MA 764 - Computer Algebra (Spring 2009)

Course by Uwe Nagel at the University of Kentucky.

Overview

Schedule

MWF, 9:00 - 9:50 am, CB 241

Material

Many problems in science and engineering lead to equations that have to be solved. Computer Algebra is the area of mathematics that develops tools for the exact solutions of equations (if this is possible at all). It is a very active area of research. This introduction to computer algebra will focus on important algorithms and their applications. Topics will include

Chinese remainder theorem and distributed data structures, interpolation, and modular algorithms

Fast Fourier transform and applications in image compression and for multiplication of (large) integers

LLL algorithm for finding short vectors in a lattice and factorization of polynomials

Gröbner bases and solving systems of polynomial equations in several variables

The course will explain the mathematics behind widely used algorithms (that have been implemented in computer algebra systems such as MAPLE and Macaulay 2).

CONTENTS:

Literature

J. von zur Gathen, J. Gerhard, Modern computer algebra, Cambridge University Press, 1999 or 2003.

D. Cox, J. Little, D. O'Shea: Ideals, varieties and algorithms, Springer, 1998.