## 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-supported and 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.

Our PhD program offers two tracks, one for *Theoretical Mathematics* and one for *Applied Mathematics*. The tracks differ only in the course and qualifying requirements during the first two years. 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 Qualifying 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 for Admission

Competitive applicants to the **theoretical track** are expected to 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 in either track 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 generally **not** consider GRE test scores for this Autumn 2024 admissions. If you have already taken the test, please do not self-report the scores to us. In exceptional circumstances students may have the option to report unofficially.

International students whose native language is not English and are not exempt should score at least a 20 on the Speak portion of the TOEFL.

## Qualifying Requirements by Track

The qualifying requirements for the theoretical track are fulfilled by passing our Abstract Algebra course sequence (Math 6111, Math 6112) *and* our Real Analysis course sequence (Math 6211, Math 6212), each with at least an A-, *or* by passing a respective examination.

The qualifying requirements for the applied track combine a mandatory Scientific Computing course (Math 6601), one of the algebra or analysis courses, and three additional courses chosen from Math 6602, Math 6411, Math 6451, and the courses comprising the algebra and analysis sequences.

The breadth requirements in the applied track are more flexible than in the theoretical track, but also include a mandatory graduate course in a non-math STEM department from an approved list.

You can find more information about our PhD program requirement here.

## Opportunities & Outcomes

The research opportunities and academic outcomes of our doctoral program are described in detail in the Graduate Program Prospectus [pdf].

Our department has about 80 active graduate faculty on the Columbus and regional campuses. Virtually every area of mathematics is represented in our program, with a sampling displayed below.

*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*

See also our Applied Mathematics Topics List [pdf].

Our program offers many support opportunities without teaching duties as well, to allow more time for scientific endeavors. These opportunities include university fellowships, external funding, and departmental fellowships and special assignments. See the Financial Support page for more details.

The median time to degree completion in our program is below six years but also varies significantly among our students, with as little as four years for students entering with substantial prior preparations. Funding is guaranteed for six years and can be extended to seven years with advisor support and the permission of the Graduate Studies Committee.

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. Recent non-academic placements include Google, Facebook, Amazon, NSA, and prestigious financial institutions.

Students also have access to training and networking opportunities that prepare them better for careers in private industry and teaching - for example, through the Erdős Institute - and are regularly offered highly competitive positions in the industry.

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. And as a program group member of the National Math Alliance, we are dedicated to enhancing diversity in our program and the scientific community. The International students in our program come from all parts of the world with a wide variety of educational backgrounds.

## Contact

Prospective students: grad-info@math.osu.edu

Graduate Office

Department of Mathematics

The Ohio State University

231 W 18th Avenue (MA 102)

Columbus, Ohio 43210

United States of America

Phone: (614) 292-6274

Fax: (614) 292-1479

[pdf] - Some links on this page are to .pdf files. If you need these files in a more accessible format, please email math@osu.edu. PDF files require the use of Adobe Acrobat Reader software to open them. If you do not have Reader, you may use the following link to Adobe to download it for free at: Adobe Acrobat Reader.