# Mathematics (MA)

### Courses

**MA 502 Boundary Value Problems 3 Credits (3,0) **

Basic techniques of solving boundary-value problems of partial differential equations by employing the methods of Fourier series orthogonal functions, operational calculus including Laplace transforms, other integral transforms, and Cauchy's residue calculus. Applications to heat transfer, fluid mechanics, elasticity, and mechanical vibrations. Computer applications.**Prerequisites:** MA 441.

**MA 504 Theory of the Potential 3 Credits (3,0) **

Potential theory and Green's function. Method of characteristics and solution of Cauchy's initial value problem for first and second order equations. Numerical methods. Application to fluid mechanics, electromagnetic fields, heat conduction, and other areas. Computer applications.**Prerequisites:** MA 502.

**MA 505 Statistics I 3 Credits (3,0) **

Descriptive statistics and graphical depiction of data; confidence intervals and hypothesis testing for the mean, difference between two means, variance, ratio of two variances, proportion, and difference between two proportions; simple and multiple regression, including model development, inferences, residual analysis, outlier identification, and verification of assumptions; fundamental concepts of design of experiments; justification of linear models; construction and analysis of basic designs including one-way, block designs, and Latin squares; multiple comparisons.**Prerequisites:** MA 243.

**MA 506 Probability and Statistical Inference 3 Credits (3,0) **

Review of basic statistics concepts and introduce concepts in experiment design, including use factorial designs and an introduction to techniques for nonlinear or non-normally distributed data. Several nonparametric statistical techniques, including Mann- Whitney test and Kruskall-Wallis test. Advanced regression topics, including the use of transformations, weighted least squares regression. Use of statistical software packages.

**MA 510 Fundamentals of Optimization 3 Credits (3,0) **

Overview of several important general types of optimization problems; development of mathematical models; linear programming; the simplex method; introduction to sensitivity analysis, networks; applications involving Maple and Excel.**Prerequisites:** MA 243.

**MA 520 Mathematical Programming and Decision-Making 3 Credits (3,0) **

A continuation of MA 510. Development of mathematical modeling techniques with an emphasis on integer programming, nonlinear programming, and multiple-criteria decision-making techniques; case studies from aviation/aerospace involving mathematical programming and decision-making.**Prerequisites:** MA 510.

**MA 532 Numerical Linear Algebra for Engineers 3 Credits (2,1) **

Review of matrix operations. Advanced introduction to numerical linear algebra and matrix methods used in solving linear systems that arise in engineering and science. Direct and iterative methods for linear systems, eigenvalue decomposition and matrix factorization such as LU/LQ/SVD factorizations, sparse and structured matrices. Introduction to Spectral Analysis and Least Squares approximation.

**MA 540 Data Mining 3 Credits (3,0) **

Data Mining is to gather, assimilate, and make sense of large amounts of data. The course includes techniques, algorithms, and open-source software to automatically classify data, to discover novel and useful patterns, and to help predict future outcomes. Prerequisites are Statistics, Multivariate Calculus, and familiarity with either Java, C/C++, MATLAB or R.

**MA 541 Introduction to Mathematical Analysis 3 Credits (3,0) **

Careful treatment of the theoretical aspects of the calculus of functions of a real variable. Topics include the real number system, limits, continuity, derivatives, the Riemann integral, elementary notions of topology and metric spaces.

**MA 543 Complex Variables 3 Credits (3,0) **

Algebra of complex numbers; complex functions, analytic functions; mapping by elementary functions; conformal mappings and their applications; additional topics may include complex integration, power series expansion.

**MA 544 Data Visualization 3 Credits (3,0) **

Introduction to different aspects of information and scientific visualization, computer graphics and related mathematics concepts; representation of data graphically and using exploratory data analytics to gain understanding and insight into data; application software packages for interactive display and analysis of data.

**MA 546 Application-Based Advanced Engineering Mathematics 3 Credits (3,0) **

This course is designed to present a general approach of introducing a survey of core advanced engineering mathematics topics. The general approach is sought is to present a representative physical circumstance then subsequently develop the mathematical representation (mathematical model) fitting that circumstance noting areas where approximations are needed and introduced or dismissals are applied.

**MA 550 Partial Differential Equations 3 Credits (3,0) **

Physical models leading to partial differential equations. Fourier series and Fourier transforms. Solution of linear partial differential equations, including solutions of the wave, heat and Laplace's equation.

**MA 553 High Performance Scientific Computing 3 Credits (3,0) **

This course is an introduction to high performance computing in computational mathematics and sciences with practical applications. The course provides an overview of parallel computing and study of program efficiency on high performance computers. It concentrates on the two major parallelization paradigms: shared-memory parallelization with OpenMP and distributed-memory parallel programming with MPI. The main focus of the course will be on applications of parallel computing in the sciences (Engineering, Physics, Mathematics, etc.).**Prerequisites:** MA 305 or MA 348.

**MA 588 Numerical Methods in Fluids 3 Credits (3,0) **

This course explores the theory and applications of numerical methods in fluid mechanics. The topics covered will include numerical methods for incompressible flows; primitive variable and vorticity stream function on formulation; numerical treatment for inviscid and viscous flows, including restricted to incompressible flow. Emphasis will be placed on numerical methods based on finite difference, finite volume, or finite element formulations.

**MA 599 Special Topics in Mathematics 1-6 Credit**

Students may elect to perform a special, directed analysis and/or independent study in an aviation area of particular interest. A detailed proposal of the desired project must be developed and presented to the department chair or center director for faculty review and recommendation, three weeks prior to the end of registration for the term.

**MA 605 Statistical Quality Analysis 3 Credits (3,0) **

Fundamental concepts of statistical quality control, including Shewhart charts, cusum charts, EWMA charts, multivariate charts, tolerance limits, and capability analysis. Further development of concepts in statistical design of experiments including use of factorial designs, fractional factorial designs, and use of central composite designs. Several nonparametric statistical techniques, including sign test, signed rank test, rank-sum test, Kruskal-Wallis test, runs test, and Kendall's Tau. Advanced regression topics, including the use of transformations, weighted least squares regression, and detection of influential points. Throughout the course, industrial applications will be emphasized, including the use of several case studies.**Prerequisites:** MA 505.

**MA 610 Multivariate Optimization 3 Credits (3,0) **

Multiple objective optimization with an emphasis on response surface methodologies and goal programming; inclusion of group decision-making techniques in model development; case studies from aviation/aerospace emphasizing multivariate model development, and determination of optimal solutions.**Prerequisites:** MA 520 and MA 605.

**MA 615 Data Driven Modeling 3 Credits (3,0) **

Methods for complex systems & big data with emphasis on data driven modeling, model validation, and simulation; dynamic system and agent-based modeling, Monte Carlo, Markov chain, data fitting, data transformations for natural language processing and image processing; advanced data mining techniques such as cost sensitive machine learning, data compression, feature selection, and deep learning; hands- on experience on software tools such as R, MATLAB, and Python, to solve and evaluate solutions to data- enabled research problems.**Prerequisites:** MA 540 and CS 540.

**MA 625 Computing for Data Compression, Image and Signal Processing 3 Credits (2,1) **

Study of algorithms to perform linear algebra operations, matrix operations, and numerical approximations, as a foundation to understand electrical engineering and computer science concepts. Integration with other disciplines through applications in data compression, signal processing, image processing, telecommunication, and computational finance. Arithmetic complexity, accuracy, stability, and performance of algorithms in connection to numerical linear algebra problems.

**MA 630 Complex Networks and Applications 3 Credits (2,1) **

Introduction to complex network theory and its applications in big data system identification, and in capturing and exploring connections at the petabyte level of information in physics, biology and social sciences; basic graph theory and foundations of statistical physics with applications to real world networks; network models such as small world networks, scale free networks, spatial and hierarchical networks; network visualization techniques and complex network tools.**Prerequisites:** MA 540.

**MA 680 Data Science Capstone Project 3 Credits (3,0) **

Apply the Mathematics, Statistics, and computer science knowledge to solving common problems in business environment; more practical industrial techniques in data mining, visualization, and modeling to help meet deadlines; introduce practical challenges such as business problem assessment; analysis design; data collection and quality control; computer programming; analytical solutions; and technical communication.**Prerequisites:** MA 540 and CS 540.

**MA 690 Graduate Research Project 3 Credits (3,0) **

An applied problem on an aviation/aerospace topic that requires the use of optimization and/or quality- improvement skills.

**MA 699 Special Topics in Mathematics 1-6 Credit**

Students may elect to perform a special, directed analysis and/or independent study in an aviation area of particular interest. A detailed proposal of the desired project must be developed and presented to the department chair or center director for faculty review and recommendation, three weeks prior to the end of registration for the term.

**MA 700 Thesis Research 1-9 Credit**

Written and defended documentation of a research project conducted under the supervision of a faculty committee. The research must be at the level of a published paper in an appropriate journal, as determined by the faculty committee.