2010;
330 pp;
Softcover

Print ISBN: 978-0-8218-4349-9

Product Code: MBK/72

List Price: $52.00

Individual Member Price: $41.60

**Electronic ISBN: 978-1-4704-1605-8
Product Code: MBK/72.E**

List Price: $52.00

Individual Member Price: $41.60

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#### Supplemental Materials

# Mathematics Everywhere

Share this page *Edited by *
*Martin Aigner; Ehrhard Behrends*

Translated by Philip G. Spain

Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the “math inside” understandable and enjoyable. An additional attractive feature is the leisurely treatment of some hot topics that have gained prominence in recent years, such as Fermat's Theorem, Kepler's packing problem, and the solution of the Poincaré Conjecture. Or maybe you have heard about the Nash equilibrium (of “A Beautiful Mind” fame), or the strange future of quantum computers, and want to know what it is all about? Well, open the book and take an up-to-date trip into the fascinating world of the mathematics all around us.

#### Table of Contents

# Table of Contents

## Mathematics Everywhere

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface to the english translation xi12 free
- Preface to the german editions xiii14 free
- Part I. Prologue 116 free
- Math becomes a cult—description of a hope 318
- Part II. Case studies 520
- The mathematics of the compact disc 722
- Image processing and imaging for operation planning in liver surgery 1530
- The quickest path to the goal 2742
- Romeo and Juliet, spontaneous pattern formation, and Turing’s instability 5368
- Mathematics and intelligent materials 7186
- Discrete tomography: from battleship to nanotechnology 8196
- Reflections on reflections 99114
- Part III. Current topics 121136
- The role of mathematics in the financial markets 123138
- Electronic money: an impossibility or already a reality? 135150
- Spheres in the computer—the Kepler conjecture 143158
- How do quanta compute? The new world of the quantum computer 165180
- Fermat’s Last Theorem—the solution of a 300 year old problem 175190
- A short history of the Nash equilibrium 185200
- Mathematics in the climate of global change 197212
- Part IV. The central theme 217232
- Prime numbers, secret codes and the boundaries of computability 219234
- The mathematics of knots 227242
- On soap bubbles 251266
- Heat diffusion, the structure of space and the Poincaré Conjecture 261276
- Chance and mathematics: a late love 299314
- Part V. Epilogue 315330
- The prospects for mathematics in a multi-media civilization 317332
- Back Cover Back Cover1346

#### Readership

Undergraduates, graduate students, and research mathematicians interested in mathematical trends and topics in the world around us.

#### Reviews

The modern world runs on mathematics. It provides a way to make things work better and more efficiently, which is one of the ways that economies can emerge from a recession. This necessary fervor is fueled by knowledge of the latest applications of mathematics, some of which is provided in great detail by this book.

-- MAA Reviews

This collection of articles illustrates the endless impact of mathematics in the world around us while showcasing the elegance and functionality of mathematics. . . . This book is a must-read for mathematics majors. It allows them to see the wide range of places their degree can take them, many of which they would not have been exposed to in their undergraduate preparation.

-- Diane Barrett, Mathematics Teacher