# Mathematics

MAT 500        Topics in Applied Mathematics (3)

This course will introduce students to several topics in the area of mathematical methods.  Topics includes: complex numbers, determinants and matrices, ordinary differential equations, Fourier series, partial differentiation, multiple integrals and vector analysis.  Prerequisite:  Calculus II (MAT 122) or equivalent.

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 through the course. Prerequisites: MAT 340 or MAT 260 or permission of instructor.

MAT 505        Introduction to Probability

Sample space 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, transformation 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

MAT 515        Mathematical Methods in Computational Science and Engineering (3)

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 problem 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 at the undergraduate level.

MAT 521        Financial Mathematics I – Theory of Interest

Theoretical foundation and a practical understanding of interest theory in finite and continuous time will be developed. This theory includes the fundamentals of how annuity functions are applied to the concepts of present and accumulated value for various cash flow streams, and how this is used for further planning in valuation, pricing, duration, and investment. Applications to amortization of lump sums, fixed income securities, deprecation, mortgages, and related concepts will be discussed. In addition, short sales and derivatives for financial risk management will be covered. Prerequisites: MAT 505 Introduction to Probability or equivalent.

MAT 530        Number Theory and Its Applications (3)

Introductory course in Number Theory that will introduce students to the basic concepts as well as some modern applications.  Topics include: prime numbers, Greatest Common Divisors, The Euclidean Algorithm, congruences, Fermat’s Little Theorem, primality testing, etc.  Applications of Number theory:  cryptography, pseudorandom numbers, etc.

Prerequisites:  MAT 380 or MAT 381 or MAT 413 or permission of instructor.  Cross listed with MAT 430.

MAT 550 Times Series Analysis (3)

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 economic, engineering, and 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 or Equivalent.

MAT 590        Selected Topics in Mathematics (3)

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 an instructor.