Proofs from THE BOOK / by Martin Aigner, Günter M. Ziegler
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 1998 |
| 本文言語 | 英語 |
| 大きさ | VIII, 199 p : 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. The problem of the thirteen spheres 13. Touching simplices 14. Every large point set has an obtuse angle 15. Borsuk’s conjecture Analysis 16. Sets, functions, and the continuum hypothesis 17. In praise of inequalities 18. A theorem of Pólya on polynomials 19. On a lemma of Littlewood and Offord Combinatorics 20. Pigeon-hole and double counting 21. Three famous theorems on finite sets 22. Cayley’s formula for the number of trees 23. Completing Latin squares 23. The Dinitz problem Graph Theory 25. Five-coloring plane graphs 26. How to guard a museum 27. Turán’s graph theorem 28. Communicating without errors 29. Of friends and politicians 30. 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 |
| 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:Number theory LCSH:Combinatorics FREE:Mathematics FREE:Number Theory FREE:Geometry FREE:Analysis FREE:Combinatorics |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783662223437 
|
| ISBN | 9783662223437 |
| URL | http://dx.doi.org/10.1007/978-3-662-22343-7 |
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※2021年9月12日以降