# M.S. in Mathematics

## Program Guidelines

## M.S. Mathematics Program Guidelines

The Master of Science degree in mathematics at Montana State University is designed to prepare students for further graduate work or for employment in academic, industrial, business, or government forums. The prerequisites for the master’s degree program in mathematics consist of the following courses or their equivalent: 4 semesters of Calculus through Differential Equations, Linear Algebra and a proof based course in Advanced Calculus or Real Analysis.

## M.S. Mathematics Non-Thesis Plan

This plan requires both completing the coursework and passing the written comprehensive exam. At least 30 credits of coursework are required. Of these, at least 18 credits must be numbered 500 or higher. Regardless, all of the following core courses must be completed:

## M.S. Mathematics Required Courses (12 semester credits)

- M 503 Advanced Linear Algebra (every spring)
- M 504 Abstract Algebra (every spring)
- M 505 Mathematical Analysis (every fall)
- M 511 General Topology (every fall)

## Additionally students must fulfill a breadth requirement by completing at least two of the following courses

- M 441 Numerical Linear Algebra & Optimization (every fall)
- M 450 Applied Math 1 (fall odd numbered years)
- M 454 Dynamical Systems I (fall even numbered years)
- STAT 421 Probability (every fall)

Either or both of these two required courses may be replaced by the corresponding semester of the appropriate 500 level course: M 581 (numerical analysis), M 560 (applied mathematics), M 595 (dynamical systems), or STAT 501 (probability), respectively. Any other exceptions to the course requirements must be approved by the student's graduate committee and adhere to the minimum policy requirements set forth in the Graduate Catalog (Plan B). Requirements for the written comprehensive exam are listed separately below.

## M.S. Mathematics Thesis Plan

This plan requires completing the coursework, writing a thesis, and an oral defense of the thesis. At least 30 credits must be completed of which 10 must be thesis credits. Students must also complete both the core and breadth course requirements described in the Non-Thesis Plan. Any exceptions to the course requirements must be approved by the student's graduate committee and adhere to the minimum policy requirements set forth in the Graduate Catalog (Plan A). Thesis and oral defense requirements must be arranged with and approved by the student's graduate committee.

## M.S. Mathematics Comprehensive Exam

The M.S. comprehensive exam for mathematics is a written exam administered in two disjoint 3-hour components, one on Analysis (M 505) and one on Linear Algebra (M 503). Each component is graded as Ph.D. pass, M.S. pass, or fail. In order to pass the written comprehensive exam, a student must pass each component at the M.S. pass or Ph.D. pass level within two examination periods. The examinations are given in August and January with the specific dates and times for each component determined by the department. Typically, the student takes the exams in August before their third semester of study.

If the student fails one or more components in the first examination period, a failure
will be reported to The Graduate School. The student must then pass the remaining
required components in a second examination period. If the student has not passed
the remaining required components after the second examination period, a second failure
of the comprehensive exam will be reported to The Graduate School and the student
will be dismissed from the program.

## More Information

For more information, refer to The Department of Mathematics Graduate Handbook.