The department offers the doctor of philosophy degree with a major in mathematics and a master of arts degree in mathematics.

The Ph.D. degree requires proficiency in basic and advanced graduate mathematics and the completion of a dissertation containing a significant piece of original research in some area of mathematics. The scope of the research program in mathematics is broad. The Ph.D specialty and dissertation may be in any area of mathematics, including but not limited to algebra, algebraic geometry, applied mathematics, combinatorics, computational mathematics, complex analysis, differential equations, differential geometry, dynamical systems, harmonic analysis, logic, mathematical biology, number theory, probability, and topology. A complete list of faculty and their areas of expertise is available through the department website.

Students in the Ph.D. program also have the option to earn a master of arts degree.

Please consult the table below for key information about this degree program’s admissions requirements. The program may have more detailed admissions requirements, which can be found below the table or on the program’s website.

Graduate admissions is a two-step process between academic programs and the Graduate School. Applicants must meet the minimum requirements of the Graduate School as well as the program(s). Once you have researched the graduate program(s) you are interested in, apply online.

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) Not required but may be considered if available.
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 (https://grad.wisc.edu/apply/requirements/#english-proficiency).
Other Test(s) (e.g., GMAT, MCAT) The GRE subject test in Mathematics is optional but may be considered if available.
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

Accelerated: Accelerated programs are offered at a fast pace that condenses the time to completion. Students typically take enough credits aimed at completing the program in a year or two.

Evening/Weekend: ​Courses meet on the UW–Madison campus only in evenings and/or on weekends to accommodate typical business schedules.  Students have the advantages of face-to-face courses with the flexibility to keep work and other life commitments.

Face-to-Face: Courses typically meet during weekdays on the UW-Madison Campus.

Hybrid: These programs combine face-to-face and online learning formats.  Contact the program for more specific information.

Online: These programs are offered 100% online.  Some programs may require an on-campus orientation or residency experience, but the courses will be facilitated in an online format.


Minimum Credit Requirement 51 credits
Minimum Residence Credit Requirement 32 credits
Minimum Graduate Coursework Requirement Coursework taken in the Mathematics department is expected to consist only of graduate-level coursework; Details can be found in the Graduate School’s Minimum Graduate Coursework (50%) Requirement Policy: https://policy.wisc.edu/library/UW-1244
Overall Graduate GPA Requirement 3.00 GPA required. This program follows the Graduate School's policy: https://policy.wisc.edu/library/UW-1203.
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.
Graduate School Breadth Requirements All doctoral students are required to complete at least a 12-credit doctoral minor or graduate/professional certificate.

Required COURSES

Take a total of 51 graduate credits, or generally 18 courses. This includes courses in math and in breadth. 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, Topology, and Dynamics

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 breadth.


These pathways are internal to the program and represent different curricular paths a student can follow to earn this degree. Pathway names do not appear in the Graduate School admissions application, and they will not appear on the transcript.

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 19 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.


This program follows the Graduate School's Probation policy.

  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 Limits

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.


Anderson, David F
Andrews, Uri
Arinkin, Dima
Caldararu, Andrei
Craciun, Gheorghe
Denisov, Sergey
Ellenberg, Jordan
Erman, Daniel M
Feldman, Mikhail
Gong, Xianghong
Gurevich, Shamgar
Kent, Autumn Exum (Graduate Director)
Lempp, Steffen
Mari-Beffa, Gloria
Maxim, Laurentiu
Miller, Joseph S
Paul, Sean T
Poltoratski, Alexei
Roch, Sebastien
Rycroft, Christopher
Seeger, Andreas
Seppalainen, Timo
Smith, Leslie M.
Soskova, Mariya
Spagnolie, Saverio
Stechmann, Sam
Stovall, Betsy
Street, Brian Thomas (Associate Chair)
Terwilliger, Paul M.
Thiffeault, Jean-Luc (Chair)
Tran, Hung Vinh
Valko, Benedek (Undergraduate Director)
Waleffe, Fabian
Yang, Tonghai

Associate Professors

Dymarz, Tullia Maria
Guo, Shaoming
Ifrim, Mihaela
Kim, Chanwoo
Li, Qin
Marshall, Simon Lindsay
Shen, Hao
Shcherbyna, Tetyana
Wang, Botong
Zimmer, Andrew

Assistant Professors

Albritton, Dallas
Apisa, Paul
Chen, Nan
Cochran, Amy
Fabien, Maurice
Kemeny, Michael L J
Lawrence, Brian
Loving, Marissa
Lyu, Hanbaek
Ohm, Laurel
Rodriguez, Jose Israel
Uyanik, Caglar
Waldron, Alex
Wu, Chenxi
Zepeda-Nunez, Leonardo

Academic Staff

Benguria Andrews, Soledad (Calculus Coordinator)
Friedman, Tracii (Math Learning Center Director)
Grizzard, Robert (Associate Director for Instructional Programs)
Ivanov, Mikhail (Math Learning Center Instructor)
Jackson, Billy (Director of the Precalculus Program)
Keller, Mitch (Associate Director of Undergraduate Programs)
Kwon, Oh Hoon (Associate Director of the Precalculus Program)
Lindsey, Melissa (Director of Instructional Support)
Phillipson, Kaitlyn (Undergraduate Course Coordinator)
Williams, Cassie (Associate Director of Instructional and Professional Development)
Work, Grace (Associate Director of Undergraduate Research)

Enrollment Coordinator

Kyle Martinez