129 courses with the subject IEOR E, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
Introductory course for overview of modern approaches and ideas of operations research and data analytics. Through a series of interactive sessions, students engage in activities exploring OR topics with various faculty members from the IEOR department
Prerequisites: ENGI E1006; Or competency in Python. Introduction to essential data engineering methods. Potential topics include Arrays, Linked Lists, Stacks and Queues, Trees and Graphs, Hash Tables, Search Algorithms and Efficiency, Relational databases, SQL, NoSQL, and Data Wrangling. Practice both theory and applications using Python programming
Prerequisites: (ECON UN1105) ECON W1105 For undergraduates only. Examines the fundamental concepts of financial accounting and finance, from the perspective of both managers and investors. Key topics covered include principles of accrual accounting; recognizing and recording accounting transactions; preparation and analysis of financial statements; ratio analysis; pro-forma projections; time value of money (present values, future values and interest/discount rates); inflation; discounted-cash-flow (DCF) project evaluation methods; deterministic and probabilistic measures of risk; capital budgeting
Prerequisites: (IEOR E3658) and For undergraduates only. Required for all undergraduate students majoring in IE, OR:EMS, OR:FE, and OR. Must be taken during or before the fifth semester. Corequisites: IEOR E4404
Prerequisites: (IEOR E3608) and (IEOR E3658) and IEOR E3608 AND IEOR E3658 For undergraduates only. Required for all undergraduate students majoring in IE, OR:EMS, OR:FE, and OR. Must be taken during (or before) the sixth semester. Inventory management and production planning. Continuous and periodic review models: optimal policies and heuristic solutions, deterministic and probabilistic demands. Material requirements planning. Aggregate planning of production, inventory, and work force. Multi-echelon integrated production-inventory systems. Production scheduling. Term project. Recitation section required
Prerequisites: Knowledge of a programming language such as Python, C, C++ or Matlab
Prerequisites: (MATH UN2010) Corequisites: COMS W3134,COMS W3137
Prerequisites: (IEOR E3608) IEOR E3608 For undergraduates only. Required for all undergraduate students majoring in IE, OR:EMS, OR:FE, and OR. This is a follow-up to IEOR E3608 and will cover advanced topics in optimization, including integer optimization, convex optimization, and optimization under uncertainty, with a strong focus on modeling, formulations, and applications
Prerequisites: Calculus. For undergraduates only. Required for OR:FE concentration. Must be taken during or before third semester. Students who take IEOR E3658 may not take W4150 due to significant overlap. Recommended: strong mathematical skills.
Prerequisites: IEOR E3608 AND IEOR E3658 AND IEOR E4307; For IEOR undergraduates only. An overview of active research areas in Operations Research and Data Analytics, and an introduction to the essential components of research studies. This course helps students develop fundamental research skills, including paper reading, problem formulation, problem-solving, scientific writing, and research presentation. Classes are in seminar format, with students analyzing research papers, developing research projects, and presenting research findings
Prerequisites: Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design
Prerequisites: Obtained internship and approval from faculty advisor. Only for IEOR undergraduate students who need relevant work experience as part of their program of study. Final reports are required. This course may not be taken for pass/fail credit or audited
Prerequisites: Probability theory and linear programming. Required for all undergraduate students majoring in IE, OR:EMS, OR:FE, and OR. Introduction to the economic evaluation of industrial projects. Economic equivalence and criteria. Deterministic approaches to economic analysis. Multiple projects and constraints. Analysis and choice under risk and uncertainty
Prerequisites: Refer to course syllabus. A graduate course only for MS＆E, IE, and OR students. This is also required for students in the Undergraduate Advanced Track. For students who have not studied linear programming. Some of the main methods used in IEOR applications involving deterministic models: linear programming, the simplex method, nonlinear, integer and dynamic programming
Prerequisites: Linear algebra. This graduate course is only for M.S. Program in Financial Engineering students. Linear, quadratic, nonlinear, dynamic, and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering are discussed
Prerequisites: Linear programming, basic probability theory.
Prerequisites: Students should be familiar with Python programming. A basic understanding of probability and statistics at the level of IEOR E4150 (or equivalent) is required.
Prerequisites: Understanding of single- and multivariable calculus. Probability and simulation. Statistics building on knowledge in probability and simulation. Point and interval estimation, hypothesis testing, and regression. A specialized version of IEOR E4150 for MSE and MSBA students who are exempt from the first half of IEOR E4101. Must obtain waiver for E4101
Prerequisites: Understanding of single- and multivariable calculus. MSE and MSBA students only. Basic probability theory, including independence and conditioning, discrete and continuous random variable, law of large numbers, central limit theorem, and stochastic simulation, basic statistics, including point and interval estimation, hypothesis testing, and regression; examples from business applications such as inventory management, medical treatments, and finance. A specialized version of IEOR E4150 for MSE and MSBA students
Prerequisites: IEOR E4101 Introduction to stochastic processes and models, with emphasis on applications to engineering and management; random walks, gambler’s ruin problem, Markov chains in both discrete and continuous time, Poisson processes, renewal processes, stopping times, Wald’s equation, binomial lattice model for pricing risky assets, simple option pricing; simulation of simple stochastic processes, Brownian motion, and geometric Brownian motion. A specialized version of IEOR E4106 for MSE students
Prerequisites: (STAT GU4001) or IEOR E4150 This graduate course is only for IE and OR students. Also required for students in the Undergraduate Advanced Track. Corequisites: IEOR E4403
Prerequisites: IEOR E3402 or instructor's permission. MS IEOR students only.
Prerequisites: Probability and statistics at the level of IEOR E3658 and E4307 or STAT GU4001, and Deterministic Models at the level of IEOR E3608 or IEOR E4004, or instructor permission. For MS-MS&E students only.
Prerequisites: Calculus, including multiple integration. Covers the following topics: fundamentals of probability theory and statistical inference used in engineering and applied science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference: pint and confidence interval estimation, hypothesis tests, linear regression. For IEOR graduate students
Innovative solutions to complex problems that are both novel and useful. Focuses on The Think Bigger Innovation Method, uses decision-making theory, cognitive science, and industry practice to facilitate creativity and innovation. Designed to foster new ideas during the beginning of the semester that will then function as the seeds for entrepreneurially minded. Culminates in a final project with presentation of formal and polished pitch of an innovative idea in front of a distinguished panel of successful minds from across the city
Zero-credit course. Primer on quantitative and mathematical concepts. Required for all incoming MSOR and MSIE students
Lect: 3. Sensory and cognitive (brain) processing considerations in the design, development, and operations of systems, products, and tools. User or operator limits and potential in sensing, perceiving decision making, movement coordination, memory, and motivation. Fall 2026: IEOR E4207 Course Number Section/Call Number Times/Location Instructor Points Enrollment IEOR 4207 001/14692 M 4:10pm - 6:40pm 627 Seeley W. Mudd Building Leon Gold 3.00 48/52
Prerequisites: (IEOR E4207) or IEOR E4207; IEOR E4207 or instructor’s permission. An elective for undergraduate students majoring in IE. An in-depth exploration of the application potential of human factor principles for the design of products and processes. Applications to industrial products, tools, layouts, workplaces, and computer displays. Consideration to environmental factors, training and documentation. Term project
Surveys tools available in Python for getting (web scraping and APIs) and visualizing data (charts and maps). Introduction to analytics through machine learning (ML algorithms, model evaluation, text analytics, network algorithms, deep learning)
Prerequisites: IEOR E2000 (or sufficient coding background in Python); IEOR 3608 (or CSOR 4231 Analysis of Algorithms I); IEOR E3658 (or another probability course); IEOR E4212 (or machine learning background from other courses
Prerequisites: probability, linear algebra. Descriptive statistics, central limit theorem, parameter estimation, sufficient statistics, hypothesis testing, regression, logistic regression, goodness-of-fit tests, applications to operations research models
Zero-credit course. Primer on quantitative and mathematical concepts. Required for all incoming MSOR and MSIE students
points. underlying Corporate Finance, such as CAPM, Miller Modigliani, Fama French factors, Smart Beta, etc. Interpret financial statements, build cash flow models, value projects, value companies, and make Corporate Finance decisions. Additional topics include: cost of capital, dividend policy, debt policy, impact of taxes, Shareholder/Debtholder agency costs, dual-class shares, using option pricing theory to analyze management behavior, investment banking activities, including equity underwriting, syndicated lending, venture capital, private equity investing and private equity secondaries. Application of theory in real-world situations: analyzing financial activities of companies such as General Electric, Google, Snapchat, Spotify, and
Prerequisites: Probability theory and linear programming Required for students in the Undergraduate Advanced Track. Key measures and analytical tools to assess the financial performance of a firm and perform the economic evaluation of industrial projects. Deterministic mathematical programming models for capital budgeting. Concepts in utility theory, game theory and real options analysis
Prerequisites: (IEOR E3658) and (IEOR E4307) or (STAT GU4001) and Required for all undergraduate students majoring in IE, OR:EMS, OR:FE, and OR. Also required for MSOR. Corequisites: IEOR E3106,IEOR E4106
Prerequisites: (IEOR E3608) and (IEOR E3658) and IEOR E3608 AND IEOR E3658; Computer programming. Required for undergraduate students majoring in IE and OR. Job shop scheduling: parallel machines, machines in series; arbitrary job shops. Algorithms, complexity, and worst-case analysis. Effects of randomness: machine breakdowns, random processing time. Term project
Prerequisites: (IEOR E4004) or (IEOR E3608) and (IEOR E4106) or (IEOR E3106) and Familiarity with differential equations and computer programming; or instructor’s permission.
Lect: 3. Required for undergraduate students majoring in IE. Statistical methods for quality control and improvement: graphical methods, introduction to experimental design and reliability engineering and the relationships between quality and productivity. Contemporary methods used by manufacturing and service organizations in product and process design, production and delivery of products and services.
Prerequisites: A background in optimization and/or algorithms is strongly encouraged and may be obtained concurrently. Background in probability and/or stochastic processes is also strongly encouraged and may be obtained concurrently. Prior coding experience encouraged Transportation, primarily focused on the movement of people, and logistics, primarily focused on the movement of goods, are two of the most fundamental challenges to modern society. To address many problems in these areas, a wide array of mathematical models and analytics tools have been developed. This class will introduce many of the foundational tools used in transportation and logistics problems, relying on ideas from linear optimization, integer optimization, stochastic processes, statistics, and simulation. We will address problems such as optimizing the routes of cars and delivery trucks, positioning emergency vehicles, and controlling traffic behavior. Moreover, we will discuss modern issues such as bicycle sharing, on-demand car and delivery services, and humanitarian logistics. Concepts will be reinforced with technical content as well as real-world data and examples
Prerequisites: Students should have a good background in calculus, probability, and linear algebra. Some basic prior knowledge of finance will be helpful (but not necessary).
Prerequisites: Computer programming or instructor’s approval. Required for undergraduate students majoring in OR:FE. We will take a hands-on approach to developing computer applications for Financial Engineering. Special focus will be placed on high-performance numerical applications that interact with a graphical interface. In the course of developing such applications we will learn how to create DLLs, how to integrate VBA with C/C programs, and how to write multithreaded programs. Examples of problems settings that we consider include simulation of stock price evolution, tracking, evaluation and optimization of a stock portfolio; optimal trade execution. In the course of developing these applications, we review topics of interest to OR:FE in a holistic fashion
Corequisites: IEOR E4523
Zero-credit course. Primer on Python for analytics concepts. Required for MSBA students
Aims to give the student a broad overview of the role of Operations Research in public policy. The specific areas covered include voting theory, apportionment, deployment of emergency units, location of hazardous facilities, health care, organ allocation, management of natural resources, energy policy, and aviation security. Draws on a variety techniques such as linear and integer programming, statistical and probabilistic methods, decision analysis, risk analysis, and analysis and control of dynamic systems. Spring 2026: IEOR E4505 Course Number Section/Call Number Times/Location Instructor Points Enrollment IEOR 4505 001/13283 M W 11:40am - 12:55pm 717 Hamilton Hall Eric Stratman 3.00 32/50
IEOR students only. Understand digital businesses, apply scientific, engineering thinking to digital economy. Data-driven digital strategies and operating models. Sectors: ecommerce, advertising technology, and marketing technology. Automation of the marketing, sales, and advertising functions. Algorithms, patents, and business models. Business side of the digital ecosytem and the digital economy
Prerequisites: (IEOR E3608) and (IEOR E3658) and (IEOR E4307) For senior undergraduate Engineering students: SIEO W3600: Introduction to Probability and Statistics and IEOR E3608: Introduction to Mathematical Programming; For Engineering graduate students (MS or PhD): Probability and Statistics at the level of SIEO W4150, and Deterministic Models at the level of IEOR E4004. For Healthcare Management students: P8529: Analytic Methods for Health Services Management.
Prerequisites: (IEOR E4004) or (IEOR E3608) IEOR E4004 OR IEOR E3608 Management of complex projects and the tools that are available to assist managers with such projects. Topics include project selection, project teams and organizational issues, project monitoring and control, project risk management, project resource management, and managing multiple projects
Teams of students work on real-world projects in analytics. Focus on three aspects of analytics: identifying client analytical requirements; assembling, cleaning and organizing data; identifying and implementing analytical techniques (e.g., statistics and/or machine learning); and delivering results in a client-friendly format. Each project has a defined goal and pre-identified data to analyze in one semester. Client facing class. Class requires 10 hours of time per week and possible client visits on Fridays
Prerequisites: B.S. in engineering or applied sciences; professional experience recommended; calculus, probability and statistics, linear algebra. Introduction to fundamental methods used in systems engineering. Rigorous process that translates customer needs into a structured set of specific requirements; synthesizes a system architecture that satisfies those requirements and allocates them in a physical system, meeting cost, schedule, and performance objectives throughout the product life-cycle. Sophisticated modeling of requirements optimization and dependencies, risk management, probabilistic scenario scheduling, verification matrices, and systems-of-systems constructs are synthesized to define the meta-workflow at the top of every major engineering project
Prerequisites: B.S. in engineering or applied sciences; probability and statistics, optimization, linear algebra, and basic economics. Applications of SE tools and methods in various settings. Encompasses modern complex system development environments, including aerospace and defense, transportation, energy, communications, and modern software-intensive systems
Prerequisites: (IEOR E4501) Prior exposure to some programming language is helpful, and you should either have taken or be concurrently registered in the IEOR E4501 Tools for Analytics class.
Lect: 3. MSBA students only. Groups of students will work on real world projects in analytics, focusing on three aspects: identifying client analytical requirements; assembling, cleaning, and organizing data; identifying and implementing analytical techniques (statistics, OR, machine learning); and delivering results in a client-friendly format. Each project has a well-defined goal, comes with sources of data preidentified, and has been structured so that it can be completed in one semester. Client-facing class with numerous on-site client visits; students should keep Fridays clear for this purpose. Spring 2026: IEOR E4524 Course Number Section/Call Number Times/Location Instructor Points Enrollment IEOR 4524 001/13287 Th 7:10pm - 9:40pm 301 Pupin Laboratories Hardeep Johar 3.00 255/260 IEOR 4524 002/13288 T 4:10pm - 6:40pm 327 Seeley W. Mudd Building Yaren Kaya 3.00 21/30
Prerequisites: Optimization, applied probability, statistics, and knowledge of or experience in computer programming. MS IEOR students only. Introduction to machine learning, practical use of ML algorithms and applications to financial engineering and operations. Supervised learning: regression, classification, resampling methods, regularization, support vector machines (SVMs), and deep learning. Unsupervised learning: dimensionality reduction, matrix decomposition, and clustering algorithms
Prerequisites: IEOR E4501 and IEOR E4523 IEOR E4501 AND IEOR E4523 To introduce students to programming issues around working with clouds for data analytics. Class will learn how to work with infrastructure of cloud platforms, and discussion about distributed computing, focus of course is on programming. Topics covered include MapReduce, parallelism, rewriting of algorithms (statistical, OR, and machine learning) for the cloud, and basics of porting applications so that they run on the cloud
Prerequisites: A course in probability and statistics 4101/4150 or equivalent, basic python programming. This course will cover the basics of game theory and market design, with a focus on how AI and optimization enables large-scale game solving and markets. We will cover the core ideas behind recent superhuman AIs for games such as Poker. Then, we will discuss how AI and game theory ideas are used in marketplaces such as internet advertising, fair course seat allocation, and spectrum reallocation. This is intended to be an advanced MS level and senior undergraduate course for students in Operations Research and Financial Engineering
Data visualization and how to build a story with data. Using complex data or statistics to communicate results effectively. Learn to present analysis and results conscisely and effectively
OKR framework and different variations. Measurement techniques (A/B testing, validation, correlation, etc.) Identifying what to measure in product experience and business initiatives. Data-driven decision making
Applied Analytics focus querying and transforming data with SQL, defining and visualizing metrics, measuring impact of products / processes. Tools and techniques to convert raw data to business decisions, statistical analysis. Be able to apply these techniques to real-world datasets
Introduction to the foundations and applications of Analytics Engineering, bridging Data Engineering and Data Analysis. Potential topics include SQL fundamentals, data warehouse setup and maintenance (Snowflake), version control with GitHub, data ingestion and integration (Fivetran), data cleaning and transformations (dbt), data visualization (Preset), and orchestrating modern data architectures. Emphasizes both theoretical understanding and hands-on practice, giving students practical experience building, managing, and analyzing data pipelines and models in real-world scenarios
Prerequisites: Linear Algebra, Calculus, Probability, and some basic programming. Course covers major statistical learning methods for data mining under both supervised and unsupervised settings. Topics covered include linear regression and classification, model selection and regularization, tree-based methods, support vector machines, and unsupervised learning. Students learn about principles underlying each method, how to determine which methods are most suited to applied settings, concepts behind model fitting and parameter tuning, and how to apply methods in practice and assess their performance. Emphasizes roles of statistical modeling and optimization in data mining
Focus on advanced statistical techniques for a career in data science or business analytics. Covers the use of writing probabilistic models for data-generating processes, using Bayesian Methods/MCMC to solve such problems. Emphasizes problem identification and general problem-solving tools. Special Topics: Survival Analysis, Missing Data, Robust Statistics, Sequential Analysis, Multiple Testing. Assignments are case-based
only with adviser approval) Ethnicity and Race Minor CSER UN1010 INTRO TO COMP ETHNIC STUDIES One of the following courses: CSER UN3928 COLONIZATION/DECOLONIZATION CSER UN3942 RACE AND RACISMS Three additional CSER courses with approval from the Department Film and Media Studies Minor Students who take the minor should begin with Intro to Film and Media Studies. Lab classes and seminars will only be available to students who have declared minors in Film and Media Studies. All minors are entitled to one lab class, although they may take a second for their other elective if space permits. Students can apply only one study abroad or transfer class (3-credit equivalent) to completion of the minor. This restriction a applies to film-related classes offered in other Columbia programs. The minor consists of five courses (fifteen credits) as follows: FILM UN1000 INTRO TO FILM # MEDIA STUDIES Two of the following four courses, one of which must be FILM UN2010 or UN2020: FILM UN2010 CINEMA HIST I: BEGIN-1930 FILM UN2020 CINEMA HIST II: 1930-1960 FILM UN2030 FILM UN2040 CINEMA HIST III:1960-1990 CINEMA HISTORY IV: AFTER 1990 Any two courses offered by the Department of Film and Media Studies Only one elective can be from the following labs: • FILM UN2410 LAB IN WRITING FILM CRITICISM • FILM UN2420 LABORATORY IN SCREENWRITING • FILM UN2510 LAB IN FICTION FILMMAKING • FILM UN2520 LAB IN NONFICTION FILMMAKING French and Francophone Studies
Tools and knowledge to develop a comprehensive new venture that is scalable, repeatable, and capital efficient. Covers customer discovery, market sizing, pricing, competition, distribution, funding, developing a minimal viable product, and other facets of creating new ventures. A company blueprint and final investor pitch are deliverables
How Design Thinking can enhance innovation activities, market impact, value creation, and speed. Topics include: conceptual and practical understanding of design thinking, creative solutions, develop robust practices to lead interdisciplinary teams. Course aims to strengthen individuals and collaborative capabilities to identify customer needs, indirect and qualitative research, create concept hypotheses, develop prototype, defined opportunities into actionable innovation possibilities, and recommendations for client organizations
Technological breakthroughs driven change, disruption, and transformation of the business landscape/society. Course covers overview of deep learning and neural networks; AI and robotics; imaging and vision; photonics; blockchain; smart/digital cities; and the application of these technologies for creating new products and services
Prerequisites: Prior knowledge in quantitative and analytical methods, such as operations research (e.g., optimization or stochastic processes), business analytics (e.g., data analysis or statistical modeling), or machine learning. Explores how analytics and AI drive strategy, business models, and organizational transformation. Develops students as “analytics translators” who bridge technical models and business execution using leadership, communication, and change management alongside analytical expertise. Covers frameworks for value creation, organizational design, systems thinking, complexity, innovation, and behavioral barriers such as cognitive biases and resistance to change. Examines how firms integrate analytics into strategy and operations within evolving digital and knowledge-driven economies
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit. or Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit
Prerequisites: IEOR E4004IEOR E4106IEOR E4150 or instructor's permission. Probability and statistics, Basic optimization (e.g., familiarity with linear and convex optimization, gradient descent, basic algorithm design constructs), familiarity with Programming in python (or experience with programming in other languages like C/C++/Matlab and willingness to learn python). Knowledge of machine learning is not required, but some basic familiarity may help. This course introduces engineering undergraduates to the essential concepts, tools, and skills required to create and manage a successful technology-driven business. Students will learn through a mix of lectures, case studies, assignments, and a final business plan project, guided by a professor with an engineering background and over three decades of real-world startup experience. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit. or Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit. or Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
Prerequisites: IEOR E4004 AND IEOR E4106 AND IEOR E4150; IEOR E4150, IEOR E4004, and IEOR E4106, or instructor's permission. Special topics arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes each time it is offered, it may be repeated for credit. Consult the department for section assignment
(0 credits, First Year)
Primer on quantitative and mathematical concepts. Required for all incoming MSBA students
Prerequisites: (STAT GU4001) and (IEOR E4004) IEOR E4004 AND STAT W4001 Focus on capacity allocation, dynamic pricing and revenue management. Perishable and/or limited product and pricing implications. Applications to various industries including service, airlines, hotel, resource rentals, etc
Prerequisites: (STAT GU4001) and (IEOR E4106) IEOR E4106 AND STAT W4001 Risk management models and tools; measure risk using statistical and stochastic methods, hedging and diversification. Examples include insurance risk, financial risk, and operational risk. Topics covered include VaR, estimating rare events, extreme value analysis, time series estimation of extremal events; axioms of risk measures, hedging using financial options, credit risk modeling, and various insurance risk models
Prerequisites: (IEOR E4700) IEOR E4700 Required for undergraduate students majoring in OR:FE. Characteristics of commodities or credit derivatives. Case study and pricing of structures and products. Topics covered include swaps, credit derivatives, single tranche CDO, hedging, convertible arbitrage, FX, leverage leases, debt markets, and commodities
Prerequisites: (IEOR E4700) IEOR E4700 Models for pricing and hedging equity, fixed-income, credit-derivative securities, standard tools for hedging and risk management, models and theoretical foundations for pricing equity options (standard European, American equity options, Asian options), standard Black-Scholes model (with multiasset extension), asset allocation, portfolio optimization, investments over longtime horizons, and pricing of fixed-income derivatives (Ho-Lee, Black-Derman-Toy, Heath-Jarrow-Morton interest rate model)
Prerequisites: A solid background in probability and statistics is strongly encouraged. An optimization background is also strongly encouraged and may be obtained concurrently. Prior coding experience is encouraged. This course focuses on how to identify, evaluate, and capture business analytic opportunities that create value. The course covers basic analytic methods alongside case studies on organizations that successfully deployed these techniques. The first part of the course is on using data to develop insights and predictive capabilities with machine learning techniques. The second part focuses on the use of A/B testing, causal inference, ethics, and optimization to support decision-making
Prerequisites: (IEOR E3106) or (IEOR E4106)
Prerequisites: (STAT GU4001) STAT W4001 This graduate course is only for M.S. Program in Financial Engineering students, offered during the summer session. Review of elements of probability theory, Poisson processes, exponential distribution, renewal theory, Wald’s equation. Introduction to discrete-time Markov chains and applications to queueing theory, inventory models, branching processes
Prerequisites: (IEOR E4701) IEOR E4701 This graduate course is only for M.S. Program in Financial Engineering students. Multivariate random number generation, bootstrapping, Monte Carlo simulation, efficiency improvement techniques. Simulation output analysis, Markov-chain Monte Carlo. Applications to financial engineering. Introduction to financial engineering simulation software and exposure to modeling with real financial data. Note: Students who have taken IEOR E4404 Simulation may not register for this course for credit
Prerequisites: Students should have a good background in calculus, probability and linear algebra. Some basic prior knowledge on finance will be helpful (but not necessary).
Prerequisites: (IEOR E4701) and (IEOR E4702) and Linear algebra Corequisites: IEOR E4709
Prerequisites: (IEOR E4701) Corequisites: IEOR E4709
Prerequisites: IEOR E4702 Probability Corequisites: IEOR E4706,IEOR E4707
Prerequisites: Refer to course syllabus. An introduction to capital markets and investments providing an overview of financial markets and tools for asset valuation. Topics covered include the pricing of fixed-income securities (treasury markets, interest rate swaps futures, etc.), discussions on topics in credit, foreign exchange, sovereign ad securitized markets—private equity and hedge funds, etc
Prerequisites: (IEOR E4706) and IEOR E4706; Knowledge of derivatives valuation models. During the past 15 years the behavior of market options prices have shown systematic deviations from the classic Black-Scholes model. Examines the empirical behavior of implied volatilities, in particular the volatility smile that now characterizes most markets, the mathematics and intuition behind new models that can account for the smile, and their consequences for hedging and valuation
Prerequisites: (IEOR E4700) and IEOR E4700; Additional prerequisites will be announced depending on offering Selected topics of interest in the area of quantitative finance. Offerings vary each year; some topics include energy derivatives, experimental finance, foreign exchange and related derivative instruments, inflation derivatives, hedge fund management, modeling equity derivatives in Java, mortgage-backed securities, numerical solutions of partial differential equations, quantitative portfolio management, risk management, trade and technology in financial markets
Prerequisites: IEOR E4700; Additional prerequisites will be announced depending on offering This graduate-level course provides a rigorous foundation in quantitative portfolio construction, bridging theory with practical implementation. It develops a systematic framework for constructing optimal portfolios, beginning with the classical Markowitz model and enhancing it to address real-world portfolio objectives and constraints. Students learn how forecasts of asset returns, risk, and market impact are formulated in the optimizer objectives and constraints, and how estimation error affects portfolio construction and performance. They also study the robust estimation of key optimizer inputs such as risk models using modern statistical and econometric methods that handle noise and time-varying dynamics. Students gain hands-on experience constructing portfolios using industry-standard datasets, tools, and risk models. The course also provides a brief introduction to advanced topics such as random matrix theory, multiperiod optimization, and the use of modern machine learning methods, which represent emerging directions in quantitative portfolio research
Prerequisites: IEOR E4700 Additional prerequisites announced depending on offering.
Prerequisites: IEOR E4700; Additional Prerequisites will be announced depending on offering The course examines how large language models are transforming investment management practice. It opens with a grounding in core AI techniques (prompting strategies, Retrieval-Augmented Generation, and agentic frameworks) before mapping these onto institutional investment and wealth management workflows. The bulk of the course explores specific applications: extracting and monitoring risk factors from equity data and unstructured text using AI, building real-time news monitoring systems that score sentiment and flag portfolio-relevant events, and using LLMs to generate stress-test scenarios. Later sessions cover multi-agent systems for automated research and trading, including agent roles, guardrails, and human oversight, and how these techniques can enhance classical portfolio construction methods (risk parity, mean-variance optimization, Black-Litterman). The course includes guest lectures by industry practitioners discussing the industry's AI adoption trends
Prerequisites: IEOR E4700; Additional prerequisites will be announced depending on offering In this course, we will cover the basics of mathematical modeling of interest rates and credit derivatives. In the first part, we will cover basic interest rate derivatives, the Heath-Jarrow-Morton (HJM) framework, classic short rate models (for both interest rates and default intensities), and the numerical techniques used in practice for their calibration. In the second part, we will cover the basics of single-name derivatives modeling, and we will discuss pricing simple credit derivatives. We will also discuss correlation products and the most common techniques used for their pricing. In the third part, we will discuss some recent research papers addressing the use of adjoint algorithmic differentiation for the calculation of risk for interest rate and credit derivatives
Prerequisites: (IEOR E4700) Additional Prerequisites will be announced depending on offering
Prerequisites: IEOR E4700; Additional prerequisites will be announced depending on offering The search for better performance has led investors to explore Alternative Investments that are outside the traditional categories of exchange traded equities, Treasury Bonds, and other investment-grade fixed income products. The field of Alternative Investments covers a wide range of products such as convertible bonds, Preferred Shares, Hedge Funds, Venture Capital, and Cryptocurrencies. There is a growing need in the market for students with knowledge of these products and the practical and theoretical know how of valuing and risk managing these investments given that each product has it own nuances and anomalies. This course presents and studies some major Alternative Investment products and ways to evaluate and risk manage them
Prerequisites: IEOR E4700 Additional prerequisites will be announced depending on offering.
Prerequisites: (IEOR E4701) and (IEOR E4707) IEOR E4701 AND IEOR E4707 Introduction to quantitative modeling of credit risk, with a focus on the pricing of credit derivatives. Focus on the pricing of single-name credit derivatives (credit default swaps) and collateralized debt obligations (CDOs). Detail topics include default and credit risk, multiname default barrier models and multiname reduced form models
Prerequisites: (IEOR E4700) IEOR E4700 MS IEOR students only. Application of various computational methods/techniques in quantitative/computational finance. Transform techniques: fast Fourier transform for data de-noising and pricing, finite difference methods for partial differential equations (PDE), partial integro-differential equations (PIDE), Monte-Carlo simulation techniques in finance, and calibration techniques, filtering and parameter estimation techniques. Computational platform will be C /Java/Python/Matlab/R
Prerequisites: IEOR E4700
Prerequisites: (IEOR E4700) IEOR E4700 Foreign exchange market and its related derivative instruments—the latter being forward contracts, futures, options, and exotic options. What is unusual about foreign exchange is that although it can rightfully claim to be the largest of all financial markets, it remains an area where very few have any meaningful experience. Virtually everyone has traded stocks, bonds, and mutual funds. Comparatively few individuals have ever traded foreign exchange. In part that is because foreign exchange is an interbank market. Ironically the foreign exchange markets may be the best place to trade derivatives and to invent new derivatives—given the massive two-way flow of trading that goes through bank dealing rooms virtually 24 hours a day. And most of that is transacted at razor-thin margins, at least comparatively speaking, a fact that makes the foreign exchange market an ideal platform for derivatives. The emphasis is on familiarizing the student with the nature of the foreign exchange market and those factors that make it special among financial markets, enabling the student to gain a deeper understanding of the related market for derivatives on foreign exchange
Prerequisites: Recommended: IEOR E4700 Conceptual and practical understanding of structured and hybrid products from the standpoint of relevant risk factors, design goals and characteristics, pricing, hedging, and risk management. Detailed analysis of the underlying cash-flows, embedded derivative instruments, and various structural features of these transactions, both from the investor and issuer perspectives, and analysis of the impact of the prevailing market conditions and parameters on their pricing and risk characteristics. Numerical methods for valuing and managing risk of structured/hybrid products and their embedded derivatives and their application to equity, interest rates, commodities and currencies, inflation, and credit-related products. Conceptual and mathematical principles underlying these techniques, and practical issues that arise in their implementations in Python and other programming environments. Special contractual provisions encountered in structured and hybrid transactions, and incorporation of yield curves, volatility smile, and other features of the underlying processes into pricing and implementation framework for these products
Prerequisites: Proficiency in Python & Tensor, good understanding of calculus, knowledge of linear/matrix algebra, and basic knowledge of statistics
Covers C programming language, applications, and features for financial engineering, and quantitative finance applications. Note: restricted to IEOR MS FE students only
Selected topics of interest in area of quantitative finance. Some topics include energy derivatives, experimental finance, foreign exchange and related derivative instruments, inflation derivatives, hedge fund management, modeling equity derivatives in Java, mortgage-backed securities, numerical solutions of partial differential equations, quantitative portfolio management, risk management, trade and technology in financial markets. Note: open to IEOR students only
Prerequisites: see notes re: points probability and statistics, instruments of the financial markets, and asset pricing models. Introduces risk management principles, practical implementation and applications, standard market, liquidity, and credit risk measurement techniques, and their drawbacks and limitations. Note: restricted to IEOR students only
Prerequisites: Permission of the instructor
Prerequisites: First year MSFE Students Degree requirement for all MSFE first-year students. Topics in Financial Engineering. Past seminar topics include Evolving Financial Intermediation, Measuring and Using Trading Algorithms Effectively, Path-Dependent Volatility, Artificial Intelligence and Data Science in modern financial decision making, Risk-Based Performance Attribution, and Financial Machine Learning. Meets select Monday evenings
Primer on quantitative and mathematical concepts. Required of all incoming MSFE students
Prerequisites: approval by a faculty member who agrees to supervise the work. Prerequisite(s): Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design
A required course for undergraduate students majoring in OR:EMS. Focus on the management and consequences of technology-based innovation. Explores how new industries are created, how existing industries can be transformed by new technologies, the linkages between technological development and the creation of wealth and the management challenges of pursuing strategic innovation
Prerequisites: Obtained internship and approval from faculty adviser. Only for IEOR graduate students who need relevant work experience as part of their program of study. Final reports required. May not be taken for pass/fail credit or audited
Prerequisites: Linear algebra
Prerequisites: Linear algebra An introduction to combinatorial optimization, network flows and discrete algorithms. Shortest path problems, maximum flow problems. Matching problems, bipartite and cardinality nonbipartite. Introduction to discrete algorithms and complexity theory: NP-completeness and approximation algorithms
Discusses recent advances in fields of machine learning: kernel methods, neural networks (various generative adversarial net architectures), and reinforcement learning (with applications in robotics). Quasi Monte Carlo methods in the context of approximating RBF kernels via orthogonal transforms (instances of the structured technique). Will discuss techniques such as TD(0), TD(λ), LSTDQ, LSPI, DQN
Prerequisites: (STAT GU4001) or STAT W4001; STAT GU4001 or equivalent. Advanced treatment of stochastic modeling in the context of queueing, reliability, manufacturing, insurance risk, financial engineering and other engineering applications. Review of elements of probability theory; exponential distribution; renewal theory; Wald’s equation; Poisson processes. Introduction to both discrete and continuous-time Markov chains; introduction to Brownian motion
Prerequisites: (IEOR E6711) or equivalent.
Prerequisites: Faculty adviser’s permission. Selected topics in IEOR. Content varies from year to year. May be repeated for credit
Before registering, the student must submit an outline of the proposed work for approval by the supervisor and the chair of the Department. Advanced study in a specialized field under the supervision of a member of the department staff. May be repeated for credit
Source: Teachers College at Columbia University's catalog, linked per course · table learning_unit · CourseShelf publish 61
