The Ph.D. program in mathematics

A student in the Ph.D. program begins their career by taking three or more yearlong sequences from one of the areas where we offer preliminary examinations. Currently examinations are given in algebra, analysis, discrete mathematics, numerical analysis, partial differential equations and topology. In addition to the qualifying exams, students are asked to take a minor which may be outside the department, or an internal minor in the department. After passing three preliminary examinations and demonstrating competency in one foreign language, students begin studying a topic in depth to prepare for their oral qualifying examination. After successfully completing the oral qualifying examination, the Ph.D. candidate begins the research necessary to write a dissertation. The dissertation must be defended at a public defense.

The department offers Ph.D.'s in both pure and applied mathematics. Areas of strength for the department include combinatorial optimization, algebraic combinatorics, complex analysis, functional analysis, mathematical physics, algebra including number theory, group theory, ring theory and algebraic geometry, partial differential equations, harmonic analysis, numerical analysis including numerical linear algebra, numerical solution of partial diffential equations and image processing, topology and the mathematics of materials.

Students in the Ph.D. program are typically supported by teaching assistantships during their studies. Research assistantships may be available for advanced students working on particular projects. All students are encouraged to developing their teaching skills while at Kentucky and several special opportunities are available for the best students.