Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - CMPT 981 G200

Special Topics in Theoretical Computing Science (3)

Computer Algebra

Class Number: 7269

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Tue, 3:30–5:20 p.m.
    Burnaby

    Jan 6 – Apr 9, 2025: Thu, 3:30–4:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 23, 2025
    Wed, 9:00–9:00 a.m.
    Burnaby

Description

COURSE DETAILS:

Special Topics in Theoretical Computing Science : Symbolic Computation 
Note: The course will be given simultaneously with MATH 801 Computer Algebra

The course is about computing with mathematical objects symbolically.
This includes numbers, polynomials like f = x^3 y - 3 x y^2 + 1
and the elementary functions sqrt(x), ln(x), and exp(x).
We will answer the following questions:

 

1: How do we represent polynomials and formulas on a computer?
2: How fast can we multiply integers and polynomials?
3: Can we factor polynomials in polynomial time?
4: Does an algorithm exist for computing an indefinite integral?
5: What does it mean to simplify an algebraic expression?

Algorithms include probabilistic algorithms, modular algorithms,
and application of the Fast Fourier transform.  Maple will be
used as a programming language for implementing algorithms.
No prior knowledge of Maple is assumed. I will teach you Maple.

Topics covered include
- Integer arithmetic: Karatsuba's algorithm, Stein's binary GCD algorithm.
- Arithmetic and data structures for multivariate polynomials
- Data structures for and simplification of general formulas
- The Chinese Remainder Theorem: polynomial GCD computation
- The Fast Fourier Transform and fast and polynomial multiplication.
- Probabilistic Algorithms: factoring polynomials over finite fields.
- Hensel's Lemma and factoring polynomials with integer coefficients.
- Symbolic differentiation and integration.
- Polynomial resultants and rational function integration.
- The Risch decision procedure for elementary function integration.



 

 

Grading

NOTES:

Grading Assessment: 

6 Assignments 50%
Course mini project 10%
24 hour take home final 40%

Materials

MATERIALS + SUPPLIES:

Algorithms for Computer Algebra by Geddes, Czapor, and Labahn ISBN 978-0792392590

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.