# Computational Science, Ph.D.

**John Wallin, Program Director**

(615) 494-7735

John.Wallin@mtsu.edu

www.mtsu.edu/COMS

The Ph.D. in Computational Science is an interdisciplinary program in the College of Basic and Applied Sciences and includes faculty from Agriculture, Biology, Chemistry, Computer Science, Engineering Technology, Geosciences, Mathematical Sciences, and Physics and Astronomy. This program is research intensive and applied in nature, seeking to produce graduates with competency in the following three key areas:

- mastery of the mathematical methods of computation as applied to scientific research investigations coupled with a firm understanding of the underlying fundamental science in at least one disciplinary specialization;
- deep knowledge of programming languages, scientific programming, and computing technology so that graduates can adapt and grow as computing systems evolve; and
- skills in effective written and oral communication so that graduates are prepared to assume leadership positions in academia, national labs, and industry.

### Admission Requirements

Admission to the Doctor of Philosophy in Computational Science program is based on a comprehensive assessment of a candidate's qualifications including Graduate Record Examination (GRE) scores, undergraduate and graduate grade point average, and letters of recommendation.

Applicants who do not meet these minimums but whose application materials indicate high potential for success may be admitted conditionally. Such students must meet the conditions of their admission in the time stated to be fully admitted to the program of study.

### Application Procedures

*All application materials are to be submitted to the College of Graduate Studies.*

The application deadline is February 15 for those wishing to be considered for graduate assistantships for the following Fall. Late applications may be considered, but admission and financial support in the form of an assistantship are not guaranteed.

Applicant must

- submit an application with the appropriate application fee (online at
**www.mtsu.edu/graduate/apply.php**). Once this initial application has been accepted, the applicant will receive directions on how to enter the graduate portal to be able to submit other materials. - submit official scores for the verbal, quantitative, and analytical writing measures of the GRE that indicate potential for success in the Computational Science program. The GRE is an important measure and is given significant consideration in the admissions review process. Successful applicants typically have Verbal and Quantitative scores at or above the 50th percentile for persons intending graduate study in science with a combined V + Q score exceeding 297;
- submit official transcripts showing a GPA in previous academic work that indicates potential for success in advanced study. Successful applicants typically have a minimum 3.50 GPA in their graduate work or a minimum 3.00 GPA when entering with a bachelor's degree. Applicants should hold a bachelor's, master's, or doctoral degree in a science discipline;
- provide letters of recommendation from at least three professors or professionals that address the applicant's potential to successfully complete a Ph.D. in the Computational Science program.

It is also strongly recommended that prospective students submit a one-page statement of their background and research interests as part of the application. The statement should include a short summary of experience in mathematics, computer programming, and in science along with the types of problems they hope to work on when they join the program.

### Degree Requirements

The Ph.D. in Computational Science requires completion of a minimum of 72 semester hours.

In order to satisfy the minimum requirements for the degree, students must successfully

- complete 48 hours of approved graduate core coursework composed of foundation, core, and elective courses;
- complete 12 hours of directed research;
- complete the qualifying exam before the end of the second year in the program;
- complete 12 hours of dissertation research;
- make at least two research presentations at regional, national, or international meetings as the lead or coauthor;
- serve as lead author or make significant contributions of two articles published, in press, or under review in high quality, peer-reviewed journals;
- make a significant contribution to the development of at least one external grant proposal in collaboration with an MTSU faculty member serving as principal investigator;
- complete a dissertation, including the final oral defense.

### Curriculum: Computational Science

The following illustrates the minimum coursework requirements. In addition, a maximum of 24 hours of directed research and a maximum of 24 hours of dissertation research may be applied to degree requirements.

### Foundation Courses (11 hours)

### COMS 6100 - Fundamentals of Computational Science

**3credit hours**

Prerequisite: Admission to the Computational Science Ph.D. program or permission of instructor. Foundational overview of the mathematical and scientific underpinnings of computational science. Introduces the principles of finding computer solutions to contemporary science challenges. Offers preparation for core and elective courses in the Ph.D. program in Computational Science by reviewing essential mathematical methods and basic science principles drawn from biology, chemistry, and physics. Special topics include techniques of high performance computing and applications, parallel systems, and theory of computation, case studies in computational chemistry, physics, and mathematical biology.

### COMS 6500 - Fundamentals of Scientific Computing

**4credit hours**

Prerequisite: Graduate standing or permission of instructor. Fundamentals of problem solving approaches in computational science, including computer arithmetic and error analysis, linear and nonlinear equations, least squares, interpolation, numerical differentiation and integration, optimization, random number generations and Monte Carlo simulation. Students will gain computational experience by analyzing case studies using modern software packages such as MATLAB.

### CSCI 6050 - Computer Systems Fundamentals

**4credit hours**

Prerequisite: CSCI 6020 or COMS 6100 with minimum grade of B or equivalent. Advanced introduction to computer systems. Data representations, computer arithmetic, machine-level representations of programs, program optimization, memory hierarchy, linking, exceptional control flow, virtual memory and memory management, basic network concepts, and basic concurrent concepts and programming. Three hours lecture and two hours lab.

### Computational Science Core (19-21 hours)

### CSCI 6330 - Parallel Processing Concepts

**3credit hours**

Prerequisites: [CSCI 3130 and either (CSCI 3240 or CSCI 3250)] or CSCI 6050 and a working knowledge of either C or C++. Parallel processing and programming in a parallel environment. Topics include classification of parallel architectures, actual parallel architectures, design and implementation of parallel programs, and parallel software engineering.

### COMS 7800 - Teaching Internship

**3credit hours**

Designed for graduate students in Computational Science in order to develop better classroom skills and to build an understanding that good teaching practices can be learned and continuously improved. S/U grading.

### COMS 7950 - Research Seminar in Computational Science

**1credit hours**

Prerequisite: Admission to the Computational Science Ph.D. program or permission of instructor. Seminar course to build a broader understanding of problems and research topics in computational science through advanced reading of selected journal articles, group discussion, and presentations by both external and internal speakers in computational science.

### COMS 7900 - Computational Science Capstone

**4credit hours**

Prerequisites: COMS 6500 and CSCI 6330 or permission of instructor. Requires students to apply advanced computing and mathematics to solve problems in natural and applied sciences. Students expected to apply parallel computing, advanced simulation and data mining techniques to solve a research problem in collaboration with advisor. Course co-taught by two faculty members from different departments. Final presentations open to students, faculty, and visitors.

### COMS 7100 - Applied Computational Science

**4credit hours**

Prerequisite: Consent of instructor. Intense lecture and practice-based course in computational methods, with a research program offered. Possible topics include computational aspects of linear algebra; contemporary numerical methods (finite difference-based and boundary integral equation-based) for solving initial and boundary value problems for ordinary and partial differential equations arising in engineering, natural sciences, and economics and finance.

### COMS 7300 - Numerical Partial Differential Equations

**4credit hours**

Prerequisite: COMS 6500 or permission of instructor. Numerical methods for solving ordinary and partial differential equations, partial differential integral equations, and stochastic differential equations. Convergence and stability analyses, finite difference methods, finite element methods, mesh-free methods and fast Fourier transform also included.

OR

### CSCI 7350 - Data Mining

**3credit hours**

Prerequisite: Fundamental courses in the Computational Science Ph.D. program and CSCI 6020 or equivalent or consent of instructor. Introduction to concepts, theories, techniques, issues, and applications of data mining. Data preprocessing, association rule analysis, classification analysis, cluster and outlier analysis, deviation detection, statistical modeling, consideration of emergent technologies.

### STAT 7400 - Computational Statistics

**3credit hours**

Prerequisites: COMS 6100 and MATH 2530 or equivalent. Statistical visualization and other computationally intensive methods. The role of computation as a fundamental tool of discovery in data analysis, statistical inference, and development of statistical theory and methods. Monte Carlo studies in statistics, computational inference, tools for identification of structure in data, numerical methods in statistics, estimation of functions (orthogonal polynomials, splines, etc.), statistical models, graphical methods, data fitting and data mining, and machine learning techniques.

### Electives (16-18 hours)

Electives may come from departmental master's degree programs and the COMS program.

### COMS 7840 - Selected Topics in the Natural and Applied Sciences

**3credit hours**

Selected topics in the natural and applied sciences for Computational Science students. Provides an opportunity to study applications of computational techniques to real world problems and enhance the domain knowledge of students within the program. Rotating topics may include computational chemistry, computational physics, and computational biology.

### COMS 7700 - Advanced Concepts in Computational Science

**3 or 4credit hours**

Advanced topics and protocols specific to different subdivisions of computational science not covered in core or elective courses offered through the program. Students will work under the direct supervision of the instructor. Lecture and/or laboratory components. May be repeated for 6 to 8 credit hours.

- Other electives
**10 to 12 credit hours**

### Directed Research (12-24 hours)

Students must complete 12 hours of directed research before advancement to candidacy. Student may not take more than 6 credit hours of directed research per semester.

**Note:** No more than 24 hours of directed research may be applied toward degree requirements.

### COMS 7500 - Directed Research in Computational Science

**1 to 6credit hours**

For Ph.D. students prior to advancement to candidacy. Selection of a research problem, review of pertinent literature, protocol design, collection and analysis of data, and preparation of results for publication. S/U grading.

### Dissertation (12-24 hours)

**Note:** No more than 24 hours of dissertation research may be applied toward degree requirements.

### COMS 7640 - Dissertation Research

**1 to 6credit hours**

Prerequisite: Advancement to candidacy within the Computational Science Ph.D. program. Involves the student working with their research advisor on any of the aspects of the Ph.D. dissertation from the selection of research problem, a review of the pertinent literature, formulation of a computational approach, data analysis, and composition of the dissertation.

### Program Notes

Applicants holding a master's degree will be expected to have earned at least 21 semester hours of graduate mathematics, science, or engineering credit with evidence of strong mathematical skills and experience in computation through coursework, employment, and/or research experiences. Applicants applying from the baccalaureate level must have an appropriate science degree with evidence of strong mathematical skills and experience in computation through coursework, employment, and/or research experiences.

Students entering with a master's degree in a mathematical, science, or engineering discipline may, on the recommendation of the program coordination committee and with the approval of the graduate dean, have up to 12 credit hours accepted from their master's if it directly corresponds to coursework in the Computational Science curriculum. Students who are interested in pursuing a Master's Degree in Mathematics or Computer Science while pursuing their Ph.D. will need to consult with the program director and the respective departments to understand the additional requirements.

Applicants lacking necessary foundational coursework in previous degrees will be required to complete some remedial courses as part of their program of study in addition to the degree requirements.