Graduate Course Catalog 2012-2013
Degrees Offered: M.S., Ph.D.
The Integrated Applied Mathematics program offers both the master of science in mathematics with an option in applied mathematics, and the doctor of philosophy program in applied mathematics. Both programs are housed in the Department of Mathematics, and additional information is available here.
The essence of modern applied mathematics is the interplay between mathematical analysis, numerical computation and scientific/engineering specialization. Thus, the IAM curriculum is designed to provide applied mathematics graduate students with advanced training in these three broad, inter-related topics: (1) Mathematical Methods, (2) Scientific Computing, and (3) a Scientific or Engineering Area of Specialization.
M.S. Degree Requirements (Applied Mathematics Option)
This program requires 30 credit hours, consisting of the courses MATH 931, MATH/IAM Applied Functional Analysis, an approved two-course sequence in applied mathematics (such as MATH 967/977). In addition to these courses, the student chooses either a thesis or project option. The thesis option consists of 6 credits of Master's Thesis (MATH 899) and four elective courses. The project option consists of 3 credits of Master's Project (MATH 898) and five elective courses. The elective courses need not be in mathematics, but must be at the 800 level or higher, and at least one must be a technical course in statistics or some other department. The broad elective flexibility allows the student's application interests to have a substantial role in the content of the program. The student's full program plan must be proposed in writing to the applied mathematics faculty and approved prior to the student's second semester of study. There is no comprehensive examination in this option.
The following are the requirements of completing the Ph.D. in Applied Mathematics program:
Students are advanced to candidacy after meeting the following requirements:
1. Must take 9 courses totaling 27 credits from the following list: PHYS 931, IAM 830, IAM 851, IAM 932, IAM 933, IAM 961, IAM 962. One of the following 2-course sequences can also apply: MATH 847/IAM 950, ME 807/ME 909 or PHYS 953/PHYS 951.
2. In addition, must take a minimum of 3 technical electives totaling 9 credits from the following list: IAM 940, ME 812, ME 911, and other approved courses.
3. Pass a 3-part Ph.D. Qualifying Exam:
*Comprehensive exam in mathematical methods
*Comprehensive exam in numerical analysis and HPC
*Oral or written exam in specialization area
4. Seminar presentation of thesis proposal to dissertation committee.
Each Ph.D. student must submit a dissertation that includes original results in integrated applied mathematics.
|IAM||830||Graduate Ordinary Differential Equations||3|
|IAM||851||Introduction to High-Performance Computing||3|
|IAM||932||Graduate Partial Differential Equations||3|
|IAM||933||Applied Functional Analysis||3|
|IAM||940||Asymptotic and Perturbation Methods||3|
|IAM||950||Spatiotemporal and Turbulent Dynamics||3|
|IAM||961||Numerical Analysis I: Numerical Linear Algebra||3|
|IAM||962||Numerical Partial Differential Equations||3|