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Math 98T:
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General information:
The goal of this seminar will be to introduce students to the study of rational points on elliptic curves and to provide an introduction to the computational tools available to study them. An elliptic curve is an equation of the form y2 = x3 + Ax + B, with two whole numbers A and B. A rational point is simply a choice of two fractions for x and y which satisfy this equation. Modern number theory provides a number of answers to the obvious question, ``Why study elliptic curves?'' In addition to being important in numerous areas of mathematics, elliptic curves are finding applications all over the sciences, such as in cryptography and physics. In this seminar, we'll learn enough basic material about elliptic curves to be able to discuss some of these applications.
Schedule (Last updated 4/21/08)
Homework:
- Homework 1, due April 4, 2008
- Homework 2, due April 11, 2008
- Homework 3, due April 18, 2008
- Homework 3.5, due April 28, 2008: Turn in the first two pages of a draft of your paper.
- Homework 4, due May 2, 2008
- Homework 5, due May 9, 2008
- Homework 6, due May 16, 2008
Handouts:
- Syllabus
- Abstract algebra I
- Abstract algebra II (coming soon)
- Project ideas
Daily notes:
I'm going to post my notes here, as long as they seem useful.
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