Mathematical Software: Computer Algebra

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• The course is over.

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. Time permitting, we may consider advanced topics like Grobner bases and their applications, or an overview of the structural properties of finite fields covering some applications to cryptography or coding theory.
• 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 September 2001 (well 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. For the implementations in the assignments, C can also be used.
• Classes begin: Thursday, January 3, 2002.
  Classes end: Monday, April 1, 2002.
  Winter break: February 18-22, 2002.
• 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 7	Maple, addition and multiplication	10%
  2	February 7	March 11	Euclidean algorithm, EEA	15%
  3	March 7	March 28	Interpolation, Chinese remainder, fast algorithms	15%
  4	March 18	April 8	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 8, 2002.
• 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 2002 (html file)
• February 2002 (html file)
• March-April 2002 (html file)

Contact Information: