University of Utah Department of Computer Science Department of Mathematics

CES Course Descriptions

CS 5210/6210: Introduction to Scientific Computing (3) Prereq.: CS 3200, CS3510, MATH 3150. This course is offered every third semester, beginning in Fall 1999.
Course Outline: This course provides an introduction to existing classical and modern numerical methods and a knowledge of their algorithmic development and efficient implementation. Topics include: numerical linear algebra, approximation methods and parallel computation methods for nonlinear equations, ordinary differential equations, and partial differential equations. Students will learn about existing algorithms, and develop and implement new algorithms for parallel and distributed environments.

MATH 5610: Introduction to Numerical Analysis I (4) Sem: A. Prereq: MATH 2210, either MATH 2250 or 2270, and computing experience.
Course Outline: Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets).

CS 6220: Advanced Scientific Computing (3) Prereq.: CS 5210/6210 or MATH 5610 (Offered every third semester, beginning in Spring 2000).
Course Outline: A study of the numerical solution of two and three dimensional partial differential equations that arise in science and engineering problems. Topics include: finite difference methods, finite element methods, boundary element methods, multigrid methods, sinc methods, domain decomposition, mesh generation, storage optimization methods, and adaptive methods.

5620 Introduction to Numerical Analysis II (4) Sem: S. Recommended Prereq.: MATH 5610.
Course Outline: Computational solution of initial and boundary value problems of ordinary and partial differential equations.

MATH 5740: Mathematical Modeling (2) Sem: S. Prereq.: CS 5220 or MATH 5620 .
Course Outline: Development of mathematical models for physical, biological, engineering, and industrial phenomena and problems, using mainly ordinary and partial differential equations. Involvement of analytical and numerical tools suitable for analysis and visualization of the solutions of these problems, including packages such as LAPACK, EISPACK, Maple and Matlab.

CS 5630/6630: Scientific Visualization (3) Prereq.: CS 3510, CS 3200 or CS 5210 or MATH 5610 (Offered every third semester, beginning Fall 2000).
Course Outline: An introduction to the techniques and tools needed for the visual display of data. Students will explore mmany aspects of visualization, using a ``from concepts to results'' format. The course begins with an overview of the important issues involved in visualization, continues through an overview of graphics tools relating to visualization, and ends with instruction in the utilization and customization of a variety of scientific visualization software packages.

MATH 6790 Case Studies in Computational Engineering and Science (2) Sem: S. Prereq.: MATH 5740 and either MATH 5620 or CS 5220.
Course Outline: Two to five faculty members from various disciplines will describe in detail a project in which they are engaged that involves all ingredients of computational engineering and science: a scientific or engineering problem, a mathematical problem leading to mathematical questions, and the solution and interpretation of these questions obtained by the use of modern computing techniques. Participating faculty will vary from year to year. To be offered on the basis of need.

CS 6938/MATH 6795: Seminar in Computational Engineering and Science (1-3). Prereq.: MATH 6790.
Course Outline: Students in the final semester of the Computational Engineering and Science program will present their own CES-related research.

Students in the CES program are encouraged to take additional courses in the various areas above. Some courses that may be of interest are:

CS 5020: Algorithms and Data Structures
CS 5010: Software Practice
CS 6820: Parallel Computer Architecture
CS 7120: Information Based Complexity
CS 7240: Sinc Methods
CS 5600/6600, 5610/6610: Computer Graphics
CS 6670, 6680: Computer-Aided Geometric Design
CS 6939: Seminar in Inverse Problems (1-3).
MATH 5110, 5120 Mathematical Biology
MATH 5410, 5420 Introduction to Ordinary Differential Equations
MATH 5440 Introduction to Partial Differential Equations
MATH 5470 Applied Dynamical Systems
MATH 5660 Parallel Numerical Methods
MATH 5710, 5720 Introduction to Applied Mathematics
MATH 6610, 6620 Analysis of Numerical Methods
MATH 6630 Numerical Solutions of Partial Differential Equations
MATH 6710 Applied Linear Operator and Spectral Methods
MATH 6720 Appl Complex Variables, Asymptotic Methods
MATH 6730 Asymptotic and Perturbation Methods
MATH 6750, 6760 Continuum Mechanics: Fluids, Solids
MATH 6770, 6780 Mathematical Biology