# Master’s in Math and Applied Math

The M.S. degrees are designed to ensure that the student acquires a reasonably broad background in either mathematics or applied mathematics and studies one or more areas in depth. The two degree options are the M.S. degree with project and the Option B master’s degree, which is usually completed by students in a Ph.D. program. Both degrees are offered in mathematics and applied mathematics.

The M.S. degrees in mathematics and applied mathematics require a minimum of 27 hours of coursework (nine courses).

For the M.S. in mathematics, the student takes a four-course core consisting of

- MA 515 (Analysis)
- MA 551 (Topology) or MA 518 (Manifolds)
- MA 520 (Linear Algebra) or MA 523 (Matrix Theory)
- MA 521 (Algebra)

For the M.S. in applied mathematics, the four-course core is

- MA 515 (Analysis)
- MA 580 (Numerical Analysis)
- Two courses from among:
- MA 505 (Linear Programming)
- MA 531 (Control)
- MA 532 (Ordinary Differential Equations)
- MA 534 (Partial Differential Equations)
- MA 546 (Probability)
- MA 523 (Matrix Theory) or MA 520 (Linear Algebra)

In addition, for either degree, there is an in-depth study requirement of two two-course sequences, or one group of three related courses. This requirement can be met, for example, by taking follow-up courses to two of the core courses. Thus, it can be met with as few as two courses in addition to the core courses, which leaves room for three electives. Another way to meet the in-depth study requirement is to complete a three-course minor in a mathematics-related area. The M.S. programs allow up to three courses in mathematics-related disciplines.

For the M.S. in applied mathematics with a concentration in computational mathematics, the student’s coursework must include MA 780 and one course from a list of computational mathematics courses. This list includes the department’s advanced numerical analysis and computer algebra courses, as well as various computer science courses and computationally intensive courses from other disciplines .

Additional requirements for the Option B master’s degree, which does not require a project, are described

here.

For the M.S. degree with project, the student completes a three-credit-hour project. An advisory committee of three faculty members oversees the project. A written report on the project is presented at a final oral examination, which includes a short lecture describing the project.

M.S. projects are sometimes directed by a faculty member from the student’s minor department. Other M.S. projects have grown out of jobs with local companies or research organizations.

## Timetable

- Students are assigned a beginning advisor who can assist them with questions concerning their program and related issues. Students may change their advisor at any time.
- After two semesters of graduate work, you should choose a project advisor. If you begin graduate work in the fall, the summer after your first year is a good time to start the project. Projects often take more than one semester to complete. The project advisor need not be the same faculty member who has been your advisor up to this point.
- In consultation with your project advisor, choose two additional faculty members for your advisory committee. If you have a minor, one member of your committee must come from the minor department or program.
- Yoy should complete a Plan of Graduate Work (a list of the courses you have taken or plan to take) online through MyPack Portal after consultation with your advisor and advisory committee.

Before the Plan of Work is submitted, you must have signed and submitted a patent agreement form. - As soon as possible after you begin to work with your project advisor, you should submit to your advisory committee a proposal for your master’s project. This proposal is described below. The advisory committee must approve the proposal.
- When all requirements except completion of the course work in the final semester are satisfied, you should schedule the final oral examination with your advisory committee, and submit a Permit to Schedule Final Oral Examination form to the Mathematics Department graduate program office. This must be done at least five weeks before the date of the exam. The graduate program office will reserve a room for the exam. At the examination students give a presentation on their project (see below) and answer questions related to the project and the topics in their Plan of Work. To graduate in a given semester, you must pass the exam before the Graduate School deadline for that semester, approximately six weeks before graduation
- Complete a Diploma Order Request from the Mathematics Department graduate program office at the beginning of the semester in which you anticipate graduating.

## Master’s Project Proposal

The proposal for a student’s master’s project should establish for their advisory committee that the level of the project is appropriate for a master’s student. The proposal should include the following features.

- Introduction: Describe the general setting of the project. For an applied project, describe the application; for a project within mathematics, describe how the project relates to a wider body of mathematics.
- State precisely what the project is, and what the student plans to do.
- Show that the project involves substantial mathematics. For example, if you plan to describe a theorem and study how it applies to a problem, write about this plan. If you plan to study a mathematical model, you should describe what is being modeled, the model itself, and what you plan to do in your study: analysis, numerical analysis, computer experiments, etc. Applied projects can involve a subject outside mathematics, provided substantial mathematics is included in the project report.

## Master’s Project Report

The report is produced with guidance from the advisor. It is typically 10–20 pages long and is organized in the same way a thesis or a published paper is organized. The first page should be a title page, giving the title of the project, the author and other pertinent details. There should be an introduction, describing the topic and the relationship with other parts of mathematics or science and giving references. There should be one or more sections giving the treatment of the topic, followed by a bibliography.