MAT 502 Linear Algebra
This course is a graduate level Linear Algebra course, with an emphasis on applications including linear models and linear estimation. The student will build on the knowledge obtained in undergraduate math courses such as Linear Algebra and Differential Equations, learn about special matrices, singular value decomposition, pseudo inverse, quadratic forms, Hilbert spaces and least squares, and acquire an introduction to linear models and linear estimation, A computational environment is integrated throughout the course. Prerequisite: MAT 340 Linear Algebra or MAT 260 Differential Equations or consent of Instructor.
MAT 515 Mathematical Methods in Computational Science and Engineering
Essential to the practicing applied mathematician is the ability to analyze and solve problems from science and engineering. This course provides the student with a context for problems solving at a mature level with a review and further development of topics in linear algebra, including applications to networks, structures, and estimation. Optimization is covered, including Lagrange multipliers. Much of the language of applied mathematics is based on differential equations. This course explores analytic and numerical solutions to Laplace’s equation and potential flow; boundary–value problems; minimum principles and calculus of variations. Also developed are Fourier series; the discrete Fourier transform; convolutions, and applications. Students are expected to have mastered Linear Algebra, Differential Equations, and Multivariable Calculus on the undergraduate level.
MAT 560 Numerical Differential Equations
Mathematical methods, algorithms, and numerical implementations associated with the solution of ordinary and partial differential equations are investigated. Standard methodologies including Euler, Runge-Kutta, finite difference and finite element are developed in the context of applied problems. Topics include the numerical solution of initial and applied boundary value problems, parabolic, elliptic, and hyperbolic partial differential equations. Convergence, accuracy, and appropriateness of method are developed in a systematic manner. Prerequisite: MAT 515 Mathematical Methods in Computational Science and Engineering.
Choose one from the following, depending on student interest:
MAT 550 Time Series Analysis (3 credits)
This course is an introduction to the theory and applications of time series analysis and modeling. The students will acquire a working knowledge of time series and forecasting methods as applied in economics, engineering and the natural and social sciences. Topics covered include stationary processes, ARMA and ARIMA processes, multivariate time series, state-space models, the Kalman Recursion and spectral analysis. A computational environment for simulation and data analysis is integrated throughout the course. Prerequisite: MAT 370 Applied Probability.
MAT 505 Introduction to Probability (3credits)
Sample spaces and counting, axioms and rules of probability, conditional probability and independence, modeling with discrete and continuous random variables, jointly distributed random variables, characteristics of random variables, transformations of random variables, moment generating functions. Law of large numbers and central limit theorem, statistical applications, random number generation and simulations of systems. Prerequisite: MAT 253 Calculus III.
MAT 590 Selected Topics in Mathematics (3credits)
Provides students with the opportunity to learn specific topics not offered via regular coursework. Topics will be selected by faculty and will require a mix of theoretical and applied knowledge as appropriate. Prerequisite: Permission of Instructor.