This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell’s theorem and explains the conjecture of Birch and Swinnerton-Dyer.
Elliptic Curves 2nd Edition Free Download
June 12, 2022
You may also like
ALGEBRA MATHEMATICS
Algebra 3 Homological Algebra and Its Applications by Ramji Lal PDF
April 11, 2024
This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived...
ALGEBRA MATHEMATICS
Algebra for College Students 5th Edition by Margaret L. Lial PDF
February 3, 2024
Algebra for College Students is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying...
ALGEBRA MATHEMATICS
Integral Points on Algebraic Varieties An Introduction to Diophantine Geometry by Pietro Corvaja PDF
October 18, 2023
This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on...
Recent Posts
- Algebra 3 Homological Algebra and Its Applications by Ramji Lal PDF
- Heat Transfer Physics 2nd Edition By Massoud Kaviany PDF
- Lavin’s Radiography for Veterinary Technicians, 6th Edition by Marg Brown PDF
- Principles of Physics, 10th Edition by David Halliday PDF
- The Dog Behavior Problem Solver by Teoti Anderson PDF
Add Comment