数学天书中的证明（原书第四版 英文版）
作者：（德）齐格勒 著
出版时间：2013年版
内容简介
Paul Erdos liked to talk about The Book，in which God maintains the perfect proofs for mathematical theorems， following the dictum of G. H. Hardy that there is no permanent place for ugly mathematics. Erdos also said that you need not believe in God but， as a mathematician， you should believe in The Book. A few years ago， we suggested to lum to write up a first （and very modest） approximation to The Book. He was enthusiastic about the idea and， characteristically， went to work immediately， filling page after page with his suggestions. Our book was supposed to appear in March 1998 as a present to Erdos' 85th birthday. With Paul's unfortunate death in the summer of 1996， he is not listed as a co-author. Instead this book is dedicated to his memory.
目录
Number Theory
1.Six proofs of the infinity of primes
2.Bertrand's postulate
3.Binomialcoefficients are (almost) never powers
4.Representing numbers as sums of two squares
5.The law of quadratic reciprocity
6.Every firute division ring is afield
7.Some irrational numbers
8.Three times ∏2/6
Geometry
9.Hilbert's tlurd problem: decomposing polyhedra
10.Lines in the plane and decompositions of graphs
11.The slopeproblem
12.Three applications of Euler's formula
13.Cauchy's rigidity theorem
14.Touching simplices
15.Every large point set has an obtuse angle
16.Borsuk's conjecture
Analysis
17.In praise ofinequalities
19.The fundamental theorem of algebra
20.One square and an odd number of triangles
21.A theorem of Polya on polynomials
22.On alemma of Littlewood and Offord
23.Cotangent and the Herglotz trick
24.Buffon's needle problem
Combinatorics
25.Pigeon-hole and double counting
26.Tiling rectangles
27.Three famous theorems on finite sets
28.Shuffling cards
29.Lattice paths and determinants
30.Cayley's formula for the number of trees
31.IdenMes versus bijections
32.Completing Latin squares
Graph Theory
33.The Dinitz problem
34.Five-coloring plane graphs
35.How to guard a museum
36.Turan's graph theorem
37.Communicating without errors
38.The chromatic number of Kneser graphs
39.Of friends and politicians
40.Probability makes counting (sometimes) easy
About the Illustrations
Index
