Fourier Analysis, MTH 496-001
| Instructor: | Mark Iwen |
| Time and Place: | Lectures are MWF 9:10 am -- 10:00 am, in Wells Hall A216 |
| E-mail: | markiwen@math.msu.edu |
| Office: | D220 WH |
| Office Hours: | Monday 10:00 am -- 11:00 am, Tuesday 10:30 am -- 11:30 am, and Wednesday 10:00 am -- 11:00 am |
We will discuss Discrete Fourier Transforms, the Fast Fourier Transform (FFT) algorithm, Fourier series, Orthogonal Functions, Inner Product Spaces, Convergence issues, The Fourier Transform, Distributions, and Time-Frequency Analysis.
Course website for MTH 496-001:
http://math.msu.edu/~markiwen/Teaching/MTH496/MTH496_S23.html
The course website is mandatory reading for the course. On it you will find the course schedule, the syllabus, and supplementary reading. Homework assignments will be posted on the schedule.
Textbook:
Fourier Analysis and Its Applications, by Gerald B. Folland.
International Thompson Publishing Company, 1992.
The majority of the course will be spent covering Chapters 2, 3, 7, and 9 of Folland's book.
Supplementary Texts:
We will also utilize material from Foundations of Time-Frequency Analysis by Karlheinz Gröchenig, as well as from other pdf sources provided by the instructor on D2L. It's not necessary to buy either of these books (though both are good).
D2L:
Additional reading materials are available on D2L (https://d2l.msu.edu). This website also contains your raw grades, and a lot of good information about potential student projects.
Homework:
Homework assignments will be given every other week and will constitute 40% of your final grade. The homework questions will be assigned on the web with their due dates. Posting of new assignments will be announced in class. You must submit your homework solutions during the class period on the due date unless prior permission has been granted to submit otherwise. Late homework assignments will never be graded. The lowest two homework scores will be dropped when computing your average homework grade. Homework solutions must be original copies in the student's own handwriting. No other submissions will be graded. Solutions must be clear and neatly written to receive credit. A subset of the homework problems will be graded on each assignment.
Midterm Exam:
There will be a midterm exam in class on March 3, 2023. It will constitute 20% of your final grade.
Final Exam:
There will be a final exam on Tuesday May 2, 2023 from 12:45 pm -- 2:45 pm in Wells Hall A216. It will constitute 40% of your final grade.
Project Option:
If a student wishes to skip the final exam, they may instead replace it with a project to be presented to the class during the last week of class. Such a final project will consist of two parts: (i) A 20 minute presentation to be delivered during the last week of class, and (ii) a written report summarizing in 7 to 10 pages your project research topic (due the last day of class). You should expect to spend a good deal of time researching the topic in the library, and looking at books and research articles. A rough draft of the paper should be turned in to me for comments about three weeks before the semester ends. Students are encouraged to work in groups of two or three. If your project involves writing any computer code, then this should also be turned in and will be graded as part of the project report. To pursue this option interested students must receive written authorization of their chosen project topic by the instructor before the end of March 17, 2023.
The project grade will graded based on the project report (60%), and the project presentation and slides/notes (40%). Copies of all presentation notes/slides must be submitted the day of the presentation. A hard copy of the project report is due at the beginning of the last class. Project reports should be written in LaTeX using this template. Project presentation slides should be done in either power point or LaTeX. If a chalk talk is done instead, then a neatly written copy of the notes should be turned in beforehand.
Grading:
Your final course percentage will be determined by averaging your homework, midterm exam, and final exam (or replacement project) percentages with the following weights: Homework (40%), Midterm Exam (20%), and the Final Exam (or replacement project) (40%). The result of this weighted average will then be rounded to the nearest integer.
Your final grade (e.g., 3.5, 4.0, etc.) will be assigned according to a class ranking. That is, the weighted averages calculated as above for all the students in the class will be rank ordered. Finally, threshold scores (e.g., a score above which a 4.0 is earned) will be determined, thereby establishing each student's final grade in the class. The threshold scores for each grade will never be higher than those indicated in following table.
| 90% -- 100% | A | 4.0 |
| 85% -- 89% | A-/B+ | 3.5 |
| 80% -- 84% | B | 3.0 |
| 75% -- 79% | B-/C+ | 2.5 |
| 70% -- 74% | C | 2.0 |
| 65% -- 69% | C-/D+ | 1.5 |
| 60% -- 64% | D | 1.0 |
| 0% -- 59% | F | 0.0 |
Incomplete grades will be given only in unusual cases of illness or other personal emergency, which causes the student to miss a significant amount of the course. This grade cannot be given for any other reason.
Academic Integrity:
You are encouraged to work with your peers on solving homework assignments. However, all submitted homework solutions must be written up individually in your own words. Submitting another student's written work as your own will be considered plagiarism.