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# AMCS Graduate Curriculum

AMCS students study theoretical mathematics, applied mathematics, and an outside area in which mathematics is applied. Then they do dissertation research on a problem involving the outside area. The goals of the AMCS graduate curriculum are:

- To develop the competence of all AMCS students in several core areas
- To give AMCS students the opportunity to get early starts on their research.
- To have an AMCS curriculum that facilitates transfers to and from Mathematics.

## Section 1: Summary of Requirements

### Subsection 1.1 Required Courses in Core Areas

- Analysis: Introduction to Analysis I-II (MATH:5200 - MATH:5210)
- Differential Equations with Numerical Methods: Nonlinear Dynamics with Numerical Methods (MATH:5600) - Partial Differential Equations with Numerical Methods (MATH:5700)
- Numerical Analysis: Numerical Methods I & II (MATH:5800-MATH:5810)

Every student must pass (grade of B- or higher in each course) all three core course sequences (or be exempted -- see details in Section 2) in the first two years of graduate study. Detailed course descriptions are available at the Department of Mathematics home page https://math.uiowa.edu/ by following the link to Graduate Program and then Course Information. These core courses are accessible to students who have completed single and multivariable calculus, linear algebra, and an introduction to analysis.

### Subsection 1.2. Ph.D. Qualifying Examinations

Every student must pass Ph.D. qualifying examinations within two years after beginning graduate study. Details on the Ph.D. Qualifying Examinations can be found in Section 2 below.

### Subsection 1.3. Outside Area Preparation Course and First-Year Seminars

Every student must take and pass at least one outside area preparation course in the first two years of graduate study among (the list is not exhaustive)

- BAIS:6300: Dynamic Programming (Spring)
- BAIS:6480: Knowledge Discovery (Fall)
- BAIS:6600: Linear Programming (Spring)
- BAIS:6700: Discrete Optimization (Fall)
- BAIS:6900: Heuristic Search (Spring)
- BIOS:5710-5720: Biostatistical Methods I (Fall) - II (Spring)
- BME:5200: Biomedical Signal Processing (Spring)
- BME:5210: Medical Imaging Physics (Fall)
- CBE:5412: Atmospheric Modeling (Spring)
- CS:4310: Design and Implementation of Algorithms (Spring)
- CS:4700: High Performance and Parallel Computing (Fall)
- CS:5350: Design and Analysis of Algorithms (Fall)
- CS:5370: Computational Geometry (Spring)
- CS:5430: Machine Learning (Spring)
- ECE:5450: Machine Learning (Fall)
- ECE:5460: Digital Signal Processing (Fall)
- ECE:5480: Digital Image Processing (Fall)
- ECE:5600: Control Theory (Fall)
- ECE:5995: Contemporary Topics in Electrical and Computer Engineering (Fall and Spring)
- MATH:4060: Discrete Mathematical models (Spring)
- MATH:4700: Partial Differential Equations with Applications
- MATH:4820: Optimization techniques (Spring)
- MATH:4840: Mathematics of Machine Learning (Fall)
- ME:4111: Scientific Computing and Machine Learning (Spring and Fall)
- ME:5114: Nonlinear Control in Robotic Systems (Spring)
- PHYS:4731: Plasma Physics I (Fall every other year)
- PHYS:4860: Computational Physics (Spring)
- PHYS:5710: Classical Mechanics (Fall)
- PHYS:5730: Statistical Mechanics I (Spring)
- PHYS:5741-5742: Quantum Mechanics I (Fall) - II (Spring)
- PHYS:5811-5812: Classical Electrodynamics I (Fall) - II (Spring)
- PHYS:5905: Special Topics in Physics (Spring)
- STAT:4100-4101: Mathematical Statistics I (Fall) - II (Spring)
- Other courses: to be approved by the AMCS Director.

Every student must take and pass the two first-year seminars in the first two years of graduate study

- MATH:5900: First-Year Graduate Seminar (Fall)
- AMCS:5900: Seminar: Appl Math & Computational Sci (Spring).

### Subsection 1.3. Outside Area Courses

Every student must take and pass two outside area Ph.D. level courses at 6000-level or higher. An outside area is defined as an area outside of mathematics, in which mathematics is applied. In case it is difficult to find two such Ph.D. level courses sequence in the outside area, the student should contact the AMCS Director for an appropriate arrangement of equivalent courses.

### Subsection 1.4. Ph.D. Comprehensive Examination

Every student must pass a Ph.D. Comprehensive Examination over the outside research area within three and a half years after beginning graduate study. The Ph.D. Comprehensive Examination is typically based on the outside area courses and/or directed reading. Details on the Ph.D. Comprehensive Examination can be found in Section 3 below.

### Subsection 1.5. Mathematics Course Requirement

In order to establish a solid foundation in mathematics, all AMCS students must take and pass at least two courses among

- MATH:5000: Abstract Algebra I (Fall)
- MATH:5010: Abstract Algebra II (Spring)
- MATH:5400: General Topology or Fundamental Groups and Covering Spaces
- MATH:5410: Introduction to Smooth Manifolds (Spring)
- MATH:5750: Mathematical Biology I (Fall)
- MATH:5760: Mathematical Biology II (Spring)

and at least 12 credit hours of graduate mathematics courses numbered from MATH:6000 to MATH:7999 with the exception of the seminars. The courses in the student's written plan of study should be chosen to obtain mathematical breadth and must be approved by the AMCS Director.

### Subsection 1.6. Non-Required Outside Courses

Any outside course not listed in Section 1 and not required for the AMCS PhD degree requires pre-approval by the AMCS Director.

## Section 2: Details on the Ph.D. Qualifying Examinations

Every student is required to demonstrate competence in core areas, either by passing (grade of B- or higher in each course) the core course sequences, or by passing the relevant portion of the Ph.D. Qualifying Examinations with a mark of PhD level pass. Graduate courses transferred from other universities may be used to satisfy the core course and mathematics course requirements, subject to approval of the AMCS Director.

The student must pass the Ph.D. Qualifying Exams within the first two years of graduate study based on the three MATH:5000-level core course sequences listed in Subsection 1.1 and also possibly in either algebra or topology to substitute for at most one of the core areas. The Ph.D. Qualifying Exams will be offered in all areas (as needed by student registration) at the beginning of each fall and spring semester. A Ph.D. student must register for the Ph.D. Qualifying 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. Qualifying Exam session. After this date, any examination area not taken will be marked as "fail".

The Ph.D. Qualifying Exams consist of examinations in core areas (see Section 1) chosen by the Ph.D. student. Each examination area is three hour long and can be taken during different sessions. For each examination area, the 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. To pass the Ph.D. Qualifying Exams, the student must pass three different examination areas with the mark of "Ph.D. level pass". Each examination area can be attempted at most three times. For a repeated examination area the best result counts, i.e., a mark of "fail" does not replace that of "Master's level pass". An examination area passed with a "Ph.D. level pass" cannot be repeated. A first exception rule for passing the Ph.D. Qualifying Exams is as follows: A Ph.D. student is considered as having passed the Ph.D. Qualifying Exams if the result of three examination areas taken during the first Fall session (1st semester of study), the first Spring session (2nd semester of study), and the consecutive Fall session (3rd semester of study) consists of two "Ph.D. level passes" and one "Master's level pass". A second exception rule for passing the Ph.D. Qualifying Exams is as follows: A Ph.D. student is considered as having passed the Ph.D. Qualifying Exams in the situation that at least three examination areas are taken during the same session and the result of three of those examinations consists at least of two "Ph.D. level passes" and one "Master's level pass".

Sample Timelines: The core course requirements and Ph.D. Qualifying Exams system allow

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

These new rules will start to be applied to the new class of students entering in Fall 2020 and also to current first year students opting for these new rules before August 10, 2020.

## Section 3: Details on the Ph.D. Comprehensive Examination

It is required that every Ph.D. candidate must pass an oral Ph.D. Comprehensive Examination within three and a half years after beginning graduate study. To request the Comprehensive Exam, a student must submit a written Ph.D. Comprehensive Examination proposal to the AMCS Director for approval. The proposal is one to two pages long, and it must include names of the examining committee members, the date and time of the exam, and an abstract of presentation material. The examining committee must contain at least four faculty members, and at least two of the four members should be AMCS affiliated faculty. The chair of the committee is usually the student's Ph.D. thesis advisor. Note that we must submit an exam request form to the Graduate College at least two weeks before the exam date. Typically the Comprehensive Exam would build on the outside area courses and/or directed readings. The student would give an oral presentation of the material (usually about one hour) and be questioned over the material by the committee. When the Comprehensive Exam is requested, the AMCS Director fills a Plan of Study form with the student on what additional courses will be required for the completion of the Ph.D.

## Section 4: Academic Registration

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. Students must be registered in the semester in which they earn their degree.

## Section 5: Ph.D. Dissertation

See Section XII. Doctor's Degrees, M. Dissertation for the Doctoral Degree of the Graduate College Manual of Rules and Regulations. The dissertation consists of original work for the most part and not of a collection of results found in the scientific literature. A minimum of 100 pages is generally expected.

## Section 6: Time to degree

The expected time-to-degree is 5 years. Financial support from the University of Iowa in the form of teaching assistantships or fellowships is limited to a maximum of 6 years. Students are required to complete their PhD within 7 years after beginning graduate study and failure to graduate within this time frame will result in dismissal from the Program. Only under exceptional circumstances would a student be allowed to remain longer than 7 years in the Program and it would require approval by the AMCS Director.