Doctor of Philosophy in Mathematics

Entrance Requirements

In addition to meeting the entrance requirements of the Graduate School, the applicant should have the mathematical training equivalent to that obtained from a master’s degree in mathematics. Well-qualified students with a bachelor’s degree in mathematics, or students who have had advanced work in other areas, would usually enroll in the M.S. program in mathematics until they pass Part I of the qualifying examination. However, this is not a requirement.

Entering students will have a diagnostic and advising interview with the Graduate Director to plan an appropriate program of study.

General Requirements

• A minimum of 72 credit hours beyond the bachelor’s degree – all at the 300 level or above


• Two thirds of the course work should be in mathematics


• Course work in mathematics must be at the 400 level or above in order to be used towards the 72 credit hour requirement


• 3.0 GPA must be maintained in all course work


• 3.0 GPA must be maintained in all mathematics courses at the 400 level or above, excluding work in seminars and doctoral research


• No more than 24 credit hours of research/thesis may be counted towards the 72 credit hour requirement


• The Seminar Requirement must be satisfied – at most two additional credits beyond the two allowed for the MS may be counted towards the 72 hour requirement


• At most 1 hour of MATH 584 (Supervised College Teaching) may be counted towards the 72 credit hour requirement


• MATH 530 may not be counted toward the 72 hour requirement

Students entering with a master’s degree in mathematics may receive up to 30 credit hours towards the 72 credit hour requirements. For these students, a minimum of 42 credits must be earned at CSU after admission to a doctoral program, and at least 21 credits beyond the master’s degree must be earned in courses numbered 500 or above. For students enrolled in a continuous master’s/Ph.D. program at Colorado State University, all courses taken during the master’s program may be applied to the doctoral degree, even if the total master’s degree credits exceed 30.

It must be stated on the Ph.D. program of study that all credits earned on the MS will be counted toward the PhD; furthermore, this must be approved by the student’s advisory committee, the Department of Mathematics, and the Graduate School. For more detailed information on university-wide Ph.D. requirements, please consult the Graduate School website:

http://graduateschool.colostate.edu/

Breadth Requirement

To fulfill the breadth requirement for the Ph.D., all students will be required to take and pass, with a grade of B- or better, at least 14 three (or more) credit Mathematics courses at the 500 level or above excluding:

• MATH 530
• MATH 699
• MATH 798
• MATH 799

Students entering with a master’s degree in mathematics from another institution may use courses approved to count towards the 72 credit hour requirement to also count towards this requirement. 

At least two courses must be chosen from each of the lists below. This breadth requirement may be completed over the course of the student’s graduate program. Credit earned for comparable courses taken at other institutions may be evaluated by the Graduate Director, at the student’s request, to determine suitability for substitution for particular course(s) in the lists below.

List I	List II	List III
MATH 501	MATH 517	MATH 510
MATH 502	MATH 518	MATH 520
MATH 566	MATH 519	MATH 545
MATH 567	MATH 617	MATH 546
MATH 570	MATH 618	MATH 560
MATH 571	MATH 619	MATH 561
MATH 601	MATH 717	MATH 620
MATH 602	MATH 718	MATH 621
MATH 666		MATH 640
MATH 667		MATH 641
MATH 672		MATH 645
MATH 673		MATH 646

Departmental Qualifying Examination

The departmental Ph.D. qualifying exam consists of two examinations, parts I and II.

Part I of the qualifying examination

Part I of the qualifying examination will consist of a student's request for the evaluation of their portfolio. Generally, a portfolio will consist of the final exams taken from the courses MATH 517, MATH 519, MATH 566, MATH 617 and one out of the two courses MATH 560, MATH 567. Student requests for the evaluation of their portfolio may be submitted to the qualifying examination committee (QEC) at the end of each semester. All portfolios must be submitted to the QEC by the end of the student's fourth semester of residency in the program. Regular faculty on the QEC may vote to a) pass, b) fail or c) conditionally pass a candidate. In case c), the QEC may require that either one or more of the regularly scheduled portfolio course final examinations be retaken in a subsequent semester or that a portfolio be augmented by one or more additional final examinations from advanced coursework in mathematics. A conditional pass must be resolved within one year.

Students who have previously received credit for one or more courses comparable to any of the designated portfolio classes may sit the regularly scheduled examination with or without registering for the course.

Students may, with approval of their faculty advisor and the graduate director, petition the QEC to consider additional, or alternative, evidence as part of the portfolio.

All portfolios will be reviewed by the QEC in May of the student's first year of residency in our program and the student will be advised regarding his or her academic progress. Satisfactory progress is required to retain GTA support.

Part II of the qualifying examination

After the selection of a permanent advisor, the student together with the Ph.D. advisor, and sometimes in consultation with additional faculty, will devise a second evaluation to be completed by the student before the preliminary examination, and after the completion of Part I of the qualifying examination. This evaluation must be completed within two academic years following the passing of Part I of the qualifying examination. The student should demonstrate proficiency on material approximately at the 600-level.

Departmental Preliminary Examination

At some time after a Ph.D. advisor and committee have been assigned, the student will be required to pass an oral preliminary examination prepared and administered by the student’s committee. This examination must be passed at least one academic year (two semesters; the summer session may be included) before defense of the dissertation. The purpose of this oral examination is to evaluate the student’s proposed research project.

Two weeks prior to the examination, the student must provide to the Ph.D. committee a written copy of the dissertation proposal, including a survey of the relevant literature, a description of the problem to be investigated, and an outline of methodology to be considered. The student either passes, passes provisionally (certain additional conditions must be met), or fails. In case the student fails the examination, it may be repeated once subject to Graduate School regulations. After this examination has been passed, the student becomes a Ph.D. candidate. 

A written report of the examination will become part of the student’s file.

PhD Dissertation and Final Examination

Each Ph.D. candidate must prepare a dissertation containing original mathematical research that is acceptable to the students committee. The student must successfully defend this dissertation in an open oral examination before the committee as well as other interested parties.  This examination can be given no sooner than two semesters (including summer) after the student becomes a Ph.D. candidate.  

The Thesis:

The format of the thesis must strictly adhere to the requirements of the Graduate School.   A format Requirements Checklist and sample pages of the Title page, Copyright page, Signature page, and Abstract page are available on the Graduate School website:

http://graduateschool.colostate.edu/index.asp?url=publications

The thesis must be submitted to the Graduate School by the published deadline.

http://graduateschool.colostate.edu/index.asp?url=gradinfo

 

Three additional forms are required for the PhD and can be found on the Graduate School website:

http://graduateschool.colostate.edu/index.asp?url=publications

• Doctoral  Dissertation Agreement Form
• Survey of Earned Doctorates
• Dissertation Release Form

 

The Graduate Coordinator will assist with room scheduling once the date and time for the defense have been established with your committee.  

The student’s committee must have adequate time to review the thesis before the final examination.  Therefore, the committee must have the thesis at least two weeks (including two weekends) before the final examination which meets the following standards: 

• The Thesis must be in final form


• The Print is letter quality, and a uniform style has been used throughout.


• Figures, printouts, etc. are clear and easy to read.


• Text is double-spaced and printed on only one side of the paper.


• Spiral bound

Results of the final oral examination will be reported on the GS24.  Voting is limited to the members of the student’s committee, and a majority vote is necessary to pass the examination. A tie vote is interpreted as failure to pass the examination. All committee members must vote to either Pass or Fail the student; there is no option to withhold a signature.  Committee members who are not academic faculty do not have a vote on the final examination. 

If significant revisions to the thesis are required by the committee after the final oral examination is complete, a reasonable amount of time must be given for committee members to re-review the thesis once the revisions have been made.

A candidate who fails the final examination may be reexamined once and, for the reexamination, may be required to complete further work. The reexamination must be held not later than 12 months after the first examination. The examination must not be held earlier than two months after the first examination unless the student agrees to a shorter time period. Failure to pass the second exam results in dismissal from the Graduate School.