Hardcover ISBN:  9780821805879 
Product Code:  MMONO/170 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Electronic ISBN:  9781470445850 
Product Code:  MMONO/170.E 
List Price:  $103.00 
MAA Member Price:  $92.70 
AMS Member Price:  $82.40 

Book DetailsTranslations of Mathematical MonographsVolume: 170; 1997; 185 ppMSC: Primary 11; 14; 33;
This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is selfcontained and assumes as prerequisites only the standard oneyear courses of algebra and analysis.
ReadershipUndergraduate students, graduate students, research mathematicians and physicists interested in elliptic functions.

Table of Contents

Chapters

Geometry of cubic curves

Elliptic functions

Arcs of curves and elliptic integrals

Abel’s theorem on division of lemniscate

Arithmetic of cubic curves

Algebraic equations

Theta functions and solutions of quintic equations


Additional Material

Reviews

A wonderful choice of topics, delivered in a concrete and lively style … provide a lively introduction to many classical topics that lie at the foundations of contemporary algebra, number theory and algebraic geometry.
Mathematical Reviews 
The strong point of [this] book is the intertwining of complex analysis with algebraic geometry. The book is in fact an elementary introduction to the arithmetic of elliptic curves as well as a treatment of the theory of elliptic functions. the ideal book for a reading course!
Mathematische Semesterberichte 
Provides a great panoramic view for the beginner in the field. The style of writing is very cultured, with a sympathetic understanding and respect of the pioneering work of the old masters, and with a delightful sense of aesthetics and beauty. This book really breathes the charm and the fine art of the mathematics of Abel's era, and it is mainly this particular feature that makes the book under review fairly unique and highly valuable. Experts and teachers can benefit from the reading of this text likewise.
Zentralblatt MATH


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This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is selfcontained and assumes as prerequisites only the standard oneyear courses of algebra and analysis.
Undergraduate students, graduate students, research mathematicians and physicists interested in elliptic functions.

Chapters

Geometry of cubic curves

Elliptic functions

Arcs of curves and elliptic integrals

Abel’s theorem on division of lemniscate

Arithmetic of cubic curves

Algebraic equations

Theta functions and solutions of quintic equations

A wonderful choice of topics, delivered in a concrete and lively style … provide a lively introduction to many classical topics that lie at the foundations of contemporary algebra, number theory and algebraic geometry.
Mathematical Reviews 
The strong point of [this] book is the intertwining of complex analysis with algebraic geometry. The book is in fact an elementary introduction to the arithmetic of elliptic curves as well as a treatment of the theory of elliptic functions. the ideal book for a reading course!
Mathematische Semesterberichte 
Provides a great panoramic view for the beginner in the field. The style of writing is very cultured, with a sympathetic understanding and respect of the pioneering work of the old masters, and with a delightful sense of aesthetics and beauty. This book really breathes the charm and the fine art of the mathematics of Abel's era, and it is mainly this particular feature that makes the book under review fairly unique and highly valuable. Experts and teachers can benefit from the reading of this text likewise.
Zentralblatt MATH