Proofs from the Book

Name: Proofs from the Book
Price: 31.31 USD
Availability: InStock
ISBN: 9783540404606

ISBN-10: 3540404600

ISBN-13: 9783540404606

Edition: 3rd 2004 (Revised)

Authors: Martin Aigner, Gï¿½nter M. Ziegler, K. H. Hofmann

List price: $49.95

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Description:

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 "... the style is clear and entertaining, the level is close to elementary ... and the proofs are…

Book details

List price: $49.95
Edition: 3rd
Copyright year: 2004
Publisher: Springer
Publication date: 11/13/2003
Binding: Hardcover
Pages: 240
Size: 8.25" wide x 9.75" long x 0.75" tall
Weight: 1.892
Language: English



Number Theory


Six proofs of the infinity of primes


Bertrand's postulate


Binomial coefficients are (almost) never powers


Representing numbers as sums of two squares


Every finite division ring is a field


Some irrational numbers


Geometry


Hilbert's third problem: decomposing polyhedra


Lines in the plane and decompositions of graphs


The slope problem


Three applications of Euler's formula


Cauchy's rigidity theorem


Touching simplices


Every large point set has an obtuse angle


Borsuk's conjecture


Analysis


Sets, functions, and the continuum hypothesis


In praise of inequalities


A theorem of Polya on polynomials


On a lemma of Littlewood and Offord


Cotangent and the Herglotz trick


Buffon's needle problem


Combinatorics


Pigeon-hole and double counting


Three famous theorems on finite sets


Lattice paths and determinants


Cayley's formula for the number of trees


Completing Latin squares


The Dinitz problem


Graph Theory


Five-coloring plane graphs


How to guard a museum


Turan's graph theorem


Communicating without errors


Of friends and politicians


Probability makes counting (sometimes) easy


About the Illustrations


Index