Fearless Symmetry : Exposing the Hidden Patterns of Numbers - New Edition / Robert Gross, Avner Ash.

Format:

Book

Author/Creator:

Ash, Avner, author.

Gross, Robert, author.

Language:

English

Subjects (All):

Number theory.

Local Subjects:

Number theory.

Physical Description:

1 online resource (307 p.)

Edition:

New edition with a New preface by the authors

Place of Publication:

Princeton, NJ : Princeton University Press, [2008]

Language Note:

English

Summary:

Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

Contents:

Frontmatter

Contents

Foreword

Preface To The Paperback Edition

Preface

Acknowledgments

Greek Alphabet

Part One. Algebraic Preliminaries

Chapter 1. Representations

Chapter 2. Groups

Chapter 3. Permutations

Chapter 4. Modular Arithmetic

Chapter 5. Complex Numbers

Chapter 6. Equations and Varieties

Chapter 7. Quadratic Reciprocity

Part Two. Galois Theory and Representations

Chapter 8. Galois Theory

Chapter 9. Elliptic Curves

Chapter 10. Matrices

Chapter 11. Groups of Matrices

Chapter 12. Group Representations

Chapter 13. The Galois Group Of A Polynomial

Chapter 14. The Restriction Morphism

Chapter 15. The Greeks Had a Name for it

Chapter 16. Frobenius

Part Three. Reciprocity Laws

Chapter 17. Reciprocity Laws

Chapter 18. One- And Two-Dimensional Representations

Chapter 19. Quadratic Reciprocity Revisited

Chapter 20. A Machine for Making Galois Representations

Chapter 21. A Last Look at Reciprocity

Chapter 22. Fermat's Last Theorem and Generalized Fermat Equations

Chapter 23. Retrospect

Bibliography

Index

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9786612964893

9781282964891

1282964895

9781400837779

1400837774

OCLC:

705944534