MARC details
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05057nmm a22003495i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20230705150634.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
180614s2018 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783662572658 |
| -- |
978-3-662-57265-8 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.7 |
| Edition number |
23 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Aigner, Martin. |
| 9 (RLIN) |
20267 |
| 245 ## - TITLE STATEMENT |
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| Title |
Proofs from THE BOOK |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Martin Aigner, Günter M. Ziegler. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
6th ed. 2018. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Berlin, Heidelberg : |
| Name of publisher, distributor, etc. |
Springer Berlin Heidelberg : |
| -- |
Imprint: Springer, |
| Date of publication, distribution, etc. |
2018. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
VIII, 326 p. |
| Other physical details |
online resource. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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. The law of quadratic reciprocity -- 6. Every finite division ring is a field -- 7. The spectral theorem and Hadamard's determinant problem -- 8. Some irrational numbers -- 9. Three times π2/6 -- Geometry: 10. Hilbert's third problem: decomposing polyhedral -- 11. Lines in the plane and decompositions of graphs -- 12. The slope problem -- 13. Three applications of Euler's formula -- 14. Cauchy's rigidity theorem -- 15. The Borromean rings don't exist -- 16. Touching simplices -- 17. Every large point set has an obtuse angle -- 18. Borsuk's conjecture -- Analysis: 19. Sets, functions, and the continuum hypothesis -- 20. In praise of inequalities -- 21. The fundamental theorem of algebra -- 22. One square and an odd number of triangles -- 23. A theorem of Pólya on polynomials -- 24. Van der Waerden's permanent conjecture -- 25. On a lemma of Littlewood and Offord -- 26. Cotangent and the Herglotz trick -- 27. Buffon's needle problem -- Combinatorics: 28. Pigeon-hole and double counting -- 29. Tiling rectangles -- 30. Three famous theorems on finite sets -- 31. Shuffling cards -- 32. Lattice paths and determinants -- 33. Cayley's formula for the number of trees -- 34. Identities versus bijections -- 35. The finite Kakeya problem -- 36. Completing Latin squares -- Graph Theory: 37. Permanents and the power of entropy -- 38. The Dinitz problem -- 39. Five-coloring plane graphs -- 40. How to guard a museum -- 41. Turán's graph theorem -- 42. Communicating without errors -- 43. The chromatic number of Kneser graphs -- 44. Of friends and politicians -- 45. Probability makes counting (sometimes) easy -- About the Illustrations -- Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Number theory. |
| 9 (RLIN) |
20268 |
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| Topical term or geographic name entry element |
Geometry. |
| 9 (RLIN) |
20269 |
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| Topical term or geographic name entry element |
Mathematical analysis. |
| 9 (RLIN) |
20270 |
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| Topical term or geographic name entry element |
Discrete mathematics. |
| 9 (RLIN) |
20271 |
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| Topical term or geographic name entry element |
Graph theory. |
| 9 (RLIN) |
20272 |
|
|---|
| Topical term or geographic name entry element |
Computer science-Mathematics. |
| 9 (RLIN) |
20273 |
|
|---|
| Topical term or geographic name entry element |
Number Theory. |
| 9 (RLIN) |
20274 |
|
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| Topical term or geographic name entry element |
Geometry. |
| 9 (RLIN) |
20269 |
|
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| Topical term or geographic name entry element |
Analysis. |
| 9 (RLIN) |
20275 |
|
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| Topical term or geographic name entry element |
Discrete Mathematics. |
| 9 (RLIN) |
20276 |
|
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| Topical term or geographic name entry element |
Graph Theory. |
| 9 (RLIN) |
20277 |
|
|---|
| Topical term or geographic name entry element |
Mathematics of Computing. |
| 9 (RLIN) |
20278 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Ziegler, Günter M. |
| Relator term |
author. |
| Authority record control number or standard number |
(orcid)0000-0003-1502-1915 |
| Real World Object URI |
https://orcid.org/0000-0003-1502-1915 |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
20279 |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-3-662-57265-8">https://doi.org/10.1007/978-3-662-57265-8</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
e-Book |
