Mathematical Software: Computer Algebra

Current announcements

This space will be used for announcements. Check it regularly.

• The course is over. The final marks are now posted outside of my door's office in HP4372.

General Information

• 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 could be taken into account. An overview of the structural properties of finite fields covering some applications to cryptography or coding theory may be considered.
• 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.
• Tentative lecture schedule (html file) as of December 2000 (before classes start).
  The actual material covered in each lecture is below.
• Textbook: Modern Computer Algebra by Joachim von zur Gathen and Jurgen Gerhard, Cambridge University Press, 1999.
• Language: Maple, a system for symbolic mathematical computation. Here is a list of Maple manuals and books that present mathematical material with the help of Maple.
• Classes begin: Wednesday, January 3, 2001.
  Classes end: Tuesday, April 3, 2001.
  Winter break: February 19-23, 2001.
• Term mark:
  There will be four assignments for a total of 50% of the mark. The tentative schedule of assignments is below.

  Assignment	Hand-out Date	Due Date	Contents	Worth
  1	January 17	February 5	Maple, addition and multiplication	10%
  2	February 5	March 5	Euclidean algorithm, EEA	15%
  3	March 5	March 26	Interpolation, Chinese remainder, fast algorithms	15%
  4	March 15	April 2	DFT, Newton's iteration, factoring polynomials	10%

• Evaluation:
  Term mark is 50% and final examination is 50%.
• Withdrawal: The last day for withdrawal from the course is March 9, 2001.
• Students with Disabilities: Students with Disabilities who require academic accommodations please feel free to see me, and contact the Paul Menton Centre to complete the required forms.
• Some files may be in postcript format. If you don't have a software to view postscript files, you may download a ghostview software.

Lectures per month

• January 2001 (html file)
• February 2001 (html file)
• March-April 2001 (html file)

Assignments (postcript form)

• Assignment 1;
• Assignment 2;
• Assignment 3;
• Assignment 4

Contact Information: