Courses

This course will introduce students to the fundamental ideas of scientific computing on high performance architectures. The principal objective of this course is to enable students to use high performance computers in all aspects of scientific computing to support research activities. At the end of the class, you should be able to: design and implement efficient algorithms for high performance computing related to a variety of research areas, use MPI, OpenMP and other special tools used to program large multi-processor computers, understand the basic operating principles of these machines, and, analyze the performance of your codes.

Course number: MAE 609, PHY 515, MTH 667, CE 620

Introduction to fundamental ideas of scientific computing, with particular attention given to algorithms that are well-suited to high performance computer architectures. Concentration on scientific computing in applications, including stochastic methods, FFTs, and finite element and finite difference methods.

Course number: MAE 610

Spectral methods are high order methods based on global polynomials such as the trigonometric or orthogonal polynomials, and they yield the so-called exponential or spectral convergence when smooth problems are considered. Due to such high order accuracy, spectral methods have been actively applied to various problems in applied mathematics. This course will introduce spectral methods with emphasis on both the theory and applications. The methodology of spectral methods will be derived for various PDEs such as wave equations, heat equations, and nonlinear hyperbolic conservation laws. Recent developments of the spectral methods for non-smooth problems and the discontinuous Galerkin methods will be also covered. Students who take this course will have an understanding of the spectral methods and be able to apply them to real computational problems.

Course number: MTH 637 

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.