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 end of the first 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.
