Spring 2003
Freshman Seminar 21n:
Mathematical and Computational Aspects of Elliptic Curves

William Stein


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Lecture Notes / Handouts / Homework

An elliptic curve is a cubic curve of the form y2 = x3 + Ax + B with A and B whole numbers. The seminar will explore many incarnations of elliptic curves in number theory and computer science.

We will spend the first half of the semester building a solid foundation about the basics of elliptic curves. You will each read about elliptic curves, then give presentations to each other about what you read. I will not assume that you come into the seminar knowing any number theory at all.

Depending on your taste, and how far we get with the basics, we will examine some of the following topics:

Things To Read

  1. Silverman and Tate: Rational Points on Elliptic Curves [link to Amazon.com].
  2. Ribet and Hearst's excellent review of [Silverman-Tate]: PDF, dvi, Postscript
  3. Barry Mazur's article Number Theory as Gadfly: PDF.
  4. The book Elementary Number Theory and Elliptic Curves that I'm writing.
  5. Hellegouarch's book "Invitation to the Mathematics of FERMAT-WILES" (see this review).

Other Resources

  1. Andrew Wiles's proof of Fermat's Last Theorem: PDF (860kB pdf file instead of huge JSTOR scan, thanks to Derek Buchanan), TeX file
  2. Complete solution to Hilbert's 10 problem in 21 pages: PDF
  3. Stillwell's article The Evolution of Elliptic Curves: PDF
  4. Very dated list of elliptic curve resources

Some books you might want to look at

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