## The department of Mathematics and Statistics at University of Michigan-Dearborn currently offers a Master of Science Degree in Applied and Computational Mathematics.

The key components of this evening program involve the integration of applied mathematics, mathematical modeling and numerical analysis.

## More about the program

Effective use of advanced mathematical techniques has become more important in industrial settings in recent years owing to the fact that the applications of industry are addressed by implementing algorithms on the computer rather than by hand. The demand has increased for people who understand what algorithms do and how to implement mathematical algorithms knowledgeably and efficiently. The efficiency of an algorithm and of its implementation are issues which are often of major interest within a company. In-depth knowledge concerning this issue on the part of an employee or job applicant can increase greatly that individual’s value and ability to contribute. More generally, the skill of making advanced mathematical methods accessible is of increasing value both for research and for industrial applications. Development of skills in these areas is the primary purpose of the Master’s Degree Program in Applied and Computational Mathematics.

Provide graduate-level education in applied mathematics in order to develop comprehension of principles of applied mathematics and skills in employing those principles in industrial or scientific settings.

### Themes

- General principles and theories of applied mathematics.
- Construction and analysis of mathematical models.
- Development and efficient execution of computational mathematical algorithms.
- Opportunities for independent or collaborative work.

- Individuals in established careers who want or require further training for their current positions.
- Individuals in the workforce who wish to retrain for new career directions, in some cases preparing for a more mathematically-oriented assignment with their current employer.
- Recent graduates who desire a deeper understanding of applied mathematics as an aid in launching a career.

1. 30 semester hours of graduate course work with a cumulative grade point average of B or better. The 30 hours must be selected from lists of approved courses and be approved by the student's graduate advisor. At least fifteen of the hours must be Mathematics and Statistics courses. Up to six credit hours toward the degree may be granted by the Graduate Program Committee to a student through the transfer of credit for approved graduate-level courses. Such courses must have been completed within the past five years with a grade of B or better at an accredited institution and not have been applied in whole or in part toward another degree or certificate.

In addition to the specific degree requirements listed here, the general Master's degree policies and requirements also apply. Note: Students admitted through Summer 2019 to the Applied and Computational Math graduate program fall under Rackham Graduate School Academic Policies.

2. One course from each of the following Core Areas A, B, and C. At most nine hours from these Core Areas may count toward the 30 hours. Equivalent courses taken elsewhere may be used to satisfy the requirement, but may not count toward the 30 hours (with the exception of the six hours specified in 1 above which may count toward the 30 hours).

A. Mathematical Analysis

i. MATH 551 Advanced Calculus I

ii. MATH 554 Fourier Series and Boundary Value Problems

iii. MATH 555 Complex Variables

B. Numerical Methods

i. MATH 572 Introduction to Numerical Analysis

ii. MATH 573 Matrix Computation

C. Modeling

i. MATH 562 Mathematical Modeling

3. At least four courses from the Modeling Specialization Areas listed below. Not all four may be from the same area. Equivalent courses taken elsewhere may be used to satisfy the requirement, but may not count toward the 30 hours (with the exception of the six hours specified in 1 above which may count toward the 30 hours).

A. Linear and Discrete Models

i. MATH 523 Linear Algebra with Applications

ii. STAT 530 Applied Regression Analysis

iii. MATH 558 Introduction to Wavelets

iv. MATH 573 Matrix Computation

B. Differential Models

i. MATH 504 Dynamical Systems

ii. MATH 514 Finite Difference Methods for Differential Equations

iii. MATH 516 Finite Element Methods for Differential Equations

iv. MATH 554 Fourier Series and Boundary Value Problems

C. Statistical Models

i. MATH 520 Stochastic Processes

ii. MATH 525 Mathematical Statistics II

iii. STAT 530 Applied Regression Analysis

iv. STAT 535 Data Analysis and Modeling

v. STAT 545 Reliability and Survival Analysis

vi. STAT 550 Multivariate Statistical Analysis

vii. STAT 560 Time Series

4. MATH 599, Independent Research Project, taken for three credits.

5. Six hours of cognates outside the Department of Mathematics and Statistics. The courses should be selected from an approved list (Appendix B).

The following courses count toward the degree. Many of these courses have prerequisites beyond those required for admission to the program. If a student has only the courses required for admission to the program, the following courses should be accessible: IMSE 500, ME 510, ME 518, DS 570, OM 521. If a student takes IMSE 500, then IMSE 505 should be accessible. If a student has taken a course in probability and statistics equivalent to IMSE 317, then the courses ECE 552, ECE 555, ECE 585 should be accessible.

1. Computer and Information Science

CIS 505 Algorithm Design and Analysis

CIS 515 Computer Graphics

CIS 527 Computer Networks

CIS 537 Advanced Networking

CIS 544 Computer and Network Security

CIS 551 Advanced Computer Graphics

CIS 552 Information Visualization and Multimedia Gaming

CIS 568 Data Mining

CIS 574 Compiler Design

CIS 575 Software Engineering Management

CIS 652 Information Visualization and Computer Animation

2. Economics

ECON 515 Introduction to Econometrics

3. Electrical and Computer Engineering

ECE 552 Fuzzy Systems

ECE 555 Stochastic Processes

ECE 560 Modern Control Theory

ECE 565 Digital Control

ECE 567 Non-linear Control Systems

ECE 585 Pattern Recognition

ECE 665 Optimal Control

4. Industrial and Manufacturing Systems Engineering

IMSE 500 Models of Operations Research

IMSE 505 Optimization

IMSE 510 Probability and Statistical Models

IMSE 511 Design and Analysis of Experiments

IMSE 514 Multivariate Statistics

IMSE 520 Managerial Decision Analysis

IMSE 567 Reliability Analysis

5. Management

DS 570 Management Science

OM 521 Operations Management

OM 660 Analysis and Design of Supply Chains

6. Mechanical Engineering

ME 510 Finite Element Methods

ME 518 Advanced Engineering Analysis

7. Physics

PHYS 503 Electricity and Magnetism

PHYS 553 Quantum Mechanics

8. Other graduate courses outside the Department of Mathematics and Statistics approved by the graduate advisor.