Elementary Applied Algebra

Class Info

Class Number: Math 431
Dates: Mar 02 2010 - Jun 05 2010
Room: NS 319
Meeting time:
Tuesday 10:30 - 12:00
Thursday 9:00 - 10:30

Text: Rational Points on Elliptic Curves, Joseph H. Silverman and John Tate, Springer Verlag 1992
Links
Homework
Material covered

Midterm Exam: April 20, 10:30 - 12:00, room NS 319

Answers for the midterm test

Final Exam: June 17, 9:00 - 11:00, room NS 319

Answers for the final exam

Syllabus

Week Chapters Topics
1 Introduction Introduction
2 1.1 Rational Points on Conics
3 1.2-3 Geometry of Cubic Curves, Weierstrass Normal Form
4 1.4 Explicit Formulas for the Group Law
5 2.1 Points of Order Two and Three
6 2.2 Real and Complex Points on Cubic Curves
7 2.3-4 Points of Finite Order have Integer Coordinates
8 Midterm Exam
9 2.5 The Nagell-Lutz Theorem
10 3.1-3 The Group of Rational Points, Height and Descent
11 3.4 A Useful Homomorphism
12 3.5,4.1 Mordell's Theorem, Rational Points over Finite Fields
13 4.2 A Theorem of Gauss (*)
14 4.4 Factorization Algorithm using Elliptic Curves
15 Final Exam
(*) A Theorem of Gauss will not be part of the Final Exam.

Grading

We will have a mid-term test in April, and a final exam in June.
The grades will be accorded the following weights.
Attendance 10%
Mid-term: 40%
Final: 50%

Homework

I will assign homework every Thursday for the material covered that week.
It will be due to hand in on the following Thursday .
Last modified: Sun Apr 04 14:54:32 KST 2010