Mathematics everywhere:
Saved in:
| Other Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2010]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Item Description: | Translated from the German: Alles Mathematik. 3rd edition, Wiesbaden : Vieweg + Teubner, 2009 |
| Physical Description: | xiv, 330 Seiten Illustrationen, Diagramme, Karten 26 cm |
| ISBN: | 9780821843499 |
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MARC
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| 130 | 0 | |a Alles Mathematik | |
| 245 | 1 | 0 | |a Mathematics everywhere |c Martin Aigner ; Ehrhard Behrends editors, translated by Philip G. Spain |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Mathematics everywhere
Autor: Aigner, Martin
Jahr: 2010
Contents
Preface to the English Translation xi
Prefaces to the German Editions xiii
Preface to the first German Edition xiii
Preface to the second German Edition xiv
Preface to the third German Edition xiv
Part 1. Prologue 1
Chapter 1. Math Becomes a Cult—Description of a Hope
Gero von Randow 3
Part 2. Case Studies 5
Chapter 2. The Mathematics of the Compact Disc
Jack H. van Lint 7
Words and codes 7
A simple example 7
From music to audiobits 9
Reed-Solomon codes 9
The compact disc 12
References 14
Chapter 3. Image Processing and Imaging for Operation Planning in Liver
Surgery
Heinz-Otto Peitgen, Carl Evertsz, Bernhard Preim,
Dirk Selle, Thomas Schindewolf, and Wolf Spindler 15
1. Introduction 15
2. Medical background 16
3. Architecture of a surgery planning system 17
4. Liver and tumor segmentation 18
5. Vessel segmentation and analysis 20
6. Visualization and exploration of the analysed data 23
7. Summary 25
8. Prospect 26
References 26
Chapter 4. The Quickest Path to the Goal
Ralf Borndorfer, Martin Grotsciiel and Andreas
Lobel 27
1. Historical overture 27
CONTENTS
2. Combinatorics of shortest paths 33
3. Combinations of paths , 43
4. Outlook 49
5. Further reading 30
6. Solutions to the questions 31
Chapter 5. Romeo and Juliet, Spontaneous Pattern Formation, and Turing s
Instability
Bernold Fiedler 53
1. Turing dreams 53
: 2. Romeo and Juliet 54
3. Roberto and Julietta 55
4. When sisters gossip ... 57
5. ... and brothers brag 50
6. Turing s theorem 53
7. Mathematical summary 54
8. Outlook 56
References 59
Chapter 6. Mathematics and Intelligent Materials
Stefan Muller
Mathematics as a key technology
Metals with memory
Memory and microstructure
Microstructures everywhere
Microstructures as optimal forms
Mathematical chance helps—Young measures
Design of new materials through mathematics
Future challenges: multiscale mathematics,
or the bridging from atoms to materials
Protein folding, rough energy landscapes, and optimization
References
Chapter 7. Discrete Tomography: From Battleship to Nanotechnology
Peter Gritzmann 81
A glimpse into the human body 81
Behind the teacher s back 82
Duty rosters and data security 87
Reconstruction of crystalline structures ¦«: . 87
Uniqueness theorems • . 91
Complexity and algorithms 95
Stability 96
Chapter 8. Reflections on Reflections
Jurgen Richter-Gebert 99
Childhood memories 99
1. Good angles, bad angles ;• 99
2. One, two, three ... infinity 101
3. Kaleidoscopes—beauty-viewers 101
4. Number games 103
71
71
71
71
74
75
76
77
77
80
80
CONTENTS
vii
5. Light billiards, anti-stealth-boats and egoist mirrors ^ 104
6. The perfect display cupboard 106
7. The way from the right angle 108
8. Platonic beauties ¦ - 110
9. Christmas chaos -i 111
10. Circle inversions 112
11. A new universe 113
12. To infinity, and beyond 116
13. Reading and surfing tips 118
Part 3. Current Topics 121
Chapter 9. The Role of Mathematics in the Financial Markets
Walter Schachermayer 123
References 133
Chapter 10. Electronic Money:
An Impossibility or Already a Reality?
Albrecht Beutelspacher 135
1. Introduction 135
2. What is money? 135
3. Cryptographic mechanisms 136
4. Electronic money: the basic scheme 138
5. Double spending 139
6. Extra properties . 140
Summary 141
References 141
Chapter 11. Spheres in the Computer—the Kepler Conjecture
Martin Henk and Gunter M. Ziegler 143
A really hard nut 143
In the plane 145
Into the third dimension 152
A scandalous situation • j 156
A recipe? 157
Computer versus Kepler jk 161
Problems, problems 161
References 163
Chapter 12. How Do Quanta Compute?
The New World of the Quantum Computer
Ehrhard Behrends 165
1. Why are prime numbers important in cryptography? 166
2. A mathematical preparation: period lengths - 167
3. Some quantum mechanics 168
4. Qbits: the components of a quantum computer 170
5. How does one factorize large numbers with a quantum computer? 171
6. Summary 173
CONTENTS
Chapter 13. Fermat s Last Theorem—the Solution
of a 300 Year Old Problem
Jurg Kramer 175
1. Introduction 175
2. How did Fermat come to his Conjecture? 175
3. The period between 1637 and 1980 177
4. The three worlds 178
5. The bridges between the three worlds 181
6. The anti-Fermat world does not exist 182
References 183
Chapter 14. A Short History of the Nash Equilibrium
Karl Sigmund 185
Does Sherlock Holmes have a chance? 185
The art of the bluff 186
Maximin solutions 188
The Nash equilibrium 189
Ideas from evolution theory 190
The prisoners dilemma 191
Tit for Tat 192
Altruism versus self-interest 193
Chapter 15. Mathematics in the Climate of Global Change
Rupert Klein 197
Why climate and climate impact research? 197
Complexities 199
Story exercises 202
Multiple scales 204
Approximate solutions and missing lattice points 206
Multiscale asymptotics for the oscillator with small mass and damping 208
Hurricanes: an example in multiscale phenomena 212
Conclusion 214
References 215
Part 4. The Central Theme 217
Chapter 16. Prime Numbers, Secret Codes
and the Boundaries of Computability
Martin Aigner 219
1. Prime numbers 219
2. Secret codes 221
3. Boundaries of computability 224
References 226
Chapter 17. The Mathematics of Knots
Elmar Vogt 227
History 227
Wild and tame knots and the search
for the right mathematical concept 231
k
CONTENTS
Polygonal knots
The Reidemeister approach to knot theory 235
There are true knots 238
Some families of knots 244
Chapter 18. On Soap Bubbles
Dirk Ferus 251
References and picture credits 259
Chapter 19. Heat Diffusion, the Structure of Space,
and the Poincare Conjecture
Klaus Ecker 261
1. Introduction 261
2. Geometry and topology of surfaces 263
3. Geometry and topology of three-dimensional spaces 276
4. Heat diffusion and the geometry of curves 285
5. Ricci flow, geometrization and the Poincare Conjecture 288
6. Conclusion 296
References 296
Chapter 20. Chance and Mathematics: a Late Love
Eiirhard Beiirends 299
1. How did it start? 299
2. How is it done today? 300
3. Fundamental concepts 302
4. Games of chance 305
5. Randomness vanishes at infinity 307
6. The productive role of chance 309
7. Chance in the microcosmos 310
8. Philosophical 312
Part 5. Epilogue 315
Chapter 21. The Prospects for Mathematics
in a Multi-Media Civilization
Philip J. Davis „ 317
Poincare s predictions 318
What will pull mathematics into the future? 318
The inner texture (or soul) of mathematics 324
A personal illumination 329
References 330
|
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| spelling | Alles Mathematik Mathematics everywhere Martin Aigner ; Ehrhard Behrends editors, translated by Philip G. Spain Providence, Rhode Island American Mathematical Society [2010] © 2010 xiv, 330 Seiten Illustrationen, Diagramme, Karten 26 cm txt rdacontent n rdamedia nc rdacarrier Translated from the German: Alles Mathematik. 3rd edition, Wiesbaden : Vieweg + Teubner, 2009 Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematik (DE-588)4037944-9 s Anwendung (DE-588)4196864-5 s DE-604 Aigner, Martin 1942-2023 (DE-588)13205387X edt Behrends, Ehrhard 1946- (DE-588)124668631 edt Spain, Philip G. trl Erscheint auch als Online-Ausgabe 978-1-4704-1605-8 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9780821843499.pdf Inhaltsverzeichnis DE-601 pdf/application http://zbmath.org/?q=an:1200.00015 Zentralblatt MATH Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029163145&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematics everywhere Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4196864-5 (DE-588)4143413-4 |
| title | Mathematics everywhere |
| title_alt | Alles Mathematik |
| title_auth | Mathematics everywhere |
| title_exact_search | Mathematics everywhere |
| title_full | Mathematics everywhere Martin Aigner ; Ehrhard Behrends editors, translated by Philip G. Spain |
| title_fullStr | Mathematics everywhere Martin Aigner ; Ehrhard Behrends editors, translated by Philip G. Spain |
| title_full_unstemmed | Mathematics everywhere Martin Aigner ; Ehrhard Behrends editors, translated by Philip G. Spain |
| title_short | Mathematics everywhere |
| title_sort | mathematics everywhere |
| topic | Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Mathematik Mathematics Anwendung Aufsatzsammlung |
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