Proofs from THE BOOK / by Martin Aigner, Günter M. Ziegler
| データ種別 | 電子ブック |
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| 版 | Second Edition |
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 2001 |
| 本文言語 | 英語 |
| 大きさ | VIII, 215 p. 198 illus., 6 illus. in color : online resource |
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| 内容注記 | 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 Geometry 7. Hilbert’s third problem: decomposing polyhedra 8. Lines in the plane and decompositions of graphs 9. The slope problem 10. Three applications of Euler’s formula 11. Cauchy’s rigidity theorem 12. Touching simplices 13. Every large point set has an obtuse angle 14. Borsuk’s conjecture Analysis 15. Sets, functions, and the continuum hypothesis 16. In praise of inequalities 17. A theorem of Pólya on polynomials 18. On a lemma of Littlewood and Offord 19. Cotangent and the Herglotz trick 20. Buffon’s needle problem Combinatorics 21. Pigeon-hole and double counting 22. Three famous theorems on finite sets 23. Lattice paths and determinants 24. Cayley’s formula for the number of trees 25. Completing Latin squares 26. The Dinitz problem Graph Theory 27. Five-coloring plane graphs 28. How to guard a museum 29. Turán’s graph theorem 30. Communicating without errors 31. Of friends and politicians 32. Probability makes counting (sometimes) easy About the Illustrations |
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| 一般注記 | The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added |
| 著者標目 | *Aigner, Martin author Ziegler, Günter M. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Computer science LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Geometry LCSH:Number theory LCSH:Combinatorics FREE:Mathematics FREE:Number Theory FREE:Geometry FREE:Analysis FREE:Combinatorics FREE:Computer Science, general |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783662043158 
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| ISBN | 9783662043158 |
| URL | http://dx.doi.org/10.1007/978-3-662-04315-8 |
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