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**Andrew J. Christlieb, Chairperson**

Computational Mathematics, Science and Engineering is the multidisciplinary field that is concerned with the use of advanced computing capabilities to solve complex problems pertaining to computational modeling and data science. Among the areas of interest include the development and analysis of algorithms, high performance computing, including both parallel computing and heterogeneous architectures, and the application of both algorithms and high performance computing to modeling and data analysis, exploration, and visualization. The department offers a wide range of courses in computational and data science. Graduates will use their skills in large-scale computing and data science to address a wide variety of problems in science, engineering and other fields.

The Department of Computational Mathematics, Science and Engineering is administered jointly by the colleges of Natural Science, and Engineering.

The department offers a minor in Computational Mathematics, Science and Engineering. The minor is a minimum of 17 credits and builds up on the first two undergraduate CMSE courses, CMSE 201 and 202. The purpose of the minor is to teach students foundational concepts in computational modeling and data science, and to have them apply these to domain-specific challenges. Mastery of these subject areas are attained through a variety of courses offered by CMSE, augmented by discipline-specific courses and project-based work through other departments on campus. For additional information on the minor, see the Department of Computational Mathematics, Science and Engineering section in the College of Natural Science section of this catalog.

The Department of Computational Mathematics, Science and Engineering offers the programs listed below:

** Master of Science**

Computational Mathematics, Science and Engineering

** Doctor of Philosophy**

Computational Mathematics, Science and Engineering

** Graduate Certificate**

Computational Modeling

High-Performance Computing

Study for the department's graduate degree programs is administered by the College of Engineering.

The Master of Science degree in Computational Mathematics, Science, and Engineering provides students broad and deep knowledge of the fundamental techniques used in computational modeling and data science, as well as significant exposure to at least one application domain.

**Admission**

Admission to graduate study in computational mathematics, science, and engineering is primarily to the doctoral program. Under certain circumstances, the program may consider application for admission to the master’s degree program for students who wish to earn the master’s degree in preparation for the doctoral program in computational mathematics, science, and engineering, or another doctoral program, or in pursuit of other professional goals.

To be considered for admission to the master's degree, a student must:

- have a four-year bachelor’s degree in any area.
- have a strong interest in computational and/or data science.
- have taken course work in calculus through differential equations, and have a working knowledge of linear algebra, basic statistics, and basic numerical methods.
- be proficient in at least one programming language.

A total of 30 credits is required for the degree under either Plan A (with thesis) or Plan B (without thesis). The student’s program of study must be approved by the student’s guidance committee and must meet the requirements specified below.

Requirements for Both Plan A and Plan B |
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1. | Complete three of the following courses (9 credits): | ||||||||

CMSE | 820 | Mathematical Foundations of Data Science | 3 | ||||||

CMSE | 821 | Numerical Methods for Differential Equations | 3 | ||||||

CMSE | 822 | Parallel Computing | 3 | ||||||

CMSE | 823 | Numerical Linear Algebra, I | 3 | ||||||

Additional details on applicable course work can be found in the CMSE graduate handbook at www.cmse.msu.edu. |
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2. | Complete additional course work in one or more cognate areas chosen in consultation with the student’s guidance committee as specified in the CMSE graduate handbook at www.cmse.msu.edu. |
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3. | All students must complete Responsible Conduct of Research Training. | ||||||||

Additional Requirements for Plan A: |
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1. | The following course: | ||||||||

CMSE | 899 | Master’s Thesis Research | 4 to 8 | ||||||

2. | Successful completion and defense of a thesis based on original research on a problem in computational and/or data science. The thesis research will culminate in a written thesis to be submitted to, and accepted by, a guidance committee. An oral examination of the student’s work may be required. | ||||||||

Additional Requirements for Plan B: |
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1. | Completion of additional course work determined in consultation with the student’s guidance committee. | ||||||||

2. | Completion of a final examination or evaluation. |

The Doctor of Philosophy degree in Computational Mathematics, Science, and Engineering provides students broad and deep knowledge of the fundamental techniques used in computational modeling and data science, as well as significant exposure to at least one application domain, and to conduct significant original research in algorithms and/or applications relating to computational and data science.

**Admission**

Admission to graduate study in computational mathematics, science, and engineering is primarily to the doctoral program.

To be considered for admission to the doctoral degree, a student must:

- have a four-year bachelor’s degree in any area.
- have a strong interest in computational and/or data science.
- have taken course work in calculus through differential equations, and have a working knowledge of linear algebra, basic statistics, and basic numerical methods.
- be proficient in at least one programming language.

The student’s program of study must be approved by the student’s guidance committee and must meet the requirements specified below.

1. | Complete the following courses (12 credits): | ||||||||

CMSE | 820 | Mathematical Foundations of Data Science | 3 | ||||||

CMSE | 821 | Numerical Methods for Differential Equations | 3 | ||||||

CMSE | 822 | Parallel Computing | 3 | ||||||

CMSE | 823 | Numerical Linear Algebra, I | 3 | ||||||

Additional details on applicable course work can be found in the CMSE graduate handbook at www.cmse.msu.edu. | |||||||||

2. | Complete additional course work 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 guidance committee as specified in the CMSE graduate handbook at www.cmse.msu.edu. | ||||||||

3. | Complete at least 24 credits and no more than 36 credits of CMSE 999 Doctoral Dissertation Research. | ||||||||

4. | Pass a written or practical qualifying examination. | ||||||||

5. | Pass an oral or written comprehensive examination no less than six months before the defense of the student’s dissertation. | ||||||||

6. | Successfully defend the doctoral dissertation based on original research in algorithms pertaining to, or applications of computational and data science. | ||||||||

7. | All students must complete Responsible Conduct of Research Training. |

The Graduate Certificate in Computational Modeling is intended for students with interest in applying computational and data science approaches to their research problems, or who generally desire broad training in computational modeling and methodology.

**Requirements for the Graduate Certificate in Computational Modeling**

Students must complete a minimum of 9 credits from the following:

1. | Two of the following core courses (6 credits): | ||||||||

CMSE | 801 | Introduction to Computational Modeling | 3 | ||||||

CMSE | 802 | Methods in Computational Modeling | 3 | ||||||

CMSE | 820 | Mathematical Foundations of Data Science | 3 | ||||||

CMSE | 821 | Numerical Methods for Differential Equations | 3 | ||||||

CMSE | 822 | Parallel Computing | 3 | ||||||

CMSE | 823 | Numerical Linear Algebra I | 3 | ||||||

2. | One or more additional courses selected from the following: | ||||||||

AST | 911 | Numerical Techniques in Astronomy | 2 | ||||||

CEM | 883 | Computational Quantum Chemistry | 3 | ||||||

CEM | 888 | Computational Chemistry | 3 | ||||||

CMSE | 801 | Introduction to Computational Modeling | 3 | ||||||

CMSE | 802 | Methods in Computational Modeling | 3 | ||||||

CMSE | 820 | Mathematical Foundations of Data Science | 3 | ||||||

CMSE | 821 | Numerical Methods for Differential Equations | 3 | ||||||

CMSE | 822 | Parallel Computing | 3 | ||||||

CMSE | 823 | Numerical Linear Algebra I | 3 | ||||||

CSE | 836 | Probabilistic Models and Algorithms in Computational Biology | 3 | ||||||

CSE | 845 | Multi-disciplinary Research Methods for the Study of Evolution | 3 | ||||||

CSE | 881 | Data Mining | 3 | ||||||

ECE | 837 | Computational Methods in Electromagnetics | 3 | ||||||

ME | 835 | Turbulence Modeling and Simulation | 3 | ||||||

ME | 840 | Computational Fluid Dynamics and Heat Transfer | 3 | ||||||

ME | 872 | Finite Element Method | 3 | ||||||

MTH | 451 | Numerical Analysis I | 3 | ||||||

MTH | 452 | Numerical Analysis II | 3 | ||||||

MTH | 850 | Numerical Analysis I | 3 | ||||||

MTH | 851 | Numerical Analysis II | 3 | ||||||

MTH | 852 | Numerical Methods for Ordinary Differential Equations | 3 | ||||||

MTH | 950 | Numerical Methods for Partial Differential Equations I | 3 | ||||||

MTH | 951 | Numerical Methods for Partial Differential Equations II | 3 | ||||||

MTH | 995 | Special Topics in Numerical Analysis and Operations Research | 3 to 6 | ||||||

PHY | 480 | Computational Physics | 3 | ||||||

PHY | 915 | Computational Condensed Matter Physics | 2 | ||||||

PHY | 919 | Modern Electronic Structure Theory | 2 | ||||||

PHY | 950 | Data Analysis Methods for High-Energy and Nuclear Physics | 2 | ||||||

PHY | 998 | High Performance Computing and Computational Tools for Nuclear Physics | 2 | ||||||

PLB | 810 | Theories and Practices in Bioinformatics | 3 | ||||||

QB | 826 | Introduction to Quantitative Biology Techniques | 1 | ||||||

STT | 461 | Computations in Probability and Statistics | 3 | ||||||

STT | 465 | Bayesian Statistical Methods | 3 | ||||||

STT | 802 | Statistical Computation | 3 | ||||||

STT | 874 | Introduction to Bayesian Analysis | 3 | ||||||

Courses used to fulfill requirement 1. may not be used to fulfill this requirement. Additional courses at the 400-level or above may be used to fulfill this requirement if approved by the CMSE graduate advisor. Students must have a minimum 3.0 grade-point average in courses applied to the certificate in order for it to be awarded. |

The Graduate Certificate in High-Performance Computing is intended for students with interest in applying computational and data science approaches that require parallel and/or high-performance computing to their research problems, or who generally desire broad training in parallel computational methodology.

**Requirements for the Graduate Certificate in High-Performance Computing**

Students must complete a minimum of 9 credits from the following:

1. | The following core course (3 credits): | ||||||||

CMSE | 822 | Parallel Computing | 3 | ||||||

2. | Two or more additional courses selected from the following: | ||||||||

AST | 911 | Numerical Techniques in Astronomy | 2 | ||||||

CEM | 883 | Computational Quantum Chemistry | 3 | ||||||

CEM | 888 | Computational Chemistry | 3 | ||||||

CSE | 836 | Probabilistic Models and Algorithms in Computational Biology | 3 | ||||||

CSE | 845 | Multi-disciplinary Research Methods for the Study of Evolution | 3 | ||||||

CSE | 881 | Data Mining | 3 | ||||||

ECE | 837 | Computational Methods in Electromagnetics | 3 | ||||||

ME | 835 | Turbulence Modeling and Simulation | 3 | ||||||

ME | 840 | Computational Fluid Dynamics and Heat Transfer | 3 | ||||||

ME | 872 | Finite Element Method | 3 | ||||||

MTH | 850 | Numerical Analysis I | 3 | ||||||

MTH | 851 | Numerical Analysis II | 3 | ||||||

MTH | 852 | Numerical Methods for Ordinary Differential Equations | 3 | ||||||

MTH | 950 | Numerical Methods for Partial Differential Equations I | 3 | ||||||

MTH | 951 | Numerical Methods for Partial Differential Equations II | 3 | ||||||

MTH | 995 | Special Topics in Numerical Analysis and Operations Research | 3 to 6 | ||||||

PHY | 915 | Computational Condensed Matter Physics | 2 | ||||||

PHY | 919 | Modern Electronic Structure Theory | 2 | ||||||

PHY | 950 | Data Analysis Methods for High-Energy and Nuclear Physics | 2 | ||||||

PHY | 998 | High Performance Computing and Computational Tools for Nuclear Physics | 2 | ||||||

PLB | 810 | Theories and Practices in Bioinformatics | 3 | ||||||

QB | 826 | Introduction to Quantitative Biology Techniques | 1 | ||||||

STT | 802 | Statistical Computation | 3 | ||||||

STT | 874 | Introduction to Bayesian Analysis | 3 | ||||||

Additional courses at the 800-level or above may be used to fulfill this requirement if approved by the CMSE graduate advisor. Students must have a minimum 3.0 grade-point average in courses applied to the certificate in order for it to be awarded. |