齐格勒编著的《数学天书中的证明(第4版)》介绍了40个著名数学问题的极富创造性和独具匠心的证明。其中有些证明不仅想珐奇特、构思精巧,作为一个整体更是天衣无缝。难怪,西方有些虔诚的数学家将这类杰作比喻为上帝的创造。这不是一本教科书,也不是一本专著,而是一本开阔数学视野和提高数学修养的著作。
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