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## The Queen of Mathematics: A Historically Motivated Guide to Number Theory (Hardback)"Starting in the fall of 1986, I combined my interests in number theory and history by teaching a one-year course in number theory from a historical prospective. The course used historical highlights to show the development of various topics, and I included some discussion about the lives of famous number theorists. My lecture notes for the course turned into a more formal set of notes, which turned into this book. Both the spirit and organization of material in the book remain those of my original lectures." — Jay R. Goldman, author, in the Preface ## $49.50 |

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Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** This book is in very good condition, showing only slight signs of use and wear (mostly in a slightly faded spine and front cover). The covers, pages, and spine are in very good condition, and there is no writing on the pages.

## Description

From the back cover: “This book takes the unique approach of examining number theory as it developed from the 17th through 19th centuries, leading to an understanding of today’s research problems on the basis of their historical evolution. Written as a labor of love by an author well known for his expository style, the book introduces the reader to diverse mathematical players: Fermat, Euler, Lagrange, Legendre, Dedekind, Hilbert, and more. Gauss (who gave the field of number theory its sobriquet ‘The Queen of Mathematics’) and his *Disquisitiones Arithmeticae* receive a particularly intensive treatment. The text then moves on to tackle some advanced themes including arithmetic on curves, geometry of numbers, *p*-adic numbers and valuations, and the interconnected topics of irrational and transcendental numbers and Diophantine appropriation. With its historical framework and narrative style, Goldman’s book makes both a lovely resources for mathematicians and an introductory text for students and teachers.”

**CHAPTERS**

**PART 1: FROM FERMAT TO LEGENDRE**

- The Founding Fathers
- Fermat
- Euler
- From Euler to Lagrange; The Theory of Continued Fractions
- Lagrange
- Legendre

**PART 2: GAUSS AND THE DISQUISITIONES ARITHMETICAE**

- Gauss
- Theory of Congruence 1
- Theory of Congruence 2
- Primitive Roots and Power Residues
- Congruences of the Second Degree
- Binary Quadratic Forms 1: Arithmetic Theory
- Binary Quadratic Forms 2: Geometric Theory
- Cyclotomy

**PART 3: ALGEBRAIC NUMBER THEORY**

- Algebraic Number Theory 1: The Gaussian Integers and Biquadratic Reciprocity
- Algebraic Number Theory 2: Algebraic Numbers and Quadratic Fields
- Algebraic Number Theory 3: Ideals in Quadratic Fields

**PART 4: ARITHMETIC ON CURVES**

- Arithmetic on Curves 1: Rational Points and Plane Algebraic Curves
- Arithmetic on Curves 2: Rational Points and Elliptic Curves
- Arithmetic on Curves 3: The Twentieth Century

**PART 5: MISCELLANEOUS TOPICS**

- Irrational and Transcendental Numbers, Diophantine Approximations
- Geometry of Numbers
- p-adic Numbers and Valuations

The book concludes with Bibliography and Index.

## Details

- SKU:
- 3021
- Subject:
- Number Theory
- Author:
- Goldman, Jay R.
- Publisher:
- A K Peters
- Publish Date:
- 2004
- Format:
- Hardback
- Weight (pounds):
- 1.73
- Dimensions (W”xL”xH”):
- 6.3″x9.3″x1.2″
- ISBN-13:
- 9781568810065
- ISBN-10:
- 1568810067
- Grade Level:
- College

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