Program Overview

Introduction to the Applied Mathematical & Computational Sciences Program

The Applied Mathematical & Computational Sciences (AMCS) program at the University of Iowa is designed to provide students with a comprehensive education in theoretical mathematics, applied mathematics, and an outside area in which mathematics is applied. The program aims to develop the competence of all AMCS students in several core areas, give students the opportunity to get an early start on their research, and facilitate transfers to and from Mathematics.

Program Requirements

Core Course Requirements

• 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 in the first two years of graduate study.

Ph.D. Qualifying Examinations

Every student must pass Ph.D. qualifying examinations within two years after beginning graduate study. The Ph.D. Qualifying Examinations consist of examinations in core areas chosen by the Ph.D. student. Each examination area is three hours long and can be taken during different sessions.

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. The student must also 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)

Outside Area Courses

Every student must take and pass two outside area Ph.D. level courses at the 6000-level or higher. An outside area is defined as an area outside of mathematics, in which mathematics is applied.

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.

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 (Fall)
• 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.

Details on the Ph.D. Qualifying Examinations

Every student is required to demonstrate competence in core areas, either by passing the core course sequences or by passing the relevant portion of the Ph.D. Qualifying Examinations with a mark of PhD level pass. The Ph.D. Qualifying Exams will be offered in all areas at the beginning of each fall and spring semester.

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. The examining committee must contain at least four faculty members, and at least two of the four members should be AMCS affiliated faculty.

Academic Registration

According to 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.

Ph.D. Dissertation

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.

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.