# Spring 2021 - MATH 701 G100

## Overview

• #### Course Times + Location:

Tu 2:30 PM – 4:20 PM
REMOTE LEARNING, Burnaby

Th 2:30 PM – 3:20 PM
REMOTE LEARNING, Burnaby

• #### Exam Times + Location:

Apr 23, 2021
9:00 AM – 9:00 AM
TAKE HOME-EXAM, Burnaby

## Description

#### CALENDAR DESCRIPTION:

Data structures and algorithms for mathematical objects, including long integers, polynomials, and general 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, and polynomial factorization. Students will use a computer algebra system such as Maple for calculations and programming. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

#### 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 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.
• Probabilisitic algorithms for polynomial factorization over finite fields.
• Hensel's lemma and polynomial factorization over the integers.
• Resultants and rational function integration methods.
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.

#### COURSE DELIVERY

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

Note: this is a cross-listed course with MACM 401/ MATH 801

• 5 Assignments (10% each) 50%
• Final Exam (24 hour take-home) 50%

#### 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:

• Ability to scan documents (phone app acceptable)

## Materials

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

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.