Introductory Courses

MTH 511, Advanced Mathematical Analysis: This course is a review of basic results of calculus: power series, directional derivatives and gradient, extrema and Lagrange multipliers, and multiple integration. Advanced topics in calculus are covered: uniform convergence of sequences of functions, uniform convergences of series of functions, implicit function theorems, and functions defined by integrals. Topics in linear algebra include: solution of systems of equations and matrices, vector spaces, and eigenvalue problems. Also covered are the following multivariate calculus topics: directional derivatives, chain rule, Lagrange multipliers, Taylor’s formula, the mean value theorem, the inverse and implicit mapping theorems, iterated integrals and Fubini’s theorem. 3 Cr. Hrs.

MBA 620, Financial Analysis and Markets: This course is an overview of finance to include the analysis of financial statements, valuation concepts, capital budgeting techniques, capital structure analysis, working capital management, and capital market. 3 Cr. Hrs.

Required Courses

MTH 538, Introduction to Financial Mathematics: This course covers Markov random processes, Brownian motion in financial markets, stochastic integral, stochastic differential equation, Ito calculus, European style stock options, Single-agent consumption and investment, and equilibrium in a complete market. 3 Cr. Hrs.

MTH 525, Stochastic Processes: This is a basic course on stochastic processes. Topics to be covered include a review of fundamental probability theory, Markov chains, Poisson process, birth and death process, renewal processes, Random walk and Brownian motion, and Martingales. 3 Cr. Hrs.

MTH 556, Numerical Analysis II: This course discusses numerical solution of partial differential equations. The course materials include finite difference methods, stability, convergence, error estimate, numerical treatments of the Black-Scholes equation, splitting method, adaptive method, binomial trees and Monte Carlo computational methods. 3 Cr. Hrs.

MTH 544, Time Series: This course covers Stochastic models for discrete time series in the time-domain, smoothing with moving averages, autoregressive processes (ARMA, ARCH, GARCH), vector autocorrelation, Bayesian analysis, Kalman filter and model identification, parameter estimation, forecasting, and Markov chains and changes in regimes.3 Cr. Hrs.

MTH 557/MBA 622, Financial Derivatives and Risk Management: This course consists of two parts. The first part covers the usage and pricing of derivatives – subjects include the basis features of futures and options, binomial and trinomial option pricing, the Black-Scholes formula, exotic options, swaptions, interest rate based derivatives, implied binomial trees, volatility measurement, dynamic trading strategies and varieties of exotic options. It also covers arbitrage-based derivatives pricing approaches, emphasizing economic intuition and understanding of quantitative analysis. The second part of the course covers financial risk measurement and management – including market risk, credit risk, liquidity risk, settlement risk, model risk, volatility risk, and kurtosis risk. 3 Cr. Hrs.

MTH 558/MBA 623, Computational Finance and Data Mining: This is a team taught course with a faculty member from the Department of Economics and Finance and a faculty member from the Department of Mathematics. Students study topics relevant to solving partial differential equations that arise in finance, topics relevant to simulation methods that arise in the analysis of financial derivatives, and topics relevant to optimization methods in finance. Partial differential equations topics include finite difference methods with connection to binomial models and interest rate models. Topics also include non-traditional methods such as neural networks, the genetic Algorithm, Fuzzy Logic, etc. Topics related to simulation methods include random variable generation, variance reduction methods, statistical analysis of simulation output, importance sampling, Martingale control variables and stratification. With respect to optimization, both linear and nonlinear methods will be introduced. 3 Cr. Hrs.

Elective Courses

MBA 625, Investments and Financial Markets: This is a study of investment principles and techniques used by both individual and institutional investors. Topics include bond and stock markets, security valuation methods, portfolio theory and management, and investment institutions. 3 Cr. Hrs.

MTH 534, Optimal Control Theory and Applications in Finance and Economics: This course deals with the optimal control theory and its applications in finance and economics. The first part of the course covers the basic optimal control theories and methods. Topics include formulation of optimal control problems, calculus of variations, the Maximum Principle under various constraints, solutions of linear quadratic regulator problems, and stochastic optimal control. The second part of the course focuses on the applications of optimal control in the fields of finance, economics and marketing. The course also provides an introduction of game theory and its application in distributed systems. 3 Cr. Hrs.

MBA 628, Fixed Income Analysis: This class will expose students to a variety of fixed income instruments that are traded in the financial markets, their investment characteristics, the state-of-the-art technology for valuing them, technique for quantifying their interest rate risk, and portfolio strategies for using them. This is a valuable course for CFA candidates, Fund Managers, Credit Risk Managers, Commercial Bankers, and anyone interested in investing in fixed income securities as alternatives to stocks. 3 Cr. Hrs.

MTH 543, Regression Analysis: Topics covered include least squares, lack of fit and pure error, correlation, matrix methods, F test, weighted least squares, examination of residuals, multiple regression, transformations and dummy variables, model building, ridge regression, stepwise regression, and multiple regression applied to analysis of variance problems. 3 Cr. Hrs.

MTH 535, Partial Differential Equations: This course covers classifications of partial differential equations, methods of solution of the wave equation, Laplace’s equation, and the heat equation, the Black-Scholes equation, applications of partial differential equations. 3 Cr. Hrs.

MTH 531, Ordinary Differential Equations: Topics include existence and uniqueness theorems, linear equations and systems, self-adjoint equations, boundary value problems, and basic nonlinear techniques. 3 Cr. Hrs.

MTH 547, Statistics for Experimenters: This course covers the design of experiments and analysis of quantitative data which are useful to anyone engaged in experimental work. The course features designed experiments using replication and blocking, the use of transformations, and applications of full and fractional factorial designs. Also covered is experimental design for developing quality into products using Taguchi methods. 3 Cr. Hrs.

MTH 551, Methods of Mathematical Physics: This course discusses linear transformations and matrix theory, linear integral equations, and calculus of variations, eigenvalue problems. 3 Cr. Hrs.

MTH 552, Methods of Appled Mathematics: Topics include dimensional analysis and scaling, regular and singular perturbation methods with boundary layer analysis, the stability and bifurcation of equilibrium solutions, and other asymptotic methods. 3 Cr. Hrs.

MTH 565, Linear Algebra: This course covers vector spaces, linear transformations and matrices, inner product spaces, invariant direct-sum decomposition and the Jordan canonical form. 3 Cr. Hrs.

MTH 583, Discrete and Continuous Fourier Analysis: This course covers Fourier representation of Complex valued functions, rules for finding Fourier transforms, mathematical operators associated with Fourier analysis, fast algorithms, wavelet analysis, and selected applications. 3 Cr. Hrs.

MTH 532, Difference Equations: Topics include the calculus of finite differences, first order equations, linear equations and systems, z-transform, stability, boundary value problems for nonlinear equations, Green’s functions, control theory, and applications. 3 Cr. Hrs.

ENM 521, Deterministic Operations Research: This course is an introduction to deterministic methods for optimization, with a focus on mathematical programming (linear, nonlinear, integer) and network methods. 3 Cr. Hrs.

ENM 522, Probabilistic Operations Research: Students are introduced to probabilistic methods for modeling and analyzing the performance of complex systems. Topics include Markov chains, queuing, forecasting, discrete event simulation, and inventory modeling. 3 Cr. Hrs.

CPS 542, Database Management Systems: This course covers physical and logical organization of data files; hierarchical, network, and relational database models; data definition language and data manipulation language of a commercial database management system, and query languages. 3 Cr. Hrs.