The Queen of Mathematics: A Historically Motivated Guide to Number Theory (Hardback)

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.

Product Details

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 hisDisquisitiones 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

1. The Founding Fathers
2. Fermat
3. Euler
4. From Euler to Lagrange; The Theory of Continued Fractions
5. Lagrange
6. Legendre

PART 2: GAUSS AND THE DISQUISITIONES ARITHMETICAE

7. Gauss
8. Theory of Congruence 1
9. Theory of Congruence 2
10. Primitive Roots and Power Residues
11. Congruences of the Second Degree
12. Binary Quadratic Forms 1: Arithmetic Theory
13. Binary Quadratic Forms 2: Geometric Theory
14. Cyclotomy

PART 3: ALGEBRAIC NUMBER THEORY

15. Algebraic Number Theory 1: The Gaussian Integers and Biquadratic Reciprocity
16. Algebraic Number Theory 2: Algebraic Numbers and Quadratic Fields
17. Algebraic Number Theory 3: Ideals in Quadratic Fields

PART 4: ARITHMETIC ON CURVES

18. Arithmetic on Curves 1: Rational Points and Plane Algebraic Curves
19. Arithmetic on Curves 2: Rational Points and Elliptic Curves
20. Arithmetic on Curves 3: The Twentieth Century

PART 5: MISCELLANEOUS TOPICS

21. Irrational and Transcendental Numbers, Diophantine Approximations
22. Geometry of Numbers
23. p-adic Numbers and Valuations

The book concludes with Bibliography and Index.