Below you will find titles and descriptions of MAT 250's and MAT 400's that have been taught in recent years. If you are a student and interested in studying a particular topic, please come talk to one of us. You may have picked the topic for the next MAT 250/400's!!

MAT 406 Introduction to Coding Theory
Mathematical stuctures of vector spaces, groups, and finite fields are used to develop efficient and reliable methods of transmitting and storing information. Several specific types of linear block codes, including Hamming, Golay, BCH, and cyclic codes, are studied. Prerequisite: MAT 240.

MAT 254: Explorations in Advanced Mathematics
A course designed to enhance the ability of students to discover and prove results in advanced mathematics. Students use the computer to explore questions and look for patterns, leading to conjectures and eventually to the proofs of mathematical theorems. Examples are taken from areas like number theory, analysis, discrete mathematics, and geometry. Prerequisite: MAT 171; CSC 117 helpful but not required.

MAT 404 Introduction to Topology
Topics include metric spaces, continuity, and homeomorphisms. Prerequisite: MAT 230 and 240.

MAT 253: Problems, Projects, and Presentations
A study of different techniques used in mathematical problem solving. Students will work in teams and use mathematical software to solve problems arising in both pure and applied math projecs. Emphasis will be placed on oral and written presentation of results. A Wednesday - Saturday field trip is planned to the national Joint Mathematics Meetings in Phoenix, Arizona during the first week of the term.

MAT 405 Theory of Integration
A study of the theory of the integral, the course begins by describing Bernhard Riemann’s 1850s formulation of the integral (used in calculus courses to integrate continuous functions). It then explains Henri Lebesgue’s reformulation (developed in 1901), which mathematicians often consider the beginning point of a modern analysis of functions. The Lebesgue integral forms a “natural” mathematical venue for many fields such as probability theory and quantum mechanics. Discussion of the Riemann integral includes Upper and Lower Riemann Sums and finishes by characterizing Riemann integrable functions. The course then introduces the Lebesgue Integral (as a generalization of the Riemann integral) for the real line only. Prerequisite: MAT 230 and MAT 240.

MAT 403 Partial Differential Equations
A study of linear partial differential equations of first and second order. Includes the introductory theory of linear partial differential equations. Also, explicit solutions of the wave equation, Laplace's equation, and heat equation are obtained using the method of separation of variables and Fourier series. Prerequisite: MAT 360 or 26.

MAT 252: Aspects of Topology
This course touches on some of the questions that led to the birth of topology as a distinct branch of mathematics. The primary focus is on the types of reasoning that are considered "topological." We will spend class in a combination of discussions and in-class projects, including puzzle solving, artistic response, art analysis/representation, and the use of knot modeling software.

MAT 251: Advanced Geometry
This course uses mathematics to study the geometry of multidimensional spaces, even when the space is "curved" (or non-Euclidean). In particular, students will review several multivariate calculus topics, such as vectors, the divergence, gradient, and curl. In addition, the course will introduce new concepts, such as "curvilinear coordinates," "tensors," and "differential forms" and will describe "coordinate-independent" formulation of vectors. The instruction will utilize many forms of learning that may include computer technology in the classroom, group problem solving, and individual guidance through workbooks. The material is useful in many different areas of mathematics, applied mathematics, and physics.

MAT 250: Modern Cryptography
This course examines the mathematics of modern cryptographic systems, which provide security and ensure authenticity of electronic messages. The course will place special emphasis on pbulic key cryptography (systems that allow anyone to use a public key to encrypt a message that only the recipient can read). Two areas of mathematics - number theory (the study of whole numbers) and abstract algebra (the study of algebraic structures) - play a crucial role in the analysis. Students will sometimes work in teams, and the course organization will provide the opportunity to solve mathematical problems in both a conventional manner and with computer software.

Introduction to Topology
Topology is concerned with the intrinsic, qualitative properties of spatial configurations that are independent of size, location, and shape. For example, a balloon may be contorted into various shapes and returned to its original shape as long as it is not "popped." Various definitions of "open" sets are used to obtain topological spaces. Topics discussed for each topological space include cluster points, closure, continuity of functions, connectedness, and compactness. We also discuss separation axioms and metric spaces.

Explorations in Advanced Mathematics
A course designed to enhance the ability of students to discover and prove results in advanced mathematics. Students use the computer to explore questions and look for patterns, leading to conjectures and eventually to the proofs of mathematical theorems. Examples are taken from areas like number theory, analysis, discrete mathematics, and geometry.

Mathematical Logic
The course is dedicated to studying the reasoning processes and the relational systems common to all fields of mathematics and the relation between truth and proof in mathematics. We begin by developing sentential logic and first-order logic, consider the soundness and completeness of these systems and study the properties of first-order theories and models. For our grand finale, we will prove the Gödel Incompleteness Theorems. Philosophical and practical implications of these results are discussed throughout the course.

Probability and Lebesgue Measure
A study of probability theory first formulated by the mathematicians Andrei Kolomogorov and Norbert Wiener in the 1930's. Topics include: why probability theory is best understood using Lebesgue measure, measure theory as an extension of the Riemann integral, and probability applications such as the Central Limit Theorem.

Applied Mathematics
This course surveys a few applied topics evolving from ideas in linear algebra. After reviewing some linear algebra concepts and setting a framework for the applications, the course covers topics such as: least squares, electrical networks, linear and nonlinear differential equations, Fourier series, and the heat and wave equations.

Game Theory
A survey of game theory and its applications based on the foundational ideas of Von Neumann, Morgenstein, and Nobel Prize winner John Nash. Topics include: finite games and their representations, making deals and finding bargaining solutions, zero sum games and applications in economics, and games with repetitions.

Application of Vector Space Methods
The description of optimization problems through the unification of a few principles of linear vector space theory. Concepts such as distance, orthogonality, and convexity produce results. Topics include: vector spaces, normed linear spaces, Fourier series, a control problem, least squares, and optimization.

Historical Development of Mathematics
A history of mathematics from different perspectives: solving problems the way they were solved originally, analyzing original documents, and learning about the people who developed mathematics.

Hiding Information and Preventing Errors
The course is divided into two three-week sections. The first half of the course develops the topics found in number theory which may be applied to create cryptographic systems such as the RSA Public Key System. The second half of the course applies abstract algebra to create error-correcting coding schemes used in computers, check-out lanes, and many types of identification numbers.