University of Toronto Spring 1997
CSC478S/2412S: Computer Algebra
Assignment dates updated February 5, 1997 Instructor: Daniel Panario, daniel@cdf (preferable), daniel@cs
Office hours: T 10-11 in SF 2304A, or by appointment.
Lectures: TR 2 in MP 118, and F 2 in LM 157.
Tutor: David Neto, at478net@cdf
Text: K. O. Geddes, S. R. Czapor and G. Labahn, ALGORITHMS FOR COMPUTER ALGEBRA, Kluwer, 1992.
Language: MAPLE, a system for symbolic mathematical computation. Optional for project: C++.
Prerequisities: mathematical maturity is recommended. Although not required, at least one undergraduate abstract algebra course may be useful. Undergraduate courses in discrete mathematics and in data structures could be helpful.
Work Handout Due Value date date A1 Jan 14 Jan 28 5 % A2 Jan 28 Feb 14 15 % A3 Feb 14 Mar 7 15 % A4 Mar 7 Mar 28 15 % A5 Mar 21 Apr 11 15 % Proj Feb 11 Apr 11 35 % ----- 100 %
Plagiarism: assignments and project have to be your own work. Plagiarism is a serious academic offense.
Course goals: This course is an introduction to basic algebraic algorithms that are useful for computer algebra systems. More specifically, operations like multiplication, division, greatest common divisors and factorization are studied over several domains including the ring of integers, finite fields, polynomial rings, and quotient rings. The basic tools considered include modular arithmetic, discrete Fourier transform, Chinese remainder theorem, Newton iteration, and Hensel techniques. Grobner bases and their applications are taken into account. An overview of the structural properties of finite fields covering some applications in detail is considered.
Course outline (some of these topics will be covered):
Feb 17-21 reading week (no classes)
Mar 7 last day to drop without penalty
Mar 28 Good Friday (University closed)
Apr 11 last lecture