PhD in Mathematical Sciences

The Doctor of Philosophy (PhD) program in Mathematical Sciences represents achievement of a broad knowledge of the various branches of mathematics, of the ability to communicate mathematics in both written and oral form, and of a demonstrated creative ability in a particular branch of mathematics.

The program prepares students for careers in academia and as professional mathematicians. Students have the opportunity to work with some of the world's leading experts in a variety of research areas. The Department has particular strength in the interrelated fields of analysis, partial differential equations, and probability. Students interested in more applied directions can work with experts in mathematical bioscience, computational finance, and cryptography..

Admission Requirements

Students applying for the program should have or be expecting to obtain a bachelor’s degree either in mathematics or a related field.

The following background is required:

  • Multivariable calculus at the level of MATH 2063
  • Ordinary differential equations at the level of MATH 2073 or MATH 2074
  • Linear algebra at the level of MATH 2076
  • Experience with reading and constructing mathematical proofs at the level of MATH 3001

The following background is recommended:

An official general GRE score is required for admission.  This requirement is waived for applicants with at least 6 graduate credits in a relevant field with a cumulative GPA of 3.2 or higher.  The requirement is also waived for UC undergraduates with a degree in a relevant field and a cumulative GPA of 3.5 or higher.  A quantitative score of 160 or higher is recommended.

Proficiency in English is required of international students whose native language is not English.  The minimum scores required for admission and to be considered for an assistantship are as follows:
  Admission Assistantship
TOEFL 80 93
IELTS (overall band) 6.5 7
Duolingo 110 115

The English proficiency requirement is met for applicants with degrees earned in English from accredited universities and colleges in the US or other English-speaking countries.

Financial Support

Most of our PhD students receive full financial support via a teaching or research assistantship, and most are supported through their entire UC career.  Travel support is available for students to attend or present their work at conferences.  

All applicants for the PhD program are automatically reviewed for graduate assistantship eligibility at the time of application. 

Application Instructions

Applicants will need to meet the minimum requirements to be considered for the program. Completed applications will be reviewed beginning February 1. We will continue to receive applications until all positions are filled.

All application materials from international students requiring a US visa must be received prior to April 1 (but sooner is better) in order to allow time for the necessary paperwork to be processed. The visa application process can often take 90 days or more to complete.

How to apply: 

1. Create an online application

2. Include these documents in your application:

  • Three letters of recommendation. The application system will automatically send an email to each of the recommenders with a link to submit their letters. 
  • Unofficial copy of transcript (official transcript will be required if you are admitted to the program). 
  • GRE general test score 
  • Statement of purpose/cover letter 
  • English Proficiency for international students

3. Pay the application fee

UC’s CEEB college code is 1833, as established by The College Board. CEEB codes are used to ensure that test scores are sent to the correct institution. 

Program Description

The credit-hour requirement includes a minimum of 90 graduate credits beyond the bachelor's degree or a minimum of 60 credits beyond a master's degree, including 7 hours in dissertation research, with a GPA of 3.3 or higher. 

All incoming PhD students are required to take the qualifying exam before the beginning of their first semester. Students who do not pass this exam at the PhD level are placed in the appropriate 6000 - level courses. The Mathematics Qualifying Exam is based on the two-semester sequence Advanced Calculus MATH6001-6002 and the one semester course Abstract Linear Algebra MATH6003. 

All PhD students must pass four preliminary examinations. Each Preliminary Exam is offered twice a year. Examinations based on a course given during Fall Semester are offered after the end of Spring Semester and at the beginning of the following Fall Semester. Examinations based on a course given during the Spring Semester are offered at the beginning of the Fall Semester and at the beginning of the following Spring Semester.

After the preliminary examinations, an advanced examination in the area of examination of the student is required. An advanced exam may either be a written exam, a presentation or a series of presentations. The exam will be administered by a committee. Generally, this committee will form the students’ dissertation committee.

Visit the curriculum guide to learn about the required courses. More details concerning the requirements of the program are explained in the Mathematical Sciences Department’s Graduate Handbook. See the course descriptions for information on the content.

About Cincinnati

Cincinnati is a big city with a small-town feel. The cost of living is low, but the quality of life is high.  Forbes named Cincinnati the #5 most affordable city and the #9 best city for raising a family. Cincinnati has ranked the best place to live in Ohio by U.S. News & World Report, also the fourth-best city in the country for parks. UC is home to over 10,500 graduate students, 20% of which are international students.


For further information, please contact the Graduate Program Director, Dr. Robert Buckingham:

See the full list of our graduate programs