There are a number of classes across the affiliated departments that can count towards the Operations Research Program requirements, detailed below. The classes that are currently active can be found in the University Course Bulletin in LionPath . Students planning on taking any of the classes listed in this page should check schedule and frequency with the corresponding departments, as these are continuously being updated.

**Colloquium requirements:** students must enroll in O R 590 Colloquium for 1 credit in each year enrolled in the major graduate program and in residence. The maximum number of OR 590 credits required for a Ph.D dual title student is 4. Any particular course may satisfy both the graduate major program and those in the Operations Research Program.

Note: some classes are considered equivalent within and across departments. When classes are equivalent, only one can count towards the credit requirements of a specific area and sub-area. Equivalent classes are detailed in the Application Forms.

**OR Courses**

**Statistical Methods:**

**ECON 501 – Econometrics**

Description: Applications of Statistical Techniques to Economics.**EEFE/ECON 510 – Econometrics I**

Description: General linear model, multicolinearity, specification error, autocorrelation, heteroskedasticity, restricted least squares, functional form, dummy variables, limited dependent variables.

Prerequisite: ECON 490 or STAT 462 or STAT 501**EEFE/ECON 511 – Econometrics II**

Description: Topics include endogeneity and moment-based estimators, linear systems of equations, maximum likelihood estimation, models for qualitative and limited dependent variables, models for time series data, models for panel data and treatment evaluation.

Prerequisite: EEFE 510**IE 511 – Experimental Design in Engineering**

Description: Statistical design and analysis of experiments in engineering; experimental models and experimental designs using the analysis of variance.

Prerequisite: IE 323**IE 555 – Statistical Process Monitoring and Analysis**

Description: Statistical techniques for univariate and multivariate monitoring of dependent and autocorrelated processes; theoretical and numerical approaches for analyzing performance.

Prerequisite: IE 323**IE 583 – Response Surface Methodology and Process Optimization**

Description: Surface Methodologies used for sequential experimentation and optimization of production processes. Statistical design and analysis of such experiments.

Prerequisite: IE 511 or STAT 501**IE 584 – Time Series Control and Process Adjustment**

Description: Design of Time Series-based process controllers for Quality Engineering. Study of the effect of autocorrelation on control chart performance.

Prerequisite: IE 423**MATH/STAT 414 – Introduction to Probability Theory**

Description: probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Prerequisite: MATH 230 or MATH 231**MATH/STAT 415 – Introduction to Mathematical Statistics**

Description: A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests.

Prerequisite: MATH 414**MATH/STAT 418 – Introduction to Probability and Stochastic Processing for Engineering**

Description: Fundamentals and axioms, combinatorial probability, conditional probability and independence, probability laws, random variables, expectation; Chebyshev’s inequality. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Prerequisite: MATH 230 or MATH 231**SC&IS 535 – Statistical Research Methods for Supply Chain and Information Systems**

Description: Current statistical research methods for modeling and analysis of supply chain and information systems.

Prerequisite: 3 credits each in undergraduate accounting, economics, and statistics**STAT 460 – Intermediate Applied Statistics**

Description: Review of hypothesis testing, goodness-of-fit tests, regression, correlation analysis, completely randomized designs, randomized complete block designs, latin squares.

Prerequisite: STAT 200, STAT 240, STAT 250, STAT 301, or STAT 401**STAT 501 – Regression Methods**

Description: Analysis of research data through simple and multiple regression and correlation; polynomial models; indicator variables; step-wise, piece-wise, and logistic regression.

Prerequisite: 6 credits in statistics or STAT 451; matrix algebra**STAT 502 – Analysis of Variance and Design of Experiments**

Description: Analysis of variance and design concepts; factorial, nested, and unbalanced data; ANCOVA; blocked, Latin square, split-plot, repeated measures designs.

Prerequisite: STAT 462 or STAT 501**STAT 503 – Design of Experiments**

Description: Design principles; optimality; confounding in split-plot, repeated measures, fractional factorial, response surface, and balanced/partially balanced incomplete block designs.

Prerequisite: STAT 462 or STAT 501; STAT 502

**Stochastic Processes:**

**EE 560 – Probability, Random Variables, and Stochastic Processes**

Description: Review of probability theory and random variables; mathematical description of random signals; linear system response; Wiener, Kalman, and other filtering.

Prerequisite: EE 350; STAT 418**IE/SC&IS 516 – Applied Stochastic Processes**

Description: Study of stochastic processes and their applications to engineering and supply chain and information systems.

Prerequisite: IE 322 or STAT 318**MATH/STAT 416 – Stochastic Modeling**

Description: Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation.

Prerequisite: MATH 318 OR MATH 414; MATH 230**MATH/STAT 516 – Stochastic Processes**

Description: Markov chains; generating functions; limit theorems; continuous time and renewal processes; martingales, submartingales, and supermartingales; diffusion processes; applications.

Prerequisite: MATH 416**MATH/STAT 519 – Topics in Stochastic Processes**

Description: Selected topics in stochastic processes, including Markov and Wiener processes; stochastic integrals, optimization, and control; optimal filtering.

Prerequisite: STAT 516, STAT 517**ME 577 – Stochastic Systems for Science and Engineering**

Description: The course develops the theory of stochastic processes and linear and nonlinear stochastic differential equations for applications to science and engineering.

Prerequisite: MATH 414 or MATH 418; ME 550 or MATH 501**STAT 515 – Stochastic Processes and Monte Carlo Methods**

Description: Conditional probability and expectation, Markov chains, the exponential distribution and Poisson processes.

Prerequisite: MATH 414, STAT 414, or STAT 513

**Linear Optimization:**

**EEFE 527 – Quantitative Methods I**

Description: The first part of the course reviews the foundations of the mathematical analysis with the goal of modeling feasibility; i.e., the set of possible choices. This prepares us to next move to modeling the optimal choice with an extended presentation on optimization theory and application in the static setting. The final part of the course moves on to the methods for engaging in dynamic optimization.

Prerequisite: EEFE 512, ECON 502**IE 405 – Deterministic Models in Operations Research**

Description: Deterministic models in operation research including linear programming, flows in networks, project management, transportation and assignment models and integer programming.

Prerequisite: MATH 220**IE 505 – Linear Programming**

Description: An accelerated treatment of the main theorems of linear programming and duality structures plus introduction to numerical and computational aspects of solving large-scale problems.

Prerequisite: IE 405**MATH 484 – Linear Programs and Related Problems**

Description: Introduction to theory and applications of linear programming; the simplex algorithm and newer methods of solution; duality theory.

Prerequisite: MATH 220; MATH 230 or MATH 231**CHE 512 – Optimization and Biological Networks**

Description: Mathematical optimization, formulation and solution techniques for linear, nonlinear, and mixed-integer problems; optimization-based tools for reconstruction, analysis, and redesign of biological networks.

**Deterministic Optimization:**

**IE 468 – Optimization Modeling and Methods**

Description: Mathematical modeling of linear, integer, and nonlinear programming problems and computational methods for solving these classes of problems.

Prerequisite: IE 405, MATH 231**IE 510 – Integer Programming**

Description: Study of advanced topics in mathematical programming; emphasis on large-scale systems involving integer variables.

Prerequisite: IE 512**IE 512 – Graph Theory and Networks in Management**

Description: Graph and network theory; application to problems of flows in networks, transportation and assignment problems, pert/CPM, facilities planning.

Prerequisite: IE 425**IE 520 – Multiple Criteria Optimization**

Description: Study of concepts and methods in analysis of systems involving multiple objectives with applications to engineering, economic, and environmental systems.

Prerequisite: IE 405 or INS 427**IE 521 – Nonlinear Programming**

Description: Fundamental theory of optimization including classical optimization, convex analysis, optimality conditions and duality, algorithmic solution strategies, variational methods in optimization.

Prerequisite: IE 505**IE 525 – Convex Optimization**

Description: This course is designed to provide students with necessary skills to recognize or build convex optimization problems coming from diverse application areas and to solve them efficiently. It consists of five parts: 1) convex sets, 2) convex functions, 3) convex optimization, 4) algorithms and 5) real life applications.

Prerequisite: IE 505**IE 588 – Nonlinear Networks**

Description: Foundation in congestion games, including elements of non-cooperative game theory, equilibrium network flows, Braess paradox, and the price of anarchy. This course examines the theory of congestion games, developed originally to describe flows on congested transport networks but recently embraced to model data networks.

Prerequisite: IE 505**IE 589 – Dynamic Optimization and Differential Games**

Description: Dynamic optimization and dynamic non-cooperative games emphasizing industrial applications. This course provides an introduction to dynamic optimization and dynamic noncooperative games from the perspective of infinite dimensional mathematical programming and differential variational inequalities in topological vector spaces.

Prerequisite: IE 425; IE 505; IE 521 (can be taken concurrently)**MATH 486 – Mathematical Theory of Games**

Description: Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.

Prerequisite: MATH 220**MATH/CSE 555 – Numerical Optimization Techniques**

Description: Unconstrained and constrained optimization methods, linear and quadratic programming, software issues, ellipsoid and Karmarkar’s algorithm, global optimization, parallelism in optimization.

Prerequisite: CMPSC 456**ME 444 – Engineering Optimization**

Description: Problem formulation, algorithms and computer solution of various engineering optimization problems.

Prerequisite: MATH 220; MATH 230 or MATH 231; CMPSC 201 or CMPSC 202 or CMPSC 200**SC&IS 525- Supply Chain Optimization**

Description: Introduction to theory and practice of optimization methods and models for analyzing and improving the performance of supply chain environments.

Prerequisite: prior coursework in linear algebra and calculus

**Stochastic Optimization:**

**IE/SC&IS 519 – Dynamic Programming**

Description: This course presents the basic theory and applications of dynamic programming. The focus of the course will be on the theory of Markov decision processes (MDP), which provides an analytical tool to optimally control the behavior of a Markov Chain. The students will learn fundamental MDP models, computational methods and applications in supply chain and information systems, including production and inventory control, quality control, logistics, scheduling, queueing network, and economic problem.

Prerequisite: IE 516 or SC&IS 516 or equivalent

**Numerical Methods:**

**MATH/CMPSC 451 – Numerical Computations**

Description: Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast FOURIER transform, and differential equations emphasizing computational properties and implementation. Students may take only one course for credit from MATH 451 and 455.

Prerequisite: CMPSC 201C, CMPSC 201, or CSE 103; MATH 230 or MATH 231**MATH 455/CMPSC – Introduction to Numerical Analysis I**

Description: Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455.

Prerequisite: CMPSC 201C, CMPSC 201F, or CSE 103; MATH 220; MATH 230 or MATH 231**MATH/CMPSC 456 – Introduction to Numerical Analysis II**

Description: Polynomial and piecewise polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations.

Prerequisite: MATH 455**MATH/CSE 550 – Numerical Linear Algebra**

Description: Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors.

Prerequisite: MATH 441 or MATH 456**MATH 553 – Introduction to Approximation Theory**

Description: Interpolation; remainder theory; approximation of functions; error analysis; orthogonal polynomials; approximation of linear functionals; functional analysis applied to numerical analysis.

Prerequisite: MATH 401, 3 credits in Computer Science and Engineering

**Simulation Methods:**

**IE 453 – Simulation Modeling for Decision Support**

Description: Introduction of concepts of simulation modeling and analysis, with application to manufacturing and production systems.

Prerequisite: CMPSC 201C or CMPSC 201F ;IE 323, IE 425**IE 522 – Discrete Event Systems Simulation**

Description: Fundamentals of discrete event simulation, including event scheduling, time advance mechanisms, random variate generation, and output analysis.

Prerequisite: IE 425**IE 540 – Manufacturing Systems Simulation**

Description: Use of simulation in design and process improvement of manufacturing systems. Analysis of simulation language structure. Readings in current literature.

Prerequisite: IE 453**SC&IS 545 – Supply Chain Systems Simulation**

Description: Application of computer simulation to analysis and design of supply chain and information systems design; simulation experiments in SC&IS research.

Prerequisite: 3 credits of computer programming

**Data Science / Data Analytics (*pending approval):**

**BAN 540 – Business Analytics**

Description: The course objectives are to demonstrate the benefits of using a systematic and analytical approach to marketing decision-making, and to build the skills and confidence of students for undertaking such analyses and decision-making in a modern enterprise.**CMPSC 410 – Programming Models for Big Data**

Description: This course introduces modern programming models and related software stacks for performing scalable data analytics and discovery tasks over massive and/or high dimensional datasets. The learning objectives of the course are that the students are able to choose appropriate programming models for a big data application, understand the tradeoff of such choice, and be able to leverage state-of-the art cyber infrastructures to develop scalable data analytics or discovery tasks..

Enforced Prerequisite: CMPSC 122 and DS 220. Recommended Preparation: DS 310 or CMPSC 448**CMPSC 448 – Machine Learning and Algorithmic AI**

Description: Evaluation and use of machine learning models; algorithmic elements of artificial intelligence.

Prerequisite: IE 453**CSE 584 – Machine Learning: Tools and Algorithms**

Description: Computational methods for modern machine learning models, including applications to big data and non-differentiable objective functions.**EE 456 – Introduction to Neural Networks**

Description: Artificial Neural Networks as a solving tool for difficult problems for which conventional methods are not applicable.

Prerequisite: CMPSC201 or CMPSC202; MATH 220**EE 556 – Graphs, Algorithms, and Neural Networks**

Description: Examine neural networks by exploiting graph theory for offering alternate solutions to classical problems in signal processing and control.**EE 582 – Adaptive and Learning Systems**

Description: Adaptive and learning control systems; system identification; performance indices; gradient, stochastic approximation, controlled random search methods; introduction to pattern recognition.

Prerequisite: EE 580**IE 561 – Data Mining Driven Design**

Description: The study and application of data mining/machine learning (DM/ML) techniques in multidisciplinary design.**IE 562 – Computational Foundations of Smart Systems**

Description: Intelligent computational techniques for the design and implementation of smart systems.**IE 575 – Foundations of Predictive Analytics**

Description: Survey course on the key topics in predictive analytics.

Prerequisite: IE 323, STAT 500 or equivalent**IE 582 – Engineering Analytics**

Description: Students will learn advanced information technology, network science, big data, descriptive and predictive analytics, for manufacturing and service systems.**STAT 557 – Data mining I**

Description: This course on data mining will cover methodology, major software tools and applications in this field. By introducing principal ideas in statistical learning, the course will help students to understand conceptual underpinnings of methods in data mining.

Prerequisite: STAT 318 or STAT 416 and basic programming skills**STAT 558 – Data mining II**

Description: Advanced data mining techniques: temporal pattern mining, network mining, boosting, discriminative models, generative models, data warehouse, and choosing mining algorithms.

Prerequisite: STAT 557 or IST 557

**ABE 559 – Biological and Agricultural Systems Simulation**

Description: Continuous simulation modeling of biological and physical systems, numerical simulation techniques, validation and verification, difference measures, sensitivity analysis.

Prerequisite: MATH 111 or MATH 141**BRS 429W – Biorenewable Systems Analysis and Management**

Description: Systems analysis and optimization techniques including an introduction to systems theory, qualitative and quantitative analysis, linear programming, waiting line models, PERT/CPM, minimal spanning tree, calculus methods, simulation modeling for decision making, inventory, and energy audits. All topics are presented in the form of case studies that require the students to solve problems in realistic production and processing scenarios. The course also provides a writing-intensive structure.

Prerequisite: BRS 422**CE 525 – Transportation Operations**

Description: Tools for analyzing transportation operations, including: properties of traffic streams, queuing, traffic dynamics, networks, probability and estimation of traffic properties.

Prerequisite: CE 423**CMPEN 431 – Introduction to Computer Architecture**

Description: ntroduction to Computer Architecture (3) This course will introduce students to the architecture-level design issues of a computer system. They will apply their knowledge of digital logic design to explore the high-level interaction of the individual computer system hardware components. Concepts of sequential and parallel architecture including the interaction of different memory components, their layout and placement, communication among multiple processors, effects of pipelining, and performance issues, will be covered.

Prerequisite: CMPEN331 or CMPEN371m**CMPSC 431W – Database Management Systems**

Description: Topics include: conceptual data modeling, relational data model, relational query languages, schema normalization, database/Internet applications, and database system issues.**CMPSC 442 – Artificial Intelligence**

Description: Introduction to the theory, research paradigms, implementation techniques, and philosophies of artificial intelligence.

Prerequisite: CMPSC122 or equivalent; Concurrent: CMPSC465**CMPSC 465 – Data Structures and Algorithms**

Description: Fundamental concepts of computer science: data structures, analysis of algorithms, recursion, trees, sets, graphs, sorting.

Prerequisite: CMPSC122; CMPSC360 or MATH 311W**CSE 556 – Finite Element Methods**

Description: Sobolev spaces, variational formulations of boundary value problems; piecewise polynomial approximation theory, convergence and stability, special methods and applications.

Prerequisite: MATH 502 , MATH 552**CSE 562 – Probabilistic Algorithms**

Description: Design and analysis of probabilistic algorithms, reliability problems, probabilistic complexity classes, lower bounds.

Prerequisite: CSE 565**CSE 564 – Complexity of Combinatorial Problems**

Description: NP-completeness theory; approximation and heuristic techniques; discrete scheduling; additional complexity classes.

Prerequisite: CSE 565**CSE 565 – Algorithm Design and Analysis**

Description: An introduction to algorithmic design and analysis.

Prerequisite: CMPSC 465**ECON 500 – Introduction to Mathematical Economics**

Description: Mathematical Economics: Applications of Mathematical Techniques to Economics.**ECON 521 – Advanced Microeconomic Theory**

Description: Theory of consumer behavior; theory of the firm; price determination in product and factor markets; introduction to welfare economics.**ECON 589 – Seminar in Econometric Theory**

Description: Theories and methods relevant to the application of statistical methods to economics.

Prerequisite: ECON 510**EE 581 – Optimal Control**

Description: Variational methods in control system design; classical calculus of variations, dynamic programming, maximum principle; optimal digital control systems; state estimation.

Prerequisite: EE 580**EEFE 530 – Applied Microeconomics II**

Description: This course is designed to: (1) expose students to the most common econometric and statistical techniques used in applied microeconomic research and (2) give students an overview of the different types of micro data and the most common methods used to manipulate these data to create additional data sets and variables.

Prerequisite: EEFE 512, EEFE 510**EEFE 531 – Applied Microeconomics I**

Description: In this course, we will study microeconometrics, a subfield that encompasses specification as well as a variety of estimation, computational, and simulation methods that allow us to pursue specification and parameterization of econometric models suitable for analyzing micro-level data. We will see that these methods support an enriched basis for examining the validity of microeconomic theory, and also extend the analytics feasibly tackled by microeconomics. At the micro-level of empirical analysis, we will see our theory predicts high frequencies of corner solutions, abrupt switching, and discontinuities.

Prerequisite: EEFE 512 or ECON 502, EEFE 510 or ECON 510, EEFE 511 or ECON 510**EEFE 532 – Applied Computational Economics**

Description: Economists often find themselves in situations where closed-form solutions do not exist or econometric estimation is inappropriate due to data limitations or the nature of the problem. In these cases, numerical approaches, using computer-based methods, may be an economist’s best option. In this course, we will explore four topics in the field of computational economics: computable general equilibrium modeling, growth modeling, uncertainty and formal monte carlo analysis, and agent-based modeling.

Prerequisite: EEFE 512**ERM 412 – Resource Systems Analysis**

Description: The concept of systems; techniques of analysis, including input/output, mathematical programming, and simulation; application to resource systems.

Prerequisite: BIOL 220W, ERM 151, ERM 300, and STAT 240; MATH 111 or MATH 141**GEOG 560 – Seminar in Geographic Information Science**

Description: Geographic information science problems/theory, e.g. GIS, cartography, remote sensing, spatial analysis, modeling.**IE 402 – Advanced Engineering Economy**

Description: Concepts and techniques of analyses useful in evaluating engineering projects under deterministic and uncertain conditions.

Prerequisite: IE 302, IE 322, IE 405**IE 425 – Stochastic Models in Operations Research**

Description: An introduction to the method and techniques of mathematical decision making, including inventory, replacement, allocation, and waiting line problems.

Prerequisite: IE 405**IE 454 – Applied Decision Analysis**

Description: Theory and practice of decision analysis applied to engineering problems.

Prerequisite: IE 322**IE 507 – Operations Research: Scheduling Models**

Description: Scheduling models with simultaneous job arrival and probabilistic job arrival, network scheduling, and scheduling simulation techniques.

Prerequisite: IE 425**IE 509 – Operations Research: Waiting Line Models**

Description: Waiting line models including models with infinite queues, finite queues, single and multiple servers under various priorities and disciplines.

Prerequisite: IE 516**IE 532 – Reliability Engineering**

Description: Mathematical definition of concepts in reliability engineering; methods of system reliability calculation; reliability modeling, estimation, and acceptance testing procedures.

Prerequisite: IE 323 or 3 credits in probability and statistics with a prerequisite of calculus**IE 566 – Quality Control**

Description: Advanced quality assurance and control topics, including multivariate methods, economic design for control and acceptance, dimensioning, tolerancing, and error analysis.

Prerequisite: IE 423**IE 570 – Supply Chain Engineering**

Description: Use of operations research models and methods for solving problems in supply chain systems.

Prerequisite: IE 405, IE 425 or SC&IS 510**MATH 485 – Graph Theory**

Description: Introduction to the theory and applications of graphs and directed graphs. Emphasis on the fundamental theorems and their proofs.

Prerequisite: MATH 311W**MATH 486 – Mathematical Theory of Games**

Description: Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.

Prerequisite: MATH 220**ME 565 – Optimal Design of Mechanical and Structural Systems**

Description: Application of numerical optimization techniques to design mechanical and structural systems; design sensitivity analysis.**MKTG 555 – Marketing Models**

Description: Topics in the model building approach to marketing decision making, focusing on current research issues.**PNG 430 – Reservoir Modeling**

Description: The numerical simulation of petroleum reservoir processes by the use of models; scaling criteria and network flow.

Prerequisite: MATH 251, PNG 410; CMPSC 201C or CMPSC 201F**PNG 511 – Numerical Solution of the Partial Differential Equations of Flow in Porous Media**

Description: Differencing schemes for the partial differential equations of single-phase flow; application to flow of gas and mixing in porous media**PNG 512 – Numerical Reservoir Simulation**

Description: Mathematical analysis of complex reservoir behavior and combination drives; numerical methods for the solution of behavior equations; recent developments.**SC&IS 505 – Management Information Systems Research**

Description: Research problems and issues in supply chain and information systems.**SC&IS 510 – Introduction to Supply Chain and Information Systems**

Description: Introduction to the strategic framework, issues, and methods for integrating supply and demand management within and across companies.**SC&IS 520 – Principles of SC&IS I**

Description: Initial course on principles of supply chain and information systems with special emphasis on potential research topics.

Prerequisite: SC&IS 510**SC&IS 530 – Principles of SC&IS II**

Description: Sequel on principles of supply chain and information systems with special emphasis on potential research topics.

Prerequisite: SC&IS 510**STAT 510 – Applied Time Series Analysis**

Description: Identification of models for empirical data collected over time. Use of models in forecasting.

Prerequisite: STAT 462 or STAT 501 or STAT 511**STAT 513 – Theory of Statistics I**

Description: Probability models, random variables, expectation, generating functions, distribution theory, limit theorems, parametric families, exponential families, sampling distributions.

Prerequisite: MATH 230**STAT 514 – Theory of Statistics II**

Description: Sufficiency, completeness, likelihood, estimation, testing, decision theory, Bayesian inference, sequential procedures, multivariate distributions and inference, nonparametric inference.

Prerequisite: STAT 513**STAT 540 – Statistical Computing**

Description: Computational foundations of statistics; algorithms for linear and nonlinear models, discrete algorithms in statistics, graphics, missing data, Monte Carlo techniques.

Prerequisite: STAT 501 or STAT 511; STAT 415; matrix algebra

**ABE 559 – Biological and Agricultural Systems Simulation**

Description: Continuous simulation modeling of biological and physical systems, numerical simulation techniques, validation and verification, difference measures, sensitivity analysis.

Prerequisite: MATH 111 or MATH 141**BAN 540 – Business Analytics**

Description: The course objectives are to demonstrate the benefits of using a systematic and analytical approach to marketing decision-making, and to build the skills and confidence of students for undertaking such analyses and decision-making in a modern enterprise.**BRS 429W – Biorenewable Systems Analysis and Management**

Description: Systems analysis and optimization techniques including an introduction to systems theory, qualitative and quantitative analysis, linear programming, waiting line models, PERT/CPM, minimal spanning tree, calculus methods, simulation modeling for decision making, inventory, and energy audits. All topics are presented in the form of case studies that require the students to solve problems in realistic production and processing scenarios. The course also provides a writing-intensive structure.

Prerequisite: BRS 422**CE 525 – Transportation Operations**

Description: Tools for analyzing transportation operations, including: properties of traffic streams, queuing, traffic dynamics, networks, probability and estimation of traffic properties.

Prerequisite: CE 423**CHE 512 – Optimization and Biological Networks**

Description: Mathematical optimization, formulation and solution techniques for linear, nonlinear, and mixed-integer problems; optimization-based tools for reconstruction, analysis, and redesign of biological networks.**CMPEN 431 – Introduction to Computer Architecture**

Description: ntroduction to Computer Architecture (3) This course will introduce students to the architecture-level design issues of a computer system. They will apply their knowledge of digital logic design to explore the high-level interaction of the individual computer system hardware components. Concepts of sequential and parallel architecture including the interaction of different memory components, their layout and placement, communication among multiple processors, effects of pipelining, and performance issues, will be covered.

Prerequisite: CMPEN331 or CMPEN371m**CMPSC 410 – Programming Models for Big Data**

Description: This course introduces modern programming models and related software stacks for performing scalable data analytics and discovery tasks over massive and/or high dimensional datasets. The learning objectives of the course are that the students are able to choose appropriate programming models for a big data application, understand the tradeoff of such choice, and be able to leverage state-of-the art cyber infrastructures to develop scalable data analytics or discovery tasks..

Enforced Prerequisite: CMPSC 122 and DS 220. Recommended Preparation: DS 310 or CMPSC 448**CMPSC 431W – Database Management Systems**

Description: Topics include: conceptual data modeling, relational data model, relational query languages, schema normalization, database/Internet applications, and database system issues.**CMPSC 442 – Artificial Intelligence**

Description: Introduction to the theory, research paradigms, implementation techniques, and philosophies of artificial intelligence.

Prerequisite: CMPSC122 or equivalent; Concurrent: CMPSC465**CMPSC 448 – Machine Learning and Algorithmic AI**

Description: Evaluation and use of machine learning models; algorithmic elements of artificial intelligence.

Prerequisite: IE 453**CMPSC 465 – Data Structures and Algorithms**

Description: Fundamental concepts of computer science: data structures, analysis of algorithms, recursion, trees, sets, graphs, sorting.

Prerequisite: CMPSC122; CMPSC360 or MATH 311W**CSE 556 – Finite Element Methods**

Description: Sobolev spaces, variational formulations of boundary value problems; piecewise polynomial approximation theory, convergence and stability, special methods and applications.

Prerequisite: MATH 502 , MATH 552**CSE 562 – Probabilistic Algorithms**

Description: Design and analysis of probabilistic algorithms, reliability problems, probabilistic complexity classes, lower bounds.

Prerequisite: CSE 565**CSE 564 – Complexity of Combinatorial Problems**

Description: NP-completeness theory; approximation and heuristic techniques; discrete scheduling; additional complexity classes.

Prerequisite: CSE 565**CSE 565 – Algorithm Design and Analysis**

Description: An introduction to algorithmic design and analysis.

Prerequisite: CMPSC 465**CSE 584 – Machine Learning: Tools and Algorithms**

Description: Computational methods for modern machine learning models, including applications to big data and non-differentiable objective functions.**ECON 500 – Introduction to Mathematical Economics**

Description: Mathematical Economics: Applications of Mathematical Techniques to Economics.**ECON 501 – Econometrics**

Description: Applications of Statistical Techniques to Economics.**ECON 521 – Advanced Microeconomic Theory**

Description: Theory of consumer behavior; theory of the firm; price determination in product and factor markets; introduction to welfare economics.**ECON 589 – Seminar in Econometric Theory**

Description: Theories and methods relevant to the application of statistical methods to economics.

Prerequisite: ECON 510**EE 456 – Introduction to Neural Networks**

Description: Artificial Neural Networks as a solving tool for difficult problems for which conventional methods are not applicable.

Prerequisite: CMPSC201 or CMPSC202; MATH 220**EE 556 – Graphs, Algorithms, and Neural Networks**

Description: Examine neural networks by exploiting graph theory for offering alternate solutions to classical problems in signal processing and control.**EE 560 – Probability, Random Variables, and Stochastic Processes**

Description: Review of probability theory and random variables; mathematical description of random signals; linear system response; Wiener, Kalman, and other filtering.

Prerequisite: EE 350; STAT 418**EE 581 – Optimal Control**

Description: Variational methods in control system design; classical calculus of variations, dynamic programming, maximum principle; optimal digital control systems; state estimation.

Prerequisite: EE 580**EE 582 – Adaptive and Learning Systems**

Description: Adaptive and learning control systems; system identification; performance indices; gradient, stochastic approximation, controlled random search methods; introduction to pattern recognition.

Prerequisite: EE 580**EEFE/ECON 510 – Econometrics I**

Description: General linear model, multicolinearity, specification error, autocorrelation, heteroskedasticity, restricted least squares, functional form, dummy variables, limited dependent variables.

Prerequisite: ECON 490 or STAT 462 or STAT 501**EEFE/ECON 511 – Econometrics II**

Description: Topics include endogeneity and moment-based estimators, linear systems of equations, maximum likelihood estimation, models for qualitative and limited dependent variables, models for time series data, models for panel data and treatment evaluation.

Prerequisite: EEFE 510**EEFE 527 – Quantitative Methods I**

Description: The first part of the course reviews the foundations of the mathematical analysis with the goal of modeling feasibility; i.e., the set of possible choices. This prepares us to next move to modeling the optimal choice with an extended presentation on optimization theory and application in the static setting. The final part of the course moves on to the methods for engaging in dynamic optimization.

Prerequisite: EEFE 512, ECON 502**EEFE 530 – Applied Microeconomics II**

Description: This course is designed to: (1) expose students to the most common econometric and statistical techniques used in applied microeconomic research and (2) give students an overview of the different types of micro data and the most common methods used to manipulate these data to create additional data sets and variables.

Prerequisite: EEFE 512, EEFE 510**EEFE 531 – Applied Microeconomics I**

Description: In this course, we will study microeconometrics, a subfield that encompasses specification as well as a variety of estimation, computational, and simulation methods that allow us to pursue specification and parameterization of econometric models suitable for analyzing micro-level data. We will see that these methods support an enriched basis for examining the validity of microeconomic theory, and also extend the analytics feasibly tackled by microeconomics. At the micro-level of empirical analysis, we will see our theory predicts high frequencies of corner solutions, abrupt switching, and discontinuities.

Prerequisite: EEFE 512 or ECON 502, EEFE 510 or ECON 510, EEFE 511 or ECON 510**EEFE 532 – Applied Computational Economics**

Description: Economists often find themselves in situations where closed-form solutions do not exist or econometric estimation is inappropriate due to data limitations or the nature of the problem. In these cases, numerical approaches, using computer-based methods, may be an economist’s best option. In this course, we will explore four topics in the field of computational economics: computable general equilibrium modeling, growth modeling, uncertainty and formal monte carlo analysis, and agent-based modeling.

Prerequisite: EEFE 512**ERM 412 – Resource Systems Analysis**

Description: The concept of systems; techniques of analysis, including input/output, mathematical programming, and simulation; application to resource systems.

Prerequisite: BIOL 220W, ERM 151, ERM 300, and STAT 240; MATH 111 or MATH 141**GEOG 560 – Seminar in Geographic Information Science**

Description: Geographic information science problems/theory, e.g. GIS, cartography, remote sensing, spatial analysis, modeling.**IE 402 – Advanced Engineering Economy**

Description: Concepts and techniques of analyses useful in evaluating engineering projects under deterministic and uncertain conditions.

Prerequisite: IE 302, IE 322, IE 405**IE 405 – Deterministic Models in Operations Research**

Description: Deterministic models in operation research including linear programming, flows in networks, project management, transportation and assignment models and integer programming.

Prerequisite: MATH 220**IE 425 – Stochastic Models in Operations Research**

Description: An introduction to the method and techniques of mathematical decision making, including inventory, replacement, allocation, and waiting line problems.

Prerequisite: IE 405**IE 453 – Simulation Modeling for Decision Support**

Description: Introduction of concepts of simulation modeling and analysis, with application to manufacturing and production systems.

Prerequisite: CMPSC 201C or CMPSC 201F ;IE 323, IE 425**IE 454 – Applied Decision Analysis**

Description: Theory and practice of decision analysis applied to engineering problems.

Prerequisite: IE 322**IE 468 – Optimization Modeling and Methods**

Description: Mathematical modeling of linear, integer, and nonlinear programming problems and computational methods for solving these classes of problems.

Prerequisite: IE 405, MATH 231**IE 505 – Linear Programming**

Description: An accelerated treatment of the main theorems of linear programming and duality structures plus introduction to numerical and computational aspects of solving large-scale problems.

Prerequisite: IE 405**IE 507 – Operations Research: Scheduling Models**

Description: Scheduling models with simultaneous job arrival and probabilistic job arrival, network scheduling, and scheduling simulation techniques.

Prerequisite: IE 425**IE 509 – Operations Research: Waiting Line Models**

Description: Waiting line models including models with infinite queues, finite queues, single and multiple servers under various priorities and disciplines.

Prerequisite: IE 516**IE 510 – Integer Programming**

Description: Study of advanced topics in mathematical programming; emphasis on large-scale systems involving integer variables.

Prerequisite: IE 512**IE 511 – Experimental Design in Engineering**

Description: Statistical design and analysis of experiments in engineering; experimental models and experimental designs using the analysis of variance.

Prerequisite: IE 323**IE 512 – Graph Theory and Networks in Management**

Description: Graph and network theory; application to problems of flows in networks, transportation and assignment problems, pert/CPM, facilities planning.

Prerequisite: IE 425**IE/SC&IS 516 – Applied Stochastic Processes**

Description: Study of stochastic processes and their applications to engineering and supply chain and information systems.

Prerequisite: IE 322 or STAT 318**IE/SC&IS 519 – Dynamic Programming**

Description: This course presents the basic theory and applications of dynamic programming. The focus of the course will be on the theory of Markov decision processes (MDP), which provides an analytical tool to optimally control the behavior of a Markov Chain. The students will learn fundamental MDP models, computational methods and applications in supply chain and information systems, including production and inventory control, quality control, logistics, scheduling, queueing network, and economic problem.

Prerequisite: IE 516 or SC&IS 516 or equivalent**IE 520 – Multiple Criteria Optimization**

Description: Study of concepts and methods in analysis of systems involving multiple objectives with applications to engineering, economic, and environmental systems.

Prerequisite: IE 405 or INS 427**IE 521 – Nonlinear Programming**

Description: Fundamental theory of optimization including classical optimization, convex analysis, optimality conditions and duality, algorithmic solution strategies, variational methods in optimization.

Prerequisite: IE 505**IE 522 – Discrete Event Systems Simulation**

Description: Fundamentals of discrete event simulation, including event scheduling, time advance mechanisms, random variate generation, and output analysis.

Prerequisite: IE 425**IE 525 – Convex Optimization**

Description: This course is designed to provide students with necessary skills to recognize or build convex optimization problems coming from diverse application areas and to solve them efficiently. It consists of five parts: 1) convex sets, 2) convex functions, 3) convex optimization, 4) algorithms and 5) real life applications.

Prerequisite: IE 505**IE 532 – Reliability Engineering**

Description: Mathematical definition of concepts in reliability engineering; methods of system reliability calculation; reliability modeling, estimation, and acceptance testing procedures.

Prerequisite: IE 323 or 3 credits in probability and statistics with a prerequisite of calculus**IE 540 – Manufacturing Systems Simulation**

Description: Use of simulation in design and process improvement of manufacturing systems. Analysis of simulation language structure. Readings in current literature.

Prerequisite: IE 453**IE 555 – Statistical Process Monitoring and Analysis**

Description: Statistical techniques for univariate and multivariate monitoring of dependent and autocorrelated processes; theoretical and numerical approaches for analyzing performance.

Prerequisite: IE 323**IE 561 – Data Mining Driven Design**

Description: The study and application of data mining/machine learning (DM/ML) techniques in multidisciplinary design.**IE 562 – Computational Foundations of Smart Systems**

Description: Intelligent computational techniques for the design and implementation of smart systems.**IE 566 – Quality Control**

Description: Advanced quality assurance and control topics, including multivariate methods, economic design for control and acceptance, dimensioning, tolerancing, and error analysis.

Prerequisite: IE 423**IE 570 – Supply Chain Engineering**

Description: Use of operations research models and methods for solving problems in supply chain systems.

Prerequisite: IE 405, IE 425 or SC&IS 510**IE 575 – Foundations of Predictive Analytics**

Description: Survey course on the key topics in predictive analytics.

Prerequisite: IE 323, STAT 500 or equivalent**IE 582 – Engineering Analytics**

Description: Students will learn advanced information technology, network science, big data, descriptive and predictive analytics, for manufacturing and service systems.**IE 583 – Response Surface Methodology and Process Optimization**

Description: Surface Methodologies used for sequential experimentation and optimization of production processes. Statistical design and analysis of such experiments.

Prerequisite: IE 511 or STAT 501**IE 584 – Time Series Control and Process Adjustment**

Description: Design of Time Series-based process controllers for Quality Engineering. Study of the effect of autocorrelation on control chart performance.

Prerequisite: IE 423**IE 588 – Nonlinear Networks**

Description: Foundation in congestion games, including elements of non-cooperative game theory, equilibrium network flows, Braess paradox, and the price of anarchy. This course examines the theory of congestion games, developed originally to describe flows on congested transport networks but recently embraced to model data networks.

Prerequisite: IE 505**IE 589 – Dynamic Optimization and Differential Games**

Description: Dynamic optimization and dynamic non-cooperative games emphasizing industrial applications. This course provides an introduction to dynamic optimization and dynamic noncooperative games from the perspective of infinite dimensional mathematical programming and differential variational inequalities in topological vector spaces.

Prerequisite: IE 425; IE 505; IE 521 (can be taken concurrently)**MATH/STAT 414 – Introduction to Probability Theory**

Description: probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Prerequisite: MATH 230 or MATH 231**MATH/STAT 415 – Introduction to Mathematical Statistics**

Description: A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests.

Prerequisite: MATH 414**MATH/STAT 416 – Stochastic Modeling**

Description: Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation.

Prerequisite: MATH 318 OR MATH 414; MATH 230**MATH/STAT 418 – Introduction to Probability and Stochastic Processing for Engineering**

Description: Fundamentals and axioms, combinatorial probability, conditional probability and independence, probability laws, random variables, expectation; Chebyshev’s inequality. Students may take only one course from MATH(STAT) 414 and 418 for credit.

Prerequisite: MATH 230 or MATH 231**MATH/CMPSC 451 – Numerical Computations**

Description: Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast FOURIER transform, and differential equations emphasizing computational properties and implementation. Students may take only one course for credit from MATH 451 and 455.

Prerequisite: CMPSC 201C, CMPSC 201, or CSE 103; MATH 230 or MATH 231**MATH 455/CMPSC – Introduction to Numerical Analysis I**

Description: Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455.

Prerequisite: CMPSC 201C, CMPSC 201F, or CSE 103; MATH 220; MATH 230 or MATH 231**MATH/CMPSC 456 – Introduction to Numerical Analysis II**

Description: Polynomial and piecewise polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations.

Prerequisite: MATH 455**MATH 484 – Linear Programs and Related Problems**

Description: Introduction to theory and applications of linear programming; the simplex algorithm and newer methods of solution; duality theory.

Prerequisite: MATH 220; MATH 230 or MATH 231**MATH 485 – Graph Theory**

Description: Introduction to the theory and applications of graphs and directed graphs. Emphasis on the fundamental theorems and their proofs.

Prerequisite: MATH 311W**MATH 486 – Mathematical Theory of Games**

Description: Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.

Prerequisite: MATH 220**MATH/CSE 555 – Numerical Optimization Techniques**

Description: Unconstrained and constrained optimization methods, linear and quadratic programming, software issues, ellipsoid and Karmarkar’s algorithm, global optimization, parallelism in optimization.

Prerequisite: CMPSC 456**MATH/STAT 516 – Stochastic Processes**

Description: Markov chains; generating functions; limit theorems; continuous time and renewal processes; martingales, submartingales, and supermartingales; diffusion processes; applications.

Prerequisite: MATH 416**MATH/STAT 519 – Topics in Stochastic Processes**

Description: Selected topics in stochastic processes, including Markov and Wiener processes; stochastic integrals, optimization, and control; optimal filtering.

Prerequisite: STAT 516, STAT 517**MATH/CSE 550 – Numerical Linear Algebra**

Description: Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors.

Prerequisite: MATH 441 or MATH 456**MATH 553 – Introduction to Approximation Theory**

Description: Interpolation; remainder theory; approximation of functions; error analysis; orthogonal polynomials; approximation of linear functionals; functional analysis applied to numerical analysis.

Prerequisite: MATH 401, 3 credits in Computer Science and Engineering**ME 444 – Engineering Optimization**

Description: Problem formulation, algorithms and computer solution of various engineering optimization problems.

Prerequisite: MATH 220; MATH 230 or MATH 231; CMPSC 201 or CMPSC 202 or CMPSC 200**ME 565 – Optimal Design of Mechanical and Structural Systems**

Description: Application of numerical optimization techniques to design mechanical and structural systems; design sensitivity analysis.**ME 577 – Stochastic Systems for Science and Engineering**

Description: The course develops the theory of stochastic processes and linear and nonlinear stochastic differential equations for applications to science and engineering.

Prerequisite: MATH 414 or MATH 418; ME 550 or MATH 501**MKTG 555 – Marketing Models**

Description: Topics in the model building approach to marketing decision making, focusing on current research issues.**PNG 430 – Reservoir Modeling**

Description: The numerical simulation of petroleum reservoir processes by the use of models; scaling criteria and network flow.

Prerequisite: MATH 251, PNG 410; CMPSC 201C or CMPSC 201F**PNG 511 – Numerical Solution of the Partial Differential Equations of Flow in Porous Media**

Description: Differencing schemes for the partial differential equations of single-phase flow; application to flow of gas and mixing in porous media**PNG 512 – Numerical Reservoir Simulation**

Description: Mathematical analysis of complex reservoir behavior and combination drives; numerical methods for the solution of behavior equations; recent developments.**SC&IS 505 – Management Information Systems Research**

Description: Research problems and issues in supply chain and information systems.**SC&IS 510 – Introduction to Supply Chain and Information Systems**

Description: Introduction to the strategic framework, issues, and methods for integrating supply and demand management within and across companies.**SC&IS 520 – Principles of SC&IS I**

Description: Initial course on principles of supply chain and information systems with special emphasis on potential research topics.

Prerequisite: SC&IS 510**SC&IS 525- Supply Chain Optimization**

Description: Introduction to theory and practice of optimization methods and models for analyzing and improving the performance of supply chain environments.

Prerequisite: prior coursework in linear algebra and calculus**SC&IS 530 – Principles of SC&IS II**

Description: Sequel on principles of supply chain and information systems with special emphasis on potential research topics.

Prerequisite: SC&IS 510**SC&IS 535 – Statistical Research Methods for Supply Chain and Information Systems**

Description: Current statistical research methods for modeling and analysis of supply chain and information systems.

Prerequisite: 3 credits each in undergraduate accounting, economics, and statistics**SC&IS 545 – Supply Chain Systems Simulation**

Description: Application of computer simulation to analysis and design of supply chain and information systems design; simulation experiments in SC&IS research.

Prerequisite: 3 credits of computer programming**STAT 460 – Intermediate Applied Statistics**

Description: Review of hypothesis testing, goodness-of-fit tests, regression, correlation analysis, completely randomized designs, randomized complete block designs, latin squares.

Prerequisite: STAT 200, STAT 240, STAT 250, STAT 301, or STAT 401**STAT 501 – Regression Methods**

Description: Analysis of research data through simple and multiple regression and correlation; polynomial models; indicator variables; step-wise, piece-wise, and logistic regression.

Prerequisite: 6 credits in statistics or STAT 451; matrix algebra**STAT 502 – Analysis of Variance and Design of Experiments**

Description: Analysis of variance and design concepts; factorial, nested, and unbalanced data; ANCOVA; blocked, Latin square, split-plot, repeated measures designs.

Prerequisite: STAT 462 or STAT 501**STAT 503 – Design of Experiments**

Description: Design principles; optimality; confounding in split-plot, repeated measures, fractional factorial, response surface, and balanced/partially balanced incomplete block designs.

Prerequisite: STAT 462 or STAT 501; STAT 502**STAT 510 – Applied Time Series Analysis**

Description: Identification of models for empirical data collected over time. Use of models in forecasting.

Prerequisite: STAT 462 or STAT 501 or STAT 511**STAT 513 – Theory of Statistics I**

Description: Probability models, random variables, expectation, generating functions, distribution theory, limit theorems, parametric families, exponential families, sampling distributions.

Prerequisite: MATH 230**STAT 514 – Theory of Statistics II**

Description: Sufficiency, completeness, likelihood, estimation, testing, decision theory, Bayesian inference, sequential procedures, multivariate distributions and inference, nonparametric inference.

Prerequisite: STAT 513**STAT 515 – Stochastic Processes and Monte Carlo Methods**

Description: Conditional probability and expectation, Markov chains, the exponential distribution and Poisson processes.

Prerequisite: MATH 414, STAT 414, or STAT 513**STAT 540 – Statistical Computing**

Description: Computational foundations of statistics; algorithms for linear and nonlinear models, discrete algorithms in statistics, graphics, missing data, Monte Carlo techniques.

Prerequisite: STAT 501 or STAT 511; STAT 415; matrix algebra**STAT 557 – Data mining I**

Description: This course on data mining will cover methodology, major software tools and applications in this field. By introducing principal ideas in statistical learning, the course will help students to understand conceptual underpinnings of methods in data mining.

Prerequisite: STAT 318 or STAT 416 and basic programming skills**STAT 558 – Data mining II**

Description: Advanced data mining techniques: temporal pattern mining, network mining, boosting, discriminative models, generative models, data warehouse, and choosing mining algorithms.

Prerequisite: STAT 557 or IST 557