The Art of Mathematics: Coffee Time in Memphis

Front Cover
Cambridge University Press, Sep 14, 2006 - Mathematics - 359 pages
3 Reviews
Can a Christian escape from a lion? How quickly can a rumor spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.
  

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Contents

The Problems
1
Contents ix
13
The Hints
36
The Solutions
45
Erdos Problems for Epsilons
48
Points on a Circle
50
Partitions into Closed Sets
52
Triangles and Squares
53
Triangles Touching a Triangle
192
Even and Odd Graphs
193
the MoonMoser Theorem
194
Filling a Matrix
197
the ErdosMordell Theorem
199
Perfect Difference Sets
203
Difference Bases
205
the HardyLittlewood Maximal Theorem
208

Polygons and Rectangles
55
African Rally
56
Fixing Convex Domains
58
Nested Subsets
61
Almost Disjoint Subsets
63
Loaded Dice
64
An Unexpected Inequality
65
the ErdosSelfridge Theorem
66
Independent Sets
68
Expansion into Sums 2i3j
69
A Tennis Match
70
Another Erdos Problem for Epsilons
71
Planar Domains of Diameter 1
73
Orienting Graphs
74
A Simple Clock
75
Neighbours in a Matrix
76
Separately Continuous Functions
77
Boundary Cubes
78
Lozenge Tilings
79
A Continuum Independent Set
83
Separating Families of Sets
84
Bipartite Covers of Complete Graphs
86
the Theorems
88
of Radon and Caratheodory
89
Hellys Theorem
90
Judicious Partitions of Points
92
Further Lozenge Tilings
93
Two Squares in a Square
95
the SylvesterGallai Theorem
98
The Spread of Infection on a Square Grid
104
The Spread of Infection in a ddimensional Box
106
an Easy Erdos Problem for Epsilons
110
the Champernowne Number
111
Random Walks on Graphs
113
Simple Tilings of Rectangles
114
Ltilings
116
Borsuks Theorem
117
Borsuks Problem
120
Napoleons Theorem
124
Morleys Theorem
126
Connected Subgraphs
129
Subtrees of an Infinite Tree
133
Twodistance Sets
134
Gossiping Dons
136
the de BruijnErdos Theorem
140
an Extension of the de BruijnErdos Theorem
142
Bell Numbers
144
Circles Touching a Square
147
Gambling
149
Complex Sequences
151
Partitions of Integers
153
Emptying Glasses
157
Distances in Planar Sets
159
Monic Polynomials
161
Odd Clubs
163
A Politically Correct Town
164
Lattice Paths
165
Triangulations of Polygons
168
Zagiers Inequality
169
Squares Touching a Square
170
Infection with Three Neighbours
171
The Spread of Infection on a Torus
173
Dominating Sequences
174
Sums of Reciprocals
175
Absentminded Passengers
176
Airline Luggage
177
the ErdosKoRado Theorem
179
the MYBL Inequality
180
Five Points in Space
183
Triads
184
Colouring Complete Graphs
186
a Theorem of Besicovitch
187
Independent Random Variables
190
Random Words
212
Crossing a Chess Board
214
Powers of Paths and Cycles
216
Powers of Oriented Cycles
217
Perfect Trees
218
Circular sequences
220
Infinite Sets with Integral Distances
222
Finite Sets with Integral Distances
223
Thues Theorem
224
the ThueMorse Theorem
226
the CauchyDavenport Theorem
229
the ErdosGinzburgZiv Theorem
232
Subwords of Distinct Words
237
Prime Factors of Sums
238
Catalan Numbers
240
Permutations without Long Decreasing Subsequences
242
a Theorem of Justicz Scheinerman and Winkler
244
the BrunnMinkowski Inequality
246
Bollobass Lemma
251
Saturated Hypergraphs
252
Hardys Inequality
253
Carlemans Inequality
257
Triangulating Squares
259
Strongly Separating Families
262
Strongly Separating Systems of Pairs of Sets
263
The Maximum EdgeBoundary of a Downset
265
Partitioning a Subset of the Cube
267
Frankls Theorem
269
Even Sets with Even Intersections
271
Sets with Even Intersections
273
Even Clubs
275
Covering the Sphere
276
Lovaszs Theorem
277
Partitions into Bricks
279
Drawing Dense Graphs
280
Szekelys Theorem
282
PointLine Incidences
284
Geometric Graphs without Parallel Edges
285
Shortest Tours
288
Density of Integers
291
Kirchbergers Theorem
293
Chords of Convex Bodies
294
Neighourly Polyhedra
296
Perles Theorem
299
The Rank of a Matrix
301
a Theorem of Frankl and Wilson
303
Families without Orthogonal Vectors
306
the KahnKalai Theorem
308
Periodic Sequences
311
the FineWilf Theorem
313
Wendels Theorem
315
Planar and Spherical Triangles
318
Hadˇziivanovs theorem
319
A Probabilistic Inequality
321
Cube Slicing
322
the HobbyRice Theorem
324
Cutting a Necklace
326
the RieszThorin Interpolation Theorem
328
Uniform Covers
332
Projections of Bodies
333
the Box Theorem of Bollobas and Thomason
335
the RayChaudhuri Wilson Inequality
337
the FranklWilson Inequality
340
Maps from Sn
342
Hopfs Theorem
344
Spherical Pairs
345
Realizing Distances
346
A Closed Cover of S2
348
the Friendship Theorem of Erdos Renyi and Sos
349
Polarities in Projective Planes
352
Steinitzs Theorem
353
The PointLine Game
356
Copyright

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About the author (2006)

Béla Bollobás is a Senior Research Fellow at Trinity College, Cambridge and is the Jabie Hardin Chair of Excellence in Combinatorics at the University of Memphis. He has held visiting positions from Seattle to Singapore, from Brazil to Zurich. This is his tenth book.

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