Undergraduate Courses

A first introduction to probability and statistics. This course will provide background to understand and produce rigorous statistical analysis including estimation, confidence intervals, hypothesis testing and regression and classification. Applicability and limitations of these methods will be illustrated using a variety of modern real world data sets and manipulation of the statistical software R.
**Exam option: Some students may have substantial prior knowledge of engineering statistics. For them, the “Core Requirement” aspects of ORF 245, Fundamentals of Engineering Statistics, can be satisfied by a “core-requirement exam”. The 3-hour exam is administered in January to student(s) who have applied to the ORFE Director of Undergraduate Studies prior to the previous December 1 for permission to take the exam, and received authorization by the ORF 245 Exam Committee. The application should clearly state (including supporting documentation) why the student feels they already have a firm grasp of the Fundamentals of Engineering Statistics. Note: passing the exam satisfies the “Core Requirement of ORF 245” but does not contribute a course to the BSE degree’s “36 courses” requirement and it increases ORFE’s “Departmental Elective” requirement from 10 to 11, one of which must now be an advanced statistics course. In short, the “Core Requirement” for statistics can be satisfied by either taking and passing ORF 245 or for those with sufficient advanced knowledge, passing the ORF 245 exam and passing an advanced statistics course.
Many real-world problems involve maximizing a linear function subject to linear equality and/or inequality constraints. Such problems are called Linear Programming (LP) problems. Examples include min-cost network flows, portfolio optimization, options pricing, assignment problems and two-person zero-sum games to name but a few. The theory of linear programming will be developed with a special emphasis on duality theory. Attention will be devoted to efficient solution algorithms. These algorithms will be illustrated on real-world examples such as those mentioned.
An introduction to probability and its applications. Topics include: basic principles of probability; Lifetimes and reliability, Poisson processes; random walks; Brownian motion; branching processes; Markov chains
A survey of quantitative approaches for making optimal decisions under uncertainty, including decision trees, Monte Carlo simulation, and stochastic programs. Forecasting and planning systems are integrated in the context of financial applications. Machine learning methods are linked to the stochastic optimization models.
Financial Mathematics is concerned with designing and analyzing products that improve the efficiency of markets, and create mechanisms for reducing risk. This course develops quantitative methods for these goals: the notions of arbitrage and risk-neutral pricing in discrete time, specific models such as Black-Scholes and Heston in continuous time, and calibration to market data. Credit derivatives, the term structure of interest rates, and robust techniques in the context of volatility options will be discussed, as well as lessons from the financial crisis.
The amount of data in our world has been exploding and analyzing large data sets is a central challenge in society. This course introduces the statistical principles and computational tools for analyzing big data. Topics include statistical modeling and inference, model selection and regularization, scalable computational algorithms, and more.
Predictive analytics and decision modeling are two key components of business analytics. They provide decision makers with the fundamental rationality in evaluating performance, making decisions, designing strategies, and managing risk. ORF360 focuses on both popular decision models arising from real applications, as well as mathematical decision-making tools and concepts. The first half of the course introduces the basic decision models in revenue management and pricing. The second half of the course consists of a series of business themes, such as airlines, finance, healthcare, and games, and focuses on data-driven real-world applications.
An introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, and techniques for dealing with uncertainty and intractability in optimization problems. Extensive hands-on experience with high-level optimization software. Applications drawn from operations research, statistics and machine learning, economics, control theory, and engineering.
Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member.
This course showcases how networks are widespread in society, technology, and nature, via a mix of theory and applications. It demonstrates the importance of understanding network effects when making decisions in an increasingly connected world. Topics include an introduction to graph theory, game theory, social networks, information networks, strategic interactions on networks, network models, network dynamics, information diffusion, and more.
Electronic commerce, traditionally the buying and selling of goods using electronic technologies, extends to essentially all facets of human interaction when extended to services, particularly information. The course focuses on both the software and the hardware aspects of traditional aspects as well as the broader aspects of the creation, dissemination and human consumption electronic services. Covered will be the physical, financial and social aspects of these technologies
An introduction to popular statistical approaches in regression and time series analysis. Topics will include theoretical aspects and practical considerations of linear, nonlinear, and nonparametric modeling (kernels, neural networks, and decision trees).
This is an introduction to the stochastic models inspired by the dynamics of resource sharing. Topics discussed include: early motivating communication systems (telephone and computer networks); modern applications (call centers, healthcare operations, and urban planning for smart cities); and key formulas (from Erlang blocking and delay to Little's law). We also review supporting stochastic theories like equilibrium Markov chains along with Markov, Poisson and renewal processes.
An introduction to the uses of simulation and computation for analyzing stochastic models and interpreting real phenomena. Topics covered include generating discrete and continuous random variables, stochastic ordering, the statistical analysis of simulated data, variance reduction techniques, statistical validation techniques, nonstationary Markov chains, and Markov chain Monte Carlo methods. Applications are drawn from problems in finance, manufacturing, and communication networks. Students will be encouraged to program in Python. Office hours will be offered for students unfamiliar with the language.
Students will develop mathematical modeling skills in the context of sequential decisions under uncertainty. Students will learn the five elements of a sequential decision problem: state variables, identifying and modeling decisions, uncertainty quantification, creating transition functions, and designing objective junctions. They will learn how to design policies, and the principles of policy search and evaluation in both offline and online settings. All concepts will be taught through a series of carefully chosen problems designed to bring out specific modeling features.
This course develops several methods that are central to modern optimization and learning problems under uncertainty. These include dynamic programming, linear quadratic regulator, Kalman filter, multi-armed bandits and reinforcement learning. Representative applications and numerical methods are emphasized.
This course covers the basic concepts of measuring, modeling and managing risks within a financial optimization framework. Topics include single and multi-stage financial planning systems. Implementation from several domains within asset management and goal based investing. Machine learning algorithms are introduced and linked to the stochastic planning models. Python and optimization exercises required.
An introduction to the theory and practice of high frequency trading in modern electronic financial markets. We give an overview of the institutional landscape and basic empirical features of modern equity, futures, and fixed income markets. We discuss theoretical models for market making and price formation. Then we dig into detailed empirical aspects of market microstructure and how these can be used to construct effective trading strategies. Course work will be a mixture of theoretical and data-driven problems. Programming environment will be a mixture of the R statistical environment, with the Kdb database language.
This course is an introduction to commodities markets (oil, gas, metals, electricity, etc.), and quantitative approaches to capturing uncertainties in their demand and supply. We start from a financial perspective, and traditional models of commodity spot prices and forward curves. Then we cover modern topics: game theoretic models of energy production (OPEC vs. fracking vs. renewables); quantifying the risk of intermittency of solar and wind output on the reliability of the electric grid (mitigating the duck curve); financialization of commodity markets; carbon emissions markets. We also discuss economic and policy implications.
Studied is the transportation sector of the economy from a technology and policy planning perspective. The focus is on the methodologies and analytical tools that underpin policy formulation, capital and operations planning, and real-time operational decision making within the transportation industry. Case studies of innovative concepts such as "value" pricing, real-time fleet management and control, GPS-based route guidance systems, automated transit systems and autonomous vehicles will provide a practical focus for the methodologies. Class project in lieu of final exam focused on major issue in Transportation Systems Analysis.
Over recent decades, novel data sources and machine learning models have enabled rapid evolution across financial services. This course focuses on ongoing innovations in consumer lending. The technical material spans finance and machine learning topics, including fairness and explainability, important in lending and also more broadly. The class integrates technical topics with critical explorations of business practices informed by readings, class discussion and outside speakers, and includes work with industry data sets.
An introduction to the theory and practice of high frequency trading in modern electronic financial markets. We give an overview of the institutional landscape and basic empirical features of modern equity, futures, and fixed income markets. We discuss theoretical models for market making and price formation. Then we dig into detailed empirical aspects of market microstructure and how these can be used to constructe effective trading strategies. Course work will be a mixture of theoretical and data-driven problems. Programming environment will be a mixture of the R statistical environment, with the Kdb database language.
An introduction to network games. Topics will include: A crash course on state games, introduction to graph theory and network games, games with incomplete information and auctions, non-atomic games, signals and correlated equilibria.
A formal report on research involving analysis, synthesis, and design, directed toward improved understanding and resolution of a significant problem. The research is conducted under the supervision of a faculty member, and the thesis is defended by the student at a public examination before a faculty committee. The senior thesis is equivalent to a year-long study and is recorded as a double course in the Spring.
Students conduct a one-semester project. Topics chosen by students with approval of the faculty. A written report is required at the end of the term.