Simon Fraser University
Engaging the World

Course Outlines

Summer 2025 - MATH 819 G100

Algebra: Selected Topics (4)

Computer Algebra

Class Number: 4958

Delivery Method: In Person

Overview

  • Course Times + Location:

    Location: TBA

Description

COURSE-LEVEL EDUCATIONAL GOALS:

This is a second course in Computer Algebra designed to prepare students to undertake research in Computer Algebra. This includes learning more tools and doing a research project. Prerequisite includes MACM 401 or MATH 801 or permission of the instructor. Programming in Maple is required.

Topics

  1. Algorithms for Linear Algebra
  2. The Fast Fourier Transform (FFT) and Applications
  3. Computing with Multivariate Polynomials
  4. Groebner Bases and Applications
  5. Sparse Multivariate Polynomial Interpolation
  6. Computing with Algebraic Numbers
  7. Miscellaneous topics
  8. Multivariate Hensel lifting
  9. Automatic Differentiation

Grading

  • Assignments (six assignments, 10% each) 60%
  • Course Project (presentation as a written report + Maple code) 40%

NOTES:

For the Course Project students may choose a research problem from a list of pre-selected topics provided by the instructor. The project will involve reading a paper from the literature, implementing  one or more algorithms in Maple, studying the mathematical basis for the algorithm(s), comparing the algorithms theoretically and experimentally and presenting their work as a written report in LaTeX.

Materials

RECOMMENDED READING:

  • Modern Computer Algebra by von zur Gathen and Gerhard.
  • Ideals, Varieties and Algorithms by Cox, Little and O'Shea.
  • Algorithms for Computer Algebra by Geddes, Czapor and Labahn.
  • Various research papers.

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.