{"id":3014,"date":"2021-12-31T19:59:53","date_gmt":"2022-01-01T00:59:53","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/fgarvan\/?page_id=3014"},"modified":"2026-03-19T08:11:12","modified_gmt":"2026-03-19T12:11:12","slug":"mat-6932-seminar-in-number-theory-spring-2022","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/fgarvan\/mat-6932-seminar-in-number-theory-spring-2022\/","title":{"rendered":"MAT 6932 SEMINAR IN NUMBER THEORY SPRING 2022"},"content":{"rendered":"\r\n
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MAT 6932 SEMINAR IN NUMBER THEORY SPRING 2022<\/h1>\n\n\n\n

This syllabus is subject to change. Last change was made 9:43pm, December 31, 2021.<\/span>
\nCourse:<\/strong> MAT 6932 (Seminar in Number Theory) (3 credits)<\/p>\n\n\n\n\n\n

Topic:<\/strong> Modular Forms and Mock-Theta Functions<\/p>\n\n\n\n\n\n

Lecturer:<\/strong> Dr. F. Garvan (Office: LIT 498; Email: fgarvan@ufl.edu;
\nPhone: 294-4305)<\/p>\n\n\n\n\n\n

Section:<\/strong> 1014 (Spring 2022)<\/p>\n\n\n\n\n\n

Location:<\/strong> BLDG 105<\/a> Room 234<\/p>\n\n\n\n\n\n

Time:<\/strong> MWF 6 (12:50 – 1:40pm)<\/p>\n\n\n\n\n\n

Office Hours:<\/strong> TBA or by appointment.<\/p>\n\n\n\n\n\n

Prerequisites:<\/strong>
\nA basic knowledge of analysis and complex function theory.<\/p>\n\n\n\n\n\n

Outline:<\/strong>
\nRamanujan introduced mock theta functions in his last to Hardy in 1920. We follow the development of Ramanujan’s mock theta functions up until the present time. Along the way we cover some theory of basic hypergeometric functions and classical modular forms. In 1987 Freeman Dyson issued the challenge of developing the group theoretic structure of mock theta functions analogous to the theory of classical modular forms. The first major advance
\nwas in 2003 when Sander Zwegers showed how Ramanujan’s mock-theta functions fit into the theory of real analytic modular forms. We will study how modern mathematics has taken up Dyson’s challenge and cover any needed background material.<\/p>\n\n\n\n\n\n

Text<\/strong>:
\nThere is no required text. Links to online reading will be given.<\/p>\n\n\n\n\n\n

Grading:<\/strong>
\nGrades will be based on either some homework or a class presentation.<\/p>\n\n\n\n\n\n

Homework Assignments:<\/strong>
\nHomework assignments will be assigned regularly and graded.<\/p>\n\n\n\n

Additional Information: <\/strong><\/p>\n\n\n\n\n\n

Grades. <\/i><\/p>\n\n\n\n

Grading will be in accord with the UF policy stated at<\/dl>\n\n\n\n

https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/grades.aspx<\/a><\/p>\n\n\n\n

. Also see<\/dl>\n\n\n\n

the current UF policy on assigning grade points. <\/a> Academic Honesty. <\/i><\/p>\n\n\n\n

The course will be conducted in accordance with the University honor code and academic honesty policy<\/dl>\n\n\n\n

UF students are bound by The Honor Code Pledge which states, \u201cWe, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code.\u201d On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: \u201cOn my honor, I have neither given nor received unauthorized aid in doing this assignment.\u201d<\/strong> The Honor Code <\/strong><\/a> specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have questions or concerns please consult with the instructor.<\/i> Accommodation for students with disabilities. <\/i><\/p>\n\n\n\n

Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565,<\/dl>\n\n\n\n

https:\/\/disability.ufl.edu\/<\/a><\/p>\n\n\n\n

) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.<\/dl>\n\n\n\n

Online Evaluations. <\/i><\/p>\n\n\n\n

\u201cStudents are expected to provide feedback on the quality of instruction in this course by completing online evaluations at<\/dl>\n\n\n\n

https:\/\/evaluations.ufl.edu<\/a><\/p>\n\n\n\n

. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https:\/\/evaluations.ufl.edu\/results\/.\u201d<\/dl>\n\n\n\n

Additional Information- Health and Wellness: <\/strong><\/p>\n\n\n\n