Applied and Computational Mathematics

The Applied and Computational Mathematics (ACM) Master's program provides graduate-level education in applied mathematics. The program develops the principles of applied mathematics and statistics, and provides students with the skills to employ those principles in industrial or scientific settings. It has three central themes: general principles and theories of applied mathematics and statistics, the construction and analysis of mathematical and statistical models, and the development and efficient execution of computational mathematical algorithms. Effective use of advanced applied mathematical techniques has become increasingly important in industrial and scientific settings as the amount of sophisticated simulation software and specialized open-source packages has greatly increased. Professionals are needed to assist engineers, scientists and managers in the precise formulation of complex problems and in selecting the analytical methods and software appropriate for their solutions. These professionals should understand the algorithms underlying mathematical software and be able to implement additional mathematical algorithms knowledgeably and efficiently in the framework of existing software. Finally, these professionals need to interpret the results of computations for others. It is the goal of the program to equip students with these skills so that they will become professionals in the needed fields.

The Program

The key components of this evening/late-afternoon program involve the integration of applied mathematics, mathematical modeling, numerical analysis and statistics. The ACM program provides not only coursework in various areas of applied mathematics, but also opportunities for independent or collaborative work. These approaches to learning contribute to a student’s outlook and depth of understanding. The program supports the development and enhancement of students’ skills in high-demand industrial and scientific careers, and in other careers that primarily focus on applied mathematics. It is geared toward three groups of prospective students: 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, and recent graduates who desire a deeper understanding of applied mathematics to help in launching a career. 

Admission and Prerequisites

Admission to the ACM program as a regular student requires a B.A. or a B.S. degree in mathematics, statistics, computer and information science, engineering, a physical science or a life science, earned in a program at an accredited institution with an average grade of B or better. Individuals with degrees in other fields not listed above or with grades less than a B average may be considered for conditional admission and may be required to submit evidence of potential for success in the ACM program. An entering student must have completed three courses in Calculus, including multivariate Calculus, plus an introductory course in Linear Algebra (or a combined course in Differential Equations with Linear Algebra) and an introductory course in Probability or Statistics. In exceptional cases, an applicant may be admitted without some prerequisite courses. If an applicant is admitted to the program without some prerequisite courses, the applicant must make up the missing prerequisites after entrance to the Graduate Program. However, credits received in courses elected to make up the missing prerequisites do not count toward the degree.

See the application instructions for information in how to apply

A complete application consists of the following:

  1. Official transcripts from all universities and colleges attended.
  2. A one-page statement of purpose stating the applicant’s career goals and personal objectives in pursuing the program.
  3. Two letters of recommendation are required. At least one letter must address the applicant's academic background.
  4. Students whose native language is not English are also required to satisfy the English Language Requirements for Admission which can be found in the General Information section of this catalog.

For more information, visit the ACM website or call 313-583-6321.

Undergraduate students admitted to the Applied and Computational Mathematics 4+1 option may count 16 credits in the graduate program toward their undergraduate Mathematics degree. At least one additional year of graduate work after completing their undergraduate degree would be needed to complete the rest of the ACM's degree requirements. Undergraduate students interested in the 4+1 option are strongly encouraged to apply in their sophomore year and start the program in their junior year.

Advanced Standing

Up to 9 credit hours, or their equivalent,  toward the degree may be granted by the Graduate Program Committee to a student through the transfer of credit for approved graduate-level courses. These courses must have been completed within the past five years with a grade of B or better at an accredited institution with graduate degree programs and not have been applied in whole or in part toward another degree or certificate. 

Graduate credit may be transferred from other University of Michigan campuses (Flint or Ann Arbor) for up to half of the credits required for the degree.

Major Requirements

Minimum of 30 semester hours of graduate course work with a cumulative grade point average of B or better.

The minimum of 30 hours must be selected from approved courses listed below and be approved by the student's graduate advisor. At least 15 credit hours of the courses must be in Mathematics and Statistics. 

Undergraduate students admitted to the Applied and Computational Mathematics 4+1 option may count 16 credits in the graduate program toward their undergraduate Mathematics degree.

In addition to the specific degree requirements listed here, the general Master's degree policies and requirements also apply. 

Core Courses
All of the following are required (9 credits):
MATH 525Statistical Inference 1,23
or STAT 530 Applied Regression Analysis
MATH 562Mathematical Modeling 13
MATH 572Introduction to Computational Mathematics 13
Total Credit Hours9

Electives
Select four courses from the following (12-13 credits):12-13
Dynamical Systems 3
Stochastic Processes 1
Applied Linear Algebra 1
Statistical Inference 1
Advanced Calculus 1
Fourier Series and Boundary Value Problems 2
Functions of a Complex Variable with Applications 2
Applied Regression Analysis 2
Machine Learning and Computational Statistics 2
Design and Analysis of Experiments 2
Time Series Analysis 2,3
Total Credit Hours12-13
1

Students enrolled in the 4+1 option can double count Math 520, MATH 523, MATH  525, MATH 551, Math 562, and Math 572 toward both undergraduate math degree and ACM degree.

2

Students enrolled in the 4+1 option can double count toward both undergraduate math degree and ACM degree one course from Math 554 and Math 555, and one course from Stat 530, STAT 531, Stat 540, and Stat 560. Alternatively, two courses from Stat 530, STAT 531, Stat 540, and Stat 560 can be double counted.

3

Offered infrequently.

 
 
Independent Research Project
Three credits from one of the following:3
Independent Research Project
Independent Research Project
Total Credit Hours3
Cognate Courses
Two courses or 6 credit hours of cognates outside the Department of Mathematics and Statistics should be selected from the list of preapproved courses below. Some of these courses have additional prerequisites. Other cognates are possible with the approval of the graduate director 46
Computer and Information Science
Algorithm Analysis and Design
Introduction to Natural Language Processing
Computer Graphics and Visual Computing
Computer Networks
Text Mining and Information Retrieval
Advanced Networking and Distributed Systems
Computer and Network Security
Data Security and Privacy
Advanced Computer Graphics
Information Visualization with Parallel Computing
Software Engineering
Database Systems
Introduction to Big Data
Electronic Commerce
Data Mining
Advanced Data Mining
Object Oriented Systems Design
Compiler Design
Software Engineering Mgmt
Artificial Intelligence
Deep Learning
Advanced Artificial Intelligence
Advanced Data Management
Advanced Information Visualization and Virtualization
Research Advances in Data Management
Economics
Introduction to Econometrics
Electrical and Computer Engineering
Math Mthds for Elec & Comp Eng
Analytic and Comp Math
Intro to Multimedia Sys
Interactive Media
Multimedia Secur & Forensics
Cloud Computing
Data Mining
Intr to Pwr Mgmt & Reliability
Intro Robot Syst
Fuzzy Systems
Intro. to CPS Security
Stochastic Processes
Modern Control Theory
Digital Control Systems
Nonlinear Control Systems
Intelligent Systems
Digital Signal Processing
Artificial Neural Networks
Pat Rec & Neural Netwks
Pattern Recognition
Multidimen Digital Signal Proc
Optimal Control Systems
Industrial and Manufacturing Systems Engineering
Models of Oper Research
Optimization
Probability & Statistical Mod
Design and Analysis of Exp
Multivariate Statistics
Managerial Decision Analysis
Data Management
Applied Data Analytics and Modeling for Enterprise Systems
Reliability Analysis
Big Data Aanal & Visuliztn
Advanced Optimization
Advanced Stochastic Processes
Management
Prescriptive Business Analytics
Operations Management
Supply Chain Analytics
Mechanical Engineering
Finite Element Methods
Advanced Engineering Analysis
Computational Fluid Mechanics and Heat Transfer
Physics
Electricity & Magnetism
Quantum Mechanics
Total Credit Hours6
4

Exceptions can be made to use a course not from the above list as a cognate course. For such an exception, the student is required to receive an approval from the ACM Program Advisor by petition prior to registering the course. 

Learning Goals

  1. Comprehension of the principles and theories of applied mathematics and statistics.
  2. Skill in the construction and analysis of mathematical models.
  3. Skill in the analysis and development of efficient computational mathematical algorithms
  4. Ability to apply the first three items in industrial and scientific settings.