# PhD program details

### Expected student background

Students who wish to pursue a PhD in Computational Mathematics, Science and Engineering should have a four-year bachelor's degree in any area of science and engineering, and have a strong interest in computational and/or data science. In terms of mathematical background, students are expected to have taken courses in calculus through differential equations, and to have a working knowledge of linear algebra and basic statistics. In addition, students are expected to be proficient in at least one commonly-used programming language (such as C, C++, Java, Fortran, or Python) and to have knowledge of basic numerical methods (at the level of CMSE 802). Profiles of successful domestic and international applicants can be found at the bottom of this page.

### The PhD program

Students pursuing a Doctorate of Philosophy in Computational Mathematics, Science and Engineering must fulfill several requirements pertaining to both coursework and research, as detailed in the CMSE graduate handbook. These requirements include:

- Demonstrate competency in the following subject areas by passing a subject exam in each topic:
- The mathematical foundations of data science (e.g., CMSE 820, 3 credits)
- Numerical methods for differential equations (e.g., CMSE 821, 3 credits)
- Methods for parallel computing (e.g., CMSE 822, 3 credits)
- Numerical methods for linear algebra (e.g., CMSE 823, 3 credits)

- Complete coursework to total a minimum of 30 credits beyond the bachelor's degree in one or more cognate areas chosen in consultation with the student's dissertation committee. Typically, courses at the 800 level and above will fulfill this requirement.
- Complete a minimum of 24, and maximum of 36, dissertation research credits (CMSE 999).
- Pass a comprehensive examination that tests students' understanding of their chosen area of specialization, their ability to communicate scientific methods and results in written and oral form, and their ability to construct a realistic and detailed plan of research for their dissertation. This examination must be passed no less than six months before the defense of the student’s dissertation.
- Meet annually with their dissertation committee to report on progress and receive guidance. This annual meeting must include a written annual report.
- Complete and orally defend a dissertation based on original research in algorithms pertaining to, and/or applications of, computational and/or data science.
- Complete Responsible Conduct of Research training.

CMSE doctoral students are expected to form a dissertation committee by the end of their first year in the graduate program; given the flexibility inherent in this PhD program, the purpose of this committee is to assist students in determining a coherent set of coursework in addition to providing guidance regarding their research activities.

### Profiles of successful applicants

- A general profile of successful domestic applicants is as follows:
- Highly ranked in their bachelor's class.
- An overall GPA of 3.5 or better.
- GRE (general) scores are generally above 159 for the quantitative portion. GRE Verbal scores less than 146 and Analytical scores less than 3.0 will generally not be considered acceptable.

- A general profile of successful international applicants is as follows:
- Graduate of a highly ranked school.
- In the upper 10% of their class.
- TOEFL scores of a total of 80 or higher (19 in each category except Writing which is 22), or an IELTS score of 6.5 or higher.
- GRE (general) scores are generally above 159 for the quantitative portion. GRE Verbal scores less than 146 and Analytical scores less than 3.0 will generally not be considered acceptable.

Instructions on how to apply to the CMSE PhD program can be found here. If you have any questions, please email the CMSE Graduate Director.