The graduate program in mathematics offers courses of study leading
to the degrees of master of science and doctor of philosophy. Possible
areas of specialization include algebraic geometry, category theory and
topos theory, commutative algebra, theory of computation, differential
geometry, discrete mathematics, functional analysis, geometric measure
theory, group theory, harmonic analysis on Euclidean spaces, Lie
theory, logic, mathematical physics, nonlinear analysis, number theory,
numerical analysis, ordinary differential equations, operations
research, partial differential equations, probability theory, ring
theory, mathematics underlying string theory, system and control
theory, and algebraic and geometric topology.

The program in
mathematics is housed in the Hill Center for the Mathematical Sciences,
a seven-story building on the Busch campus. Hill Center and the
adjoining CoRE Building house the computer science and statistics
departments, the Center for Discrete Mathematics and Theoretical
Computer Science, and the Mathematical Sciences Library. The library
contains more than 27,000 volumes and subscribes to more than 300
research journals in pure and applied mathematics. Office space is
provided to all full-time graduate students in mathematics. The
graduate programs in biology, chemistry, physics, and engineering are
located nearby.

Applicants to the Ph.D. programs must have a
strong undergraduate background in mathematics and must submit scores
from both the general and subject tests of the Graduate Record
Examination (GRE). Financial aid through fellowships and teaching
assistantships is available to qualified doctoral students. Application
for financial support should be made by February 1.

Applicants
to the master`s programs should have an undergraduate degree in
mathematics or a related area. Preferably, they should have taken
courses in linear algebra and advanced calculus. Both the general and
subject tests of the GRE are required for master`s applicants.

It also is possible to apply for admission as a nondegree student. The
GRE is not required for these applicants. As many as 12 credits of
course work taken as a nondegree student can count toward a degree if
the student is subsequently admitted to a degree program.

All
doctoral students must pass a two-stage qualifying examination before
officially commencing work on their thesis. The first examination, a
written one, is designed to ensure that Ph.D. graduates know certain
basic material. Normally, it is taken at the beginning of the student's
second year. The second examination, which is oral, normally is taken
by the beginning of the second term of the student`s third year.

Students pursuing a Ph.D. in mathematics must take 48 credits in
approved courses. Normally, this curriculum will include 16:
640:501,502 Theory of Functions of a Real Variable, 16:640:503 Theory
of Functions of a Complex Variable I, and 16:640:551,552 Abstract
Algebra. Students should choose a program that gives them knowledge in
a broad range of mathematics and/or its applications. In addition,
students in the sequence must take 16:640:616,617 Seminar in
Mathematics; acquire a reading knowledge of French, German, or Russian;
complete 24 credits of research; and submit a doctoral dissertation.
There is no residency requirement. Ordinarily, the courses
16:642:527,528 Methods of Applied Mathematics, 16: 642:550 Linear
Algebra and Applications, and 16: 642:593 Mathematical Foundations for
Industrial and Systems Engineering are not approved for the Ph.D.
program in mathematics.

For the M.S. in mathematics, students
select, with the approval of the graduate director, 30 credits of
course work. At least 18 of these credits must come from courses
offered by the Graduate Program in Mathematics. Specific requirements
are: (1) one of the following courses: 16:640:501 Theory of Functions
of a Real Variable I, 16:640:503 Theory of Functions of a Complex
Variable I, 16:640:515 Ordinary Differential Equations, and 16:642:516
Applied Partial Differential Equations; (2) 16: 640:551 Abstract
Algebra I; and (3) a course in computer science, statistics, or some
other area of applied mathematics offered by the department. There is
no residency requirement, but a master's essay is required.

Not all graduate courses listed below are given every year. Each course
is scheduled subject to student demand and at the discretion of the
graduate faculty.