Mathematics

M.S. Mathematics

Ph.D. Mathematics

Program Admission Requirements:

• 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. 

Program Admission Requirements:

• By the time of entry into the Ph.D. 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. A proof-based course in Linear Algebra (M 333), An additional proof--based course in advanced Linear Algebra, Functional Analysis, or Abstract Algebra is preferred, but not required.
2. A proof-based course in Advanced Calculus or Introduction to Analysis I (M 383).  A second semester of Analysis is preferred, but not required. 
3. A record of undergraduate coursework in rigorous proof-based mathematics (or M.S. level coursework if applicable). Additionally, demonstration of original mathematical research is preferred, but not required.

Mathematics M.S. Comprehensive Exams:

• The components of the M.S. Written Comprehensive exam test competency with the contents of the following respective courses.
  • Principles of Mathematical Analysis (M 505).
  • Advanced Linear Algebra (M 503)
• 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.  

Mathematics Ph.D. Qualifying Examination:

• The Ph.D. Qualifying exam consists of two components, administered on different days of the exam period.  (It is identical to the M.S. Mathematics Written Comprehensive exam.)  
• The components of the M.S. Written Comprehensive exam test competency with the contents of the following respective courses.
  • Principles of Mathematical Analysis (M 505).
  • Advanced Linear Algebra (M 503)
• 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.  

Mathematics Ph.D. Comprehensive Exam:
Written Comprehensive:

• The Ph.D. Written Comprehensive exam consists of two components.  Each component is a 6-hour written exam.
• The content of each component is selected from the following list

1. Measure Theory (M 547)​​​​ - Complex Analysis (M 551) 
2. General Topology (M 511) -  Geometry & Algebraic Topology (M 512) 
3. Abstract Algebra (M 504) - Abstract Algebra II (M 554)
4.  Dynamical Systems I (M 595) - Dynamical Systems II (M 596) 
5.  Functional Analysis I (M 584) - Functional Analysis II (M 585) 
6.  Numerical Solution of Partial Differential Equations I (M 581) - Numerical Solution of Partial Differential Equations II (M 582)  
7. Partial Differential Equations I (M 544) - Partial Differential Equations II (M 545) 
8. Methods of Applied Mathematics I (M 560)  -  Methods of Applied Mathematics II (M 561)
9. At most one component not from the list above.
   • To implement this option, the student must file a petition form in consultation with their Graduate Committee.

• Each attempt of a given component is graded as Pass or Fail

Oral Comprehensive Exam:

The Oral Comprehensive exam involves three components, described as follows. 

1. The oral presentation component is a 1-hour presentation in which the student's Graduate Committee is present, and the general public is invited to be in the audience.  Typically, the Oral Comprehensive exam is a thesis topic proposal in which the student’s ability to conduct the proposed research is assessed by their Graduate Committee. 
2. The Question and Answer component of the exam takes place after the presentation, and it is closed to the general public: only the student and the student's Graduate Committee (including a Graduate Representative if that is requested by the student) are present.   
3. The written component is a professionalized document, written by the student.  All members of the student’s Graduate Committee must have access to this document at least one (1) week prior to the oral presentation component. 

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. 

Mathematics Ph.D. Dissertation Requirements
A Ph.D. student’s Dissertation is a document prepared by the student that is suitable for publication in a peer-reviewed venue.  The Dissertation is expected to record the results of extended research by the student, be an original contribution to knowledge, and include new material worthy of publication. All members of the student’s Graduate Committee must have access to a final draft of the Dissertation at least four (4) weeks prior to the Final Defense. The student’s Dissertation must be submitted to the Graduate School in final form as an electronic dissertation no later than 14 working days before the end of the term in which graduate work is completed.   

Mathematics Ph.D. Final Defense
Department policies on the final defense and all other administrative procedures regarding the degree completion are exactly those as set out by The Graduate School with the exception of the following.  The Final Defense is to be organized by the student and their Advisor.  If any member of their Graduate Committee has had insufficient time to prepare, a Final Defense must not take place and must be rescheduled.