The State Education Department and the Chancellor of the State
University of New York have approved an Advanced (Graduate)
Certificate in Computational Science at the University at Buffalo.
Computational Science is an emerging discipline, uniting ideas in
mathematics and computer science together with applications arising
in science and engineering. Because it complements theoretical and
experimental investigations, Computational Science is often
referred to as "the third science". The Certificate recognizes a
student's special training in scientific computing and
applications. This Certificate is a cooperative program involving
the Center for Computational Research and the Departments of
Mathematics, Physics, Chemical Engineering and Mechanical and
Aerospace Engineering; other departments have expressed an interest
in joining the program.

The University at Buffalo has made a significant investment in creating the Center for Computational Research, a facility that provides leading edge computing and visualization resources to the University and Western New York communities. The Certificate Program and the new courses in High Performance Computing were designed to help train UB students in the methods of scientific computing on modern computing hardware available at CCR.

The Certificate requires a total of 15 hours of graduate coursework (usually 5 courses). A two-semester course in High Performance Computing is common for all students in the program; the remaining nine hours consists of options chosen from computing and applications courses specific to each participating department. By exposing students to some of the fundamental methods in computational science, while also providing them with an understanding of the application of computing within their chosen discipline, the requirements highlight the interdisciplinary nature of computational science.

(Excerpts from the proposal to the State University of New York and the State Education Department)

This Advanced (Graduate) Certificate in Computational Science is designed to provide students at the University at Buffalo with training in advanced scientific computing in combination with specialized education in traditional disciplines of science and engineering. Computational Science is an emerging discipline, uniting ideas of Mathematics and Computer Science together with applications arising in science and engineering. Computational Science must be distinguished from Computer Science. Computer Science concerns the design of hardware and software for the computer systems of the future. Computational Science concerns the exploitation of current hardware and software to address large-scale computational problems that arise in fields of engineering and science. As computers become more integrated into the working environment of business and industry, students will require thorough and systematic training in computational science in order to secure employment in advanced technology fields. This Advanced Certificate program is designed to address this need. The Program provides for coursework in current techniques of high performance computing, and for advanced study in a chosen discipline.

More specifically, Computational Science applies techniques from Mathematics and Computer Science to problems of applied interest. Active areas of research in Computational Science include the design of fast algorithms for the solution of linear algebra and differential equations, optimization, database management, and visualization. In addition, solving cutting-edge problems in any of these fields necessitates exploiting advanced computer architectures. Thus working in computational science requires a background in high performance computing (the knowledge of computational methods on advanced architectures) together with training in an application area (differential equations or linear algebra or optimization or database or visualization or management of advanced computing systems, among others).

Because of the inherently interdisciplinary nature of Computational Science, the program of study for this Advanced Certificate is designed as a cooperative venture among several departments and organized research units. Part of the program (high performance computing) is common to all students, and part is specific to participating departments. This arrangement promotes the study of the methods of scientific computing while simultaneously advancing the study of disciplinary science and engineering. Study in computational science complements study in traditional departmental sub-specialties, and a Certificate Program thus broadens the educational background of students.

This Certificate Program will be comprised of several options. The Certificate Program requires a total of 15 hours of graduate coursework, 6 hours (40%) of this coursework is common to all students in the Program and consists of a two-semester course in High Performance Computing, while the remaining 9 hours (60%) consists of options chosen from approved disciplinary courses related to computing, computational simulations, and numerical modeling. This arrangement exposes students to some of the fundamental methods of computational science, while also providing them with an understanding of the application of computing within their chosen discipline.

Students wishing to earn this Advanced Certificate must be admitted into a department participating in the Certificate Program, either in the graduate program (for a degree or for the Certificate) or in an approved 5-Year Combined BA-MA degree program. All coursework, including the course hours in High Performance Computing, must be approved by the participating departments for graduate credit within their programs and must be applicable toward a registered graduate degree. At present, there are four departments participating in this Certificate Program, each of which has registered graduate programs leading to Masters and Ph.D. degrees. The participating departments are:

- Chemical Engineering
- Mathematics
- Mechanical and Aerospace Engineering
- Physics

Thus, an Advanced (Graduate) Certificate in Computational Science provides unique training for students in science and engineering. Approval of the Certificate by the State Education Department will provide appropriate recognition of the special education earned by these students through their work in Computational Science.

Requirements for the Advanced Certificate consist of:

- Acceptance into the graduate or combined BA-MA degree program of a participating department
- Completion of 15 hours of coursework, including:
- 6 credit hours consisting of the required courses High Performance Computing I and High Performance Computing II;
- 9 credit hours of elective coursework consisting of departmentally approved courses as detailed below.

Students must maintain a B average in all Certificate courses and must be in good academic standing in their home department. The courses High Performance Computing I and II (HPC I and II) were created in Spring, 1999, through the efforts of the University at Buffalo's Center for Computational Research (CCR), and serve to educate students in the methods of scientific computing on modern hardware architectures. HPC I and II are cross-listed among CCR and three departments participating in the Certificate Program, ensuring departmental acceptance of this coursework toward their degree programs. [ Note. Physics has agreed to cross-list the HPC course, and is preparing the necessary paperwork. In the interim, the Physics Department will accept the currently listed HPC courses as applying towards a degree in Physics. ] The participating departments and CCR will coordinate the instruction assignments for HPC I and II.

In addition to the required HPC courses, students must complete elective courses in their home departments, chosen from a program designed by the individual departments. This additional coursework falls into four options, one from each of the departments:

- Option in Chemical Engineering. In addition to High Performance Computing I and II, students must take CE 531 Chemical Engineering Analysis I. Students must also choose two additional courses from among: CE 532, Chemical Engineering Analysis II, CE 526 Statistical Mechanics, CE 533 Introduction to Finite Elements, or CE 580 Nonlinear Analysis. Students may request a waiver to allow a substitution for these requirements, but any substitution requires prior approval of the Director of Graduate Studies in consultation with the Director of CCR.
- Option in Mathematics. In addition to High Performance Computing I and II, students must take MTH 537, Introduction to Numerical Analysis I and MTH 538, Introduction to Numerical Analysis II, and one course from among MTH 545 Introduction to Ordinary Differential Equations, MTH 549, Introduction to Partial Differential Equations, MTH 645, Advanced Ordinary Differential Equations, MTH 649, Partial Differential Equations, MTH 543, Fundamentals of Applied Mathematics, MTH 539, Methods of Applied Mathematics. Students may request a waiver to allow a substitution for these requirements, but any substitution requires prior approval of the Director of Graduate Studies in consultation with the Director of CCR.
- Option in Mechanical and Aerospace Engineering. In addition to High Performance Computing I and II, students must take three courses from among: MAE 510, Virtual Reality, MAE 529, Finite Element Structural Analysis, MAE 541, Topics in Finite Element Analysis, MAE 542, Engineering Applications of Computational Fluid Dynamics, MAE 550, Optimization in Engineering Design, MAE 564, Manufacturing Automation, Sys 500, 506, 507, 508, 509 Special Topics in System Identification, Sys 571, System Analysis, Sys 581, Optimal Estimation Methods. Students may request a waiver to allow a substitution for these requirements, but any substitution requires prior approval of the Director of Graduate Studies in consultation with the Director of CCR.
- Option in Physics. In addition to High Performance Computing I and II, students must take three courses from among PHY 501, Mathematical Physics, PHY 505, Computational Physics I, PHY 506, Computational Physics II, PHY 507, Quantum Mechanics I, PHY 508, Quantum Mechanics II, PHY 509, Classical Dynamics, PHY 513 Electrodynamics I, PHY 514, Electrodynamics II, and PHY 519 Statistical Mechanics I, PHY 520, Statistical Mechanics II. Students may request a waiver to allow a substitution for these requirements, but any substitution requires prior approval of the Director of Graduate Studies in consultation with the Director of CCR.

Participating departments, in consultation with the Director of CCR, will approve the awarding of the Advanced Certificate for students registered in that department.

Faculty participating in the initiative in high performance computing are drawn from the several participating departments at the University at Buffalo.

The coursework required for this Advanced Certificate consists of classes drawn from regularly scheduled departmental offerings, and the specialized, required courses High Performance Computing I and II are cross-listed by several participating departments. Responsibility for staffing departmental courses resides with those departments. UB's Center for Computational Research (CCR) will help coordinate the program and course offerings. The CCR is not an academic department and provides no credit-bearing course instruction. The CCR does provide hardware, software and consulting support for those faculty and students using high performance computing facilities. CCR thus provides access to the tools required for applying the methods and techniques learned as part of the Certificate coursework to current research problems in science and engineering. This combination of specialized training in computational science, advanced education in a field of science and engineering, and access to a leading center of academic computing, offers students the opportunity for a program of advanced study unmatched in the State of New York.