Graduate Program in Scientific Computation

Scientific computing encompasses the modeling, simulation, and visualization activities increasingly used in science to complement, enhance, and extend traditional methods of scientific research. An emerging new focus in scientific computation is symbolic mathematical computation, also known as computer algebra. Research accomplishments in this area are behind such systems as DERIVE, MAPLE, MATHEMATICA, MACSYMA, REDUCE, and SCRATCHPAD. Our program emphasizes computer algebra and opportunities in numerical computing guided jointly by faculty in the Computer and Information Sciences (CIS) Department and the Mathematical Sciences Department. In CIS we have a strong group of faculty with research activities in computer algebra, and MATH has a strong group of faculty in numerical computing. These resources provide a tremendous opportunity for the student of scientific computation at the University of Delaware.

CIS faculty research interests are in parallel algebraic algorithms, use of randomization in algebraic algorithms, algorithms for integration in finite terms, algorithms for solving differential equations in closed form, symbolic/numeric methods in linear algebra, solution of polynomial equations and related issues, and algebraic computations over algebraic number and function fields. In the Department of Mathematical Sciences, faculty members investigate problems in partial differential equations and integral equations arising in such areas as elasticity, electromagnetic theory, fluid dynamics, and viscoelasticity as well as image processing, wave propagation, and mathematical biology. Applications include linear and nonlinear boundary value problems, direct and inverse scattering problems and signal processing. The methods include direct and iterative procedures, collocation, finite difference and finite element techniques and boundary element methods.

Current Faculty

• B. F. Caviness, Professor (joint apptointment with Mathematical Sciences)
• B. D. Saunders, Professor (joint appointment with Mathematical Sciences)
• D. H. Wood, Research Assosciate Professor

Course Offerings

CISC 621 Design and Analysis of Algorithms
CISC 623 Applied Symbolic Computation
CISC 821 Algebraic Algorithms
CISC 823 Analytic Algorithms
CISC 829 Adv Topics in Scientific & Algebraic Computation
MATH 610 Intro to Partial Differential Equations
MATH 611 Intro. to Numerical Analysis I
MATH 612 Intro to Numerical Analysis II
MATH 650 Abstract Algebra
MATH 672 Vector Spaces
MATH 846 Modern Higher Algebra II (Field Theory)
MATH 838 Numerical Methods for Partial Differential Equations I
MATH 839 Numerical Methods for Partial Differential Equations II