M.S. in Mathematics

M.S. in Mathematics

The Master of Science (M.S.) degree in Mathematics at Montana State University is designed to prepare students for conducting independent research in mathematics, either by pursuing further graduate work or pursuing a professional career in academia, business, industry or government. 

Earning an M.S. degree in mathematics at MSU requires an M.S. student to complete required coursework as well as achieve the following milestones, in consultation with their Graduate Committee. 

  1. Form a Graduate Committee of at least three members. 

  2. Earn a Pass on the M.S. Written Comprehensive exam demonstrating competence in linear algebra and analysis. 

For additional information about the program, please refer to http://www.math.montana.edu/.

Program Admission Requirements

Admission to the program is based on a holistic assessment of a student’s total academic record as well as demonstrable promise to complete an M.S. in mathematics at MSU.  The minimum requirements for an applicant to be considered for admission to the M.S. program are as follows.   

  • By the time of entry into the M.S. program, the applicant must have received a Bachelor’s degree from an accredited college or university in the U.S., or equivalent from a non-U.S. institution.  

  • The applicant must have earned an overall grade-point average of 3.0 (B), or equivalent, in the most recent two years of study.   

  • The applicant must have received a grade of B or better in the following courses, or an equivalent grade from an equivalent course.  (Please refer to the MSU course description within each link for a list of topics covered in the course.) 

  1. Four semesters of Calculus through Differential Equations, 
  2. Linear Algebra (M 333), 
  3. A proof-based course in Advanced Calculus or Introduction to Analysis I (M 383).  A second semester of Analysis is preferred, but not required. 

International Students: Please refer to The Graduate School's page International Application Process for a detailed description of additional admission requirements, such as demonstrating English proficiency which apply to some countries. 

  • In order to be eligible for admission to the program, the department requires that the applicant demonstrate a minimum score on one of the following  TOEFL: 80-internet-based [iBT] or 550-PBT, or IELTS: 6.5: 54, or  Duolingo: 120. 
  • In order to be eligible for a Graduate Teaching Assistantship position, the applicant must provide documentation of a minimum score of TOEFL: 93-internet-based [iBT] or 550-PBT, or IELTS: 7.0: 65, or Duolingo: 135

Program Requirements

The Master of Science degree can include a thesis or not, and each plan is described below.  In the thesis plan, the student is required to complete course work, pass a comprehensive exam, and to write and defend a thesis that is based on original scholarship.  In the non-thesis plan, the student is required to complete course work and pass a comprehensive exam.

Non-Thesis Plan

This plan requires both completing the course work and passing the written comprehensive exam. At least 30 credits of course work 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 503Advanced Linear Algebra3
M 504Abstract Algebra3
M 505Principles of Mathematical Analysis3
M 511General Topology3
Additionally, students must fulfill a breadth requirement by completing at least two of the following: *6
Numerical Linear Algebra & Optimization
Applied Mathematics I
Introduction of Dynamical Systems I
Probability Theory
*

Either or both of these two required courses may be replaced by the corresponding semester of the appropriate 500 level course: M 581 Numerical Solution of Partial Differential Equations I, M 560 Methods of Applied Mathematics I, M 595 Dynamical Systems I, M 507 Mathematical Optimization , M 508 Mathematics of Machine Learning or STAT 501 Intermediate Probability and Statistics, 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 Handbook.

Requirements for the written comprehensive exam are listed below.

M.S. in Mathematics Comprehensive Exam

The M.S. Written Comprehensive exam is a tool to ensure that M.S. students have demonstrated competence in two principal subjects in mathematics.   

The M.S. Written Comprehensive exam is described and recorded as follows. 

  • The M.S. Written Comprehensive exam consists of two written exam components.

  • The components of the M.S. Written Comprehensive exam test competency with the contents of the following respective courses.

  1. Principles of Mathematical Analysis (M 505).
  2. Advanced Linear Algebra (M 503)

  • Each attempt of a given component is graded as a Ph.D. Pass, M.S. Pass, or Fail.  

  • To pass the M.S. Written Comprehensive exam is to earn a Ph.D. Pass or an M.S. Pass on both components of the exam.  

A student may attempt, or reattempt, components of the M.S. Written Comprehensive exam according to the following policies. 

  • An M.S. student must attempt both components of the M.S. Written Comprehensive exam within one (1) year of entry into the program.

  • There are two exam periods for each component of the M.S. Written Comprehensive exam: one in August and one in January (the exact dates are determined by the Department).

  • An M.S. student can attempt a given component of the M.S. Written Comprehensive exam at most twice (2); a student’s second attempt of a given component of the M.S. Written Comprehensive exam must take place in the next exam period.

  • If, after two (2) attempts, a M.S. student does not pass the M.S. Written Comprehensive exam, the student's Graduate Committee will convene to consider dismissing the student from the M.S. in Mathematics program.  A decision to dismiss an M.S. student will be based their exam submission(s) in addition to evidence (e.g. coursework, research performance) that the M.S. student has not adequately progressed toward earning an M.S.  If it is decided that an M.S. student be dismissed from the M.S. program, their Fail will be recorded to the Graduate School and their dismissal will be enacted at the end of the term in which the decision is made.​

Any exceptions to the above policies must be approved by the student’s Graduate Committee, must have the consent of the Department Head, and must comply with the Graduate School's requirements https://www.montana.edu/gradschool/policy/degreq_doctoral.html

Thesis Plan

This plan requires completing at least 20 credits of course work, writing a thesis, and an oral defense of the thesis, and passing the written comprehensive exam. At least 30 credits must be completed, of which, 10 must be thesis credits. Students must  complete both the core and breadth course requirements described in the Non-Thesis Plan above. 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 Handbook. Thesis and oral defense requirements must be arranged with and approved by the student's graduate committee.

Accelerated M.S. Plan

The Accelerated M.S. Program (AMSP) is designed to provide MSU undergraduates a path to earning both the B.S. and the M.S. in Mathematics in a total of five years.  Undergraduate students earning a B.S. in Mathematics at Montana State University may accelerate their program through any combination of Advanced Placement Credit, transfer credit, and higher semester credit loads so that they may receive their B.S. degree after four years and their M.S. degree after the fifth year. The undergraduate student can complete specific graduate level course work during year 4 of the undergraduate program.  These courses can be reserved for graduate credit towards the M.S. degree.  With careful planning by the student and the academic advisor, this can compress the time required to fulfill requirements of both the B.S. and M.S. degrees to a total of five years.  The M.S. degree is typically a non-thesis degree (course work and exams only), and all M.S. requirements described above in the Non-Thesis Plan must be fulfilled, unless otherwise approved by the student's graduate committee. 

AMSP Application and Timeline Information

Students typically apply to the AMSP program during spring term of the third year of the B.S. degree program.  A minimum of 90 undergraduate credits must be completed at the time of application.  Normally the B.S. will be awarded at the end of the student's senior (transition) year, and enrollment in the M.S. degree program will commence at the start of the fifth (graduate) year.  All M.S. program admission prerequisites listed above and all application procedures required by both the Department of Mathematical Sciences and the Graduate School apply.  This includes the application fees.  

Students apply to the AMSP program by applying to the Graduate School and selecting the term that they intend to start their graduate program, i.e. the term after they finish their undergraduate degree.

Reserved Credits:  Students planning to apply to the AMSP program should seek permission to register in graduate level courses during the second semester of their third year.  In total, a student at MSU may take up to fifteen graduate level credits to reserve towards a graduate degree.  The coursework used for reserved credits may not be counted toward the B.S. degree requirements.  In order to obtain permission to register in graduate level courses and to reserve credits toward the M.S. degree, the student must request approval through the department’s advisor overseeing the AMSP.  The Advisor must approve the request and document the specific courses to be reserved within DegreeWorks.

AMSP Program Requirements

  • The AMSP degree requirements are exactly the same as those in the Non-Thesis Plan described above.
  • Prospective students are required to keep their undergraduate coursework cumulative GPA at 3.3 or higher and their graduate coursework cumulative GPA at 3.0 or higher in order to be admitted to the AMSP.
  • If accepted into the AMSP program, students will be granted graduate status and be eligible for graduate assistantships and tuition waivers only after the B.S. degree confers.
  • At least 15 credits of graduate level coursework must be taken once the student obtains graduate status.  

Participation in the AMSP requires significant planning of coursework and application procedures.  Interested students should discuss this option with their undergraduate academic advisor within the Department of Mathematical Sciences as early as the first year of the B.S. degree program.  Students must also consult the Graduate Program Coordinator within the department as early as possible.  

For more information, refer to the Department of Mathematical Sciences.