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The Ph.D. in mathematics is intended for students who wish to advance mathematical knowledge itself, apply such knowledge to problems confronting society and science, and educate others in mathematical methods and ways of thinking.

The Mathematics Department offers students the possibility of designing study plans to meet their individual goals and interests. In particular, we offer a broad spectrum of possible research areas for our Ph.D. students, including algebra, analysis, coding theory, computational harmonic analysis, partial and ordinary differential equations, dynamical systems, financial mathematics, mathematical biology, numerical analysis, optimal control theory, set theory, statistics, stochastic processes, and topology.

Most doctoral students are trained and financially supported as teaching assistants and have the opportunity to teach classes as the primary instructor.

Mathematics Ph.D. Courses & Degree Requirements

This is a full-time program. Normative time to completion is five academic years if students have MS degree from elsewhere or six years from starting our MS program.

The first phase in doctoral education in Mathematics is to understand a few subjects deeply and a range of subjects in less detail. Our program accomplishes this through a system of courses and written examinations. An exceptionally well-prepared student can attempt the examinations early and spend relatively little time doing coursework.

The second phase is to become the expert on a specific problem and produce new mathematical results on it suitable for a dissertation. In our program this phase is done one-on-one with a faculty advisor or in a small research group. The dissertation is a scholarly work demonstrating the ability to understand, organize, improve, and present mathematical ideas of outstanding importance, depth, or interest. It must include original mathematical research and be worthy of publication.

Preparing for Comprehensive Exams

Advice from the Graduate Chair

Copies of old exams are available from the graduate chair. We recommend that you get copies of the exams in your chosen subjects before you start the core courses in that subject. Each week look at the exams and see if you have covered the material to enable you to do any more questions, and then try to do those questions, getting help as needed. At the end of the course, you will have done most or all of the old exam questions and have a firm foundation for your study.

Looking for a Dissertation Adviser

When you entered our program, you are assigned an academic adviser to help you decide on your coursework, exams, etc. We try to select a faculty member who works in the area in which you indicated interest, but this academic adviser may or may not be your dissertation adviser. We recommend that you talk to several potential advisers about their research and ask for a recent paper of theirs to read so you can see what their field is like. You can then talk to a few of them about potentially being their student. They may give you a small problem to work on to determine if you like the subject, if you like working with them, and if they like working with you. Although finding an adviser is an immensely important decision, it often is determined by you and the faculty member feeling that you are a good match.

Culminating Experience

All tracks require students to successfully complete at least three courses (minimum 3 hours each) numbered above 5999 as a capstone experience. Students in MS3101 will complete this requirement with three MATH courses. Computational Track students may count courses from computer science and mathematics, with at least one from each of those fields. These courses are at the doctoral level and require students to synthesize and apply knowledge gained through preparatory coursework.

In addition, students have the option to complete a thesis or project as part of their work.

Resources

• Advice from the Graduate Chair on How to Succeed
• Expectations Regarding Recitations
• MATH 5960 Seminar
• Mathematics Career Information
• ÃÛèÖÊÓƵ Fellowships page

Research Opportunities

• Faculty Research Areas
• Doctoral Dissertations