The Queen of mathematics

A historically motivated guide to number theory

Jay R. Goldman

550 pages, parution le 21/07/2003

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Résumé

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 approximation. With its historical framework and narrative style, Goldman's book makes both a lovely resource for mathematicians and an introductory text for students and teachers.

From Fermat to Legendre
- The founding fathers
- Fermat
- Euler
- From Euler to Lagrange; The theory of continued fractions
- Lagrange
- Legendre

Gauss and the 'disquisitions arithmeticae'
- Gauss
- Theory of congruence 1
- Theory of congruences 2
- Primitive roots and power residues
- Congruences of the second degree
- Binary quadratic forms 1 : Arithmetic theory
- Binary quadratic forms 2 : Geometric theory
- Cyclotomy

Algebraic number theory
- Algebraic number theory 1 : The Gaussian integers and biquadratic reciprocity
- Algebraic number theory 2 : Algebraic number and quadratic fields
- Algebraic number theory 3 : Ideals in quadratic fields

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

Miscellaneous topics
- Irrational and transcendental numbers, diophantine approximation
- Geometry of numbers
- p-adic numbers and valuations

Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	AK Peters
Auteur(s)	Jay R. Goldman
Parution	21/07/2003
Nb. de pages	550
Format	15,5 x 23,5
Couverture	Relié
Poids	840g
Intérieur	Noir et Blanc
EAN13	9781568810065
ISBN13	978-1-56881-006-5