Ph.D in Mathematics

Exploring New Theories at the Forefront of Mathematics and its Applications

Doctoral studies form our core graduate program.  The faculty in the department excel in numerous areas of applied mathematics and are well versed in many related disciplinary fields, thus they are highly qualified to train graduate students and mentor them in producing high-quality research and dissertations at the intersection of mathematics and the sciences or engineering.  Our Ph.D. training opens doors to research careers in academia, government laboratories, and industry and our department has a strong record of placing Ph.D. students in prestigious postdoctoral positions at top-tier universities and labs, and in industrial positions.

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office of Graduate Education.


Program of Study

The Ph.D. degree results from following a program of study in mathematics or in applied mathematics.


  • At least six, four-credit (nonthesis) graduate mathematics courses (i.e., those with numbers MATH-6xxx or MATP-6xxx).
  • At least one three- or four-credit course at the graduate (6000) level outside the department (i.e., not coded MATH or MATP and not cross listed with any department course), selected in consultation with the math adviser.
  • At least two-thirds of the total credit hours, excluding thesis, must contain the suffix numbers 6000—6999 with the further limitation that no more than 21 credits hours of 4000—4990 courses are allowed.
  • All doctoral students must pass a written preliminary exam as well as an oral qualifying examination, and complete an oral candidacy presentation.

In addition, the course MATH-6591 Research in Mathematics is strongly suggested. Any deviations from these requirements must have the approval of the Department’s Graduate Committee.

Program Outcome

Students who successfully complete this program will be able to:

  • Demonstrate mastery of graduate-level courses covering a range of topics, including mathematical analysis, mathematical methods and modeling, computational mathematics, and operations research.
  • Demonstrate mastery of graduate-level courses in at least one area outside of mathematics.
  • Conduct high-quality original research on a topic in mathematics or applied mathematics with results suitable for journal publications and technical presentations.
  • Read and interpret research level articles in mathematics and develop new mathematical concepts.
  • Develop mathematical formulation and solution of scientific problems from a range of disciplines.
  • Communicate sophisticated mathematical ideas and concepts concisely and effectively in both oral and written form.

Financial Aid

There are several potential ways that a Math Sciences graduate student can get financial support while enrolled at RPI. The most common methods are:


There are many opportunities for students to obtain fellowships to support their graduate studies.  These fellowships can come from inside or outside the department or the Institute.  For example, recent fellowships have been available from the Department of Education, and there are competitive fellowships available from the National Science Foundation. The specifics of fellowships vary from year to year, and the  Graduate Student Coordinator has information on available fellowships and application procedures.  Your academic advisor in the department is another good source of information about fellowships.

You should be sure to consider that the Math Sciences Department has guidelines for continuation of support for doctoral students. Graduate students who receive full support from the Department should plan to complete their doctoral programs within four or five years. Students can expect that their support will continue through this period, provided that they continue to make satisfactory progress toward their degree and they continue to perform well in their teaching assignments. "Satisfactory progress" means completing courses, required examinations (preliminary, qualifying, and candidacy), selecting a research area, and making progress toward completing a thesis. If a student requires support beyond the fifth year, each situation will be considered individually.

Teaching Assistantship

TA assignments vary significantly throughout Rensselaer Polytechnic Institute. In the Department of Mathematical Sciences, TA-ships are typically one-year appointments that cannot be extended for more than two years. They tend to be of two types.

TA-ships can take the form of independent classroom teaching (often called recitations), which may include small lectures, problem solving, computer labs, grading, office hours, etc. The TA works with a TA Supervisor, who is the faculty member teaching the course. The vast majority of TA-ships are of this form.

A few teaching assistantships take the form of grading and office hours only.

All TA’s are required to participate in RPI’s TA Orientation Program as well as the Department’s TA Orientation prior to their first semester of teaching.

In addition, all TA’s must attend the TA Seminar before or during their first semester of teaching at RPI. A graduate student, the Math Sciences Department Master TA, typically teaches this one-credit course (graded as Satisfactory/Unsatisfactory). The topics of this course vary according to the needs of the participants. In the past they have included: Maple, Grading, Laptops, Composing Quizzes, Campus Resources, Academic Honesty, Proctoring Exams, Extra Help, Office Hours, Latex, Making a Syllabus, etc.  In addition, each TA has their class visited and feedback is provided.

Research Assistantship

Many faculty in the Math Sciences Department have grant money that can be used to support graduate students who are interested in doing research in their field. The Research Assistantships (RA’s) do not typically have any teaching component. This allows a graduate student to have more time to work on Master’s or Ph. D. research. This is a topic you may want to talk to your advisor about.

Academic Opportunities

Designed to promote a broad range of problem-solving skills, including mathematical modeling and analysis, scientific computation, and critical assessment of solutions.

An interdisciplinary program that integrates modeling, analysis, and computations with contemporary experimental research.

Academic awards for graduate students who demonstrated outstanding ability in his or her academic work.

SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.