Applied Mathematics Master's Program

Note: The Applied Math Master's Program is not to be confused with AIM – information on AIM can be found here.

Counseling

Applied MS Math students will receive course counseling from the MS Chair. The Graduate Program Coordinator will process departmental and Rackham paperwork. Information about minimum credits, cross-listed courses, and other matters can be found in this Course Enrollment section of the Graduate Student Handbook. Students interested in a dual degree are advised to consult Rackham’s policies for dual degree programs and double counting of credit hours.

These requirements are in force from 06-14-2021. All earlier discussions with the counselor will continue to be accepted.

Requirements

There are two options in this program. One option is a program concentrating in classical applied mathematics, differential equations, and/or numerical analysis and scientific computing; the second focuses on the mathematics of optimization, or on stochastic processes. Each option has a minimum requirement of twenty-four credit hours of coursework that includes two cognate courses. In addition, a program under the first option must satisfy conditions 1, 2 and 3, and a program under the second option must satisfy conditions, 1, 2* and 3.

1.  The program must include Math 420 and 452 or substitutes approved by the counselor. The following classes are generally approved as substitutes for Math 420: Math 481, 565, 566, 582, 593, 594. The following classes are generally approved as substitutes for Math 452: Math 525, 526, 551, 555, 575, 596, 597. The program must also include one course at the 500 level not in analysis (including probability) or classical applied mathematics such as Math 565, 566, 567, 575, 582, 590, 591, 592, 593, or 594, or a more advanced course approved by the counselor.
 

2.  The program must include five courses from Group A below. At least one of these five courses must be chosen from Group B. This part of the program can include at most two classes at the 400 level and must include at least two classes at the 500 level.

A: Math 420, 452, 481 or 582, 525, 526, 551, 555, 556, 557, 558, 565 or 566, 571, 572, 590 or 591 or 592, 593 or 594, 596, 597, 651, 652, 654, 655, 656, 658, 663, 671, 756, or other counselor approved courses.
B: Math 651, 654, 655, 656, 658, 671, 756.

2*. The program must include five courses from Group A* below. At least one of these courses must be chosen from Group B*. This part of the program can include at most two classes at the 400 level and must include at least two classes at the 500 level.

A*: Math 420, 452, 481 or 582, 525, 526, 551, 555, 561, 562, 565 or 566, 571, 572, 590 or 591 or 592, 593 or 594, 596, 597, 625, 626, 663, 773, or other counselor approved courses, possibly including at most two statistics courses at or above the 500 level.
B*: Math 596, 597, 625, 626, 663, 773.

3. Two cognate courses at the graduate level must be included in the program. These may be elected from other special areas of mathematics or from other fields. The courses chosen must be related to the student’s mathematics program.

Program Learning Goals

1. Learning Goal > Mathematical Proficiency: Developing a thorough understanding of advanced mathematical concepts and techniques used in applied mathematics, such as differential equations, numerical analysis, and statistical methods.
   • Assessment > Exams (written and oral) focused on derivations, proofs, and conceptual understanding; problem sets requiring application of specific techniques; projects involving theoretical analysis of mathematical models; presentations of advanced mathematical topics.
2. Learning Goal > Computational Skills: Gaining proficiency in computational tools and software necessary for modeling, simulation, and analysis of applied mathematics problems.
   • Assessment > Programming assignments where students implement numerical algorithms or simulations; lab exercises using specialized software (e.g., MATLAB, Python with SciPy/NumPy, R); projects requiring data analysis and visualization; code reviews. 
3. Learning Goal > Interdisciplinary Application: Learning to apply mathematical methods to solve problems in various fields such as engineering, physics, biology, finance, and other sciences.
   • Assessment > Case studies that present real-world problems from various fields requiring mathematical modeling; interdisciplinary projects where students work on a problem from another discipline; presentations or reports explaining how mathematical methods were applied to a specific field.
4. Learning Goal > Problem-Solving and Critical Thinking: Enhancing abilities in problem-solving, critical thinking, and logical reasoning to effectively address complex challenges.
   • Assessment > Complex, multi-step problem sets; open-ended projects requiring independent problem formulation and solution strategies; participation in problem-solving competitions; oral examinations where students explain their thought process. 
5. Learning Goal > Research and Innovation: Developing skills for conducting independent research, including formulating hypotheses, analyzing data, and deriving conclusions based on quantitative analysis.
   • Assessment > Independent research projects; research proposals and literature reviews; presentations of research findings (e.g., conference posters, talks); peer review of research work.
6. Learning Goal > Communication Skills: Improving the ability to effectively communicate complex mathematical ideas and findings to both technical and non-technical audiences.
   • Assessment > Written reports and technical papers; oral presentations (to both technical and non-technical audiences); participation in class discussions; creation of scientific posters or infographics; clear and concise explanations of complex concepts.
7. Learning Goal > Collaboration: Cultivating the ability to work collaboratively in interdisciplinary teams, leveraging mathematical expertise to contribute to joint projects.
   • Assessment > Group projects with clearly defined individual and team responsibilities; peer evaluations of team members' contributions; observation of group dynamics during in-class activities; reflective essays on collaborative experiences.