# Proofs from the book aigner and ziegler

## Proofs from THE BOOK | Martin Aigner | Springer

It seems that you're in Germany. We have a dedicated site for Germany. 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 This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings## Martin Aigner and Günter M. Ziegler awarded the 2018 Steele Prize for Mathematical Exposition

This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. 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. Aigner and Ziegler 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. The theorems are so fundamental, their proofs so elegant and the remaining open questio.

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In Proofs from THE BOOK Aigner and Ziegler have attempted not to write that Book itself, which would be hubris on a grand scale, but to select proofs which would be candidates for inclusion in it, restricting themselves to those which use only basic higher mathematics. A lot of solid mathematics is packed into Proofs. Its thirty chapters, divided into sections on Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory, cover a broad range of subjects: the infinity of primes, applications of Euler's formula, five-coloring of plane graphs, Latin squares, the problem of the thirteen spheres, Borsuk's conjecture, inequalities, the irrationality of pi, and so on. Each chapter is largely independent; some include necessary background as an appendix. The proofs included are all relatively accessible, but readers will want to have done the better part of an undergraduate degree in pure mathematics, or an equivalent.

Hardythat there is no permanent place for ugly mathematics. A few years ago, we suggested to him to write up a? He was enthusiastic about the idea and, characteristically, went to work immediately,? Our book was supposed to appear in March as a present to Erdos? Instead this book is dedicated to his memory. Paul Erdos We have no de? We also hope that our readers will enjoy this despite the imperfections of our exposition.

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