Programs of study in mathematics that are offered lead to
the degrees of master of science (M.S.) and doctor of philosophy (Ph.D.). The
M.S. degree comes in two options. The primary option is an M.S. with a
concentration in mathematical finance, which is described in a separate listing
in this catalog. There is also a standard option for the M.S., offering a more
traditional mathematics program, but it is used infrequently.
The graduate program in mathematics uses three
curriculum codes to organize its offerings: 640 codes courses in pure
mathematics; 642 codes courses in applied math; and 644 codes math courses for
K-12 teachers. There are currently no degree programs in math associated with
curriculum code 644.
Possible areas of specialization within the Ph.D. program
include algebra and algebraic geometry, applied analysis, discrete mathematics,
geometry and topology, Lie theory, logic, mathematical physics, nonlinear
functional analysis, number theory, partial differential equations, several
complex variables, dynamical systems, and mathematical biology.
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 Ph.D.
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 tests and mathematics subject tests of the Graduate Record Examination
(GRE). Financial aid through fellowships and teaching assistantships is
available to qualified doctoral students.
The standard master of science program is a very small
program, and students are accepted only in special circumstances. It is not
considered a bridge program to our Ph.D. program. Students who are interested
in this program are advised to contact the graduate program director
before applying in order to determine whether their interests and circumstances
are appropriate for the program.
It also is possible to apply for admission as a nondegree
student. The GRE is not required for these applicants, but letters of
recommendation are requested. Admission is given only to an applicant who has
presented convincing evidence that he or she will be successful in our
courses. A nondegree student can take no
more than 6 credits per semester, and as many as 12 credits of coursework
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 end
of the first semester 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 standard M.S. in mathematics, students select, with
the approval of the graduate director, 30 credits of coursework. 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, or 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.
The graduate program offers about 25 graduate courses each
semester from the list of graduate courses in this chapter. Courses are
scheduled based on program needs, student demand, and faculty availability.
