Department of Mathematical Sciences

Montana State University
P.O. Box 172400
Bozeman, MT 59717-2400

Tel: (406) 994-3601
Fax: (406) 994-1789
Location: 2-214 Wilson Hall

Department Chair

Dr. Ken Bowers

math@math.montana.edu

Program Guidelines

Described below are the Department of Mathematical Sciences requirements for the Ph.D. degree in Mathematics. These departmental requirements supplement those set out by the Division of Graduate Education (DGE) in the Graduate Catalog for Ph.D. Students.

There are no foreign language requirements or qualifying exam for a Ph.D. in Mathematics.

1. Ph.D. Committee

1. The Ph.D. committee must include a minimum of five members excluding the DGE-assigned Graduate Representative.
2. A committee must be formed before the end of the student's second semester of study.
3. The Committee Chairperson (Advisor) must be a faculty member within the Department of Mathematical Sciences.
4. The first three committee members listed on a candidate's Program of Study read and assess the dissertation.

2. Course Requirements

1. A minimum of 30 credit hours are required (see the Graduate Catalog for Ph.D. Students for details).
2. A minimum of 18 credit hours must be dissertation credits (M690)
3. The Ph.D. student's Program of Study listing their intended coursework must be approved by all committee members.
4. The student must take a minimum of 4 credits of the Math 500 seminar series.

Typically, a Ph.D. student takes 18 credits of mathematics in courses numbered 500 or higher to prepare for their comprehensive examination. Students are encouraged to begin some form of doctoral reading or research (either informally or in the form of M689 credits) with a committee member by their second year of study.

3. Ph.D. Comprehensive Exam

The Ph.D. Comprehensive examination consists of both a written  and an oral comprehensive examination. The candidate must  pass the written comprehensive exam before taking the oral comprehensive examination

Written Exam component: OUTLINES

Written Exam Online library of old:  EXAMS 

Written Comprehensive Exam:

How a student may choose and re-take exam components is determined by (a)-(f):

1. The written comprehensive exam consists of 4-hour exam components graded as Pass or Fail.
2. The candidate  must pass three components to pass the written comprehensive examination though they may attempt more.
3. If a candidate fails a component it may be attempted at most one more time.
4. The candidate must pass the following "required" component: 
   1. MATH 547 , MATH 551 Real and Complex Analysis
5. Normally the remaining components are from the following list of  "standard" components: 
   1. MATH 511-512 Topology
   2. MATH 595-596 Dynamical Systems
   3. MATH 584-585 Functional Analysis
   4. MATH 581-582 Numerical Analysis
   5. MATH 544-545 Partial Differential Equations
   6. MATH 560-561 Applied Mathematics
   7. MATH 547, 586 Probability
6. At most one "nonstandard" component not from (i)-(viii) may be taken. To take such a component the following petition form must be completed.

Students take components determined by the exam time line describe in (g)-(k) below:

7. Exams components are given every August intercession exam period (blue) at  dates determined by the department.
8. Fall entry students may take components the August  intercession preceding their first semester enrolled. (this rule can help M.S. students continuing on toward their Ph.D. for instance).
9. Students must attempt at least one component by Year 2.
10. A student who has not passed all 3 required exam components after the Year 3 August exam period may re-take at most one previously failed component the following January intercession No new components may be attempted that January.
11. Fall and Spring entry students take exam components according to the following time line:

 

To find out how written comprehensive exam results are reported to DGE click here. If a second failure of the written comprehensive exams is reported to DGE your program of study in the Ph.D. program in Mathematics will be terminated.

Oral Comprehensive Exam:

After passing the written comprehensive exam the candidate must pass an oral comprehensive exam at a date agreed upon by the candidate's committee. Normally the oral comprehensive exam is a thesis topic proposal where the candidate's ability to conduct research on the proposal is assessed. When this is not the case, the candidate will be informed of the nature of the oral comprehensive exam by their committee. The candidate has at most two attempts to pass the oral comprehensive examination.

4. Dessertation Requirements:

Once the Ph.D. candidate has passed the comprehensive exam (both written and oral parts) the student has at most five years to  submit a draft of their dissertation to their committee prior to their final defense. The first three committee members listed on a candidate's Program of Study  must be given a dissertation draft at least two weeks prior to the Final Defense. Regardless, all committee members must have access to a dissertation draft at least one week prior to the Final Defense. The dissertation should embody the results of extended research by the candidate, be an original contribution to knowledge, and include new material worthy of publication.  The dissertation must be submitted as an electronic dissertation, in final form to the Division of Graduate Education not later than 14 working days before the end of the term in which graduate work is completed.

5. Final Defense:

Department policies on the final defense  and all other administrative procedures regarding the degree completion are exactly those as set out by Division of Graduate Education (DGE).

 

Ph.D. Comprehensive Exam Outlines

• Abstract Algebra
• Applied Math
• Complex Analysis
• Dynamical Systems
• Functional Analysis
• Numerical Analysis
• Partial Differential Equations
• Probability
• Real Analysis
• Topology

Online library of old: EXAMS

 

Updated: 02/07/2012