New AMCS Graduate Curriculum

Section 1: Summary of Requirements

Section 1.1 Required Courses in Core Areas

• 22M:115-116 Analysis
• 22M:132-133 Topology
• 22M:142-144 Differential Equations with Numerical Methods
• 22M:170-171 Numerical Analysis

Every student in the AMCS Ph.D. program must pass all four core course sequences (or be exempted -- see details in Section 2) in the first two years of graduate study. Detailed course descriptions and sample syllabuses are available at the Department of Mathematics home page http://www.math.uiowa.edu/ by following the link to Courses or to Graduate Programs and then Core Courses under New Graduate Curriculum. These core courses are accessible to students who have completed single and multivariable calculus, linear algebra, and an introduction to analysis.

Section 1.2. Ph.D. Qualifying Examination

Every student in the AMCS Ph.D. program must pass a Ph.D. qualifying examination consisting of area examinations in three of the four core areas listed above. These area examinations are based on the 100-level core sequences given in Section 1.1. The AMCS Qualifying Examination must be passed within two and a half years after beginning graduate study.

Section 1.3. Ph.D. Comprehensive Examination

All AMCS students must pass a Ph.D. Comprehensive Examination over their outside research area within three and a half years after beginning graduate study. An outside area is defined as an area outside of mathematics, in which mathematics is applied. The Ph.D. Comprehensive Examination is based on a sequence of 200-level courses in the outside area or an equivalent combination of courses and directed reading.

Section 1.4. Advanced Mathematics Course Requirement

In order to establish a solid foundation in mathematics, all AMCS students must pass at least 12 credit hours of graduate mathematics courses numbered from 22M:200 to 22M:371 with the exception of the seminars 22M:224 and 22M:225. 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.

Section 2: Details on the Ph.D. Qualifying Examination

Every student in the AMCS Ph.D. program is required to demonstrate competence in each of the four core areas within the first two years of graduate study, either by passing the four 100-level AMCS core course sequences, or by passing the relevant portion of the Ph.D. Qualifying Examination. To ensure that students plan appropriately, all AMCS students must have their written individual plans of study approved by the AMCS Director. Graduate courses transferred from other universities may be used to satisfy the core course and advanced mathematics course requirements, subject to approval of the AMCS Director. The Qualifying Examination is given in all areas at the beginning of each fall and spring semester.

Every student in the AMCS Ph.D. program must pass a Ph.D. Qualifying Examination.

• The Qualifying Examination must be passed within two and a half years after beginning graduate study.
• The Qualifying Examination consists of area examinations in three of the four AMCS core areas (taken in the same examination period).
• The area examinations are based on the 100-level core course sequences listed above.
• Each area examination is a three-hour written examination.
• A student may take the Qualifying Examination at most twice.
• For each area examination, a student will receive a grade of Ph.D. qualifying level pass, Master’s level pass or not pass.
• In order to pass the Qualifying Examination, a student must receive Ph.D. qualifying level passes in at least two areas and at least a Master’s level pass in the third area.
• If a student needs to take the Qualifying Examination a second time, then the student may carry forward area examination score(s) of Ph.D. qualifying level pass. A student who is carrying forward two of these passes must obtain a Master's level pass in the third examination area.
• AMCS does not offer a Master’s Degree; AMCS students often obtain applied mathematics Master’s Degrees in the Department of Mathematics.

Student may satisfy core course requirements via a Qualifying Examination in three ways.

• A student who receives a Ph.D. qualifying level pass in an area on the Qualifying Examination is exempted from the core course requirement in that area.
• A student may take all four area examinations at once, having registered for three as a Ph.D. Qualifying Examination. A score of Ph.D. qualifying level pass in the fourth area is necessary to satisfy the core course requirement in that area.
• A student who has already passed a Ph.D. Qualifying Examination may take an individual area examination in a subsequent Ph.D. Qualifying Examination. A score of Ph.D. qualifying level pass is necessary to satisfy a core course requirement.

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

Each student must submit a written Ph.D. Comprehensive Examination proposal to the AMCS Director for approval. This proposal must list at least two 200-level courses to be taken in the outside area, or describe an equivalent combination of courses and directed readings to be done as preparation. The examining committee specified in the proposal must contain at least five faculty members. The Ph.D. Comprehensive Examination may be written or oral. Existing outside Ph.D. comprehensive examinations or standard practices for Ph.D. comprehensive examinations in the outside area may be used. All AMCS students must pass a Ph.D. Comprehensive Examination over their outside area within three and a half years after beginning graduate study.

The new AMCS curriculum allows the following graduate student paths. These are parallel to possible paths in the Department of Mathematics (go to http://www.math.uiowa.edu/ and follow the link to Graduate Programs and then to New Graduate Curriculum and Sample Programs).

1. Entering students with excellent preparation have the opportunity to pass the Ph.D. Qualifying Examination in August of their beginning year, and then move directly to research related activities and preparation for their Ph.D. Comprehensive Examination over their outside area.
2. Entering students with very strong preparation have the opportunity to pass some of the area examinations in August of their beginning year, and then concentrate on the remaining areas. These students could pass the Ph.D. Qualifying Examination in August of the beginning of their second year and then move quickly to research related activities and preparation for their Ph.D. Comprehensive Examination over their outside area.
3. Entering students with good preparation have the opportunity to start three core sequences in the first year and possibly pass the Ph.D. Qualifying Examination in August of the beginning of their second year. Then they could move quickly to research related activities as soon as their second year, finishing their Core Courses, Ph.D. Qualifying Examination, and Ph.D. Comprehensive Examination by the end of their second year.
4. Entering students with less preparation have the opportunity to start two core sequences in the first year and another two in the second year, so that they can pass the Ph.D. Qualifying Examination in August of the beginning of their third year. By starting preparation for their Ph.D. Comprehensive Examination in their second and third years, they could finish their Core Courses, Ph.D. Qualifying Examination, and Ph.D. Comprehensive Examination by the end of their third year.
5. The time restrictions could be modified for students with weak backgrounds or special circumstances, but the requirements regarding Core Courses, Ph.D. Qualifying Examination, and Ph.D. Comprehensive Examination must be met by all AMCS students.