OPER   327. Mathematical Modeling. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   200. Fundamental concepts of mathematical modeling. Topics may include differential equation models, optimization models and probabilistic models. Practical problems will be discussed throughout.

OPER   427. Deterministic Operations Research. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC   245 or 255, MATH/OPER   327 and MATH   310. Introduction to topics in optimization including linear programming, network models and integer programming. Focuses on constructing sound models and on solving them using appropriate software. Algorithms and model properties are also discussed. Students may not receive degree credit for both OPER   427 and OPER   527.

OPER   428. Stochastic Operations Research. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC   245 or 255, MATH/STAT   309 and MATH   310. Introduction to topics in discrete-event and Monte Carlo simulation including the application of probabilistic models in real-world situations, random number generation, random variate generation and Monte Carlo integration. Students may not receive degree credit for both OPER   428 and OPER   528.

OPER   520. Game Theory and Linear Programming. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   310. The mathematical basis of game theory and linear programming. Matrix games, linear inequalities and convexity, the mini-max theorems in linear programming, computational methods and applications. Crosslisted as: MATH   520.

OPER   527. Optimization I. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: graduate status in mathematical sciences or systems modeling and analysis, or permission of the instructor. Introduction to optimization and mathematical programming. Course addresses fundamental concepts of optimization (such as optimality conditions and duality) as well as the construction, solution, analysis and application of linear programming and network models. Emphasis is placed on using software to solve problems as well as on understanding its underlying methodology. Integer programming models will be introduced. Students may not receive degree credit for both OPER   427 and OPER   527.

OPER   528. Stochastic Simulation. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: graduate status in mathematical sciences, systems modeling and analysis, or decision sciences and business analytics, or permission of the instructor. An introduction to stochastic discrete-event simulation. The course covers simulation modeling and programming in general-purpose languages (e.g., VBA for Excel) and (briefly) in specialized simulation environments (e.g., Arena, @Risk). The probability foundations of stochastic simulation of stochastic processes, random number and variate generation, variance reduction techniques, and proper design and analysis of the simulation experiment are emphasized. Applications are drawn from manufacturing, finance, logistics and service systems. Students may not receive degree credit for both OPER   428 and OPER   528.

OPER   591. Topics in Operations Research. 1-3 Hours.

Semester course; 1-3 lecture hours. 1-3 credits. May be taken more than once for credit. Prerequisite: permission of the instructor. A detailed study of selected topics in operations research.

OPER   627. Optimization II. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER   527. This course will address basic theory and algorithms for nonlinear optimization (unconstrained and constrained). Both theoretical foundations and practical implementations of optimization algorithms will be covered.

OPER   635. Network Models and Graph Theory. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER   527 or permission of the instructor. This course will focus on optimization models for network problems, as well as on the underlying graph theoretic structure for such models. Emphasis will be on solution procedures and applications with some discussion of related implementation issues. The course will concentrate on the study of polynomial-time algorithms for well-solved problems. May also include treatment of solution techniques for NP-hard network problems. Possible topics for the course include, but are not limited to, maximum flows/minimum cuts in networks, minimum spanning trees, minimum cost flows, matching and assignment, shortest path problems, traveling salesman problems and multicommodity flows.

OPER   636. Machine Learning Algorithms. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: graduate status in mathematical sciences, systems modeling and analysis, decision sciences and business analytics, or computer science, or permission of the instructor. Includes an in-depth analysis of machine learning algorithms for data mining, equipping students with skills necessary for the design of new algorithms. Analyses will include framing algorithms as optimization problems and a probabilistic analysis of algorithms. Students will be exposed to current areas of research in the construction of data mining algorithms. Crosslisted as: STAT   636.

OPER   639. Practical Optimization. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER   527. The application of optimization theory toward the solution of practical problems in operations research. The use and analysis of computer programs available to solve such problems. The algorithms used in these programs will be discussed from a practical and theoretical point of view.

OPER   641. Stochastic Simulation and Monte Carlo Methods. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT   513 and either STAT 503 or STAT   613. Addresses the methodological foundation of applying stochastic modeling and simulation with a focus on introducing simulation concepts through examples, algorithms and experiments. Topics include simulation output analysis, input modeling, simulation optimization, steady-state simulation, variance reduction techniques, sensitivity analysis and Monte Carlo optimization.

OPER   643. Decision and Risk Analysis. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: graduate status in mathematical sciences, systems modeling and analysis, or decision sciences and business analytics, or permission of the instructor. This course presents the decision and risk analysis theory and methodology. Decision analysis applies to hard problems involving sequential decisions, major uncertainties, significant outcomes and complex values. The course includes: decision structuring with influence diagrams and decision trees; modeling uncertainty with subjective probabilities; sensitivity analysis and the value of information; and modeling preferences with utility functions. Decision and risk analysis applications in business and government are considered.

OPER   645. Queuing Theory. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: graduate status in mathematical sciences or systems modeling and analysis, or permission of the instructor. This operations research course provides a development of some basic queuing systems. Such systems will include birth-death queues, as well as the M/G/I and GI/M/S queuing systems. Other topics may include the GI/G/I queues, overflow queues and some basic queuing networks.

OPER   647. Multiobjective Decision Analysis. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: graduate status in mathematical sciences, systems modeling and analysis, or decision sciences and business analytics, or permission of the instructor. Introduction to the mathematical foundations of multiattribute utility theory. Topics covered include: structuring objectives; tradeoffs under certainty; unidimensional utility theory; multiattribute preferences under uncertainty; preferences over time; and aggregation of individual preferences. Real world applications will be discussed throughout.

OPER   648. Systems Reliability Analysis. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: graduate status in mathematical sciences or systems modeling and analysis, or permission of the instructor. An introduction to engineering reliability and risk analysis, specifically failure data analysis, maintenance problems, system reliability and probabilistic risk assessment. Applications in computer science and engineering will include stochastic characterization of wear in hardware systems and the development of failure models for software systems. Decision problems such as the optimal maintenance of repairable systems and optimal testing policies for hardware and software systems will be examined. The analysis of risk through fault trees, event trees and accident precursor analysis also will be discussed. Crosslisted as: STAT   648.

OPER   649. Statistical Quality Control. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: graduate status in mathematical sciences or systems modeling and analysis, or permission of the instructor. Demonstrates how statistics and data analysis can be applied effectively to process control and management. Topics include the definition of quality, its measurement through statistical techniques, variable and attribute control charts, CUSUM charts, multivariate control charts, process capability analysis, design of experiments, and classical and Bayesian acceptance sampling. Statistical software will be used to apply the techniques to real-life case studies from manufacturing and service industries. Crosslisted as: STAT   649.

OPER   690. Research and Communications Seminar. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: 9 graduate credits in operations research (OPER) and/or statistics (STAT) and permission of the instructor. Designed to help students attain proficiency in professional and academic communication and research in the context of statistics and operations research. The course focuses on the discipline-specific communication and research skills necessary to excel in careers or graduate studies in these disciplines. Crosslisted as: STAT   690.

OPER   691. Special Topics in Operations Research. 1-3 Hours.

Semester course; 1-3 lecture hours. 1-3 credits. May be taken more than once for credit. Prerequisite: permission of the instructor. A detailed study of selected topics in operations research.

OPER   696. Applied Project. 1-3 Hours.

Semester course; variable hours (to be arranged). 1-3 credits. A total of three credits will be applied to the M.S. in Mathematical Sciences (operations research or statistics concentration). Can be repeated for credit. Prerequisite: STAT/OPER   690 or permission of the faculty adviser. Designed to allow students to apply concepts and theories learned in other courses to a practical situation. Includes the selection, written description, completion and written report of the project and a presentation of the findings. Students may not receive credit for both OPER/STAT   696 and OPER/STAT   698. Crosslisted as: STAT   696.

OPER   697. Directed Research. 1-3 Hours.

Semester course; variable hours. 1-3 credits. May be taken more than once for credit. Prerequisite: graduate standing. Supervised individual research and study in an area not covered in the present curriculum or in one which significantly extends present coverage. Research culminates with an oral presentation and submission of a written version of this presentation to the supervising faculty member.

OPER   698. Thesis. 1-3 Hours.

Hours to be arranged. 1-3 credits. A total of 3 or 6 credits may be applied to the M.S. in Mathematical Sciences/Operations Research. (A total of 3 credits for an expository thesis or a total of 6 credits for a research thesis.) May be taken more than once for credit. Prerequisite: graduate standing. Independent research culminating in the writing of the required thesis as described in this bulletin. Grade of S/U/F may be assigned in this course.

OPER   731. Discrete Optimization. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER   627. Provides the theoretical background necessary to design and evaluate advanced solution techniques for discrete optimization problems. Topics include theory of polyhedra and valid inequalities for integer programming models, matchings, computational complexity, and sufficient conditions for integer programs to be polynomially solvable. Scheduling, packing, covering and routing models will also be examined.

OPER   732. Optimization Under Uncertainty. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: OPER   527; graduate standing in mathematical sciences or systems modeling and analysis; or permission of the instructor. Offers an exploration of issues concerning decision-making problems under uncertainty using mathematical programming tools. Topics addressed include modeling uncertainty in optimization models, two-stage stochastic programs with recourse, chance constrained programs, statistical inference in stochastic programs and robust optimization. Special attention is paid to the algorithms, approximation via sampling and applications.

OPER   736. Mathematics of Knowledge and Search Engines. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent. Investigates the mathematics, methods and algorithms for searching for and extracting structures of interest (knowledge) from large and possibly high-dimensional datasets. The motivation is the rapid and phenomenal growth of the search engine (as demonstrated by Google) as a major tool for search on the Internet, which has impacted commerce, education and the study of social, financial and scientific datasets. The development of the mathematical and statistical learning algorithms behind these search engines has led to advances in how large, high-dimensional datasets can be effectively analyzed for the extraction of knowledge. Crosslisted as: STAT   736.

OPER   741. Advanced Stochastic Simulation. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   513, OPER   528 and either OPER 503 or 613, or permission of the instructor. This is an advanced-level course on stochastic modeling and simulation. State-of-the-art topics on simulation theory and methodology will be taught through lectures and guided literature review. Tentative topics include advanced simulation output analysis, simulation optimization, steady-state simulation, nested simulation, metamodeling, variance reduction (stratification, importance sampling, quasi-Monte Carlo, etc.).

OPER   743. Decision Analysis II. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER   643 or OPER   647. Introduces the current areas of research in the field of decision analysis, which applies to hard problems involving sequential decisions, major uncertainties, significant outcomes and complex values. Includes current research in decision structuring and representation, modeling uncertainty with subjective probabilities, modeling preferences with utility functions and modeling multiattribute preferences.

OPER   791. Special Topics in Operations Research. 1-3 Hours.

Semester course; 1-3 lecture hours. 1-3 credits. May be repeated for credit. Prerequisite: permission of instructor. A detailed study of selected advanced topics in operations research.