Updated: 5/31/2020,  Implemented: 8/1/2020

Ph.D. in Mathematics Degree Requirements

Check also the section Doctor of Philosophy in the Mathematics Graduate Programs of Study.

I. Core Areas and Core Courses

The core areas and core course sequences are:

• Algebra: Abstract Algebra I-II (MATH:5000 - MATH:5010)
• Analysis: Introduction to Analysis I-II (MATH:5200 - MATH:5210)
• Topology: General Topology (MATH:5400) - Introduction to Smooth Manifolds (MATH:5410)
• Differential Equations: Nonlinear Dynamics with Numerical Methods (MATH:5600) - Partial Differential Equations with Numerical Methods (MATH:5700)
• Numerical Analysis: Numerical Analysis I-II (MATH:5800-MATH:5810)
• Biomathematics: Mathematical Biology I-II (MATH:5750 - MATH:5760)

Each Ph.D. student is required to demonstrate competence in four core areas within the first two years of graduate study, either by passing (grade of B- and higher) each of the MATH:5000-level corresponding courses or by passing the relevant area of the Ph.D. Qual Exam with a mark of "Ph.D. level pass", according to Section II.

Graduate-level courses transferred from other universities may be used to satisfy part of these requirements, subject to approval of the DGS and the Graduate Committee.

II. Ph.D. Qualifying Examinations (Ph.D. Qual Exams)

Each Ph.D. student is required to pass the Ph.D. Qual Exams within the first two years of graduate study.

The Ph.D. Qual Exams will be offered during the week before each fall and spring semester in the following five areas (as needed by student registration): Algebra, Analysis, Topology, Differential Equations, and Numerical Analysis. These five qual-examination areas are based on their corresponding MATH:5000-level core course sequences, as listed in Section I. Note that MATH:5750-MATH:5760 is a non-qual course sequence.

For each of the examination areas, the Qual Exam is three hours long and can be taken during different sessions. The Ph.D. students will choose the examination areas they want to be tested on. To pass the Ph.D. Qual Exams a Ph.D. student must pass three different qual-examination areas with the mark of "Ph.D. level pass", or according to the Exception Rule described in Section II.b.

II.a. General rules for the Ph.D. Qual Exams:

A Ph.D. student must register for the Ph.D. Qual Exams by the announced deadline, usually about a month before the start of the semester. A Ph.D. student cancelling his/her registration must do so at least one week prior to the Ph.D. Qual Exams session. After this date, any examination area not taken will be marked as "Fail".

For each examination area a student will receive a grade of "Ph.D. level pass", "Master's level pass", or "Fail". An honorific grade of "Ph.D. level pass with Distinction" will be given for exceptional performance.

For a repeated examination area, the best result will count, i.e., a mark of "Fail" does not replace a mark of "Master's level pass".

It is not mandatory for a student to retake an examination area with a mark of "Fail" or "Master's level pass" in a subsequent session. Another area can be substituted.

II.b. Exception Rule:

An Exception Rule is allowed for passing the Ph.D. Qual Exams, as follows. “A Ph.D. student is considered as having passed the Ph.D. Qual Exams if the result of three examination areas taken during the first year of graduate studies consists of two "Ph.D. level passes" and one "Master's level pass".

Note that the above statement “examination areas taken during the first year of graduate studies” includes the qual exams immediately preceding year two.

II.c. Sample Timelines:

The core course requirements and Ph.D. Qual Exams system allow for example:

• Entering Ph.D. students with exceptional preparation have the opportunity to pass the Ph.D. Qual Exams at the start of their graduate study, and move directly to research related activities, finish both core course requirements and Ph.D. Comp Examination by the beginning of their second year;
• Entering Ph.D. students with very strong preparation have the opportunity to pass some of the area exams at the start of their graduate study, and concentrate on the remaining areas, and possibly pass the Ph.D. Qual Exams at the beginning of their second year of graduate study and thus again move quickly to research related activities as soon as their second year, finish both core course requirements and Ph.D. Comp Exam by the end of their second year;
• Entering students with adequate preparation have the opportunity to start three core course sequences in the first year and pass the Ph.D. Qual Exams at the beginning of their second year and thus again move quickly to research related activities as soon as their second year, finish core course requirements by the end of their second year, and the Ph.D. Comp Exam during the beginning of their third year;
• Entering students with less preparation have the opportunity to start two core course sequences in the first year and another two in the second year, pass Ph.D. Qual Exams by the end of their  second year, while in their third year they start on Ph.D. Comp Examination preparation, finish both core course requirements and Ph.D. Comp Examination by the end of their third year.

The two-year timeframe also allows the flexibility for any Ph.D. student to switch the areas of the Ph.D. Qual. Examinations during their first two years.

III. Ph.D. Comprehensive Examination (Ph.D. Comp Exam)

Each Ph.D. student is required to submit to the DGS a Doctoral Plan of Study and a Proposal for Ph.D. Comp Exam for approval by the Graduate Committee, and then to pass the Ph.D. Comp Exam in his/her chosen area no later than August 31-st at the beginning of their fourth year of graduate study.

The preparation for the Ph.D. Comp Exam is under the supervision of a faculty. Typically the Ph.D. Comp Exam preparation would build on one of the MATH:6000-level sequences with additional readings from books and research papers. Each student must submit their Proposal for Ph.D. Comp Exam to the DGS for approval by the Graduate Committee at least one month before a presentation is scheduled. The proposal must list the examining committee consisting of at least five people including the chair and be first approved by the chair of the examining committee. During the Ph.D. Comp Exam the student would give an oral presentation of the material (usually about one hour) and be questioned over the material by the examining committee. Note that the Ph.D. Comp Exam is not open to the public (except for special requests made to the DGS).

Ph.D. students may submit to the DGS revised drafts of their Doctoral Plan of Study by August 31-st of each subsequent year. Each revised plan should highlight any differences between the current and the previous version of the document.

Modifications of rules for special circumstances may change time restrictions but may not lessen content requirements.

IV. Breadth Requirements

Important notice: 5000-level courses which are already counted towards the Core Areas and Core Courses requirement in Section I do not count for any of the breadth requirements below.

IV.a. Hours Breadth Requirement:

A Ph.D. student must pass (grade of B- and higher or S or P) at least 27 credit hours of the following graduate courses:

• Courses numbered from MATH:6000 to MATH:7900 with the exception of Seminars;
• MATH 5000-level courses that were not counted towards the Core Areas and Core Courses requirement in Section I;
• Other graduate courses if they are central to the student’s research. Registration for such courses and their inclusion in the Doctoral Plan of Study require endorsement from the student’s thesis advisor prior to submission to DGS for approval by the Graduate Committee.

At least 18 (out of 27) credit hours must be from MATH:6000-level courses. Any exception to this rule, as justified by the student’s Doctoral Plan of Study, must be approved by the DGS.

IV.b. Areas Breadth Requirement:

Among the following MATH courses, a Ph.D. student must pass (grade of B- and higher) at least two courses from each of three areas chosen from the following six areas. For all these courses the letter grade is earned based on assignments that include homework and exam(s).

• Algebra: (MATH:5000 - MATH:5010), Algebra I-II (MATH:6000 - MATH:6010); Homological Algebra (MATH:7000); Algebraic Number Theory (MATH:7020);
• Analysis: (MATH:5200 - MATH:5210), Analysis I-II (MATH:6200 - MATH:6210); Functional Analysis I-II (MATH:7200 - MATH:7210);
• Topology: (MATH:5400 - MATH:5410), Introduction to Algebraic Topology (MATH:6400), Introduction to Differential Topology (MATH:6410), Differential Geometry I-II (MATH:6500 - MATH:6510); Topology of Manifolds (MATH:7400);
• Differential Equations: (MATH:5600-MATH:5700), Ordinary Differential Equations I-II (MATH:6600 - MATH:6610), Partial Differential Equations I-II (MATH:6700 - MATH:6710);
• Numerical Analysis: (MATH:5800-MATH:5810), Theoretical Numerical Analysis I-II (MATH:6850 - MATH:6860);
• Biomathematics: Mathematical Biology I-II (MATH:5750 - MATH:5760).

Graduate-level courses transferred from other universities may be used to satisfy part of the breadth requirements, subject to approval of the DGS and the Graduate Committee.

IV.c. Sample Timeline of Course to Ph.D.:

These are only recommended timelines. They will be adjusted to respond to the specific academic and research needs of the Ph.D. student.

Year	Courses by Focus Area - Examples					Major Academic goals
	Topology	Analysis/ Differential Eqns.	Algebra/ Number Theory	Biomathematics	Numerical Analysis
1	5000-5010	5200-5210	5000-5010	5200-5210 (or 5400-5410)	5200-5210	Pass Qual Exams
	5200-5210	5600-5700	5200-5210	5600-5700	5600-5700
	5400-5410	5400-5410 (or 5800-5810)	5400-5410	5800-5810	5800-5810
	Attend MATH:5900 and AMCS:5900 (First Year Seminars)
2	Last Core Seq.	Last Core Seq.	Last Core Seq.	5750-5760	Last Core Seq.	Match with an advisor
	6400-6410	6200-6210	Choose two: 6000, 6010, 7000, 7020	Choose four: 6200, 6210, 6400, 6410, 6600, 6610, (or 6700, 6710)	Choose four: 6200, 6210, 6400, 6410, 6600, 6610, 6850, 6860	Submit Plan of Study
	Choose two: 7400or other from 6000-level in IV.b	6700-6710 (or 6600-6610)	6400-6410			Prepare for Comp Exam
3	Four other breadth and/or topics courses	Four other breadth and/or topics courses	Four other breadth and/or topics courses	Choose two: 6850-6860 or other  from IV.b.	6850-6860 if not already taken; otherwise other MATH:5000/6000-level courses	Pass Comp Exam
				Two other breadth/ topics courses (see IV.a and IV.b) as recommended by advisor	Two other breadth/ topics courses (see IV.a and IV.b) as recommended by advisor	Broader professional development / Conduct original research
	Register 6 credits for MATH:7990 Research/Independent Study
	Goal of 24 breadth hours by the end of the year
4	Other breadth and/or topics course(s)	Other breadth and/or topics course(s)	Other breadth and/or topics course(s)	7630 or other breadth/ topics course (see IV.a and IV.b) as recommended by advisor	Other breadth / topics course (see IV.a and IV.b) as recommended by advisor	Conduct original research
	Register for MATH:7990 Research/ Independent Study (or take other courses, per research interest)					Participate in conferences
	Goal of 27/18 hours breadth requirement by the end of yr. 4 Make sure 18 breadth hours are MATH:6000-level
5	Register for MATH:7990 Research/ Independent Study Goal: At least 72 credit hours total					Write thesis
						Obtain employment

 

V. Academic Registration

Registration for any course that is not listed as a Ph.D. in Mathematics Degree Requirement according to Sections I-IV, requires pre-approval by the DGS.

According to Section XII. Doctor's Degrees, C. Academic Registration Requirement of the Graduate College Manual of Rules and Regulations : All doctoral programs will contain a minimum of 72 semester hours of graduate work. Of those 72 semester hours, at least 39 must be earned while registered in The University of Iowa Graduate College. After completing 21 semester hours of graduate work under Graduate College registration and in compliance with the Graduate College policy for time limits on academic credit, i.e., courses ten years or older may not be counted toward the degree, students must complete an additional 18 semester hours to be taken as follows: (1) enrollment as a full-time student (9 semester hours minimum) in each of two semesters, or (2) enrollment for a minimum of 6 semester hours in each of three semesters. A student must be registered in the semester in which (s)he earns her/his degree.

See also the College of Liberal Arts & Sciences Academic Policies Handbook.

VI. Ph.D. Dissertation

See Section XII. Doctor's Degrees, M. Dissertation for the Doctoral Degree of the Graduate College Manual of Rules and Regulations.

VII. For information about Master of Science degree, see M.S. in Mathematics