MATH

This course is about how to find the best - or at least good - solutions to large problems frequently arising in business, industrial, or scientific settings. Students learn how to model these problems mathematically, algorithms for finding solutions to them, and the theory behind why the algorithms work. Topics include the simplex method, duality theory, sensitivity analysis, and network models. The focus is on linear models and models with combinatorial structure, but some nonlinear models are considered as well. Optimization software is used frequently.

Students learn about numerical solutions to linear systems; numerical linear algebra, polynomial approximations (interpolation and extrapolation); numerical differentiation and integration. Students also learn about error analysis and how to select appropriate algorithms for specific problems.

This course introduces partial differential equations, how they arise in certain physical situations, and methods of solving them. Topics of study include the heat equation, the wave equation, Laplace's Equation, and Fourier Series with its applications to partial differential equations and boundary value problems. Additional topics may include Green's Functions, the Fourier Transform, the method of characteristics, dispersive waves, and perturbation methods.

Ordinary differential equations (ODEs) are first introduced in the calculus sequence. This course provides a deeper look at the theory of ODEs and the use of ODEs in modeling real-world phenomena. The course includes studies of first order ODEs (both linear and nonlinear), second and higher order linear ODEs, and first order systems of ODEs (both linear and nonlinear). Existence and uniqueness of solutions is discussed in each setting. Most topics are viewed from a variety of perspectives including graphical, numerical, and symbolic.

This course covers the fundamentals of theoretical mathematics with a particular focus on writing clear and rigorous mathematical proofs. The course introduces mathematical logic, set theory, function theory, equivalence relations, cardinality, and the Axiom of Choice. It also exposes students to a variety of subfields of theoretical mathematics, which may include abstract algebra, real analysis, topology, number theory, and/or combinatorics.

In this class students are given examples of problems from an annual international mathematical modeling contest. The students, in groups and with faculty mentoring, develop approaches to the problems. The students and faculty also discuss winning solutions to the problems. The students are expected to participate in the contest and give a presentation of their solution. The course meets once per week, is graded on a pass/fail basis, is a 0 credit course, and can be repeated.

In this class, students and faculty discuss problems that cut across the boundaries of the standard courses, and they investigate general strategies of problem solving. Students are encouraged to participate in a national mathematics competition. This class meets one hour a week, is graded only on a pass/fail basis, is a 0 credit course, and may be repeated.

This course is a study of the basic concepts of linear algebra and their applications. Students will explore systems of linear equations, matrices, vector spaces, bases, dimension, linear transformations, determinants, eigenvalues, change of basis, and matrix representations of linear transformations.

This course, a continuation of the calculus sequence that starts with MATH 180 and 181, is an introduction to the study of functions that have several variable inputs and/or outputs. The central ideas involving these functions are explored from the symbolic, the graphical, and the numerical points of view. Visualization and approximation, as well as local linearity continue as key themes in the course.

This course provides an introduction to the mathematics underlying computer science. Topics include a review of basic set theory, logic (propositional and predicate), theorem proving techniques, logic as a method for representing information, equivalence relations, induction, combinatorics, and graph theory, and possibly formal languages and automata.