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Introduction to approximation theory, interpolation, numerical differentiation and integration, solutions of linear and non-linear equations, numerical solution of differential equations, optimization. Emphasis is on error analysis and stability. Several practical examples and computer programs will be covered. Prerequisite: MATH 3323, with grade C or better, and a working knowledge of a high-level programming language. 

Introduction to basic computational science skills including UNIX, scientific programming using high-level languages, message passing interface, and parallel computer architectures. Prerequisite: MATH 5329, with grade C or better, may be taken concurrently.

Computer simulation of selected practical problems from physics, engineering, geology, biology or chemistry. Students learn to create mathematical models formulate modeling assumptions, select appropriate numerical methods, implement them in the form of a computer program, and visualize the numerical results. Emphasis is given to verification and validation procedures. Prerequisite: CPS 5401, with grade C or better.

Advanced scientific computing skills including implementation of numerical methods and mathematical models in a scientific programming language, use of parallel numerical libraries, and large-scale scientific data analysis and visualization (techniques and tools). Prerequisite: CPS 5310, with grade C or better, may be taken concurrently.