The Queen of Mathematics: A Historically Motivated Guide to Number Theory / Edition 1

by Jay Goldman

Overview

This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.

Product Details

ISBN-13:	9781568810065
Publisher:	Taylor & Francis
Publication date:	11/15/1997
Edition description:	New Edition
Pages:	550
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

PART 1: FROM FERMAT TO LEGENDRE, Chapter 1. The Founding Fathers, Chapter 2. Fermat, Chapter 3. Euler, Chapter 4. From Euler to Lagrange; The Theory of Continued Fractions, Chapter 5. Lagrange, Chapter 6. Legendre, PART 2: GAUSS AND THE DISQUISfilONES ARITHMETICAE, Chapter 7. Gauss, Chapter 8. Theory of Congruence, Chapter 9. Theory of Congruences, Chapter 10. Primitive Roots and Power Residues, Chapter 11. Congruences of the Second Degree, Chapter 12. Binary Quadratic Forms 1: Arithmetic Theory, Chapter 13. Binary Quadratic Forms 2: Geometric Theory, Chapter 14. Cyclotomy, PART 3: ALGEBRAIC NUMBER THEORY, Chapter 15. Algebraic Number Theory 1: The Gaussian Integers and Biquadratic Reciprocity 1. Gauss and Biquadratic Reciprocity, Chapter 16. Algebraic Number Theory 2: Algebraic Numbers and Quadratic Fields, Chapter 17. Algebraic Number Theory 3: Ideals in Quadratic Fields, PART 4: ARITHMETIC ON CURVES, Chapter 18. Arithmetic on Curves 1: Rational Points and Plane Algebraic Curves, Chapter 19. Arithmetic on Curves 2: Rational Points and Elliptic Curves, Chapter 20. Arithmetic on Curves 3: The Twentieth Century, PART 5: MISCELLANEOUS TOPICS, Chapter 21. Irrational and Transcendental Numbers, Diophantine Approximation, Chapter 22. Geometry of Numbers, Chapter 23. p-adic Numbers and Valuations, Bibliography, Index

What People are Saying About This

From the Publisher

"A superb combination historical narrative and introductory mathematic text." -Math Works, May 2003

Editorial Reviews

A superb combination historical narrative and introductory mathematic text.
— Math Works, May 2003

"A superb combination historical narrative and introductory mathematic text." -Math Works, May 2003

From the Publisher

In his preface the author relates how a longstanding fascination with the history of math led him to teach a course in number theory (which Gauss called the "Queen of Mathematics") from a historical perspective, and then to develop and expand his lecture notes for this book. He examines number theory as it developed from the 17th through the 19th centuries, leading readers<-->advanced undergraduates, graduate students, and mathematically educated lay readers<--> to an understanding of today's research problems on the basis of their historical evolution. Annotation c. by Book News, Inc., Portland, Or.

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