Proofs from the Book

Martin Aigner, Gunter M. Ziegler

224 pages, parution le 01/12/2000 (2^eme édition)

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Résumé

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 Erdös, 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. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.

Contents

Number Theory

1 Six proofs of the infinity of primes
2 Bertrand's postulate
3 Binomial coefficients are (almost) never powers
4 Representing numbers as sums of two squares
5 Every finite division ring is a field
6 Some irrational numbers

Geometry

7 Hilbert's third problem: decomposing polyhedra
8 Lines in the plane and decompositions of graphs
9 The slope problem
10 Three applications of Euler's formula
11 Cauchy's rigidity theorem
12 The problem of the thirteen spheres
13 Touching simplices
14 Every large point set has an abtuse angle
15 Borsuk's conjecture

Analysis

16 Sets, functions, and the continuum hypothesis
17 In praise of inequalities
18 A theorem of Polya on polynomials
19 On a lemma of Littlewood and Offord

Combinatorics

20 Pigeon-hole and double counting
21 Three famous theorems on finite sets
22 Cayley's formula for the number of trees
23 Completing Latin squares
23 The Dinitz problem

Graph Theory

25 Five-coloring plane graphs
26 How to guard a museum
27 Turan's graph theorem
28 Communicating without errors
29 Of friends and politicians
30 Probability makes counting (sometimes) easy
About the Illustrations
Index

L'auteur - Martin Aigner

Freie Universität Berlin, Germany.

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L'auteur - Gunter M. Ziegler

Technische Universität Berlin, Germany.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Martin Aigner, Gunter M. Ziegler
Parution	01/12/2000
Édition	2^eme édition
Nb. de pages	224
Format	16 x 24
Couverture	Relié
Poids	779g
Intérieur	Noir et Blanc
EAN13	9773540678657

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