出版時間:2006-7 出版社:世界圖書出版公司 作者:M.Aigner,G.M.Ziegler 頁數:239
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內容概要
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復學習、理解和欣賞前輩們的工作。的確,數學中有許多不僅值得反復推敲理解,更值得細心品味和欣賞的杰作。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杰作比喻為上帝的創(chuàng)造?! ”緯驯蛔g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(yǎng)的著作。書中介紹了35個著名數學問題的極富創(chuàng)造性和獨具匠心的證明。出于可讀性的考慮,本書側重于研究生水平并且局限于數論,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,并且從中學到許多東西。
書籍目錄
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 π2/6Geometry 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 conjectureAnalysis 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 bijectionsGraph 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) easyAbout the IllustrationsIndex
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