## Required Core Courses (18 credit hours):

A student will need to pass all required core and elective courses in the respective specialization with at least a grade of **C-** by the end of the Spring Semester of the second year. The total credits earned from required core and elective courses must be at least **30** credit hours. Independent studies, group studies, and research credit hours or hours from unapproved courses not on the lists below do not count towards the required 30 hours of course work.

### Mathematics

**MATH 5401**(3 cr. hrs.) Applied Differential Equations I**MATH 5402**(3 cr. hrs.) Applied Differential Equations II**MATH 5601**(3 cr. hrs.) Essentials of Numerical Methods**MATH 5602**(3 cr. hrs.) Computational Partial Differential Equations**MATH 5603**(3 cr. hrs.) Numerical Linear Algebra**MATH 5168**(3 cr. hrs.) Introduction to the Finite Element Method (cross-listed**CIVILEN 5168**/**MECHENG 5068**)

### Allowed Substitutions of Required Courses:

The following substitutions of required core course sequences are allowed with permission of the advisor.

**MATH 5401**&**5402**may be replaced by**MATH 6411**&**6451****MATH 5601**may be replaced by**MATH 6602****MATH 5602**may be replaced by**MATH 7611**&**7612**

A student may request additional substitutions of required core courses. The request should be submitted by the advisor to the Graduate Studies Committee (GSC) for approval.

## Summer Project:

## Elective Courses (12 credit hours):

At least three elective courses must be chosen from the list below and must add up to at least 12 credit hours. At least two electives must be from the same sub-specialization listed below. A student may request to use other courses to satisfy the elective requirement. The request should be submitted by the advisor to the Graduate Studies Committee (GSC) for approval.

### Computational Methods

**MATH 7611**(3 cr. hrs.) Computational Partial Differential Equations I**MATH 7612**(3 cr. hrs.) Computational Partial Differential Equations II**CSE 5441**(3 cr. hrs.) Introduction to Parallel Computing**CSE 5449**(2 cr. hrs.) Intermediate Studies in Parallel Computing**MATH 8610**(3 cr. hrs.) Topics in Applied Mathematics

### Computational Electromagnetics (Electrical & Computer Engineering)

**ECE 5510**(3 cr. hrs.) Introduction to Numerical Methods for Electromagnetics**ECE 6010**(3 cr. hrs.) Electromagnetic Field Theory I**ECE 7010**(3 cr. hrs.) Electromagnetic Field Theory II**ECE 7011**(3 cr. hrs.) Computational Electromagnetics

### Computational Fluid Dynamics & Aerodynamics (Aeronautical & Astro Engineering)

**AAE 5615**(3 cr. hrs.) Introduction to Computational Aerodynamics**AAE 5771**(3 cr. hrs.) Viscous Fluid Flow: Laminar and Transitional**AAE 8802**(3 cr. hrs.) Advanced Mathematical Methods in Engineering**AAE 8873**(3 cr. hrs.) Computational Fluid Dynamics

### Signal Processing (Electrical & Computer Engineering)

**ECE 5200**(3 cr. hrs.) Introduction to Digital Signal Processing**ECE 6200**(3 cr. hrs.) Digital Signal Processing**ECE 5602**(3 cr. hrs.) Medical Imaging**ECE 5460**(3 cr. hrs.) Digital image processing**ECE 6202**(3 cr. hrs.) Stochastic Digital Signal Processing

### Algorithms & Graphics (Computer Science & Engineering)

**CSE 5331**(2 cr. hrs.) Foundations II: Data Structures and Algorithms**CSE 5339**(2 cr. hrs.) Intermediate Studies in Algorithms**CSE 6331**(3 cr. hrs.) Algorithms**CSE 6332**(3 cr. hrs.) Advanced Algorithms**CSE 6333**(3 cr. hrs.) Distributed Algorithms**CSE 5541**(3 cr. hrs.) Computer Animation**CSE 5543**(3 cr. hrs.) Geometric Modeling**CSE 5544**(3 cr. hrs.) Introduction to Scientific Visualization**CSE 5545**(3 cr. hrs.) Advanced Computer Graphics

### Computational Mechanics (Mechanical Engineering)

**MECHENG 6505**(3 cr. hrs.) Intermediate Fluid Dynamics**MECHENG 7511**(3 cr. hrs.) Computational Fluid Dynamics**MECHENG 6507**(3 cr. hrs.) Intermediate Numerical Methods**MECHENG 7518**(3 cr. hrs.) Advanced Mathematical Methods in Mechanical Engineering

## Thesis:

By the end of the Autumn Semester of the second year each student must select a thesis advisor, and submit a Change of Advisor Form to the Math Graduate Office. The thesis advisor needs to be a mathematics department faculty member of category M level or higher. Typically (but not necessarily) this is the mathematics mentor for the summer project. Thesis research and writing will occur during the second year, and should be completed at the end of the Spring Break of the second year. During this time students should generally be signed up for **MATH 6999** with the supervising Master's Faculty Advisor (Thesis).

**MATH 6999**(1 + cr. hrs.) Graduate Thesis Research

## Thesis Defense & Graduation:

The thesis will be written during the second year under the supervision of the thesis advisor, and prepared in compliance with university rules. The thesis should be completed early during the spring semester. All students are expected to apply to graduate with Masters of Mathematical Sciences (MMS) degree via the Thesis-Option before the second Friday of the Spring Semester of their second year with the Graduate School. In order to apply a student also has to choose a second member of the examination committee by the beginning of the same semester. This has to be a Graduate Faculty member but may be from anther OSU unit related to the specialization. Typically (but not necessarily) this can be the second mentor of the summer project. The Non-thesis Option is not open to MMS students. The oral examination has to be scheduled and passed during the Spring Semester of the second year, after submission of a draft of the thesis. An additional written examination is not required. The thesis needs to follow university formatting guidelines, be approved by the committee, and be submitted to the Graduate School and OhioLink.

For further details see Section VI of the Graduate School Handbook.

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