# Free Electives

### Choose from the following list of courses with Graduate Advisor's approval:

**(Note: Extra courses previously taken in the list of Prescribed Electives can be used as free electives. See Degree Requirements for details.)**

### Computer Science (CS courses)

**CS 5310 Computer Graphics**

Computer representation and display of graphical information including line, character, and curve generation, two- and three-dimensional graphical techniques, interactive methods, and advanced topics. Prerequisite: CS 3370.

**CS 5317 Human-Computer Interaction**

Models and methods of human-computer interaction. Theory of human-computer interaction. Development of methods for interfaces such as user-centered design, prototyping and participatory design. Evaluation and testing techniques such as heuristic evaluation, the cognitive walk through, and usability testing. User-interface programming. Ethical and societal issues. Prerequisite: instructor approval.

**CS 5340 Advanced Operating Systems**

A review of process synchronization, deadlocks and memory allocation paradigm, followed by in depth coverage of distributed systems, computer security, and queuing theory. Prerequisite: CS 4375 or instructor approval.

**CS 5351 Interval Computations**

An overview of interval computations that take into account how input uncertainties influence the computation result. A review of the main ideas behind interval computations, main interval techniques, and applications to practical problems such as robotics, computer graphics, control, and bioinformatics. Prerequisite: instructor approval.**CS 5353 Topics in Emerging Computing Paradigms**

Introduction to emerging, revolutionary computing paradigms, such as quantum computing, and to the design and development of highly efficient algorithms in these paradigms. Topics may include quantum, chemical and biological computing. May be repeated for credit when topic varies. Prerequisite: instructor approval.**CS 5354 Topics in Intelligent Computing**

Introduction to advanced concepts and techniques of intelligent and soft computing and their applications. Topics may include neural computations, fuzzy computations, evolutionary computations, intelligent control and intelligent web design. Prerequisite: instructor approval.**CS 5382 Topics in Software Development**

The study of the production of high-quality software systems. Topics may include process improvement models, deductive and inductive program synthesis, clean-room programming, and software project management. Prerequisite: instructor approval.**CS 5383 Topics in Software Assurance**

The study of methods and approaches to software quality assurance particularly as it applies to high-assurance, high-consequence, and safety-critical systems. Topics may include software specification methods, formal methods of software development, formal methods in software verification, and high-assurance software engineering and system safety. Prerequisites: CS 5303 and CS 4311.

### Mathematics and Statistics (MATH or STAT courses)

**MATH 5310 Introduction to Applied Functional Analysis**

Review of finite-dimensional linear spaces, subspaces, sums and direct sums, projections, infinite-dimensional linear spaces, norm, normed spaces, convergence, open and closed sets, completeness, Banach spaces, Hahn-Banach theorem, Lebesgue spaces, basic inequalities, inner product, generalized angle and orthogonality, Hilbert spaces, orthogonal projections, Riesz theorem, and Sobolev spaces. Prerequisites: linear or matrix algebra and advanced calculus.**MATH 5311 Applied Mathematics**

This topics course is designed to introduce the students into various areas of mathematics that are directly related to engineering and science, such as mathematical modeling, differential equations, Fourier transformation, calculus of variations, theory of algorithms, and others. The course may be repeated if different topics are covered. Prerequisite: instructor approval**MATH 5314 Partial Differential Equations**

Partial derivatives and differential operators, classification of second-order partial differential equations (PDEs), examples from engineering and science, maximum principle and well-posedness, boundary conditions, weak formulations, energy norm and energetic inner product, Lax-Milgram lemma, overview of existence and uniqueness results for elliptic, parabolic, and hyperbolic PDEs. First-order hyperbolic conservation laws. Transport theorem, derivation of Euler equations of compressible inviscid flow. Compressible and incompressible Navier-Stokes equations. PDEs describing linear elasticity. Maxwell's equations. Prerequisite: MATH 5310.**MATH 5315 Finite Element Methods I**

Galerkin method and its convergence, piecewise-affine and higher-order FEM in one spatial dimension, adaptivity, general concept of nodal elements, unisolvency, local and global finite element interpolants, conformity, continuous elements in two and three dimensions. Prerequisites: MATH 5310, MATH 5343, and a working knowledge of a high-level programming language.**MATH 5335 Techniques in Optimization**

An introduction to the formulation of optimization problems and their numerical solution with application to problems in science and engineering. Emphasis on deterministic and stochastic techniques such as Newton type methods and simulated annealing. Prerequisites: MATH 1312 and a working knowledge of a high-level programming language.**MATH 5346 Interior-Point Methods for Linear Programming**

Optimization of linear objective functions subject to linear constraints. Development of theory and algorithmic strategies for solving linear programming problems using interior-point methodology. Prerequisites: MATH 2313, MATH 3323, and a working knowledge of a high-level programming language.**STAT/MATH 5386: Stochastic Processes**

Random walks, discrete time Markov chains, and Poisson process. Further topics such as continuous time Markov chains, branching processes, renewal theory, and estimation in branching processes. Prerequisites: MATH 4341, and STAT 3330 or MATH 5380.**STAT/MATH 5388 Multivariate Data Analysis**

Statistical analysis of a multivariate response. Multivariate multiple linear regression, principal components, factor analysis, canonical correlation, and discriminate analysis. Applications with the use of statistical packages will be considered. Prerequisite: MATH 5385 or equivalent.**STAT/MATH 5391 Time Series Analysis**

Time domain and frequency domain aspects of discrete time stationary processes, correlation functions, power spectra, filtering, linear systems, and ARMA models for non-stationary series. An introduction to the analysis of multiple time series. Some use of statistical software will be included. Prerequisite: MATH 5380.**MATH 6311 Topics in Applied Mathematics**

The topics may vary each semester. Each section is dedicated to a different topic. Course may be repeated for credit. Prerequisite: Permission of the instructor.**MATH 6345 Topics in Optimization**

The topics may vary each semester. Course may be repeated for credit. Prerequisite: MATH 5345, or instructor approval.

### Science and Engineering (STEM courses other than CS, MATH, and STAT)

**BINF 5351 Intro. Bioinformatics I**

Introduction to Bioinformatics I: Basic Sequence Comparisons (2-3) Theory and practice of sequence analysis, with an emphasis on nucleic acid comparisons and homologue determination. Includes understanding and use of Internet and computational tools with both public sequencing databases and experimental data.

**BINF 5352 Intro. Bioinformatics II**

Introduction to Bioinformatics II: Gene Finding and Genomic Comparisons (2-3) A continuation of BINF 5351 with an emphasis on the analysis of protein structural information. Also includes gene annotation and whole genome comparisons.

**BINF 5341 Analysis and Modeling of Biological Structures**

Introduction to the principles and methods used for the three-dimensional structural determination and simulation of macromolecules of biological interest. Recognition techniques, conformational analysis, and molecular dynamics; ligand design and docking; and modern methods for protein structure determination. Prerequisite: instructor approval. (BINF 5341 is the same course as CHEM 5341)**BINF 5354 Post-Genomic Analysis**

The extraction and confirmation of information from entire and partially assembled genome sequences. Includes the design and use of DNA arrays, SNP's and applied proteomics in the identification and verification of expressed genes of interest. Prerequisite: instructor approval.

**BIOL 5328 Biostatistics**

Study and application of specialized numerical methods in biological sciences. Prerequisite: instructor approval

**BIOL 5316 Biosystematics**

Methods and principles of taxonomy, classification, and systematics. Prerequisite: instructor approval.**GEOP 5353 Reflection Seismic Data Processing**

The computer application of digital signal processing to reflection seismic data from environ-mental, petroleum, and crustal surveys. Topics include: definition of survey geometries, data editing techniques, amplitude recovery, bandpass filtering, deconvolution, velocity analysis, F-K filtering, and migration. Prerequisite: GEOP 4332 and

GEOP 5460, or instructor approval.**GEOP 5460 Geophysical Applications of Digital Signal Processing**

Computer application of discrete signals and systems to geophysical data in one and two dimen-sions. Properties of the FFT, DFT, Z-transform, and continuous Fourier integral transform. Digital filter design, spectral analysis, deconvolution, spatial filtering of geophysical data sets. Knowledge of FORTRAN, C, or mathematical software package required. Prerequisite: Graduate standing or instructor approval.**GEOL 5375 Quantitative Techniques in the Geological Sciences**

Introduction to techniques for quantitative analysis of geologic data. Emphasis on the extraction of maximum information from large data matrices. Specific applications to petroleum and mineral exploration. Prerequisite: instructor approval.**PHYS 5365 Advanced Statistical Mechanics**

Classical and quantum statistics of systems in equilibrium. Treatment of fluctuations and transport phenomena. Introduction to many-body problems. Prerequisite: PHYS 3331.**PHYS 5371 Solid State Physics**

Electromagnetic, elastic and particle waves in periodic lattices as applied to the electrical, magnetic and thermal properties of solids. Prerequisite: PHYS 4356 or instructor approval.**EE 5301 Computational Methods for EE**

A broad coverage of the field of numerical methods emphasizing computer techniques as they apply to Electrical Engineering. Topics generally include numerical integration and differentiation, boundary-value and eigenvalue-value problems, finite-difference and finite-elements methods, and solutions to partia, parabolicl and hyperbolic differential equaltions. Prerequisite: (MATH 2326 w/ C or betteror) OR (MATH 3326 w/ C or better). **EE 5310 Computer Graphics**

Advanced topics in two- and three-dimensional graphical techniques. Topics may vary, but course may not be repeated for credit. Prerequisite: instructor approval.**EE 5370 Operating Systems**

Fundamental concepts as they apply to multi-programmed, multi-user operating systems within distributed computer systems. Topics include an overview of the kernel, file systems, process control and scheduling, inter-process communication, memory management, and I/O. The internal algorithms of a contemporary operating system are examined. Prerequisite: CS 4375 or EE 4374.**EE 5376 Computer Architecture I**

Processing design, microprogramming, memory architecture, including memory hierarchy, cache and virtual memory, and pipelines. An introduction to multiprocessor configurations. Prerequisites: EE 4342 and EE 3376 or equivalent.**EE 5377 Computer Architecture II**

Advanced topics in computer architecture, including parallel and distributing processing. Prerequisite: EE 5376.**EE 5379 Network Protocols**

The theory and application of protocols such as TCP, IP, Sockets and RPCs that are employed in computer network communications. Concentrates on network protocols that are employed from the network, transport, and process layers of the simplified 4-layer model for computer communications. Prerequisite: EE 5370 or instructor approval.**MECH 5390 Special Topics: Advanced FEA I**

Nonlinear finite element theory, theoretical basis for implementing and performing non-linear finite element analysis. Topics covered: Eulerian and Lagrangian mesh descriptions, ALE, total and updated Lagrangian formulations, basic continuum mechanics, derivation of internal, external forces and mass matrix. Prerequisite: instructor approval.

The course below is required for the professional track MS students with curriculum structured in four modules: communication, business, law, and ethics, and may be team-taught by practicing professionals in science and technology with expertise in these areas.**CPS 5330 Professional Skills in Science and Technology**

Basic business knowledge and communication skills for scientists, engineers, and technologists in industry or government. Students will sharpen their verbal and writing skills necessary for communicating with clients, supervisors, senior management, and members of the media among others. They will develop ability to collaborate and work on a team, and awareness of the basics of project management, the budgeting, accounting, information security, intellectual property and patent laws, marketing strategies, and ethical issues in science and technology.