Proofs from "The Book"

ISBN-10: 3540636986

ISBN-13: 9783540636984

Edition: 2nd 1999

Authors: Martin Aigner, G. M. Ziegler

List price: $29.95

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Description:

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erds, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.

Book details

List price: $29.95
Edition: 2nd
Copyright year: 1999
Publisher: Springer
Publication date: 12/31/1998
Binding: Hardcover
Pages: 199
Size: 7.60" wide x 9.53" long x 0.27" tall
Weight: 1.584
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



The problem of the thirteen spheres



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 Pï¿½lya on polynomials



On a lemma of Littlewood and Offord


Combinatorics



Pigeon-hole and double counting



Three famous theorems on finite sets



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