Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MACM 401 D100

Introduction to Computer Algebra (3)

Class Number: 2786

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

  • Prerequisites:

    CMPT 307 or ((MATH 340 or MATH 342) and (CMPT 225 or MACM 204)).

Description

CALENDAR DESCRIPTION:

Data structures and algorithms for mathematical objects. Topics include long integer arithmetic, computing polynomial greatest common divisors, the fast Fourier transform, Hensel's lemma and p-adic methods, differentiation and simplification of formulae, and polynomial factorization. Students will use a computer algebra system such as Maple for calculations and programming. Quantitative.

COURSE DETAILS:

Course Description

The focus of the course is on the algebra of and computing with long integers, polynomials, rational functions, and the elementary functions. We will use Maple for calculations. 

The main topics covered will be:
  • Algorithms for long integer multiplication and GCD.
  • Non-unique factorization and unique factorization. 
  • Euclidean domains, the Euclidean algorithm and applications.
  • How do systems like Maple represent a formula on the computer?
  • Simplification and differentiation of a formula.
  • The Fast Fourier Transform and applications.
  • The Chinese remainder theorem and polynomial GCD computation.
  • The P-adic Newton iteration.
  • Probabilisitic algorithms for polynomial factorization over finite fields.
  • Hensel's lemma and polynomial factorization over the integers.
  • The Sylvester Resultant.
Maple: students will also learn to use Maple, how Maple represents formulae, and develop an in depth knowledge of what it can compute and how it works. Maple will be used for calculations and programming exercises.

Note: this is a cross-listed course with MATH 701/ MATH 801.

Grading

  • 5 Assignments 50%
  • Final Exam 50%

NOTES:

Note: all 3 courses (MATH 401, MATH 701, MATH 801) run Tuesday 2:30 - 4:20 plus Thursday 2:30 - 4:20 (lecture 2:30 - 3:20 plus tutorial 3:30 - 4:20).


THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

Course notes will be provided.

RECOMMENDED READING:

Algorithms for Computer Algebra, 1 / E
Author: KO Geddes, SR Czapor, G. Labahn
Publisher: Kluwer Academic, 1992

Students are not required to purchase this text. For those who wish to purchase a physical copy, the text is available on Amazon.
ISBN: 9781475783230

Modern Computer Algebra
Author: von zur Gathen, J & Gerhard, J.
As above, purchase of this text is not required.


ISBN: 9781107039032

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.

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.