Centre College Mathematics Program

Special Topics Courses

Each Spring Term, a member of our faculty will teach a "Special Topics" course. These courses tend to be in an area of interest to the course professor. Courses are taught on a rotating basis. Below are past courses.

MAT 415 Numerical Differential Equations: A study of how computers can be used to find approximate solutions to differential equations. We will develop algorithms for solving both initialvalue and boundary-value problems for first- and second-‐order differential equations, as well as second-order partial differential equations as time permits. For each method we will address issues related to implementation and perform appropriate error and stability analysis of the algorithm. Last taught by Kilty.

MAT 410 Graph Theory: This course focuses on the mathematical theory of graphs. Applications and algorithms are also be discussed. Fundamental topics include simple graphs, digraphs, trees, connectivity, Eulerian and Hamiltonian graphs, graph colorings, independent sets, cliques, and planar graphs. Prerequisite: MAT 190 or 290 or permission of the instructor. Last taught by Wiglesworth.

MAT 407 Mathematical Logic: The course is dedicated to studying the reasoning processes and the relational systems common to all fields of mathematics. A particularly important topic addressed is the relation between truth and proof in mathematics. The course begins by developing sentential logic and first-order logic, the mathematical systems appropriate for addressing such questions. Next, the soundness and completeness of these systems is addressed and the properties of first-order theories and models, including the consequences of the compactness theorem, are studied. Finally, the Godel Incompleteness Theorems are proved, which are among the most important mathematical results of this century. Philosophical and practical implications of these results are discussed throughout the course. Last taught by McAllister.

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. Last taught by Wilson.

MAT 417 Industrial Mathematics: In this course students will complete mathematics projects derived from real‐world problems. Students will work in groups on research problems given by local businesses, industry, and government (BIG). Students will interact in a business setting, manage deadlines, produce technical documents, and think critically to find solutions. Prerequisite: CSC 117; MAT 230 or MAT 240. Taught by Swanson.