来自圣经的证明
出版信息
M.Aigner、G.M.Ziegler / 世界图书出版公司 / 2006-7 / 39.00元
内容简介
作为一门历史悠久的学问，数学有她自身的文化和美学，就像文学和艺术一样。一方面，数学家们在努力开拓新领域、解决老问题；另一方面他们也在不断地从不同的角度反复学习、理解和欣赏前辈们的工作。的确，数学中有许多不仅值得反复推敲理解，更值得细心品味和欣赏的杰作。有些定理的证明不仅想法奇特、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。
本书已被译成8种文字。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。书中介绍了35个著名数学问题的极富创造性和独具匠心的证明。出于可读性的考虑，本书侧重于研究生水平并且局限于数论，几何，分析，组合与图论五个数学领域。但我们确信，每一个数学工作者都会喜欢这本书，并且从中学到许多东西。
目录
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
7. Three times π2/6
Geometry
8. Hilbert‘s third problem: decomposing polyhedra
9. Lines in the plane and decompositions of graphs
10. The slope problem
11. Three applications of Euler‘s formula
12. Cauchy‘s rigidity theorem
13. Touching simplices
14. Every large point set has an obtuse angle
15. Borsuk‘s conjecture
Analysis
16. Sets， functions， and the continuum hypothesis
17. In praise of inequalities
22. Pigeon-hole and double counting
23. Three famous theorems on finite sets
24. Shuffling cards
25. Lattice paths and determinants
26. Cayley's formulafor the number of trees
27. Completing Latin squares
28. The Dinitz problem
29. Identities versus bijections
Graph Theory
30. Five-coloring plane graphs
31. How to guard a museum
32. Turan's graph theorem
33. Communicating without e~ors
34. Of friends and pohtici~s
35. Probability makes counting (sometinles) easy
About the Illustrations
Index
