Simon Fraser University
Engaging the World

Course Outlines

Summer 2024 - MATH 719 G100

Linear Analysis (3)

Class Number: 2643

Delivery Method: In Person

Overview

  • Course Times + Location:

    May 6 – Aug 2, 2024: Mon, 12:30–2:20 p.m.
    Burnaby

    May 6 – Aug 2, 2024: Wed, 1:30–2:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Convergence in Euclidean spaces, Fourier series and their convergence, Legendre polynomials, Hermite and Laguerre polynomials. 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:

Topics: Fourier series, discrete Fourier and Haar analysis, the Fourier transform, wavelet transforms.
 
The text is Harmonic Analysis: From Fourier to Wavelets, by Pereyra and Ward (ISBN: 978-0821875667). It is required for the course, but an electronic copy is perfectly adequate. Electronic copies may be purchased directly from the publisher. We will be covering Chapters 1, 3-6, 9, 10 of the text.

Homework: There will be a total of 6 proper homework assignments, one due every two weeks.

Projects: Students taking Math 419 will complete a term project in groups of two or three. Students taking Math 719 will complete a term project on their own. Term project will consist of a written report between 10 and 20 pages, including figures and bibliography. Earlier in the term students will submit a rough draft, and have an opportunity to respond to feedback I give on it in their final draft.

You are encouraged to discuss the homework assignments with other students in the class. However, what you hand in must be your own work. That means that you should write up your solutions on your own. Copying another student's assignment is plagiarism. Furthermore, if you use any written or web resources other than textbook in solving the questions, the source must be acknowledged in your assignment.

MATH 719 is cross-listed with MATH 419. Students enrolled in the graduate section (MATH 719) will be assigned additional homework questions, different exam questions, and will be required to submit a more extensive project.

COURSE-LEVEL EDUCATIONAL GOALS:

Students who succeed in this class will:

  • Understand the basic objectives and methods of Harmonic analysis
  • Be familiar with discrete and continuous Fourier analysis in one dimension
  • Be familiar with the main ideas of Wavelet theory

Grading

  • Homework Assignments 30%
  • Term Project 30%
  • Final Exam 40%

Materials

REQUIRED READING:

Harmonic Analysis: From Fourier to Wavelets, by Pereyra and Ward.
ISBN: 978-0821875667

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