Graduate Programs in Mathematical Sciences
Preparing the Next Generation of Mathematical Scientists
The M.S. and Ph.D. programs in mathematical sciences are designed to develop both deep expertise and broad competence across the mathematical sciences. Whether pursuing an M.S. or a Ph.D., students engage in rigorous training across core areas such as analysis, algebra, computational mathematics, statistics and operations research, while developing advanced specialization in their chosen research field. The curriculum emphasizes not only research excellence but also the development of strong communication, teaching and mentoring skills. Students undertake significant research projects and learn to effectively disseminate their work through writing and presentation. Graduates emerge as skilled mathematical scientists who are prepared for rewarding and highly impactful careers in academia, industry and government.
Prerequisites
To be accepted into either the M.S. or Ph.D. program, students should have completed prerequisite coursework in linear algebra, differential equations, a programming language, statistics, advanced calculus or real analysis, modern abstract algebra and probability.
M.S. Program Information
Concentration Requirement
In addition to satisfying the breadth requirements, students must select an identifiable concentration area and take additional courses in that area. There are two tracks: thesis and non-thesis (project). Students pursuing the thesis option are required to pass two concentration courses in addition to the breadth courses and write a thesis. Students pursuing the project option are required to pass four concentration courses in addition to the breadth courses and complete a project.
Research
As a means of integrating the student’s program of diverse study, a master’s disquisition (project or thesis) must be completed by the end of the second year. The student makes an oral and written presentation of the master’s degree disquisition. M.S. students who are completing a master’s project should register for one hour of MATH 8920 during their last semester in the program. M.S. students who are completing a master’s thesis should register for a total of six hours of MATH 8910 during their last two semesters in the program.
Breadth Requirement
The master’s breadth requirement includes the completion of six graduate-level courses, one in each of the following: algebra, analysis, computing, operations research and statistics. An additional course is also required in either operations research or statistics. It is strongly suggested that students select from among the suggested courses listed here. Any deviation from the choices of breadth courses listed here should be pre-approved by the graduate coordinator and the student’s advisor. Area of study and suggested courses:
- MATH 8530, 8510 Algebra and Discrete Math
- MATH 8210 Analysis
- MATH 8600 Computational Math
- MATH 8100 Operations Research
- MATH 8000, 8050 Statistics
- MATH 8000, 8040, 8030, 8140 Operations Research or Statistics
Program Timeline
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Semester One
- Focus on finishing three breadth courses.
- If this is a Fall semester, attend the first-year seminar.
- International students should enroll in the language improvement course and work toward passing the Verification of English Skills Test.
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Semester Two
- Finish breadth requirements and attend first-year seminar.
- Students who are supported as TAs should participate in the department’s teacher training course (which runs in the spring only).
- Choose a research advisor.
- Work with your advisor to identify a research committee (two more faculty members) and submit a committee selection form via iROAR.
- Ideally, students will identify their research projects and get started with research at the end of the second semester.
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Semester Three
- Work with your research advisor to complete a plan of study. This should be submitted via iROAR early in the third semester.
- Students should make significant progress on their research projects by the end of the third semester.
- This is often when those on TA support begin their teaching responsibilities.
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Semester Four
- There are many things to complete this semester before you graduate. Be sure to check the Graduate School deadlines for thesis defenses and graduation applications.
- Complete your research project.
- Write up your project or thesis.
- Defend the thesis or project. The defense will need to be scheduled according to the oral presentation guidelines. If you have questions or have issues, contact Connie McClain, student services coordinator. Oral presentation guideline can be found on the Graduate Studies Overview Page.
- Graduate!
Ph.D. Program Information
Coursework
Ph.D. coursework also includes at least 24 hours of non-research, non-professional-development graduate courses at the 8000 level or above beyond the M.S. degree. In addition, a Ph.D. candidate should complete at least 18 hours of MATH 9910 (dissertation research).
Preliminary Exams
Ph.D. candidates are required to pass two preliminary exams within three years of entering the graduate program, without accumulating three fails. M.S. students are allowed to take prelims, and all passes and fails will count toward their progress.
Oral Exam
Ph.D. candidates must also successfully complete a comprehensive oral examination within one year of completing the preliminary exams.
Dissertation
The final requirement for doctoral students is the Ph.D. dissertation, which will detail your original and significant contributions to the body of research in your area of concentration, and require you to defend your work.
Transfer courses and courses completed as a master’s student en route to the Ph.D. may be counted toward this requirement.
Breadth Requirement
The breadth requirements for Ph.D. students include two courses in each of the following areas:
- Algebra and discrete math
- Analysis
- Computational math
- Operations research and stochastics
- Statistics
Typical timeline
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Year One
- Focus on completing coursework related to prelim exams.
- Attempt a prelim (or two) at the end of this year.
- Attend a graduate student seminar and a research seminar each week.
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Year Two
- Complete all prelims during this year.
- Choose a research adviser during this year as well.
- Complete a GS2 committee selection form in consultation with your research advisor.
- Attend a graduate student seminar and a research seminar each week.
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Year Three
- Begin working on research projects and develop a prospectus for your dissertation in consultation with your research advisor.
- Submit a GS2 Ph.D. coursework plan via iRoar.
- Complete your comprehensive oral exam during this year.
- Complete the Ph.D. breadth requirement.
- Attend a graduate student seminar and a research seminar each week.
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Year Four
- Focus on your research and topics coursework in your area of speciality.
- Attend a graduate student seminar and a research seminar each week.
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Year Five and Possibly Six
- Attend a graduate student seminar and a research seminar each week.
- Make sure to double check the Graduate School deadlines for graduation.
- Complete and defend your dissertation.
- Graduate!
Prelim Exams and Coursework
The first priority of a beginning Ph.D. student is to pass the preliminary exams.
Current prelim policy: Graduate students are required to receive two passes without accumulating three fails within three years of entering the graduate program. M.S. students are allowed to take prelims, and all passes and fails will count towards their progress. Any prelims taken by a graduate student become part of their permanent prelim record.
A no-show will count as a fail if a student signed up and did not withdraw by the specific withdrawal deadline unless there are unusual circumstances such as a medical excuse or family emergency.
Any exception to the no-show fail policy can be made only if a written request is submitted by the student to the associate director for graduate studies and the graduate student services coordinator and approved by the associate director for graduate studies.
Prelim Topics and Preparatory Coursework
- Algebra and Discrete Math: MATH 8510, 8530; algebra prelim topics (PDF, login required).
- Analysis: MATH 8210, 8220; analysis prelim topics (PDF, login required).
- Applied Statistics: MATH 8050, 8850; applied statistics prelim topics (PDF, login required — link coming soon)
- Computational Math: MATH 8600, 8610; computation prelim topics (PDF, login required).
- Operations Research: MATH 8100, 8130; math programming prelim topics (PDF, login required).
- Statistics: MATH 8000, 8040; statistics prelim topics (PDF, login required).
- Stochastics: MATH 8030, 8170; stochastics prelim topics (PDF, login required).
Prelim Exam Archive
A repository of past prelim exams is available to augment your prepartions.
