MAS 7216

Analytic Number Theory - II - MWF 8th period (3:00-3:50pm)
Section 8877 - LIT 219
SPRING 2010

INSTRUCTOR:

    Krishnaswami Alladi
    306 Little Hall
    392-0281 extn 227
    email: alladik@ufl.edu

HOME-PAGE FOR THIS COURSE:

http://www.math.ufl.edu/~alladik/gradnumthy/spring2010/index.html

OFFICE HOURS:

W - F 9th period (4:00 - 5:00 pm) in LIT 306 and by appointment.

PREREQUISITES:

Undergraduate course in number theory and a course in complex variable theory. MAS 7215 is NOT a prerequisite for this course.

COURSE DESCRIPTION:

This course will be an introduction to the theory of partitions and q-series. Starting with the foundational results of Euler and Sylvester, we will discuss several spectacular results of the Indian genius Srinivasa Ramanujan whose magic touch provided a glorious transformation of the subject. We will discuss the theory of Rogers-Ramanujan type identities including generalizations due to Andrews, Ramanujan's congruences for the partition function, and the celebrated Hardy-Ramanujan asymptotic formula for partitions. In addition, the role of the q-binomial coefficients, q-hypergeometric identities and transformations, and Jacobi's triple product identity for theta functions will be discussed. If time permits, towards the end of the course, the elementary proof of the Prime Number Theorem or on introduction to the Sieve will be given. This is quite different from partitions, but related to material covered in MAS 7215 in Fall 2009. However the discussion will be self contained.

TEXT:

No assigned text. I will use my own notes. A number of texts will be given as references.
 

GRADING:

The course grade will be based on four to five homework assignments.

ACCOMODATION FOR STUDENTS WITH DISABILITIES:

Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.

The url of this page is http://krishnaswami-alladi.com/gradnumthy/spring2010/syllabus.html.
Created by K. Alladi (alladik@ufl.edu) on Friday, January 01, 2010.
Last update made Wed Jan 6 15:28:47 EST 2010.

MAIL alladik@ufl.edu