AMSC Doctorate Preliminary Requirements: Scientific Computation Concentration

Scientific Computation Curriculum

Within the first two years of their admission to the program, students must successfully complete their Core Courses: Scientific Computing I & II, Computer Organization and Programming for Scientific Computing, Advanced Scientific Computing I & II and the Core Science Courses, with at least a grade of "B" or better, and with an overall grade-point average in these courses of 3.5 or better. Extensions of this two year deadline may be granted by the AMSC Graduate Committee based on the specific circumstances of individual students (e.g., part-time status, background deficiencies, or illness). There is no qualifying examination for Ph.D. students in the Concentration in Scientific Computation.

Subsequently, students must complete two Applications courses and 9 credits in electives (for a total of thirty-six graduate course credits) with a ``B" grade or better. The proposed selection of courses must be approved by the student's Study Advisory Committee and submitted in the form of a Study Advisory Plan to the AMSC Graduate Committee. In addition to the course requirements, Ph.D. students will have an oral candidacy examination and will write and defend a dissertation. These elements are governed by the same rules as in the Concentration in Applied Mathematics.

There is no foreign language requirement.

Students accepted into the Ph.D. program may have up to 24 credits of requirements waived if they have taken equivalent graduate courses at a regionally accredited institution, as long as the conditions specified in the Graduate Catalogue for the transfer of credit are met and the AMSC Graduate Committee approves. The 3.5 GPA requirement for the core courses will only apply to those courses taken at the University of Maryland, College Park.

Requirement	Ph.D	Masters with thesis	Masters w/o thesis	Certificate
Scientific Computing I & II	6 hrs	6 hrs	6 hrs	6 hrs
Computer Organization and Programming for Scientific Computing	3 hrs	3 hrs	3 hrs	3 hrs
Advanced Scientific Computing I & II	6 hrs		6 hrs
Core Science Courses	6 hrs	6 hrs	6 hrs
Applications Courses	6 hrs	3 hrs	3 hrs	3 hrs
Electives	9 hrs	6 hrs	6 hrs
Total	36 hrs	24 hrs	30 hrs	12 hrs

No course may be used to meet more than one requirement, and thesis research (799, 899) is not to be counted. For all of the students in the AMSC program a grade of B or better must be achieved in each of the five Scientific Computation Core Courses (first five courses in the list above).

Scientific Computation Core Courses

There are five core courses: Scientific Computing I & II, Computer Organization and Programming for Scientific Computing, and Advanced Scientific Computing I & II.

Scientific Computing I & Scientific Computing II (AMSC 660 & 661) will cover fundamental topics in computational methods for discrete systems, linear and nonlinear systems, optimization, ODEs, Fourier and wavelet transforms, and elliptic and time-dependent PDEs. (These courses replace MAPL 660 & 661 with the same name.)

Computer Organization and Programming for Scientific Computing (AMSC 662) will cover fundamental issues of computer hardware and software, parallel computing and data managment relevant for programming for scientific computing.

Advanced Scientific Computing I & Advanced Scientific Computing II (AMSC 663 & 664) applies the topics covered in AMSC 660 & 661 and 662 in the context of a year-long personal project to develop software designed to carry out a computational scientific task in a high performance computing environment. The project will provide each student with hands-on experience on all aspects of modern computing, including the formulation of the problem (with a faculty mentor), discretization and programming of the resulting system of equations, visualization of data, and oral and written presentation of the results.

The two sequences will be taught in parallel each year. AMSC 662 will be taught in the Fall. A student can take AMSC 662 either in the first semester (at the same time as AMSC 660 and the first Core Science course), or in the third semester (at the same time as AMSC 663).

Core Science Courses

Every Scientific Computation student is expected to apply computational methods in a science discipline. The core science courses are intended to provide students with a foundation in their chosen discipline. They must be graduate-level (600-level or above) core courses from a discipline outside Mathematics and Computer Science. (The word ``science" should be considered an abbreviation for ``physical science, life sciences, engineering, business, and social science".) Core science courses for the Scientific Computation program should be selected with the advice from the relevant science departments, subject to the approval of the Study Advisory Committee. Students planning their programs should make sure the courses they choose are being taught regularly. The following are examples of courses that might be appropriate as core science courses:

Astronomy

Geology/Geophysics

Fluid Dynamics

Atmospheric Sciences

Physics

Scientific Computation Applications Courses

Applications Courses are intended to expose students to computational methods and mathematical modeling as may be relevant to their science discipline. These courses will be selected from a list of courses offered by the various Departments and approved by the Graduate Committee for the Program. The content of approved courses must be primarily in mathematics or computational science. Each student's Study Advisory Committee, working with the student, will recommend a set of Applications courses.

Like the core science courses, Applications Courses should be selected with advice from the Departments that teach the courses. Students planning their programs should make sure the courses they choose are being taught regularly. The following examples illustrate courses that might be appropriate for the Scientific Computation program.

Optimization

Applied Numerical Methods PDE/ODE

Numerical Methods in Sciences

Mathematical/Statistical Modeling in Sciences

Electives

Any graduate level (600 and above) courses approved by the student's Study Advisory Committee may be chosen as electives, although we expect most students to use these electives to gain breadth in their science discipline.