Simon Fraser University
Engaging the World

Course Outlines

Spring 2021 - MATH 801 G100

Computer Algebra (4)

Class Number: 3910

Delivery Method: Remote

Overview

  • Course Times + Location:

    Jan 11 – Apr 16, 2021: Tue, 2:30–4:20 p.m.
    Burnaby

    Jan 11 – Apr 16, 2021: Thu, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 23, 2021
    Fri, 9:00–9:00 a.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Computing with long integers, polynomials, and mathematical formulae. Topics include computing polynomial greatest common divisors, the Fast Fourier Transform, Hensel's Lemma and p-adic methods, differentiation and simplification of formulae, polynomial factorization. Integration of rational functions and elementary functions, Liouville's principle, the Risch algorithm. Students will use a computer algebra system such as Maple for calculations and programming. Students who have credit for either MACM 401 or MATH 701 may not take this course for further credit.

COURSE DETAILS:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable

Course Description


The course is about computing with mathematical objects symbolically. This includes numbers,polynomials like x3y - 3xy2 + 3x2y - 1 and the elementary functions. We will answer the following questions:

Students will learn how to use Maple as an algebraic calculator for calculating sums, integrals, and solving systems of polynomial equations, differential equations and recurrences. Students will also use Maple as a programming language for implementing algebraic algorithms, and develop and understanding of how Maple works. Students should be comfortable with writing simple programs. No prior knowledge of Maple is assumed.

The main topics covered will be:

  • Karatsuba's integer multiplication algorithm and Stein's binary GCD algorithm.
  • Arithmetic and data structures for multivariate polynomials.
  • The Chinese Remainder Theorem and polynomial GCD computation.
  • The Fast Fourier Transform and fast integer and polynomial multiplication.
  • Factoring polynomials over finite fields using a probabilistic algorithm.
  • Hensel's Lemma and factoring polynomials with integer coeffcients.
  • Symbolic differentiation and integration.
  • Polynomial resultants and rational function integration.
  • The Risch decision procedure for elementary function integration.

COURSE DELIVERY

  •  Lecture: synchronous- lectures will be held at fixed times, on-line
  •  Final exam: synchronous; date: TBA

Note: this is a cross-listed course with MATH 701/ MACM 401

Grading

  • 6 Assignments 50%
  • Course Project 15%
  • Final Exam (24 hour take home) 35%

NOTES:

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.

REQUIREMENTS:

  • Access to strong and reliable internet.
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)

Materials

REQUIRED READING:

Algorithms for Computer Algebra, 1 / E
Author: KO Geddes, SR Czapor, G. Labahn
Publisher: Kluwer Academic, 1992
ISBN: 9781475783230

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 web site 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

TEACHING AT SFU IN SPRING 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).