Description
Book SynopsisI 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.
Trade ReviewFrom the reviews:
"The authors' goal has been to write a textbook in a technically difficult field which is accessible to the average undergraduate mathematics major, and it seems that they have succeeded admirably..."--MATHEMATICAL REVIEWS
"This is a very leisurely introduction to the theory of elliptic curves, concentrating on an algebraic and number-theoretic viewpoint. It is pitched at an undergraduate level and simplifies the work by proving the main theorems with additional hypotheses or by only proving special cases. … The examples really pull together the material and make it clear. … a great book for a first introduction to the subject of elliptic curves. … very clearly written and you will understand a lot when you are done." (Allen Stenger, The Mathematical Association of America, August, 2008)
Table of ContentsI 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.
