CS 680503 Computer Algebra I Syllabus
 Course Description
This course serves as an introduction to the foundations of symbolic
mathematical computation, drawing from both computer science and
mathematics. Topics to be covered typically include: the algebraic
definition of numerical, polynomial and rational function domains,
notation for computing time analysis, arithmetic with large integers,
rational numbers and multivariate polynomials, modular number
arithmetic, greatest common divisors of polynomials (rational function
simplification), computing with homomorphic images and the Chinese
Remainder Theorem, the modular GCD algorithm.
 Course Objective
To obtain an understanding of the design, implementation, and
analysis of computer algebra algorithms in general and algorithms
for computing with polynomials in particular.
The course will require several computational assignments utilizing
Maple, and several programming assignments using both Maple and C
or C++.
 Prerequisites
 Algorithms and Data Structures I (CS 557 or equivalent).
Also knowledge of linear algebra. Some knowledge of abstract
algebra would be helpful but is not necessary.

Instructor

Jeremy Johnson
Office: 271 Korman Center
phone: 8952893
email: jjohnson@mcs.drexel.edu
office hours: MW 13 and T 46, additional hours by appointment.

Meeting Time
 W 6:009:00 in Randell 329

Textbook

Keith Geddes, Stephen Czapor, and George Labahn
Algorithms for Computer Algebra.
Kluwer Academic Publishers, 1992.
Topics
 Algebra of polynomials, Rational functions, and power series.
 Data structures and algorithms for polynomial arithmetic.
 Homomorphisms, modular algorithms, interpolation and the
Chinese Remainder Theorem.
 Newton's iteration and Hensel lifting.
 Polynomial greatest common divisors.
 Polynomial factorization.
Grading
 Homework assignments (five) 50% (10% each)
 Programming project 50%
Created: 12/22/99 by jjohnson@mcs.drexel.edu