2024 Fall Course Syllabus - Mathematics 9041.001

Course: Mathematics 9041.001.

Course Title: Functional Analysis.

Credits: 3.

How this course will be taught: In person.

Time: TR 11:00am-12:20pm.

Place: Wachman 527.

Instructor: Mihaela Ignatova.

Instructor Office: Wachman 532.

Instructor Email: ignatova@temple.edu

Instructor Phone: Please contact me by email.

Course Web Page: This is a registered Canvas course, all additional materials, announcements, and grades will be posted there

Office Hours: TR 12:30pm-2pm.

Prerequisites: Graduate real analysis at the level of the books by Wheeden and Zygmund, Stein and Shakarchi, Folland, or Royden.

Course Materials: Haim Brezis, "Functional Analysis, Sobolev spaces and partial differential equations", Springer, 2010, ISBN: 978-0-387-70913-0. Additional materials will be posted on the Canvas course page.

Course Goals: To study fundamental topics of functional analysis with multiple applications in theoretical and applied mathematics areas such as harmonic analysis, PDEs, probability, optimization, economics, physics, etc.

Topics Covered: The Hahn-Banach theorem and applications; The uniform boundedness principle, the closed graph, and open mapping theorems; Unbounded linear operators basics; Weak topologies, duality; Compact operators and spectral decomposition.

Course Grading: It will be based on regular homework.

Exam Dates: TBA.

Attendance Policy: Attendance to the lectures is recommended.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

AI Policy: The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
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