Fall Deadline December 15
Spring Deadline This program does not admit in the spring.
Summer Deadline This program does not admit in the summer.
GRE (Graduate Record Examinations) Required.
English Proficiency Test Every applicant whose native language is not English or whose undergraduate instruction was not in English must provide an English proficiency test score and meet the Graduate School minimum requirements (
Other Test(s) (e.g., GMAT, MCAT) The GRE subject test in Mathematics is required. In exceptional cases, advanced GRE's from other sciences can be substituted for the advanced GRE in mathematics.
Letters of Recommendation Required 3

Admission is competitive. Applicants to the Ph.D. program are automatically considered for financial support. For more information about application to the Ph.D. and M.A. programs, see the department's admission website.

Graduate School Resources

Resources to help you afford graduate study might include assistantships, fellowships, traineeships, and financial aid. Further funding information is available from the Graduate School. Be sure to check with your program for individual policies and restrictions related to funding.

Program Resources

Prospective students should see the program website for funding information.

Minimum Graduate School Requirements

Review the Graduate School minimum academic progress and degree requirements, in addition to the program requirements listed below.

Major Requirements


Face to Face Evening/Weekend Online Hybrid Accelerated
Yes No No No No

Mode of Instruction Definitions


Minimum Credit Requirement 51 credits
Minimum Residence Credit Requirement 32 credits
Minimum Graduate Coursework Requirement For students in the Ph.D. program the coursework in the mathematics department is expected to consist only of graduate-level coursework; courses with the Graduate Level Coursework attribute are identified and searchable in the university's Course Guide (
Overall Graduate GPA Requirement 3.00 GPA required.
Other Grade Requirements No additional grade requirements.
Assessments and Examinations Students are required to pass at least two qualifying exams. At least one qualifying exam must be passed by the beginning of the fourth semester (the spring semester of the second year). Both qualifying exams must be passed by the beginning of their sixth semester (the spring semester of the third year).

Students must pass a preliminary exam (specialty exam) by the end of the eighth semester (end of fourth year).

Students must satisfy all the requirements for dissertator status by the end of the eighth semester (end of fourth year).
Language Requirements No language requirements.
Doctoral Minor/Breadth Requirements All doctoral students are required to complete a 12-credit minor.

Required COURSES

Take a total of 51 graduate credits, or generally 18 courses. This includes courses in math and in a minor. In the Ph.D. program, math courses numbered above 700 are for graduate credit. Math courses below 700 must  be approved by the academic advisor.

There are five general and overlapping areas of specialization1 within the department:   

  • Algebra, Algebraic Geometry, Combinatorics and Number theory
  • Analysis, Differential Equations  and Probability
  • Applied and Computational Mathematics
  • Logic
  • Geometry and Topology

There is also a specialty in Mathematics Education1. The course requirement is the same as for the other specialties except that the required 51 credits should include 18 credits in courses that relate to mathematics education, and at least one of the courses must be on research techniques in education. The 18 credits may come (wholly or in part) from courses included in the minor.

Graduate School Policies

The Graduate School’s Academic Policies and Procedures provide essential information regarding general university policies. Program authority to set degree policies beyond the minimum required by the Graduate School lies with the degree program faculty. Policies set by the academic degree program can be found below.

Major-Specific Policies

Prior Coursework

Graduate Work from Other Institutions

With program approval, students in the Ph.D. program are allowed to count no more than 22 credits of graduate coursework from other institutions. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

UW–Madison Undergraduate

No more than 7 credits from a UW–Madison undergraduate degree are allowed to count toward the degree. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

UW–Madison University Special

With program approval, students are allowed to count no more than 15 credits of coursework numbered 300 or above taken as a UW–Madison Special student. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.


The Graduate School regularly reviews the record of any student who earned grades of BC, C, D, F, or Incomplete in a graduate course (300 or above), or grade of U in research credits. This review could result in academic probation with a hold on future enrollment or in being suspended from the Graduate School.

  1. Good standing (progressing according to standards; any funding guarantee remains in place).
  2. Probation (not progressing according to standards but permitted to enroll; loss of funding guarantee; specific plan with dates and deadlines in place in regard to removal of probationary status).
  3. Unsatisfactory progress (not progressing according to standards; not permitted to enroll, dismissal, leave of absence or change of advisor or program).


Students who are not yet working with a dissertation advisor are required to meet semiannually with their academic advisor. All students must have a dissertation advisor by the end of the sixth semester.


15 credits. Minimum of 6/semester, other than dissertators.

Time Constraints

Students must complete all program requirements within eight years of beginning the program. Extensions have to be approved by the program.

A candidate for a doctoral degree who fails to take the final oral examination and deposit the dissertation within five years after passing the preliminary examination may be required to take another preliminary examination and to be admitted to candidacy a second time.

Doctoral degree students who have been absent for ten or more consecutive years lose all credits that they have earned before their absence. Individual programs may count the coursework students completed prior to their absence for meeting program requirements; that coursework may not count toward Graduate School credit requirements.

grievances and appeals

These resources may be helpful in addressing your concerns:

Students should contact the department chair or program director with questions about grievances. They may also contact the L&S Academic Divisional Associate Deans, the L&S Associate Dean for Teaching and Learning Administration, or the L&S Director of Human Resources.



Graduate School Resources

Take advantage of the Graduate School's professional development resources to build skills, thrive academically, and launch your career. 

  1. Learn a substantial body of mathematics in introductory and research level graduate courses in mathematics.
  2. Complete a dissertation under the guidance of an advisor. The dissertation should make an original and substantive contribution to its subject matter.
  3. Demonstrate breadth within the learning experiences.
  4. Present research in seminar talks, conferences or publications.
  5. Communicate complex ideas in a clear and understandable manner.
  6. Foster ethical and professional conduct.

Faculty: Professors Anderson, Angenent, Arinkin, Căldăraru, Craciun, Denisov, Ellenberg, Feldman, Gong, Kent, Lempp, Mari Beffa, Maxim, Miller, Paul, Poltoratski, Roch, Seeger, Seppäläinen (chair), Smith, Stechmann, Street, Terwilliger, Thiffeault, Valko, Waleffe, Yang; Associate Professors Andrews, Dymarz, Erman, Gorin, Gurevich, Ifrim, Kim, Li, Marshall, Soskova, Spagnolie, Stovall, Tran; Assistant Professors Chen, Cochran, Guo, Kemeny, Rodriguez, Shankar, Shcherbyna, Shen, Waldron, Wang, Wu, Zepeda-Núñez, Zimmer;  Affiliate Faculty Pimentel-Alarcón, Ron.