whole, they are unreadable for non-mathematicians, and they give no hint that the theory is applicable to problems of physics, chemistry and other sciences.
By now, there are also many physics textbooks on “chaos”. Most lack depth, and many of them are plain bad, emphasizing pictorial and computer-graphics aspects of dynamics and short changing the student on the theory. That’s a pity, as the subject in its beauty and intellectual depth ranks alongside statistical mechanics and quantum field theory, with which it shares many fundamental techniques. The book represents authors’ attempt to formulate the subject as one of the basic cornerstones of the advanced graduate physics curriculum of future.
The amount of additional information for this book is almost overwhelming, including computer programs, additional exercises (the book itself contains many) and a long list of projects written by students. I won’t try to summarize the wide range of themes covered by the book (here you have the table of contents of its three volumes–classical chaos, quantum chaos and appendices), but a very good way of getting a glimpse of its scope and fun style is reading its Overture (PS). An amazing way to become acquainted with an amazing subject!