2024 Fall Course Syllabus - Mathematics 9003.001

Course: Mathematics 9003.001.

Course Title: Modular Functions.

Credits: 3.

How this course will be taught: in person.

Time: TR 2:00--3:20.

Place: Wachman Hall 527.

Instructor: Jaclyn Lang.

Instructor Office: Wachman Hall 606.

Instructor Email: jaclyn.lang@temple.edu

Instructor Phone: Use email.

Office Hours: T 3:30-5pm, R 9:30-11am.

Prerequisites: MATH 8012 or permission of instructor.

Course Materials: A First Course in Modular Forms, by Fred Diamond and Jerry Shurman.

Course Goals: The goal of this course is for students to engage with modular forms in a way that is relevant to their mathematical interests. The lectures will provide the essential background about these objects and the project will be an opportunity for students to see how modular forms relate to a topic that is of interest to them.

Topics Covered: We aim to cover the basic theory of modular forms including Eisenstein series, modular curves, dimension formulae, and Hecke operators. Time permitting, the last few weeks will be devoted to sketching the construction of the Galois representation associated to a Hecke eigenform of weight 2. This will allow us to state (but not prove) Wiles' theorem that implies Fermat's Last Theorem.

Course Grading: Project (including planning activities, write up, and presentation): 80%; Weekly problem: 20%.

Exam Dates: no exams; student presentation dates/times TBD.

Attendance Policy: Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, they are expected to contact the instructor before class.

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.

Homework: You should turn in one "problem" every week of the class; it is due under my office door by 5pm Friday every week. (13 weeks total; last one due right before Thanksgiving break.) You get to choose which problem. (Hint: pick ones related to your project topic!) If this feels overwhelming, come talk to me and I can help. The problems can be from Diamond and Shurman, another textbook, or from the lectures. They can even be filling in details from the lectures that you did not follow in real time or that were only sketched. These will be graded for completion and effort, not for mathematical correctness.

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
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.