The doctor of philosophy degree demands breadth of knowledge, an intense specialization in one field, a substantial original contribution to the field of specialization, and a high degree of expository skill.
Five years are usually needed to complete all requirements for the PhD degree, and two years of residence are required. It is not necessary to obtain the MA degree en route to the PhD degree. Students may choose to obtain the MA in computer science and the PhD in mathematics. Any program leading to the PhD degree must be planned in consultation with and approved by the departmental Graduate Education Committee.
Possible fields of specialization for PhD candidates include algebraic geometry, analysis of algorithms, arithmetic geometry, arithmetic theory of quadratic forms, combinatorics, complex analysis, computational logic, dynamical systems, enumerative combinatorics, ergodic theory, geometric group theory, graph theory, higher order languages, homogeneous dynamics, homotopy type theory, hyperbolic geometry, information security, knot theory, logic programming, mathematical logic, metric geometry, model theory, network and data science, non-Euclidean geometry, number theory, probability theory, proof theory, and topological dynamics.
All degree-seeking graduate students are required to register for at least one credit in each semester that they are enrolled in the university. Course loads below three credits must be approved by the Graduate Education Committee.