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E-grāmata: Proofs from THE BOOK

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  • Formāts: PDF+DRM
  • Izdošanas datums: 14-Jun-2018
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662572658
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Proofs from THE BOOKPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 14-Jun-2018
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662572658
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This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.

From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"

 “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [ …] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”

From the Reviews

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "

Notices of the AMS, August 1999

"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."

LMS Newsletter, January 1999

"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... "

SIGACT News, December 2011


Number Theory
1(64)
1 Six proofs of the infinity of primes
3(6)
2 Bertrand's postulate
9(6)
3 Binomial coefficients are (almost) never powers
15(4)
4 Representing numbers as sums of two squares
19(8)
5 The law of quadratic reciprocity
27(8)
6 Every finite division ring is a field
35(4)
7 The spectral theorem and Hadamard's determinant problem
39(8)
8 Some irrational numbers
47(8)
9 Four times π2/6
55(10)
Geometry
65(60)
10 Hilbert's third problem: decomposing polyhedra
67(10)
11 Lines in the plane and decompositions of graphs
77(6)
12 The slope problem
83(6)
13 Three applications of Euler's formula
89(6)
14 Cauchy's rigidity theorem
95(4)
15 The Borromean rings don't exist
99(8)
16 Touching simplices
107(4)
17 Every large point set has an obtuse angle
111(6)
18 Borsuk's conjecture
117(8)
Analysis
125(68)
19 Sets, functions, and the continuum hypothesis
127(16)
20 In praise of inequalities
143(8)
21 The fundamental theorem of algebra
151(4)
22 One square and an odd number of triangles
155(8)
23 A theorem of Polya on polynomials
163(6)
24 Van der Waerden's permanent conjecture
169(10)
25 On a lemma of Littlewood and Offord
179(4)
26 Cotangent and the Herglotz trick
183(6)
27 Buffon's needle problem
189(4)
Combinatorics
193(66)
28 Pigeon-hole and double counting
195(12)
29 Tiling rectangles
207(6)
30 Three famous theorems on finite sets
213(6)
31 Shuffling cards
219(10)
32 Lattice paths and determinants
229(6)
33 Cayley's formula for the number of trees
235(6)
34 Identities versus bijections
241(6)
35 The finite Kakeya problem
247(6)
36 Completing Latin squares
253(6)
Graph Theory
259(62)
37 Permanents and the power of entropy
261(10)
38 The Dinitz problem
271(6)
39 Five-coloring plane graphs
277(4)
40 How to guard a museum
281(4)
41 Turan's graph theorem
285(6)
42 Communicating without errors
291(10)
43 The chromatic number of Kneser graphs
301(6)
44 Of friends and politicians
307(4)
45 Probability makes counting (sometimes) easy
311(10)
About the Illustrations 321(2)
Index 323
Martin Aigner received his Ph.D. from the University of Vienna and has been professor of mathematics at the Freie Universität Berlin since 1974. He has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, among them the Springer books Combinatorial Theory and A Course on Enumeration. Martin Aigner is a recipient of the 1996 Lester R. Ford Award for mathematical exposition of the Mathematical Association of America MAA.

Günter M. Ziegler received his Ph.D. from M.I.T. and has been professor of mathematics in Berlin first at TU Berlin, now at Freie Universität since 1995. He has published in discrete mathematics, geometry, topology, and optimization, including the Lectures on Polytopes with Springer, as well as Do I Count? Stories from Mathematics. Günter M. Ziegler is a recipient of the 2006 Chauvenet Prize of the MAA for his expository writing and the 2008 Communicator award ofthe German Science Foundation.

Martin Aigner and Günter M. Ziegler have started their work on Proofs from THE BOOK in 1995 together with Paul Erdös. The first edition of this book appeared in 1998 it has since been translated into 13 languages: Brazilian, Chinese, German, Farsi, French, Hungarian, Italian, Japanese, Korean, Polish, Russian, Spanish, and Turkish.
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