來(lái)自圣經(jīng)的證明

內(nèi)容概要

作為一門歷史悠久的學(xué)問(wèn)，數(shù)學(xué)有她自身的文化和美學(xué)，就像文學(xué)和藝術(shù)一樣。一方面，數(shù)學(xué)家們?cè)谂﹂_拓新領(lǐng)域、解決老問(wèn)題；另一方面他們也在不斷地從不同的角度反復(fù)學(xué)習(xí)、理解和欣賞前輩們的工作。的確，數(shù)學(xué)中有許多不僅值得反復(fù)推敲理解，更值得細(xì)心品味和欣賞的杰作。有些定理的證明不僅想法奇特、構(gòu)思精巧，作為一個(gè)整體更是天衣無(wú)縫。難怪，西方有些虔誠(chéng)的數(shù)學(xué)家將這類杰作比喻為上帝的創(chuàng)造。　　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(shù)學(xué)視野和提高數(shù)學(xué)修養(yǎng)的著作。書中介紹了35個(gè)著名數(shù)學(xué)問(wèn)題的極富創(chuàng)造性和獨(dú)具匠心的證明。出于可讀性的考慮，本書側(cè)重于研究生水平并且局限于數(shù)論，幾何，分析，組合與圖論五個(gè)數(shù)學(xué)領(lǐng)域。但我們確信，每一個(gè)數(shù)學(xué)工作者都會(huì)喜歡這本書，并且從中學(xué)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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