Proofs from THE BOOK / by Martin Aigner, Günter M. Ziegler
| データ種別 | 電子ブック |
|---|---|
| 版 | Fourth Edition |
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 2010 |
| 本文言語 | 英語 |
| 大きさ | VIII, 274 p. 250 illus : online resource |
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| 内容注記 | Number Theory Six proofs of the infinity of primes Bertrand’s postulate Binomial coefficients are (almost) never powers Representing numbers as sums of two squares The law of quadratic reciprocity Every finite division ring is a field Some irrational numbers Three times ?²/6 Geometry Hilbert’s third problem: decomposing polyhedra Lines in the plane and decompositions of graphs The slope problem Three applications of Euler’s formula Cauchy’s rigidity theorem Touching simplices Every large point set has an obtuse angle Borsuk’s conjecture Analysis Sets, functions, and the continuum hypothesis In praise of inequalities The fundamental theorem of algebra One square and an odd number of triangles A theorem of Pólya on polynomials On a lemma of Littlewood and Offord Cotangent and the Herglotz trick Buffon’s needle problem Combinatorics Pigeon-hole and double counting Tiling rectangles Three famous theorems on finite sets Shuffling cards Lattice paths and determinants Cayley’s formula for the number of trees Identities versus bijections Completing Latin squares Graph Theory The Dinitz problem Five-coloring plane graphs How to guard a museum Turán’s graph theorem Communicating without errors The chromatic number of Kneser graphs Of friends and politicians Probability makes counting (sometimes) easy |
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| 一般注記 | This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". 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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...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. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999 |
| 著者標目 | *Aigner, Martin author Ziegler, Günter M. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Geometry LCSH:Mathematical logic LCSH:Number theory LCSH:Combinatorics FREE:Mathematics FREE:Mathematical Logic and Foundations FREE:Mathematics, general FREE:Number Theory FREE:Geometry FREE:Combinatorics FREE:Analysis |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9783642008566 
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| ISBN | 9783642008566 |
| URL | http://dx.doi.org/10.1007/978-3-642-00856-6 |
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