The art of mathematics: coffee time in Memphis
Gespeichert in:
| Späterer Titel: | Bollobás, Béla The art of mathematics |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Contributor biographical information Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xv, 359 Seiten Illustrationen, Diagramme |
| ISBN: | 0521872286 9780521872287 9780521693950 0521693950 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
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| 100 | 1 | |a Bollobás, Béla |d 1943- |e Verfasser |0 (DE-588)109481240 |4 aut | |
| 245 | 1 | 0 | |a The art of mathematics |b coffee time in Memphis |c Béla Bollobás (University ob Memphis and University of Cambridge) |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2006 | |
| 264 | 4 | |c © 2006 | |
| 300 | |a xv, 359 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathématiques | |
| 650 | 7 | |a Recreatieve wiskunde |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics | |
| 650 | 0 | 7 | |a Problem |0 (DE-588)4175771-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 785 | 0 | 0 | |i Fortgesetzt durch |a Bollobás, Béla |t The art of mathematics |c tea time in Cambridge |d 2022 |w (DE-604)BV048357582 |
| 785 | 0 | 0 | |i Fortgesetzt durch |z 978-1-108-83327-1 |
| 785 | 0 | 0 | |i Fortgesetzt durch |z 978-1-108-97826-2 |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0703/2006299521-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0703/2006299521-t.html |3 Table of contents only | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0733/2006299521-b.html |3 Contributor biographical information | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016257292 | ||
Datensatz im Suchindex
| _version_ | 1804137288135868416 |
|---|---|
| adam_text | Contents
Preface
xiii
1
The Problems
1
2
The Hints
37
3
The Solutions
46
1.
The Lion and The Christian
46
2.
Integer Sequences:
Erdős
Problems for
Epsilons
49
3.
Points on a Circle
51
4.
Partitions into Closed Sets
53
5.
Triangles and Squares
54
6.
Polygons and Rectangles
56
7.
African Rally
57
8.
Fixing Convex Domains
59
9.
Nested Subsets
62
10.
Almost Disjoint Subsets
64
11.
Loaded Dice
65
12.
An Unexpected Inequality
66
13.
Colouring Lines: the
Erdős-Selfridge
Theorem
67
14.
Independent Sets
69
15.
Expansion into Sums
2
З·
70
16.
A Tennis Match
71
17.
A Triangle Inequality: Another
Erdős
Problem for
Epsilons
72
18.
Planar Domains of Diameter
1
74
19.
Orienting Graphs
75
20.
A Simple Clock
76
21.
Neighbours in a Matrix
77
22.
Separately Continuous Functions
78
23.
Boundary Cubes
79
24.
Lozenge Tilings
80
VII
viii Contents
25.
A Continuum Independent Set
84
26.
Separating Families of Sets
85
27.
Bipartite Covers of Complete Graphs
87
28.
Convexity and Intersecting Simplices: the Theorems
of Radon and
Carathéodory
89
29.
Intersecting Convex Sets: Helly s Theorem
91
ЗО.
Judicious Partitions of Points
93
31.
Further Lozenge Tilings
94
32.
Two Squares in a Square
96
33.
Lines Through Points: the Sylvester-Gallai Theorem
99
34.
The Spread of Infection on a Square Grid
105
35.
The Spread of Infection in a ¿/-dimensional Box
107
36.
Sums of Integers: an Easy
Erdős
Problem for
Epsilons
111
37.
Normal Numbers: the Champernowne Number
112
38.
Random Walks on Graphs
114
39.
Simple Tilings of Rectangles
115
40.
¿-tilings
117
41.
Antipodal Points and Maps: Borsuk s Theorem
118
42.
Bodies of Diameter
1 :
Borsuk s Problem
121
43.
Equilateral Triangles: Napoleon s Theorem
125
44.
Trisectors
of Angles: Morley s Theorem
127
45.
Connected Subgraphs
130
46.
Subtrees of an Infinite Tree
134
47.
Two-distance Sets
135
48.
Gossiping Dons
137
49.
Exact Covers: the
de Bruijn-Erdős
Theorem
141
50.
Constant Intersections: an Extension of the
de Bruijn-Erdős
Theorem
143
51.
Bell Numbers
145
52.
Circles Touching a Square
148
53.
Gambling
150
54.
Complex Sequences
152
55.
Partitions of Integers
154
56.
Emptying Glasses
158
57.
Distances in Planar Sets
160
58.
Monic Polynomials
162
59.
Odd Clubs
164
60.
A Politically Correct Town
165
61.
Lattice Paths
166
62.
Triangulations
of Polygons
169
Contents ix
63.
A Converse of Cauchy s Inequality: Zagier s Inequality
170
64.
Squares Touching a Square
171
65.
Infection with Three Neighbours
172
66.
The Spread of Infection on a Torus
174
67.
Dominating Sequences
175
68.
Sums of Reciprocals
176
69.
Absent-minded Passengers
177
70.
Airline Luggage
178
71.
Intersecting Sets: the
Erdôs-Ko-Rado
Theorem
180
72.
Sperner Families: the
M
YBL
Inequality
181
73.
Breaking a Stick
184
74.
Triads
185
75.
Colouring Complete Graphs
187
76.
Symmetric Convex Domains: a Theorem of Besicovitch
188
77.
Independent Random Variables
191
78.
Triangles Touching a Triangle
193
79.
Even and Odd Graphs
194
80.
Packing Squares: the Moon-Moser Theorem
195
81.
Filling a Matrix
198
82.
An Inequality Concerning Triangles: the
Erdős-Mordeli
Theorem
200
83.
Perfect Difference Sets
204
84.
Difference Bases
206
85.
Satisfied Cricketers: the Hardy-Littlewood Maximal
Theorem
209
86.
Random Words
213
87.
Crossing a Chess Board
215
88.
Powers of Paths and Cycles
217
89.
Powers of Oriented Cycles
218
90.
Perfect Trees
219
91.
Circular Sequences
221
92.
Infinite Sets with Integral Distances
223
93.
Finite Sets with Integral Distances
224
94.
Cube-free Words: Thue s Theorem
225
95.
Square-free Words: the Thue-Morse Theorem
227
96.
Addition of Residue Classes: the Cauchy-Davenport
Theorem
230
97.
Sums Congruent to Zero: the
Erdős-Ginzburg-Ziv
Theorem
233
98.
Subwords of Distinct Words
238
Contents
99.
Prime Factors of Sums
239
100.
Catalan Numbers
241
101.
Permutations without Long Decreasing Subsequences
243
102.
Random Intervals: a Theorem of Justicz, Scheinerman
and
Winkler 245
103.
Sums of Convex Bodies: the Brunn-Minkowski Inequality
247
104.
Cross-Intersecting Families:
Bollobás s
Lemma
249
105.
Saturated Hypergraphs
253
106.
The Norm of Averages: Hardy s Inequality
254
107.
The Average of Geometric Means: Carleman s Inequality
258
108.
Triangulating Squares
260
109.
Strongly Separating Families
263
110.
Strongly Separating Systems of Pairs of Sets
264
111. The Maximum Edge-Boundary of a Down-set
266
112.
Partitioning a Subset of the Cube
268
113.
Weakly Cross-intersecting Pairs:
Frankľs
Theorem
270
114.
Even Sets with Even Intersections
272
115.
Sets with Even Intersections
274
116.
Even Clubs
276
117.
Covering the Sphere
277
118.
The Kneser Graph:
Lovász s
Theorem
278
119.
Partitions into Bricks
280
120.
Drawing Dense Graphs
281
121.
Unit Distances:
Székely
s
Theorem
283
122.
Point-Line Incidences
285
123.
Geometric Graphs without Parallel Edges
286
124.
Shortest Tours
289
125.
Density of Integers
292
126.
Black and White Sheep: Kirchberger s Theorem
294
127.
Chords of Convex Bodies
295
128.
Neighourly Polyhedra
297
129.
Neighbourly Simplices:
Perles
Theorem
300
130.
The Rank of a Matrix
302
131.
Modular Intersecting
k
-uniform Set Systems: a Theorem
of
Franki
and Wilson
304
132.
Families without Orthogonal Vectors
307
133.
A Counterexample to Borsuk s Conjecture:
the Kahn-Kalai Theorem
309
134.
Periodic Sequences
312
135.
Periodic Words: the Fine-Wilf Theorem
314
Contents xi
136. Points
on a Hemisphere:
Wendei s
Theorem 316
137.
Planar and Spherical Triangles
319
138.
Hobnails:
Hadžiivanov s
Theorem
320
139.
A Probabilistic Inequality
322
140.
Cube Slicing
323
141.
Measures on
[0,1]:
the Hobby-Rice Theorem
325
142.
Cutting a Necklace
327
143.
The Norm of an Operator: the Riesz-Thorin Interpolation
Theorem
329
144.
Uniform Covers
333
145.
Projections of Bodies
334
146.
BTBT: the Box Theorem of
Bollobás
and Thomason
336
147.
Intersecting Uniform Set Systems: the Ray-Chaudhuri-
Wilson Inequality
338
148.
Intersecting Set Systems: the Frankl-Wilson Inequality
341
149.
Maps from S
343
150.
Closed Covers of
5 : Hopfs
Theorem
345
151.
Spherical Pairs
346
152.
Realizing Distances
347
153.
A Closed Cover of S2
349
154.
A Friendly Party: the Friendship Theorem of
Erdős, Rényi
and
Sós
350
155.
Polarities in
Projective
Planes
353
156.
Permutations of Vectors: Steinitz s Theorem
354
157.
An American Story
357
158.
Conway s Angel and Devil Game
359
159.
The Point-Line Game
367
|
| adam_txt |
Contents
Preface
xiii
1
The Problems
1
2
The Hints
37
3
The Solutions
46
1.
The Lion and The Christian
46
2.
Integer Sequences:
Erdős
Problems for
Epsilons
49
3.
Points on a Circle
51
4.
Partitions into Closed Sets
53
5.
Triangles and Squares
54
6.
Polygons and Rectangles
56
7.
African Rally
57
8.
Fixing Convex Domains
59
9.
Nested Subsets
62
10.
Almost Disjoint Subsets
64
11.
Loaded Dice
65
12.
An Unexpected Inequality
66
13.
Colouring Lines: the
Erdős-Selfridge
Theorem
67
14.
Independent Sets
69
15.
Expansion into Sums
2'
З·'
70
16.
A Tennis Match
71
17.
A Triangle Inequality: Another
Erdős
Problem for
Epsilons
72
18.
Planar Domains of Diameter
1
74
19.
Orienting Graphs
75
20.
A Simple Clock
76
21.
Neighbours in a Matrix
77
22.
Separately Continuous Functions
78
23.
Boundary Cubes
79
24.
Lozenge Tilings
80
VII
viii Contents
25.
A Continuum Independent Set
84
26.
Separating Families of Sets
85
27.
Bipartite Covers of Complete Graphs
87
28.
Convexity and Intersecting Simplices: the Theorems
of Radon and
Carathéodory
89
29.
Intersecting Convex Sets: Helly's Theorem
91
ЗО.
Judicious Partitions of Points
93
31.
Further Lozenge Tilings
94
32.
Two Squares in a Square
96
33.
Lines Through Points: the Sylvester-Gallai Theorem
99
34.
The Spread of Infection on a Square Grid
105
35.
The Spread of Infection in a ¿/-dimensional Box
107
36.
Sums of Integers: an Easy
Erdős
Problem for
Epsilons
111
37.
Normal Numbers: the Champernowne Number
112
38.
Random Walks on Graphs
114
39.
Simple Tilings of Rectangles
115
40.
¿-tilings
117
41.
Antipodal Points and Maps: Borsuk's Theorem
118
42.
Bodies of Diameter
1 :
Borsuk's Problem
121
43.
Equilateral Triangles: Napoleon's Theorem
125
44.
Trisectors
of Angles: Morley's Theorem
127
45.
Connected Subgraphs
130
46.
Subtrees of an Infinite Tree
134
47.
Two-distance Sets
135
48.
Gossiping Dons
137
49.
Exact Covers: the
de Bruijn-Erdős
Theorem
141
50.
Constant Intersections: an Extension of the
de Bruijn-Erdős
Theorem
143
51.
Bell Numbers
145
52.
Circles Touching a Square
148
53.
Gambling
150
54.
Complex Sequences
152
55.
Partitions of Integers
154
56.
Emptying Glasses
158
57.
Distances in Planar Sets
160
58.
Monic Polynomials
162
59.
Odd Clubs
164
60.
A Politically Correct Town
165
61.
Lattice Paths
166
62.
Triangulations
of Polygons
169
Contents ix
63.
A Converse of Cauchy's Inequality: Zagier's Inequality
170
64.
Squares Touching a Square
171
65.
Infection with Three Neighbours
172
66.
The Spread of Infection on a Torus
174
67.
Dominating Sequences
175
68.
Sums of Reciprocals
176
69.
Absent-minded Passengers
177
70.
Airline Luggage
178
71.
Intersecting Sets: the
Erdôs-Ko-Rado
Theorem
180
72.
Sperner Families: the
M
YBL
Inequality
181
73.
Breaking a Stick
184
74.
Triads
185
75.
Colouring Complete Graphs
187
76.
Symmetric Convex Domains: a Theorem of Besicovitch
188
77.
Independent Random Variables
191
78.
Triangles Touching a Triangle
193
79.
Even and Odd Graphs
194
80.
Packing Squares: the Moon-Moser Theorem
195
81.
Filling a Matrix
198
82.
An Inequality Concerning Triangles: the
Erdős-Mordeli
Theorem
200
83.
Perfect Difference Sets
204
84.
Difference Bases
206
85.
Satisfied Cricketers: the Hardy-Littlewood Maximal
Theorem
209
86.
Random Words
213
87.
Crossing a Chess Board
215
88.
Powers of Paths and Cycles
217
89.
Powers of Oriented Cycles
218
90.
Perfect Trees
219
91.
Circular Sequences
221
92.
Infinite Sets with Integral Distances
223
93.
Finite Sets with Integral Distances
224
94.
Cube-free Words: Thue"s Theorem
225
95.
Square-free Words: the Thue-Morse Theorem
227
96.
Addition of Residue Classes: the Cauchy-Davenport
Theorem
230
97.
Sums Congruent to Zero: the
Erdős-Ginzburg-Ziv
Theorem
233
98.
Subwords of Distinct Words
238
Contents
99.
Prime Factors of Sums
239
100.
Catalan Numbers
241
101.
Permutations without Long Decreasing Subsequences
243
102.
Random Intervals: a Theorem of Justicz, Scheinerman
and
Winkler 245
103.
Sums of Convex Bodies: the Brunn-Minkowski Inequality
247
104.
Cross-Intersecting Families:
Bollobás's
Lemma
249
105.
Saturated Hypergraphs
253
106.
The Norm of Averages: Hardy's Inequality
254
107.
The Average of Geometric Means: Carleman's Inequality
258
108.
Triangulating Squares
260
109.
Strongly Separating Families
263
110.
Strongly Separating Systems of Pairs of Sets
264
111. The Maximum Edge-Boundary of a Down-set
266
112.
Partitioning a Subset of the Cube
268
113.
Weakly Cross-intersecting Pairs:
Frankľs
Theorem
270
114.
Even Sets with Even Intersections
272
115.
Sets with Even Intersections
274
116.
Even Clubs
276
117.
Covering the Sphere
277
118.
The Kneser Graph:
Lovász's
Theorem
278
119.
Partitions into Bricks
280
120.
Drawing Dense Graphs
281
121.
Unit Distances:
Székely
's
Theorem
283
122.
Point-Line Incidences
285
123.
Geometric Graphs without Parallel Edges
286
124.
Shortest Tours
289
125.
Density of Integers
292
126.
Black and White Sheep: Kirchberger's Theorem
294
127.
Chords of Convex Bodies
295
128.
Neighourly Polyhedra
297
129.
Neighbourly Simplices:
Perles'
Theorem
300
130.
The Rank of a Matrix
302
131.
Modular Intersecting
k
-uniform Set Systems: a Theorem
of
Franki
and Wilson
304
132.
Families without Orthogonal Vectors
307
133.
A Counterexample to Borsuk's Conjecture:
the Kahn-Kalai Theorem
309
134.
Periodic Sequences
312
135.
Periodic Words: the Fine-Wilf Theorem
314
Contents xi
136. Points
on a Hemisphere:
Wendei's
Theorem 316
137.
Planar and Spherical Triangles
319
138.
Hobnails:
Hadžiivanov's
Theorem
320
139.
A Probabilistic Inequality
322
140.
Cube Slicing
323
141.
Measures on
[0,1]:
the Hobby-Rice Theorem
325
142.
Cutting a Necklace
327
143.
The Norm of an Operator: the Riesz-Thorin Interpolation
Theorem
329
144.
Uniform Covers
333
145.
Projections of Bodies
334
146.
BTBT: the Box Theorem of
Bollobás
and Thomason
336
147.
Intersecting Uniform Set Systems: the Ray-Chaudhuri-
Wilson Inequality
338
148.
Intersecting Set Systems: the Frankl-Wilson Inequality
341
149.
Maps from S"
343
150.
Closed Covers of
5" : Hopfs
Theorem
345
151.
Spherical Pairs
346
152.
Realizing Distances
347
153.
A Closed Cover of S2
349
154.
A Friendly Party: the Friendship Theorem of
Erdős, Rényi
and
Sós
350
155.
Polarities in
Projective
Planes
353
156.
Permutations of Vectors: Steinitz's Theorem
354
157.
An American Story
357
158.
Conway's Angel and Devil Game
359
159.
The Point-Line Game
367 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bollobás, Béla 1943- |
| author_GND | (DE-588)109481240 |
| author_facet | Bollobás, Béla 1943- |
| author_role | aut |
| author_sort | Bollobás, Béla 1943- |
| author_variant | b b bb |
| building | Verbundindex |
| bvnumber | BV023053957 |
| callnumber-first | Q - Science |
| callnumber-label | QA93 |
| callnumber-raw | QA93 |
| callnumber-search | QA93 |
| callnumber-sort | QA 293 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SN 100 |
| classification_tum | MAT 001f |
| ctrlnum | (OCoLC)77004619 (DE-599)BVBBV023053957 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV023053957 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:25:51Z |
| indexdate | 2024-07-09T21:09:54Z |
| institution | BVB |
| isbn | 0521872286 9780521872287 9780521693950 0521693950 |
| language | English |
| lccn | 2006299521 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016257292 |
| oclc_num | 77004619 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-11 DE-188 DE-355 DE-BY-UBR DE-824 DE-523 DE-521 DE-739 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-11 DE-188 DE-355 DE-BY-UBR DE-824 DE-523 DE-521 DE-739 |
| physical | xv, 359 Seiten Illustrationen, Diagramme |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut The art of mathematics coffee time in Memphis Béla Bollobás (University ob Memphis and University of Cambridge) Cambridge Cambridge University Press 2006 © 2006 xv, 359 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathématiques Recreatieve wiskunde gtt Mathematik Mathematics Problem (DE-588)4175771-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s DE-604 Problem (DE-588)4175771-3 s Erscheint auch als Online-Ausgabe 978-0-511-81657-4 Fortgesetzt durch Bollobás, Béla The art of mathematics tea time in Cambridge 2022 (DE-604)BV048357582 Fortgesetzt durch 978-1-108-83327-1 Fortgesetzt durch 978-1-108-97826-2 http://www.loc.gov/catdir/enhancements/fy0703/2006299521-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0703/2006299521-t.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0733/2006299521-b.html Contributor biographical information Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016257292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bollobás, Béla 1943- The art of mathematics coffee time in Memphis Mathématiques Recreatieve wiskunde gtt Mathematik Mathematics Problem (DE-588)4175771-3 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4175771-3 (DE-588)4037944-9 (DE-588)4143389-0 |
| title | The art of mathematics coffee time in Memphis |
| title_auth | The art of mathematics coffee time in Memphis |
| title_exact_search | The art of mathematics coffee time in Memphis |
| title_exact_search_txtP | The art of mathematics coffee time in Memphis |
| title_full | The art of mathematics coffee time in Memphis Béla Bollobás (University ob Memphis and University of Cambridge) |
| title_fullStr | The art of mathematics coffee time in Memphis Béla Bollobás (University ob Memphis and University of Cambridge) |
| title_full_unstemmed | The art of mathematics coffee time in Memphis Béla Bollobás (University ob Memphis and University of Cambridge) |
| title_new | Bollobás, Béla The art of mathematics |
| title_short | The art of mathematics |
| title_sort | the art of mathematics coffee time in memphis |
| title_sub | coffee time in Memphis |
| topic | Mathématiques Recreatieve wiskunde gtt Mathematik Mathematics Problem (DE-588)4175771-3 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathématiques Recreatieve wiskunde Mathematik Mathematics Problem Aufgabensammlung |
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