Graduate Math Courses
MATH 6353 - History of Mathematics
An overview of the history of mathematics from the time of the ancient Egyptians to the present day. Appropriate for undergraduate math and math education majors as well as students working toward master's degrees in math/science education.Prerequisite: MATH 2014
MATH 6403 - Advanced Calculus I
Rigorous review of elementary calculus, real number system, continuous functions, Taylor's formula, infinite series, convergence criteria.Prerequisites: MATH 3033 and MATH 3073
MATH 6413 - Advanced Calculus II
Coordinate transformations, vectors, multiple integrals, Green's theorem, theory of integration, Fourier series.Prerequisite: MATH 4003
MATH 6483 - Introduction to Topology
An introduction to point-set topology. Sets, Cartesian products, relations, mappings, sequences, topological spaces, metric spaces.Prerequisite: MATH 3033
MATH 6523 - Linear Algebra and Matrix Theory
Systems of linear equations, eigenvalues, eigenvectors, finite dimensional vector spaces, and linear transformations with applications. Numerical solutions of systems of linear equations.Prerequisite: MATH 2024
Note: Not allowed for M.S. program in applied mathematics
MATH 6533 - Introduction to Complex Functions
Algebra of complex numbers. Properties of complex functions, derivatives, complex integrals, Cauchy's integral formula. Conformal mapping with applications to potential theory.Prerequisite: MATH 3073
MATH 6543 - Introduction to Partial Differential Equations
Continuation of Math 3073. Green's Theorems, Fourier series, Laplace transforms, partial differential equations including boundary conditions, exact solutions, classifications of equations, separation of variables, and solutions by transformation techniques.Prerequisite: MATH 3073
MATH 6603 - Introduction to Numerical Methods
Error analysis of computer arithmetic, solution of nonlinear equations, roots of polynomials, interpolation and approximation methods, numerical differentiation and integration, initial value problems for ordinary differential equations.Prerequisites: MATH 2073, CS 2503, or permission of instructor
MATH 6633 - Scientific Software Environments
Selected case studies from the sciences and engineering are used to discuss the interplay of mathematical modeling, scientific computing, and the applied sciences and engineering. Issues of high performance architectures, software engineering methodology for large-scale codes, and visualization of large data sets are discussed.Prerequisites: MATH 3073 and either CS 2503 or CS 2003
Co-listed with CS 6693
STAT 6613 - Probability
Introduction to probability theory. Probability spaces, random variables, distribution functions, expectation, conditional probability, and conditional expectation.Prerequisite: MATH 2073
STAT 6813 - Statistical Methods for Scientists and Engineers
Elementary probability, random variables and distributions, tests of significance, test of hypotheses, elementary experimental design, simple Regression, and correlation.Prerequisite: MATH 2014
MATH 7013 - Advanced Mathematical Modeling
The process of construction, analysis, and validation of dynamic and discrete mathematical models for the physical and life sciences. Computer implementation and subsequent assessment of mathematical models. Introduction to the Mathematica programming environment.Prerequisites: MATH 3073 and MATH 4123 or consent of instructor
MATH 7023 - Discrete Modeling
An introduction to the application of discrete mathematical models to the social, behavioral, biological, environmental, and physical sciences. The course will especially emphasize graph models and optimization strategies that are applied to engineering problems in communication and transportation.Prerequisite: Graduate standing
MATH 7033 - Professional Skills of Industrial Mathematics
Training in the non-mathematical skills necessary for work in an industrial setting. Written and oral communication, reports and presentations, teams, internal consulting skills, business economics and accounting, and other topics. The course will include group work and student presentations.Prerequisite: Graduate standing
MATH 7103 - Advanced Differential Equations
Fundamentals of ordinary and partial differential equations, initial value and boundary value problems, including numerical methods. Course includes an introduction to the Matlab programming environment.Prerequisite: MATH 3073
MATH 7243 - Computational Linear Algebra
Computational techniques for the solution of systems of linear and non-linear algebraic equations. Emphasis on the intelligent use of existing software packages. Laboratory exercises using matrix based computational environments required.Prerequisite: MATH 4123
MATH 7253 - Numerical Optimization
An introduction to numerical techniques for unconstrained and constrained optimization. Applications to nonlinear regression and science and engineering problems.MATH 7273 - Numerical Differential Equations
Numerical analysis of engineering and scientific problems with special emphasis on discrete techniques for ordinary and partial differential equations and on problem formulation and solution.Prerequisites: MATH 3073, CS 1043 or CS 2503 or consent of instructor.
MATH 7353 - Discrete and Integral Transforms
Fourier, Laplace, Wavelet and other discrete and continuous transforms with applications to the analytical solution of partial differential equations, data compression, image processing and filtering.MATH 7413 - Mathematical Problems from Industry
Students explore the possible solution of mathematical problems postulated by visiting scientists and engineers from industrial and commercial concerns. Topics vary from term to term and may include issues from engineering, natural sciences, finance, insurance etc. May be repeated: maximum graduate credit six hours.Prerequisites: Mathematical Modeling and at least two core applied mathematics graduate courses, or consent of instructor.
MATH 7503 - Stochastic Simulation and Queuing
Random number generation and stochastic simulation with applications.Prerequisite: STAT 3813, STAT 4413 or consent of instructor
MATH 7533 - Applied Regression
Methods for fitting deterministic models to data in the presence of noise. Least squares, statistical analysis, empirical response surface optimization in the presence of noise, and non-linear models.Prerequisite: STAT 3813
MATH 7913 - Group Report
Students work in groups to analyze a realistic industrial problem using the complete modeling paradigm. Problem identification and analysis, model development, model solution method and implementation, solution assessment and evaluation. Group reports, presentation, and documentation.MATH 7961 - Graduate Residency
MATH 7971-3 - Mathematical Internship in Industry
Internship at an industrial or government facility. The internship culminates in a written report for evaluation by the instructor.Pre-requisites: Advanced Mathematical Modeling and at least two core mathematical sciences graduate courses, or consent of instructor.