滿額折
數學天書中的證明(第4版)（簡體書）
商品資訊
ISBN13：9787510061486
出版社：世界圖書(北京)出版公司
作者：(德)G.M.齊格勒
出版日：2013/10/01
裝訂／頁數：平裝／274頁
規格：23.5cm*16.8cm (高/寬)
版次：4
商品簡介
目次
商品簡介
Paul Erdos liked to talk about The Book，in which God maintainsthe perfect proofs for mathematical theorems， following the dictumof G. H. Hardy that there is no permanent place for uglymathematics. Erdos also said that you need not believe in God but，as a mathematician， you should believe in The Book. A few yearsago， we suggested to lum to write up a first （and very modest）approximation to The Book. He was enthusiastic about the idea and，characteristically， went to work immediately， filling page afterpage with his suggestions. Our book was supposed to appear in March1998 as a present to Erdos 85th birthday. With Pauls unfortunatedeath in the summer of 1996， he is not listed as a co-author.Instead this book is dedicated to his memory.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。 本書是第4版，在第3版的基礎上新增加了5章，這5章講述一些經典的結果，如代數基礎理論、平鋪問題、和一些最新的證明結果，像圖論中的Kneser連通。新的版本中也講述了一些更深層次的內容，只要細細體會，總會有新的發現。《來自聖經的證明(第3版)》已被譯成十餘種不同的文字，這新版本會產生更加持久深遠的影響。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。書中介紹了多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，書的內容側重于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她，並從中學到許多東西。讀者對象：數學專業的研究生，以及對數學感興趣的廣大讀者。
目次
Number Theory
1.Six proofs of the infinity of primes
2.Bertrands 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.Hilberts tlurd problem: decomposing polyhedra
10.Lines in the plane and decompositions of graphs
11.The slopeproblem
12.Three applications of Eulers formula
13.Cauchys rigidity theorem
14.Touching simplices
15.Every large point set has an obtuse angle
16.Borsuks 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.Buffons 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.Cayleys 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.Turans 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
1.Six proofs of the infinity of primes
2.Bertrands 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.Hilberts tlurd problem: decomposing polyhedra
10.Lines in the plane and decompositions of graphs
11.The slopeproblem
12.Three applications of Eulers formula
13.Cauchys rigidity theorem
14.Touching simplices
15.Every large point set has an obtuse angle
16.Borsuks 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.Buffons 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.Cayleys 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.Turans 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
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