Integral Calculus
Topics covered include: transcendental functions, improper integrals, indeterminate forms, sequences, infinite series, Taylor series, numerical methods, and differential equations.
Introduction to Discrete Mathematics
A survey of discrete mathematics including informal proof techniques and mathematical induction, set theory with emphasis on functions and inverse functions, cardinality of sets, graph theory, enumeration, and discrete probability theory. This course stresses algorithmic thinking and precise mathematical expression.
Matrix Algebra
Solutions of linear systems, matrices, vector spaces, linear transformations, determinants, similar matrices, spectral theory, applications to differential equations.
Multivariable Calculus
Calculus of real-valued functions of two and three variables. Topics covered include: polar coordinates, curves and surfaces in space, partial derivatives and multiple integration.
History of Mathematics
A study of the rise of modern mathematics from the mathematics of antiquity and the Middle Ages, with a detailed investigation of the development of one or more of the central concepts of current mathematical thought.
Introduction to Algebra
Groups and their fundamental properties, permutation groups, cyclic groups, subgroups, Lagrange's theorem, and homomorphisms and isomorphisms of groups. Introduction to rings.
Complex Variables
Concepts of complex analysis, holomorphic functions, residue theory, contour integration, conformal mapping.
Analysis
Line and surface integrals, Green's theorem, the divergence theorem, and Stoke's theorem. Properties of real numbers, convergence of sequences and series, and analysis of functions of one variable including metric topology, limits, continuity, uniform continuity, differentiability, and Riemann integrability.
Ordinary Differential Equations
First order differential equations in one independent variable; constructive existence and uniqueness proofs, solutions containing parameters, continuation of solutions; extension to higher order differential equations, vector spaces and systems of linear differential equations.
Introduction to Probability Theory
This course is a calculus-based introduction to the theory of probability. It is designed for the prospective secondary school mathematics teacher. Topics include: the algebra of sets, the probability function, conditional probability, discrete and continuous random variables, simulation, sampling distributions and an introduction to game theory and Markov chains. Technology will be implemented in simulation exercises and data analysis.
Partial Differential Equations and Orthogonal Functions
This course is a continuation of ordinary differential equations and orthogonal sets of functions. Fourier series, Fourier integrals, boundary value problems, linear partial differential equations.
Economics
Principles of Microeconomics
Provides an understanding of the following topics: demand and supply analysis, the production possibilities frontier, marginal analysis, and the concept of opportunity cost, perfect competition, monopoly, monopolistic competition, oligopoly, and contestable markets.
Principles of Macroeconomics
A complete model of aggregate demand and supply is studied, and then used to explain the classical, Keynesian, monetarist, new Keynesian, and new classical models of macroeconomic equilibria. Adaptive and rational expectation models of expectation formation are examined and compared. The effectiveness of monetary and fiscal policy under each of these models is also analyzed.
Managerial Economics
An introductory discussion is followed by a discussion of several mathematical tools that can be used to assist managerial decision making. These tools include linear programming and regression analysis. The primary focus is on the application of these tools to managerial problems. Alternative forecasting techniques are examined and compared.
Money and Banking
The objective of this course is to impart a comprehensive understanding of the role that interest rates and the quantity of money play in determining other macroeconomic variables, such as the unemployment rate, inflation, and the Gross Domestic Product (GDP). This course consists of four parts: 1) Interest rate measurement and determination, 2) the history, structure, and regulation of the banking industry, 3) the Federal Reserve System and the conduct of monetary policy, and 4) monetary theory.
Banking and Financial Markets
The goal of this course is to impart a comprehensive understanding of financial markets, financial institutions, and the management of risky financial assets. his course deals with the measurement and determination of interest rates, as well as theories and empirical evidence about the differences in interest rates across assets and maturities. The relevant concepts in this class include, yield-to-maturity, present value, zero-coupon bonds, default premiums, and the term structure of interest rates. Monetary policy, the Federal Reserve System, interest rate determination, and risk management are also covered.
Introduction to Labor Economics
After this introductory discussion, the focus of the course turns to a discussion of the theory of labor demand. Students examine the short-run and long-run determinants of labor demand. The determinants of the elasticity of labor demand, and the importance of demand. Students examine the tradeoff that occurs between the number of workers hired and the length of the work week. his is followed by a discussion of the household production model in which individuals must choose to allocate time among market and various types of nonmarket activities. The effects of alternative types of welfare, unemployment compensation, and social security systems on labor supply are then examined. The course concludes with an examination of the economics of education, unions, discrimination, compensating wage differentials, and other determinants of wage differences.