Office Rm. Blocker 614A
E-mail: kuchment@math.tamu.edu, Home Page: http://www.math.tamu.edu/~kuchment
Section: 600
Time: MW 4:10 - 5:25 PM on ZOOM
Fourier series and Fourier Transform; discrete(fast) Fourier transform; discrete cosine transform; local cosine transform; Radon transform; filters; harmonic analysis on the sphere; radial, periodic, and spherical basis functions; compressed sensing . Prerequisites: MA 304, MA 308 or equivalent.
Harmonic analysis (also called Fourier analysis) is one of the major pillars of the whole mathematics and its applications in physics, engineering, and practically any other area. Thus, the word “applied” in the title neither adds, nor subtracts anything from the content. In the most general terms, the idea of harmonic analysis is:
if your problem has symmetries – use them! I will be happy to present it to you.
MATH 304 and MATH 308 or equivalent. It is highly recommended to overview some linear algebra before the class: Eigenvalues and eigenvectors, self-adjoit (Hermitian) operators, Unitary operators. A wonderful book by Gilbert Strang Linear algebra and applications is available electronically through libcat.tamu.edu.
Gerald Folland, Fourier Analysis and its Applications. Various editions are available from Wadsworth & Brooks/Cole and more recently from the AMS.
A very good by Brad Osgood Lectures on the Fourier transform and its applications is also available electronically through the libcat.
Besides these books, I will be distributing some extensive handouts, as well as references to some parts of books available electronically through the A&M library.
The rough plan of the class looks as follows:
Every week I will post on eCampus additional materials when needed, as well
as bi-weekly homework.
Take home Mid-Term and Final Exams will be given
I will set up a discussion board for the class, where you can exchange opinions, recommendations, questions, etc. (as long as this would not amount to cheating ). I will be monitoring the board and thus will be able to help when needed.
You will be able to communicate with me individually by e-mail, or through ZOOM (in the latter case please arrange the time by e-mail). Questions during the class will be also encouraged.
Dates | Topic | Reference | Work |
January 20 | Introduction | ||
January 25-27 | Linear algebra, symmetries, and harmonic analysis | A handout | HW 1 |
February 1 | shifts and rotations | handout | |
February 3 - 15 | Fourier series | Ch 2 | HW 2 |
Feb 17 - 22 | Discrete and finite Fourier transform | Sect. 7.6 | HW 3 |
February 24 - March 3 | Distributions | Ch 9 | |
March 8 - 22 | Fourier transform | Ch. 7 | Midterm exam. HW 4 |
March 24 - April 14 | Other transforms, miscellanea. | Section 7.6, Handouts | HW 5 |
April 19 - 26 | A glimpse at non-commutative harmonic analysis | Handouts | HW 6 |
May | Final Exam |
Attendance Policy: University rules related to excused and unexcused absences are located on-line at http://studentrules.tamu.edu/rule07.
Late Work Policy: No late work is accepted for unexcused absences per Section 7.4 of the University Student Rules Policy.
Make-up Policy: Students may be excused from turning in an assignment for the reasons stated in Section 7.1 (http://student-rules.tamu.edu/rule7.htm) or other reason deemed appropriate by the instructor. To be excused the student must notify the instructor in writing (acknowledged e-mail message is acceptable) prior to the date of absence if such notification is feasible. In cases where advance notification is not feasible (e.g. accident, or emergency) the student must provide notification by the end of the second working day after the absence. This notification should include an explanation of why notice could not be sent prior to the class. For approved excuses for missed assignments, an appropriate modified due date will be set by the instructor.
Absences related to Title IX of the Education Amendments of 1972 may necessitate a period of more than 30 days for make-up work, and the timeframe for make-up work should be agreed upon by the student and instructor” (Student Rule 7, Section 7.4.1).
“The instructor is under no obligation to provide an opportunity for the student to make up work missed because of an unexcused absence” (Student Rule 7, Section 7.4.2).
Students who request an excused absence are expected to uphold the Aggie Honor Code and Student Conduct Code. (See Student Rule 24.)
“Texas A&M University students are responsible for authenticating all work submitted to an instructor. If asked, students must be able to produce proof that the item submitted is indeed the work of that student. Students must keep appropriate records at all times. The inability to authenticate one’s work, should the instructor request it, may be sufficient grounds to initiate an academic misconduct case” (Section 20.1.2.3, Student Rule 20).
For
additional information please visit: http://aggiehonor.tamu.edu/.
> • The incident is reasonably believed to be discrimination or harassment.
• The incident is alleged to have been committed by or against a person who, at the time of the incident, was (1) a student enrolled at the University or (2) an employee of the University.
Mandatory Reporters must file a report regardless of how the information comes to their attention – including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Although Mandatory Reporters must file a report, in most instances, you will be able to control how the report is handled, including whether or not to pursue a formal investigation. The University’s goal is to make sure you are aware of the range of options available to you and to ensure access to the resources you need.
Students wishing to discuss concerns in a confidential setting are encouraged to make an appointment with Counseling and Psychological Services (CAPS).
Students can learn more about filing a report, accessing supportive resources, and navigating the
Title IX investigation and resolution process on the University’s Title IX web page.
Campus Safety Measures
To promote public safety and protect students, faculty, and staff during the coronavirus pandemic,
Texas A&M University has adopted policies and practices for the Fall 2020 academic term to limit
virus transmission. Students must observe the following practices while participating in
face-to-face courses and course-related activities (office hours, help sessions, transitioning to
and between classes, study spaces, academic services, etc.):
Personal Illness and Quarantine
Students required to quarantine must participate in courses and course-related activities remotely
and must not attend face-to-face course activities. Students should notify their instructors of the
quarantine requirement. Students under quarantine are expected to participate in courses and
complete graded work unless they have symptoms that are too severe to participate in course
activities.
Students experiencing personal injury or Illness that is too severe for the student to attend
class qualify for an excused absence (See Student Rule 7, Section 7.2.2.) To receive an excused
absence, students must comply with the documentation and notification guidelines outlined in
Student Rule 7. While Student Rule 7, Section 7.3.2.1, indicates a medical confirmation note from
the student's medical provider is preferred, for Fall 2020 only, students may use the Explanatory
Statement for Absence from Class form in lieu of a medical confirmation. Students must submit the
Explanatory Statement for Absence from Class within two business days after the last date of
absence.