Mathematics PhD

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.

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.

A bachelor’s degree from a regionally accredited U.S. institution or a comparable degree from an international institution is required. International applicants must have a degree comparable to a regionally accredited U.S. bachelor’s degree. You must have completed your undergraduate degree, or similar, before starting graduate school.

A minimum undergraduate grade-point average (GPA) of 3.00 on the equivalent of the last 60 semester hours (approximately two years of work) or a master’s degree with a minimum cumulative GPA of 3.00 is required. Applicants from an international institution must demonstrate strong academic achievement comparable to a 3.00 for an undergraduate or master’s degree. The Graduate School will use your institution’s grading scale. Do not convert your grades to a 4.00 scale.

Every applicant whose native language is not English, or whose undergraduate instruction was not in English, must provide an English proficiency test score. TOEFL scores must be submitted electronically via ETS. IELTS scores can be submitted electronically or by paper.  Our office address is: UW-Madison Graduate School, Office of Admissions, 232 Bascom Hall, 500 Lincoln Drive, Madison, WI 53706.  Your score will not be accepted if it is more than two years old from the start of your admission term. Country of citizenship does not exempt applicants from this requirement. Language of instruction at the college or university level and how recent the language instruction was taken are the determining factors in meeting this requirement.

Applicants are exempt if: