Number Theory | Department of Mathematics

The Department of Mathematics at the University of Illinois at Urbana-Champaign has long been known for the strength of its program in number theory. The department has a large and distinguished faculty noted for their work in this area, and the graduate program in number theory attracts students from throughout the world. At present over twenty students are writing dissertations in number theory. Each semester upper level graduate courses are offered in a variety of topics in analytic, algebraic, combinatorial, and elementary number theory.

Weekly Seminars

One or two regularly scheduled seminars are held each week, with lectures being given by faculty, graduate students, and visiting scholars. The lectures may be elementary introductions, surveys, or expositions of current research.

Number Theory Conferences

Illinois has hosted a long running series of number theory conferences:

Analytic and Combinatorial Number Theory: The Legacy of Ramanujan, June 6-9, 2019
2007 Illinois Number Theory Fest
2009 Illinois Number Theory Celebration
2010 Illinois Number Theory Conference
2011 Illinois Number Theory Conference
2014 Illinois Number Theory: A Conference in Memory of the Batemans and Heini Halberstam
2015 Illinois Number Theory Conference

In addition, every two of three years Illinois hosts the Midwest Graduate Number Theory conference for Graduate Students and recent PhDs, a unique type of conference organized almost entirely by graduate students.

Courses

Each year, the following one semester courses are offered:

Math 453, Elementary Theory of Numbers (upper undergraduate level)
Math 530, Algebraic Number Theory (beginning graduate course)
Math 531, Analytic Theory of Numbers, I (beginning graduate course)

In addition, at least four topics courses are also offered each year, with student input helping to determine the choice of the topics courses. In recent years, enrollment in these courses has been excellent, typically ranging from 10 to 25. We list below some of the topics courses taught between 2005 and 2013:

Algebraic: Class field theory, elliptic curves, modular forms, Iwasawa theory, algorithmic number theory, cryptography, Abelian varieties.
Analytic: Exponential sums, Asymptotic methods in analysis, Riemann zeta-function and L-functions, sieve methods, probabilistic number theory, elliptic functions, Continued fractions, Modular forms, Theory of partitions, additive number theory, Uniform distribution, Distribution of sequences, hypergeometric functions, Diophantine approximation, polynomials, elementary methods, anatomy of integers.

Graduate Awards

The Bateman Prize and the Bateman Fellowship are given annually for outstanding research in number theory. They are named for former Professor Paul T. Bateman, who was on the faculty from 1950 to 1989 and continued being active in the group's activities until shortly before his death in 2012. Bateman served as Department Head for the years 1965-1980.

Recipients of the Bateman Prize in Number Theory

Recipients of the Bateman Fellowship in Number Theory