The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" stresses this interplay as it develops the basic theory, thereby providing an opportunity for advance undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make "Rational Points on Elliptic Curves" an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.

Autorentext

Dr. Jeffrey Hoffstein has been a professor at Brown University since 1989 and has been a visiting professor and tenured professor at several other universities since 1978. His research areas are number theory, automorphic forms and cryptography. He has authored more than 50 publications. Dr. Jill Pipher has been a professor at Brown University since 1989. She has been an invited lecturer and has received numerous awards and honors. Her research areas are harmonic analysis, elliptic PDE, and cryptography. She has authored over 40 publications. Dr. Joseph Silverman has been a professor at Brown University since 1988. He served as the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards and is a frequently invited lecturer. His research areas are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has authored more than 130 publications and has had more than 20 doctoral students.

Inhalt
I Geometry and Arithmetic.- II Points of Finite Order.- III The Group of Rational Points.- IV Cubic Curves over Finite Fields.- V Integer Points on Cubic Curves.- VI Complex Multiplication.- Appendix A Projective Geometry.- 1. Homogeneous Coordinates and the Projective Plane.- 2. Curves in the Projective Plane.- 3. Intersections of Projective Curves.- 4. Intersection Multiplicities and a Proof of Bezout's Theorem.- Exercises.- List of Notation.