MATH 18 and computer language Number systems and errors, interpolation by polynomials, linear systems, scalar algebraic equations and systems, optimization, approximation theory, integration, initial, and boundary value problems. Finite difference and finite element methods for elliptic, parabolic, and hyperbolic problems. Study of properties such as consistency, convergence, stability, conservation, and discrete maximum principles. Math 363 Mathematical Modeling 3 hr. This course is concerned with construction, analysis, and interpretation of mathematical models that shed light on important problems in the sciences.
Emphasis is on the simplification, dimensional analysis, and scaling of mathematical models.
The course concentrates on the typical methods of set theory, transfinite induction, and Zorn's Lemma with emphasis on their applications outside set theory. The fundamentals of logic and basic set theory are included. Math 403 Adv. Math 407 Adv. Topics in Combinatorics 3 hr.