Areas of study include algebraic geometry, algebraic groups, algebraic topology, differential geometry, Hodge theory, mathematical physics, number theory, partial differential equations, representation theory, and several complex variables. In the seven basic graduate courses on algebraic geometry, algebraic topology, Lie groups and Lie algebras, number theory, partial differential equations, Riemannian geometry, and several complex variables, students gain fundamental preparation for research. Higher-level topics courses keep students abreast of current developments and prepare them for research in their chosen field. They must then write a dissertation. Students usually begin working on the dissertation with a faculty adviser in their third year, while continuing to take classes.
Most successful students obtain their Ph.D. degrees in about five years.
This is usually done in one or two years. The University's Milton S. Eisenhower Library maintains an extensive collection of mathematical books and journals, and students have access to the stacks. The department also administers a small reference library. Students share departmental offices, and study space can also be reserved in the University library. Students use the department's computers as well as the University Academic Computing Center's terminals located in the same building.