Mathematics and Computer Science

A continuation of MTH 120. Techniques and applications of integration. Infinite sequences and series. Prerequisite: MTH 113 or 120 with a grade of C- or better. Fall and spring, every year.

A thorough treatment of the techniques of formal reasoning. Topics include truth-functional logic, quantification logic and construction of correct deductions. Prerequisite: MTH 105 or higher mathematics course. Spring, even-numbered years.

A study of the techniques and theory of solving ordinary and partial differential equations. Topics may include series solutions, numerical methods, Fourier and Laplace transforms, linearization, stability theory, periodic orbits, and bifurcations and chaos. Prerequisite: MTH 310 or PHY 304. Spring, typically odd-numbered years.

A college-level approach to Euclidean and non-Euclidean geometries. The course will pursue an in-depth investigation into the following topics: Hilbert's postulates for Euclidean geometry, the parallel postulates, neutral geometry and non-Euclidean geometry. Prerequisite: MTH 220. Fall, odd-numbered years.

Game theory is the study of the interaction of rational decision makers. This course uses game theory to study incentives and strategic behavior in practical situations of inter-dependent decision making and negotiations. The course will develop basic theoretical concepts in tandem with applications from a variety of areas, including bargaining, competition, and strategic voting. Prerequisite: MTH 310 or MTH. Spring, typically even-numbered years.

This course serves as an introduction to the formulation, analysis and interpretation of mathematical models in the study of problems in the natural, management and social sciences. Topics may include optimization, dimensional analysis, Markov chains and autonomous systems. The course will require the use of the Eaton Corporation Computer Laboratory and the software packages R, Mathematica, and Matlab. Prerequisite: MTH 310. Spring, every year.

A course on mathematical interest theory. Topics discussed will include the time value of money, annuities and cash flows, loans, bonds, the yield rate of an investment, the term structure of interest rates, duration, and immunization. The course may also include topics from financial economics. Prerequisite: MTH 220 with a grade of C- or better. Offered as needed.

A study of the historical development of various branches of mathematics from antiquity through the end of the nineteenth century. Topics include mathematics prior to classical antiquity, mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of the calculus, and the nineteenth century evolution of algebra, geometry, and analysis. The course will emphasize primary source materials. Prerequisites: MTH 310 and 320. Fall, even-numbered years.

A rigorous treatment of the calculus of one variable, including limits, continuity, sequences, differentiation and Riemann integrals. This course should be taken in the junior or senior year. 

The theory of functions of a single complex variable. Complex numbers, elementary complex functions, differentiation and integration of complex functions, complex series and residue theory. Prerequisite: MTH 320. Fall, even-numbered years.

Numerical methods for approximation of roots, systems of linear equations, interpolation and curve fitting, numerical integration and differentiation, and differential equations. Problems are generally approached through structured algorithms. Prerequisite: MTH 310 and 320. Fall, every year.

An introduction to the theory of algebraic structures, including the elementary properties of groups, rings and fields. This course should be taken in the junior or senior year. Prerequisite: MTH 310 and and one of the following: MTH 330, MTH 335, or MTH 360. Fall, every year.

An introductory course in the fundamental concepts of general topology, including metric spaces, topological spaces, connectedness and compactness. Prerequisite: MTH 310 and one of the following: MTH 335 or MTH 360. Spring, even-numbered years.

Students will be introduced to contemporary mathematics literature with an emphasis on undergraduate research. Instruction will be given on how to read and write mathematics papers, how to give and receive math talks, what to do at math conferences, how to perform literature searches, and other skills related to the mathematics profession and the practice of mathematics beyond the classroom. Prerequisite: MTH 310 and MTH 320.