Math MLB Requirements

Coursework 

The Math MLB MS program must include at least one course in each of the following four core areas:

(1) linear algebra: 419§, 420, 571.
(2) algebra: 412§, 475, 493, 567, 575, 593, 594 or other 500-level algebra courses
(3) analysis: 451§, 452, 525, 526, 555, 596, 597, or other 500-level analysis courses
(4) topology/geometry: 490§, 537, 590, 591, or other 500-level topology/geometry courses

The marked (§) courses in the above list indicate mandatory minimum core competency courses; all students will demonstrate mastery in these courses, either by passing these courses or being exempted from them by the MLB director on the basis of work done at another institution or another course at UM. We encourage students to examine the syllabi, homework, and final exams for the (§)-marked courses, in order to help assess their own readiness to substitute a higher-level course for the (§)-marked courses (for example, to take Math 590 instead of Math 490). This can be done in consultation with their MLB advisor, who can, for example, assess the student’s work on such exams before the semester begins.

Some CS courses in machine learning can be used to meet the linear algebra requirement, with permission of the MLB director or Associate Chair. In this case, students should have demonstrated a good understanding of linear algebra through prior course work.

Our MLB students are diverse in their backgrounds and preparation for graduate study in mathematics, so there is considerable flexibility in satisfying the core course requirement. We expect that many scholars will have completed work at the level of one or more of the §-marked courses before. In this case, students will take another course to satisfy the core requirement in each of the four subjects. If the MLB advisor determines, for example, that the student has succeeded in a course similar to Math 412 at their prior institution, MLB scholars are still expected to earn 3 credits for an algebra course at UM, typically at a level higher than Math 412. Each Math MLB student will take at least one course in each of the four core areas above, regardless of preparation in each subject.

In addition, MLB Math students should take at least four mathematics courses at the 500 level or above. These four courses may overlap with the courses taken to satisify the four core area requirements.  To maximize flexibility, we do not require any specific courses beyond the core ones listed above, which we feel are essential to eventual success in the PhD program.

For example, a student might complete their 30 credits as follows: 

• Math 420,  451, 490 (covering 3 of the four core area MLB requirements)
• Math 593 (covering the core requirement in algebra in year 2)
• Math 567, 551, and 590 (giving the remaining needed 4 courses at 500 level)
• EECS 402 (giving the computing requirement)
• Math 700 TWICE with two different  professors, or with the same professor. 

Alternatively, the student could complete the 30 credits as follows:

• Math 419, 412  451, 490 (covering the four core area MLB requirements)
• Math 420,  566, 567,  551,  590
• Math 700  in their final semester with their MLB advisor;  the  MLB thesis incorporates coding for the computing requirement.

Students can focus on a particular area of interest, perhaps related to their MLB thesis, or they can explore a wide variety of topics, as they like. However, course selections should be approved in advance by their MLB advisor. Substitutions can be made (for example, counting certain 400-level courses or courses in other departments) with the permission of the MLB director or Associate Chair for Graduate Studies. Students intending to enter the PhD program following their MS might want to focus on preparing for at least some of the QR requirements for the Math PhD program.
 

The MLB Thesis

MLB students will work closely with a research mentor to do mathematics together on a topic of mutual interest. The MLB thesis may contain original research, but this is not a requirement. In most cases, we expect the thesis will be an expository work on a topic that may eventually become the area of the student’s PhD dissertation research.

Students are encouraged to seek out a research mentor for their MLB thesis as earlier as possible. MLB students are expected to remain on campus the summer between their first and second year, and are provided with a Rackham fellowship for this purpose. The summer should be used to work with a particular faculty mentor on a topic of mutual interest, which in many cases will naturally lead to an advising relationship and a start on their thesis work. It is acceptable, however, for the student to explore different areas, and to work with a different faculty member in their second year for their MLB thesis.

Students will assemble a MLB thesis committee by the beginning of their second year in the program, and write a “MLB Thesis Proposal”—a brief but technically precise synopsis of their project—to be read and approved by their committee and the MLB director. The committee will include their thesis advisor, one other faculty member (typically their MLB advisor, the MLB director, or the Associate Chair), and one PhD student.

All finishing MLB scholars, in both Math and AIM, will participate in the MLB Symposium, where they will present their MLB thesis work to the wider departmental community.
 

Independent Research Reading Credit

Students are required to earn at least 3 credits in independent research or reading credit with a faculty member. Typically, this will be work done with their MLB thesis advisor in the final semester.

Students are encouraged to enroll in 3-credit independent reading courses with a mathematics faculty member in any (or all) of their semesters at Michigan. This flexibility ensures that students can study topics of particular interest to them and will develop strong mentoring relationships with different faculty. Students can use this opportunity to delve deeply into a particular research area or to explore different areas and styles of mathematics.

We encourage students to consider taking advantage of the opportunity to enroll in independent reading courses with faculty in their first semester of the program.

Computing

Computing is an essential part of mathematical research today. All mathematics MLB students are expected to develop their facility with computing. This requirement is quite flexible and at the discretion of the MLB director and/or Associate Chair. A typical way to satisfy this requirement will be through the MLB thesis requirement: the student may incorporate some computing as part of their project. The requirement can also be satisfied by taking or teaching a cognate course in which coding or computing is expected, including Math 571.
 

Additional Requirements

Math M.S. Students accepted into the Marjorie Lee Browne Scholars Program will have additional opportunities related to the enhanced content of this degree program:

• Students may participate in the RMF Connection, a summer program that focuses on successful transition to graduate study, access to campus resources, building personal networks, and developing research and scholarly expertise.