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Bibliographic Details
Title:	Proofs from THE BOOK
From:	Martin Aigner, Günter M. Ziegler ; incuding illustrations by Karl H. Hofmann
Person:	Aigner, Martin 1942-2023 Verfasser aut Ziegler, Günter M. Hofmann, Karl H. 1963- 1932-
Main Authors:	Aigner, Martin 1942-2023 (Author), Ziegler, Günter M. 1963- (Author)
Other Authors:	Hofmann, Karl H. 1932- (Illustrator)
Format:	Book
Language:	English
Published:	Berlin, Germany Springer [2018]
Edition:	Sixth edition
Notation:	SK 110 SK 130
Subjects:	Mathematics Number Theory Geometry Analysis Combinatorics Graph Theory Mathematics of Computing Computer science / Mathematics Mathematical analysis Analysis (Mathematics) Number theory Graph theory Mathematik Beweis Beweisführung Mathematische Methode Mathematische Logik Beispielsammlung
Online Access:	https://d-nb.info/1156793122/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030498321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Rückendeckel: "This revised and enlarged sixth edition of ... features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters."
Physical Description:	VIII, 326 Seiten Illustrationen, Diagramme
ISBN:	9783662572641

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Record in the Search Index

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adam_text	TABLE OF CONTENTS NUMBER THEORY ____________________________ 1 1. SIX PROOFS OF THE INFINITY OF PRIM ES ................................................... 3 2. BERTRANDS POSTULATE............................................................................ 9 3. BINOMIAL COEFFICIENTS ARE (ALMOST) NEVER POWERS ............................ 15 4. REPRESENTING NUMBERS AS SUMS OF TWO SQUARES .............................. 19 5. THE LAW OF QUADRATIC RECIPROCITY....................................................... 27 6. EVERY FINITE DIVISION RING IS A FIE LD ................................................. 35 7. THE SPECTRAL THEOREM AND HADAMARDS DETERMINANT PROBLEM ......... 39 8. SOME IRRATIONAL NUMBERS................................................................... 47 9. FOUR TIMES 7 T 2 / 6 ................................................................................55 GEOMETRY ________________________________ 65 10. HILBERTS THIRD PROBLEM: DECOMPOSING POLYHEDRA.............................67 11. LINES IN THE PLANE AND DECOMPOSITIONS OF GRAPHS .......................... 77 12. THE SLOPE PROBLEM ............................................................................ 83 13. THREE APPLICATIONS OF EULERS FORM ULA .............................................. 89 14. CAUCHYS RIGIDITY THEOREM .............................................................. 95 15. THE BORROMEAN RINGS DONT EXIST ................................................... 99 16. TOUCHING SIMPLICES ....................................................................... 107 17. EVERY LARGE POINT SET HAS AN OBTUSE AN G LE ..................................... I L L 18. BORSUKS CONJECTURE.........................................................................117 ANALYSIS ________________________________ 125 19. SETS, FUNCTIONS, AND THE CONTINUUM HYPOTHESIS ............................ 127 20. IN PRAISE OF INEQUALITIES ................................................................ 143 21. THE FUNDAMENTAL THEOREM OF ALGEBRA .............................................. 151 22. ONE SQUARE AND AN ODD NUMBER OF TRIANGLES..................................155 23. A THEOREM OF POLYA ON POLYNOMIALS ............................................ 163 24. VAN DER WAERDENS PERMANENT CONJECTURE ....................................... 169 25. ON A LEMMA OF LITTLEWOOD AND OFFORD ......................................... 179 26. COTANGENT AND THE HERGLOTZ TRIC K .................................................. 183 27. BUFFONS NEEDLE PROBLEM .............................................................. 189 COMBINATORICS ___________________________ 193 28. PIGEON-HOLE AND DOUBLE COUNTING.................................................. 195 29. TILING RECTANGLES.............................................................................. 207 30. THREE FAMOUS THEOREMS ON FINITE SETS ........................................... 213 31. SHUFFLING C A RD S ................................................................................ 219 32. LATTICE PATHS AND DETERMINANTS ....................................................... 229 33. CAYLEYS FORMULA FOR THE NUMBER OF TRE E S ....................................... 235 34. IDENTITIES VERSUS BIJECTIONS .............................................................. 241 35. THE FINITE KAKEYA PROBLEM.............................................................. 247 36. COMPLETING LATIN SQUARES ............................................................ 253 GRAPH THEORY ____________________________ 259 37. PERMANENTS AND THE POWER OF ENTROPY.............................................261 38. THE DINITZ PROBLEM ......................................................................... 271 39. FIVE-COLORING PLANE GRAPHS ........................................................... 277 40. HOW TO GUARD A MUSEUM ..................................................................281 4L TURAEN*S GRAPH THEOREM .................................................................. 285 42. COMMUNICATING WITHOUT ERRO RS ....................................................... 291 43. THE CHROMATIC NUMBER OF KNESER GRAPHS........................................301 44. OF FRIENDS AND POLITICIANS................................................................ 307 45. PROBABILITY MAKES COUNTING (SOMETIMES) EASY ............................ 311 ABOUT THE ILLUSTRATIONS _____________________ 321 INDEX___________________________________323
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author	Aigner, Martin 1942-2023 Ziegler, Günter M. 1963-
author2	Hofmann, Karl H. 1932-
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author_facet	Aigner, Martin 1942-2023 Ziegler, Günter M. 1963- Hofmann, Karl H. 1932-
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discipline	Mathematik
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spellingShingle	Aigner, Martin 1942-2023 Ziegler, Günter M. 1963- Proofs from THE BOOK Mathematics Number Theory Geometry Analysis Combinatorics Graph Theory Mathematics of Computing Computer science / Mathematics Mathematical analysis Analysis (Mathematics) Number theory Graph theory Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd Beweisführung (DE-588)4227233-6 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Logik (DE-588)4037951-6 gnd
subject_GND	(DE-588)4037944-9 (DE-588)4132532-1 (DE-588)4227233-6 (DE-588)4155620-3 (DE-588)4037951-6 (DE-588)4144384-6
title	Proofs from THE BOOK
title_auth	Proofs from THE BOOK
title_exact_search	Proofs from THE BOOK
title_full	Proofs from THE BOOK Martin Aigner, Günter M. Ziegler ; incuding illustrations by Karl H. Hofmann
title_fullStr	Proofs from THE BOOK Martin Aigner, Günter M. Ziegler ; incuding illustrations by Karl H. Hofmann
title_full_unstemmed	Proofs from THE BOOK Martin Aigner, Günter M. Ziegler ; incuding illustrations by Karl H. Hofmann
title_short	Proofs from THE BOOK
title_sort	proofs from the book
topic	Mathematics Number Theory Geometry Analysis Combinatorics Graph Theory Mathematics of Computing Computer science / Mathematics Mathematical analysis Analysis (Mathematics) Number theory Graph theory Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd Beweisführung (DE-588)4227233-6 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Logik (DE-588)4037951-6 gnd
topic_facet	Mathematics Number Theory Geometry Analysis Combinatorics Graph Theory Mathematics of Computing Computer science / Mathematics Mathematical analysis Analysis (Mathematics) Number theory Graph theory Mathematik Beweis Beweisführung Mathematische Methode Mathematische Logik Beispielsammlung
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