This space will be used for announcements. Check it regularly.
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 and polynomial rings.
The basic tools considered include modular arithmetic,
discrete Fourier transform, Chinese remainder theorem
and Newton iteration. Time permitting, we may consider
advanced topics like Grobner bases and their applications,
or symbolic integration and summation.
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 and algorithms could be helpful.
Tentative lecture schedule
(html file) as of December 2008 (before classes start).
The actual material covered in each lecture is below.
Textbook:
Modern Computer Algebra by Joachim von zur Gathen
and Jurgen Gerhard, 2nd edition, Cambridge University Press, 2003.
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. Other languages could be used but
this have to be arranged with the professor.
Classes begin: Monday, January 5, 2009. Classes end: Wednesday, April 1, 2009. Winter break: February 16-20, 2009.
Term mark:
There will be two assignments and a midterm test for a total of 50%
of the mark. The tentative schedule of assignments is below.
Assignment
Hand-out Date
Due Date
Contents
Worth
1
February 2
February 23
Multiplication, gcd, EEA
15%
2
March 2
March 23
Interpolation, Chinese remainder,
fast algorithms, DFT
15%
Evaluation:
In addition to the two assignments there is a midterm test on
Wednesday February 25, 2009 worth 20% of the final mark.
Term mark is 50% and final examination is 50%.
Withdrawal:
The last day for withdrawal from the course without academic
penalties is March 6, 2009.
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.