Introduction to Computational Number Theory and Algebra

G22.3033-012 Fall 2003

Instructor: Victor Shoup

Lectures: Tuesdays and Thursdays, 1:15-2:45pm, room 513 WWH

Text: A Computational Introduction to Number Theory and Algebra, by the instructor. Available on line. Printed versions are available for purchase at Unique Copy, at 252 Greene Street.

Grading: There will be a few problem sets.

Course description:

We shall study algorithms for computing with integers, polynomials, and other algebraic objects. These algorithms play an essential role in the technologies underlying modern systems for storing and transmitting data, especially in the areas of error correcting codes and cryptography, and we shall study some of these applications as well.

As for mathematical prerequisites, the lectures should be easily accessible to students who have had undergraduate courses in abstract algebra, linear algebra, and probability theory; however, the textbook for the course develops all of the necessary mathematics from scratch, and so students with some gaps in their mathematical background can fill any such gaps by reading the textbook.

As for computer science prerequisites, all that is assumed is a basic understanding of programming, as well as some experience in algorithm analysis, roughly at the level of an undergraduate course on algorithms and data structures.

Course Outline (tentative)