本書已被譯成8種文字。這不是一本教科書，也不是一本專著，而是一本開闊數學視野和提高數學修養的著作。書中介紹了35個著名數學問題的極富創造性和獨具匠心的證明。出於可讀性的考慮，本書側重於研究生水平並且局限於數論，幾何，分析，組合與圖論五個數學領域。但我們確信，每一個數學工作者都會喜歡這本書，並且從中學到許多東西。
基本介紹
- 作者：M.Aigner / G.M.Ziegler
- ISBN：9787506282253
- 頁數：239
- 定價：39.00元
- 出版社：世界圖書出版公司
- 出版時間：2006-7
- 裝幀：平裝
- 原作名：Proofs from THE BOOK
內容介紹,作品目錄,
內容介紹
作為一門歷史悠久的學問，數學有她自身的文化和美學，就像文學和藝術一樣。一方面，數學家們在努力開拓新領域、解決老問題；另一方面他們也在不斷地從不同的角度反覆學習、理解和欣賞前輩們的工作。的確，數學中有許多不僅值得反覆推敲理解，更值得細心品味和欣賞的傑作。有些定理的證明不僅想法奇特、構思精巧，作為一個整體更是天衣無縫。難怪，西方有些虔誠的數學家將這類傑作比喻為上帝的創造。
作品目錄
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
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
