Gamma : exploring Euler's constant / Julian Havil.

Format:

Book

Author/Creator:

Havil, Julian, 1952-

Series:

Princeton Science Library

Princeton Science Library ; 53

Language:

English

Subjects (All):

Mathematical constants.

Euler, Leonhard, 1707-1783.

Euler, Leonhard.

Physical Description:

1 online resource (291 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, 2009.

Language Note:

English

Summary:

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

Contents:

Frontmatter

Contents

Foreword

Acknowledgements

Introduction

Chapter One. The Logarithmic Cradle

Chapter Two. The Harmonic Series

Chapter Three. Sub-Harmonic Series

Chapter Four. Zeta Functions

Chapter Five. Gamma's Birthplace

Chapter Six. The Gamma Function

Chapter Seven. Euler's Wonderful Identity

Chapter Eight. A Promise Fulfilled

Chapter Nine. What Is Gamma . . . Exactly?

Chapter Ten. Gamma as a Decimal

Chapter Eleven. Gamma as a Fraction

Chapter Twelve. Where Is Gamma?

Chapter Thirteen. It's a Harmonic World

Chapter Fourteen. It's a Logarithmic World

Chapter Fifteen. Problems with Primes

Chapter Sixteen. The Riemann Initiative

Appendix A. The Greek Alphabet

Appendix B. Big Oh Notation

Appendix C. Taylor Expansions

Appendix D. Complex Function Theory

Appendix E. Application to the Zeta Function

Name Index

Subject 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)

Includes bibliographical references and index.

ISBN:

0-691-17810-0

1-282-53141-7

9786612531415

1-4008-3253-5

OCLC:

609856392