Mathematics

An introduction to areas of applied math that use the skills of first year algebra. There are many topics that could be covered: Linear Systems, Matrix Theory, Linear Programming, Counting and Probability, Game Theory, Markov Processes, Finance Models, Graph Theory. The specific topics covered are at the discretion of the professor and can be tailored to the backgrounds of the students. This course contains topics of particular interest to students studying business or business-related topics. It is an excellent choice for those students who are also seeking a minor in mathematics.

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. Topics include vectors and the basic analytic geometry of three-space; the differential calculus of scalar-input, vector-output functions; the geometry of curves and surfaces; and the differential and integral calculus of vector-input, scalar-output functions.

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 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.

The calculus of functions with complex numbers as inputs and outputs has surprising depth and richness. The basic theory of these functions is developed in this course. The standard topics of calculus (function, limit, continuity, derivative, integral, series) are explored in this new context of complex numbers leading to some powerful and beautiful results. Applications include using conformal mappings to solve boundary-value problems for Laplace’s equation.

This course presents a rigorous study of abstract algebra, with an emphasis on writing proofs. Modern applications of abstract algebra to problems in chemistry, art, and computer science show this is a contemporary field in which important contributions are currently being made. Topics include groups, rings, integral domains, field theory, and the study of homomorphisms. Applications such as coding theory, public-key cryptography, crystallographic groups, and frieze groups may also be covered.