To receive the Ph.D. degree in mathematics, a candidate meet several requirements and carry out some duties described below. For additional policies or rules not covered here, consult the Division of Graduate Education (DGE).
The candidate forms a committee of five or more willing faculty, including the thesis advisor as chair. The first three members listed on the candidate's Program of Study have the responsibility to read and evaluate the thesis. The DGE will assign one additional member, the graduate representative.
The candidate must pass at least 60 graduate credit hours, including at most 30 credit hours from a previously earned master's degree and at least 18 dissertation credit hours (MATH 690). Before the completion of the Ph.D., the candidate must take a minimum of four credits of the MATH 500 seminar.
The student must pass written Ph.D. exams
in three subject areas. Individual areas are graded Pass/Fail. The Ph.D.
examination period is in late August, and the student has a second
chance the next August to record a Pass in any area not passed during
the first examination period.
When? The student must
take at least two exams during the first August examination period
after having been enrolled for two semesters. The following August the
student must take any additional exams required to pass a total of
three exams.
One exam must be
| Real and Complex Analysis | (MATH 547, MATH 551). |
Two exams must be chosen from the areas
| (a) Applied Mathematics | (MATH 560-61) |
| (b) Dynamical Systems | (MATH 595-96) |
| (c) Functional Analysis | (MATH 584-85) |
| (d) Numerical Analysis | (MATH 581-82) |
| (e) Partial Differential Equations | (MATH 544-45) |
| (f) Topology | (MATH 511-12) |
| (g) Probability | (MATH 547, MATH 586) |
The Exception: The Ph.D. committee may replace exactly one of the required exam areas (a)-(g) by a different topic. All members of the committee must concur with the change.
There are syllabi of exam areas at the http://www.math.montana.edu//Documents/Comps/phd_math/Outlines
Mathematical Sciences website.
Details. If, after one
or two August examination periods, the student has passed three exams,
the written component has been successfully completed.
If the student has passed two, but not three, the student may retake one failed
component in the intersession in the January
immediately following the second August examination period. If the
student has not passed at least two exams in two August examination
periods, the student has failed the written exam and will not continue
in the Ph.D. Program.
After passing the written exams, the candidate must pass an oral comprehensive exam at a date set by the Ph.D. committee. The candidate is allowed at most two attempts to pass the oral examination. The Ph.D. Committee will convey the format of the examination to the candidate. A pass signifies that the student is ready to begin research on a sound and original thesis topic.
After passing the written and oral parts of the comprehensive exam, a candidate has up to five years to submit a draft of the thesis to his or her Ph.D. committee. The three readers must receive the draft at least two weeks prior to the Final Defense. All committee members must have a draft by a week before the defense. The main results in the dissertation must embody original research by the candidate and be worthy of publication. An electronic version of the final form of the thesis must be submitted at least 14 working days prior to the end of the term in which the defense is held.
The Mathematical Sciences Department follows the policies of the Division of Graduate Education.