The art of mathematics - take two: Tea time in Cambridge
Gespeichert in:
| Vorheriger Titel: | Bollobás, Béla The art of mathematics |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom
Cambridge University Press
2022
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 333 Seiten Illustrationen |
| ISBN: | 9781108978262 9781108833271 |
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Datensatz im Suchindex
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| adam_text |
Contents Preface page xi 1 The Problems The Hints 33 The Solutions 45 1. Real Sequences - An Interview Question 47 2. Vulgar Fractions - Sylvester’s Theorem 49 3. Rational and Irrational Sums 53 4. Ships in Fog 55 5. A Family of Intersections 56 6. The Basel Problem - Euler’s Solution 58 7. Reciprocals of Primes - Euler and Erdős 61 8. Reciprocals of Integers 65 9. Completing Matrices 66 10. Convex Polyhedra - Take One 68 11. Convex Polyhedra - Take Two 70 12. A Very Old Tripos Problem 72 13. Angle Bisectors - the Lehmus-Steiner Theorem 74 14. Langley’s Adventitious Angles 76 15. The Tantalus Problem - from The Washington Post 79 16. Pythagorean Triples 81 17. Fermat’s Theorem for Fourth Powers 84 18. Congruent Numbers - Fermat 86 v
Contents vi Contents vii 19. A Rational Sum 89 51. Banach’s Matchbox Problem 164 20. A Quartic Equation 92 52. Cayley’s Problem 166 21. Regular Polygons 95 53. Min vs Max 168 22. Flexible Polygons 99 54. Sums of Squares 170 100 55. The Monkey and the Coconuts 172 - Philon of Byzantium 105 56. Complex Polynomials 174 25. Circumscribed Quadrilaterals - Newton 108 57. Gambler’s Ruin 175 26. Partitions of Integers 111 58. Bertrand’s Box Paradox 179 27. Parts Divisible by m and 2m 114 59. The Monty Hall Problem 181 28. Unequal vs Odd Partitions 115 60. Divisibility in a Sequence of Integers 185 29. Sparse Bases 117 61. Moving Sofa Problem 187 30. Small Intersections - Sarkozy and Szemerédi 119 62. Minimum Least Common Multiple 191 31. The Diagonals of Zero-One Matrices 122 63. Vieta Jumping 193 32. Tromino and Tetronimo Tilings 123 64. Infinite Primitive Sequences 195 33. Tromino Tilings of Rectangles 126 65. Primitive Sequences with a Small Term 197 128 66. Hypertrees 199 35. Halving Circles 129 67. Subtrees 200 36. The Number of Halving Circles 131 68. AH in a Row 201 37. A Basic Identity of Binomial Coefficients 134 69. An American Story 203 38. Tepper’s Identity 136 70. Six Equal Parts 205 39. Dixon’s Identity - Take One 138 71. Products of Real Polynomials 208 40. Dixon’s Identity - Take Two 140 72. Sums of Squares 210 41. An Unusual Inequality 143 73. Diagrams of Partitions 212 42. Hilbert’s Inequality 145 74. Euler’s Pentagonal Number Theorem 214 43. The Central Binomial Coefficient 147 75. Partitions - Maximum and Parity 218 76. Periodic Cellular Automata 220 77. Meeting
Set Systems 223 78. Dense Sets of Reals - An Application of the Baire Category Theorem 225 79. Partitions of Boxes 227 80. Distinct Representatives 229 81. Decomposing a Complete Graph: The Graham-Pollak Theorem - Take One 230 23. Polygons of Maximal Area 24. Constructing 34. Number of Matrices 44. Properties of the Central Binomial Coefficient 149 45. Products of Primes 151 46. The Erdős Proof of Bertrand’s Postulate 153 47. Powers of 2 and 3 155 48. Powers of 2 Just Less Than a Perfect Power 156 49. Powers of 2 Just Greater Than a Perfect Power 158 50. Powers of Primes Just Less Than a Perfect Power 159
viii Contents Contents 82. Matrices and Decompositions: The Graham-Pollak Theorem Take Two 232 83. Patterns and Decompositions: The Graham-Pollak Theorem Take Three 234 84. Six Concurrent Lines 236 85. Short Words - First Cases 237 86. Short Words - The General Case 239 87. The Number of Divisors 241 88. Common Neighbours 243 89. Squares in Sums 244 90. Extension of Bessel’s Inequality - Bombieri and Selberg 245 91. Equitable Colourings 247 92. Scattered Discs 249 93. East Model 251 94. Perfect Triangles 254 95. A Triangle Inequality 256 96. An Inequality for Two Triangles 258 97. Random Intersections 260 98. Disjoint Squares 262 99. Increasing Subsequences - Erdős and Szekeres 264 100. A Permutation Game 266 101. Ants on a Rod 267 102. Two Cyclists and a Swallow 268 103. Almost Disjoint Subsets of Natural Numbers 270 104. Primitive Sequences 272 105. The Time of Infection on a Grid 274 106. Areas of Triangles: Routh’s Theorem 276 107. Lines and Vectors - Euler and Sylvester 282 108. Feuerbach’s Remarkable Circle 284 109. Euler’s Ratio-Product-Sum Theorem 286 110. Bachet’s Weight Problem 288 111. Perfect Partitions 291 112. Countably Many Players 294 ix 113. One Hundred Players 296 114. River Crossings: Alcuin of York - Take One 298 115. River Crossings: Alcuin of York - Take Two 301 116. Fibonacci and a Medieval Mathematics Tournament 303 117. Triangles and Quadrilaterals - Regiomontanus 305 118. The Cross-Ratios of Points and Lines 308 119. Hexagons in Circles: Pascal’s Hexagon Theorem - Take One 312 120. Hexagons in Circles: Pascal’s Theorem - Take Two 315 121. A
Sequence in Zp 318 122. Elements of Prime Order 319 123. Flat Triangulations 320 124. Triangular Billiard Tables 322 125. Chords of an Ellipse: The Butterfly Theorem 324 126. Recurrence Relations for the Partition Function 326 127. The Growth of the Partition Function 328 128. Dense Orbits 332 |
| adam_txt |
Contents Preface page xi 1 The Problems The Hints 33 The Solutions 45 1. Real Sequences - An Interview Question 47 2. Vulgar Fractions - Sylvester’s Theorem 49 3. Rational and Irrational Sums 53 4. Ships in Fog 55 5. A Family of Intersections 56 6. The Basel Problem - Euler’s Solution 58 7. Reciprocals of Primes - Euler and Erdős 61 8. Reciprocals of Integers 65 9. Completing Matrices 66 10. Convex Polyhedra - Take One 68 11. Convex Polyhedra - Take Two 70 12. A Very Old Tripos Problem 72 13. Angle Bisectors - the Lehmus-Steiner Theorem 74 14. Langley’s Adventitious Angles 76 15. The Tantalus Problem - from The Washington Post 79 16. Pythagorean Triples 81 17. Fermat’s Theorem for Fourth Powers 84 18. Congruent Numbers - Fermat 86 v
Contents vi Contents vii 19. A Rational Sum 89 51. Banach’s Matchbox Problem 164 20. A Quartic Equation 92 52. Cayley’s Problem 166 21. Regular Polygons 95 53. Min vs Max 168 22. Flexible Polygons 99 54. Sums of Squares 170 100 55. The Monkey and the Coconuts 172 - Philon of Byzantium 105 56. Complex Polynomials 174 25. Circumscribed Quadrilaterals - Newton 108 57. Gambler’s Ruin 175 26. Partitions of Integers 111 58. Bertrand’s Box Paradox 179 27. Parts Divisible by m and 2m 114 59. The Monty Hall Problem 181 28. Unequal vs Odd Partitions 115 60. Divisibility in a Sequence of Integers 185 29. Sparse Bases 117 61. Moving Sofa Problem 187 30. Small Intersections - Sarkozy and Szemerédi 119 62. Minimum Least Common Multiple 191 31. The Diagonals of Zero-One Matrices 122 63. Vieta Jumping 193 32. Tromino and Tetronimo Tilings 123 64. Infinite Primitive Sequences 195 33. Tromino Tilings of Rectangles 126 65. Primitive Sequences with a Small Term 197 128 66. Hypertrees 199 35. Halving Circles 129 67. Subtrees 200 36. The Number of Halving Circles 131 68. AH in a Row 201 37. A Basic Identity of Binomial Coefficients 134 69. An American Story 203 38. Tepper’s Identity 136 70. Six Equal Parts 205 39. Dixon’s Identity - Take One 138 71. Products of Real Polynomials 208 40. Dixon’s Identity - Take Two 140 72. Sums of Squares 210 41. An Unusual Inequality 143 73. Diagrams of Partitions 212 42. Hilbert’s Inequality 145 74. Euler’s Pentagonal Number Theorem 214 43. The Central Binomial Coefficient 147 75. Partitions - Maximum and Parity 218 76. Periodic Cellular Automata 220 77. Meeting
Set Systems 223 78. Dense Sets of Reals - An Application of the Baire Category Theorem 225 79. Partitions of Boxes 227 80. Distinct Representatives 229 81. Decomposing a Complete Graph: The Graham-Pollak Theorem - Take One 230 23. Polygons of Maximal Area 24. Constructing 34. Number of Matrices 44. Properties of the Central Binomial Coefficient 149 45. Products of Primes 151 46. The Erdős Proof of Bertrand’s Postulate 153 47. Powers of 2 and 3 155 48. Powers of 2 Just Less Than a Perfect Power 156 49. Powers of 2 Just Greater Than a Perfect Power 158 50. Powers of Primes Just Less Than a Perfect Power 159
viii Contents Contents 82. Matrices and Decompositions: The Graham-Pollak Theorem Take Two 232 83. Patterns and Decompositions: The Graham-Pollak Theorem Take Three 234 84. Six Concurrent Lines 236 85. Short Words - First Cases 237 86. Short Words - The General Case 239 87. The Number of Divisors 241 88. Common Neighbours 243 89. Squares in Sums 244 90. Extension of Bessel’s Inequality - Bombieri and Selberg 245 91. Equitable Colourings 247 92. Scattered Discs 249 93. East Model 251 94. Perfect Triangles 254 95. A Triangle Inequality 256 96. An Inequality for Two Triangles 258 97. Random Intersections 260 98. Disjoint Squares 262 99. Increasing Subsequences - Erdős and Szekeres 264 100. A Permutation Game 266 101. Ants on a Rod 267 102. Two Cyclists and a Swallow 268 103. Almost Disjoint Subsets of Natural Numbers 270 104. Primitive Sequences 272 105. The Time of Infection on a Grid 274 106. Areas of Triangles: Routh’s Theorem 276 107. Lines and Vectors - Euler and Sylvester 282 108. Feuerbach’s Remarkable Circle 284 109. Euler’s Ratio-Product-Sum Theorem 286 110. Bachet’s Weight Problem 288 111. Perfect Partitions 291 112. Countably Many Players 294 ix 113. One Hundred Players 296 114. River Crossings: Alcuin of York - Take One 298 115. River Crossings: Alcuin of York - Take Two 301 116. Fibonacci and a Medieval Mathematics Tournament 303 117. Triangles and Quadrilaterals - Regiomontanus 305 118. The Cross-Ratios of Points and Lines 308 119. Hexagons in Circles: Pascal’s Hexagon Theorem - Take One 312 120. Hexagons in Circles: Pascal’s Theorem - Take Two 315 121. A
Sequence in Zp 318 122. Elements of Prime Order 319 123. Flat Triangulations 320 124. Triangular Billiard Tables 322 125. Chords of an Ellipse: The Butterfly Theorem 324 126. Recurrence Relations for the Partition Function 326 127. The Growth of the Partition Function 328 128. Dense Orbits 332 |
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| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut The art of mathematics - take two Tea time in Cambridge Béla Bollobás, University of Cambridge and University of Memphis Cambridge, United Kingdom Cambridge University Press 2022 © 2022 xiii, 333 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Problem (DE-588)10320914-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematics MATHEMATICS / General (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematik (DE-588)4037944-9 s Problem (DE-588)10320914-1 b DE-604 Erscheint auch als Online-Ausgabe 978-1-108-97388-5 Fortsetzung von 978-0-521-69395-0 Fortsetzung von Bollobás, Béla The art of mathematics Coffee time in Memphis 2006 0-521-87228-6 (DE-604)BV023053957 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033736827&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | The art of mathematics - take two Tea time in Cambridge |
| title_auth | The art of mathematics - take two Tea time in Cambridge |
| title_exact_search | The art of mathematics - take two Tea time in Cambridge |
| title_exact_search_txtP | The art of mathematics - take two Tea time in Cambridge |
| title_full | The art of mathematics - take two Tea time in Cambridge Béla Bollobás, University of Cambridge and University of Memphis |
| title_fullStr | The art of mathematics - take two Tea time in Cambridge Béla Bollobás, University of Cambridge and University of Memphis |
| title_full_unstemmed | The art of mathematics - take two Tea time in Cambridge Béla Bollobás, University of Cambridge and University of Memphis |
| title_old | Bollobás, Béla The art of mathematics |
| title_short | The art of mathematics - take two |
| title_sort | the art of mathematics take two tea time in cambridge |
| title_sub | Tea time in Cambridge |
| topic | Problem (DE-588)10320914-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Problem Mathematik Aufsatzsammlung |
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