CMSC 456/656
Symbolic & Algebraic Processing

Fall Semester 1999

Course Description

The primary thrust of CMSC456/656 is algebraic algorithms. Maple (which is secondary) will be used as a means of gaining a better understanding of these algorithms through hands-on experience.

We begin by studying and applying such algebraic constructs as groups, rings, fields, ideals, quotient rings, etc., with an emphasis on algebraic algorithms. Next we move on to study Groebner bases, elimination theory, polynomial & rational functions on a variety. We then study the application of symbolic & algebraic processing to robotics & automatic geometric theorem proving. Various projects in Maple will be given to illustrate these concepts.

This is not a programming language course. It is a course in which the high level programming language Maple is used as a vehicle to learn algebraic algorithms. However, the course will begin with some prelimary lectures and lab sessions devoted to learning Maple. There will also be lab sessions to help with the various Maple projects.

The course grade will be computed as follows:

25% Exam I
25% Exam II
25% Homework & Projects
25% Final Exam

Prerequisites:

CMSC 203 Discrete Math (or equivalent)
CMSC 221 Linear Algebra (or equivalent)
A reasonable amount of mathematical & algorithmic maturity

Course texts:

The text for symbolic computation is:
Cox, David, John Little, and Donal O'Shea, "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra," Springer- Verlag (1992).

The text for Maple is:
Heck, Andre, "Introduction to Maple," Springer (1996) (Second Edition)

Last Modified: August 16, 1999