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

The PhD 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 PhD 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 PhD 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 exclusively in English, must provide an English proficiency test score earned within two years of the anticipated term of enrollment. Refer to the Graduate School: Minimum Requirements for Admission policy: https://policy.wisc.edu/library/UW-1241.
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 PhD program are automatically considered for financial support. For more information about applications, 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

Mode of Instruction

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.

Curricular Requirements

Minimum Credit Requirement 51 credits
Minimum Residence Credit Requirement 32 credits
Minimum Graduate Coursework Requirement 51 credits must be graduate-level coursework. Refer to the Graduate School: Minimum Graduate Coursework (50%) Requirement policy: https://policy.wisc.edu/library/UW-1244.
Overall Graduate GPA Requirement 3.00 GPA required. Refer to the Graduate School: Grade Point Average (GPA) Requirement 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. Refer to the Graduate School: Breadth Requirement in Doctoral Training policy: https://policy.wisc.edu/library/UW-1200.

Required Courses

Students must take a total of 51 graduate credits, or generally 18 courses. This includes courses in math and in breadth. In the PhD 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 Credits Earned at Other Institutions

With program approval, students in the PhD program are allowed to transfer 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.

Undergraduate Credits Earned at Other Institutions or UW-Madison

No more than 7 credits from an undergraduate degree are allowed to transfer. Coursework must be at a graduate level and must request program approval. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

Credits Earned as a Professional Student at UW-Madison (Law, Medicine, Pharmacy, and Veterinary careers)

Refer to the Graduate School: Transfer Credits for Prior Coursework policy.

Credits Earned as a University Special Student at UW–Madison

With program approval, refer to the Graduate School: Transfer Credits for Prior Coursework policy.


Refer to the Graduate School: 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).

Advisor / Committee

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.

Credits Per Term Allowed

15 credits. Minimum of 6 per 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.

Refer to the Graduate School: Time Limits policy.

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.



Professional Development

Graduate School Resources

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

Learning Outcomes

  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.


Please visit the Math Department website for a complete list of faculty and instructional academic staff.