# Spring 2023 - MATH 801 G100

## Overview

• #### Course Times + Location:

Tu 2:30 PM – 4:20 PM
AQ 5037, Burnaby

Th 2:30 PM – 3:20 PM
AQ 5037, Burnaby

• #### Exam Times + Location:

Apr 21, 2023
9:00 AM – 9:00 AM
TAKE HOME-EXAM, Burnaby

• #### Instructor:

Michael Monagan
mmonagan@sfu.ca
1 778 782-4279

## 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 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.

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

• 6 Assignments 50%
• Course Project 10%
• Final Exam 40%

#### NOTES:

Note: all 3 courses (MACM 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

Course notes will be provided.

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

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

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.