Proofs from the Book

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Springer-Verlag Berlin Heidelberg, 2010 - Analysis - 274 pages
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This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". From the Reviews " ... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ... Aigner and Ziegler ... write: " ... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ..." Notices of the AMS, August 1999 " ... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999.

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If you enjoy mathematics and have a decent background, at least in topics of discrete mathematics, this book is a nice thing to carry around. It's a good way to read something interesting yet complex, and at the same time not have to stress over understanding it since the proofs are well presented, and it's not like you will be tested on it anyways :-)
As an example of myself, most of the springer books will put me to sleep after about 5 pages, the nice thing about this book is that you only need 5 pages to begin and end with a concept...
 

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