Program Synopsis and Training
The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization. They will be well prepared for research and faculty positions at academic institutions anywhere in the world. Owing to their independence, analytic abilities, and proven tenacity our PhD graduates are also sought after by private and government employers.
Applicants are required to decide on one of the tracks and applications will be evaluated subject to respective criteria described below. Once students have passed their pre-candidacy requirements the two tracks merge and there is no distinction in later examinations and research opportunities. In particular, the candidacy exam for both tracks consists of a research proposal, the graduate faculty available for advising is the same, and the final degree and thesis defense are independent of the initially chosen track.
Expected Preparations and Admission Criteria
Listed below are the criteria to consider while applying.
Students applying to the theoretical track should have strong foundations in Real Analysis and Abstract Algebra, equivalent to our Math 5201-5202 and Math 5111-5112 sequences. Expected preparations for the applied track include the equivalents of a rigorous Real Analysis course (such as Math 5201), a strong background in Linear Algebra, as well as an introductory course in Scientific Computing. Besides these basic requirements competitive applicants submit evidence for a broad formation in mathematics at the upper-division or beginning graduate level. Relevant coursework in other mathematical or quantitative sciences may also be considered, especially for the applied track.
Prior research experiences are not required for either track, and we routinely admit students without significant research background. Nevertheless, applicants are encouraged to include accounts of research and independent project endeavors as well as letters of supervising mentors in order to be more competitive for fellowship considerations. The research component is likely to have greater weight in applications to the applied track.
These prepared documents serve to provide our admission committee with a narrative overview of the applicant's mathematical trajectory. Their primary focus should, therefore, be to enumerate and describe any evidence of mathematical ability and mathematical promise. The information included in the documents should be well-organized, comprehensive, informative, specific, and relevant. This will help our committee to properly and efficiently evaluate the high number of applications we receive each year.
Our Graduate Recruitment Committee will not consider GRE math subject test scores for Autumn 2022 admission. If you have already taken the test, please do not self-report the scores to us.
International students whose native language is not English should score at least a 20 on the speak portion of the TOEFL. Due to COVID, at-home versions of the TOEFL test are being offered and we are accepting these scores to complete the English Proficiency Requirement for international students.
Opportunities & Outcomes
Most of our graduates continue their careers in academia. Post-doctoral placements in the last two years include, for example, UCLA, Stanford, ETH-Zürich, Brown University, University of Michigan, Northwestern University, University of Vienna, EPF Lausanne, Free University at Berlin, Purdue University, and University of Utah. In recent years our graduates also went to Princeton University, IAS, University of Chicago, Yale University, University of Michigan, Cal-Tech, Northwestern University, University of Texas, Duke University, SUNY Stony Brook, Purdue University, University of North Carolina - Chapel Hill, and Indiana University. Students also have access to training and networking opportunities that prepare them better for careers in private industry and teaching.
- Commutative, Non-commutative, & Quantum Algebra
- Analytic, Algebraic, Computational Number Theory
- Algebraic Geometry, Tropical Geometry
- Applied Mathematics, Mathematical Physics
- Real and Complex Analysis
- Functional Analysis, Operator Algebras
- Combinatorics and Graph Theory
- Differential Geometry
- Dynamical Systems and Ergodic Theory
- Financial and Actuarial Mathematics
- Logic and Foundations
- Probability Theory, Statistical Mechanics
- Mathematical Biology
- Ordinary and Partial Differential Equations
- Representation theory
- Scientific Computing
- Topology, Topological Data Analysis
Our department has currently over 80 active graduate faculty on the Columbus and regionals campuses. Virtually every area of mathematics is represented in our program, with a sampling displayed on the right. See also our Applied Mathematics Topics List [pdf]. Our program also offers many opportunities to be supported without teaching duties to allow more time for scientific endeavors.
Nearly half of the graduate population consists of domestic students coming from both larger universities and smaller liberal arts colleges with a solid math curriculum. International students come from all parts of the world and different educational backgrounds. As a program group member of the National Math Alliance we are dedicated to enhancing diversity in our program and the scientific community.
Median time to degree is below six years but also varies significantly among our students, ranging from as little as four years for well-prepared students to more than six years for students working on challenging topics. Funding is guaranteed for six years and can be extended with advisor support and studies committee permission to seven years.
Many more details can be found in our Graduate Program Prospectus [pdf].
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