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Ph.D. Program in Mathematics

Malgo Peszynska, Azhar Alhammali, and Choah Shin in Munich, Germany.

Ph.D. students Azhar Alhammali (L) and Choah Shin (R) with Professor Malgo Peszynska in Munich, Germany. Azhar and Choah presented at SIAM Geosciences Conference in Erlangen.

A strong path to meaningful mathematics research

The Ph.D. program in the Department of Mathematics allows students to undertake specialized study and independent research in mathematics. Areas of study represented by our graduate faculty include analysis, applied mathematics, differential geometry, financial and actuarial mathematics, mathematical biology, mathematics education, number theory, numerical analysis, probability and topology. Students can enter the Ph.D. program after demonstrating mathematical proficiency by passing the qualifying exams and finding a Ph.D. advisor from among the ranks of the faculty in mathematics. Students who enter the mathematics graduate program without a prior graduate degree are expected to complete the Ph.D. degree in six years. Students who enter with a prior master's degree typically complete the Ph.D. in five years.

During their first year, our graduate students typically enroll in courses and seminars that aim to prepare them for the qualifying examinations. The purpose of these exams is to demonstrate that the student has achieved a degree of mathematical depth and maturity in the core areas of real analysis and abstract linear algebra, has additionally cultivated advanced problem-solving skills in graduate-level mathematics, and is poised to undertake independent mathematical research.

Learning outcomes

The mathematics Ph.D. program learning outcomes are:

  1. Graduates will produce and defend an original contribution to knowledge, as evidenced by the writing and defense of a thesis involving significant original research.
  2. Graduates will demonstrate mastery of subject material, as evidenced by quality of performance in coursework, and on written and oral examinations in mathematics.
  3. Graduates will be able to communicate mathematical ideas, results, context and background effectively and professionally in written and oral form.
  4. Graduates will be able to conduct scholarly or professional activities in an ethical manner.