Analyzes the current debate over the rise of monopolies, the strategic behavior and performance of firms in imperfectly competitive markets, and the role of competition policy. Topics include monopoly power; pricing, product choice, and innovation decisions by firms in oligopoly markets; static and dynamic measurement of market performance; and incentives in organizations. Requires regular participation in class discussion and teamwork in a competitive strategy game. Students taking graduate version complete additional assignments.

Uses theoretical economic models and empirical evidence to help understand the past and likely future impacts that digitization has had on legacy markets and institutions. These models help frame class discussions on e-commerce, search, online advertising, traditional and social media, privacy, platform design, and distance learning, among other topics. Students complete a project, and those taking the graduate version have additional assignments.

Provides an applied treatment of modern causal inference with high-dimensional data, focusing on empirical economic problems encountered in academic research and the tech industry. Formulates problems in the languages of structural equation modeling and potential outcomes. Presents state-of-the-art approaches for inference on causal and structural parameters, including de-biased machine learning, synthetic control methods, and reinforcement learning. Introduces tools from machine learning and deep learning developed for prediction purposes, and discusses how to adapt them to learn causal parameters. Emphasizes the applied and practical perspectives. Requires knowledge of mathematical statistics and regression analysis and programming experience in R or Python.

Introduces key concepts and recent advances in environmental economics, and explores their application to environmental policy questions. Topics include market efficiency and market failure, methods for valuing the benefits of environmental quality, the proper role of government in the regulation of the environment, environmental policy design, and implementation challenges. Considers international aspects of environmental policy as well, including the economics of climate change, trade and the environment, and environmental challenges in developing countries. Students taking graduate version complete additional assignments.

Analyzes business and public policy issues in energy markets and in the environmental markets to which they are closely tied. Examines the economic determinants of industry structure and evolution of competition among firms in these industries. Investigates successful and unsuccessful strategies for entering new markets and competing in existing markets. Industries studied include oil, natural gas, coal, electricity, and transportation. Topics include climate change and environmental policy, the role of speculation in energy markets, the political economy of energy policies, and market power and antitrust. Two team-based simulation games, representing the world oil market and a deregulated electricity market, act to cement the concepts covered in lecture. Students taking graduate version complete additional assignments. Limited to 60.

Provides an introduction to the labor market, how it functions, and the important role it plays in people's lives. Topics include supply and demand, minimum wages, labor market effects of social insurance and welfare programs, the collective bargaining relationship, discrimination, human capital, and unemployment. Completion of or concurrent enrollment in 14.03 or 14.04,  and 14.32 recommended. Students taking graduate version complete additional assignments.

Explores the relationship between political institutions and economic development, covering key theoretical issues as well as recent empirical evidence. Topics include colonialism and its legacy, voting, vote buying, media, social media, corruption, and war. Discusses not just what we know on these topics, but how we know it, covering how to craft a good empirical study or field experiment and how to discriminate between reliable and unreliable statistical evidence. Some basic familiarity with probability and/or statistics is useful for this class. Students taking graduate version complete additional assignments.

Examines how industrial development and international trade have brought about rapid growth and large-scale reductions in poverty for some developing countries, while globalization has simply increased inequality and brought little growth for others. Also considers why, in yet other developing countries, firms remain small-scale and have not integrated with global supply chains. Draws on both theoretical models and empirical evidence to better understand the reasons for these very different experiences and implications for policy. Students taking graduate version complete additional assignments.

Analyzes business and public policy issues in energy markets and in the environmental markets to which they are closely tied. Examines the economic determinants of industry structure and evolution of competition among firms in these industries. Investigates successful and unsuccessful strategies for entering new markets and competing in existing markets. Industries studied include oil, natural gas, coal, electricity, and transportation. Topics include climate change and environmental policy, the role of speculation in energy markets, the political economy of energy policies, and market power and antitrust. Two team-based simulation games, representing the world oil market and a deregulated electricity market, act to cement the concepts covered in lecture. Students taking graduate version complete additional assignments. Limited to 60.

An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.

Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment. Topics include learning of distributions, hypothesis testing (including multiple comparison procedures), linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Students taking graduate version complete additional assignments. Recommended prerequisite: 18.06.

Hands-on analysis of data demonstrates the interplay between statistics and computation. Includes four modules, each centered on a specific data set, and introduced by a domain expert. Provides instruction in specific, relevant analysis methods and corresponding algorithmic aspects. Potential modules may include medical data, gene regulation, social networks, finance data (time series), traffic, transportation, weather forecasting, policy, or industrial web applications. Projects address a large-scale data analysis question. Students taking graduate version complete additional assignments. Limited enrollment; priority to Statistics and Data Science minors and to juniors and seniors.

Introduces principles and core techniques for programming multicore machines. Topics include locking, scalability, concurrent data structures, multiprocessor scheduling, load balancing, and state-of-the-art synchronization techniques, such as transactional memory. Includes sequence of programming assignments on a large multicore machine, culminating with the design of a highly concurrent application. Students taking graduate version complete additional assignments.

More advanced and powerful data structures for answering several queries on the same data. Such structures are crucial in particular for designing efficient algorithms. Dictionaries; hashing; search trees. Self-adjusting data structures; linear search; splay trees; dynamic optimality. Integer data structures; word RAM. Predecessor problem; van Emde Boas priority queues; y-fast trees; fusion trees. Lower bounds; cell-probe model; round elimination. Dynamic graphs; link-cut trees; dynamic connectivity. Strings; text indexing; suffix arrays; suffix trees. Static data structures; compact arrays; rank and select. Succinct data structures; tree encodings; implicit data structures. External-memory and cache-oblivious data structures; B-trees; buffer trees; tree layout; ordered-file maintenance. Temporal data structures; persistence; retroactivity.

Covers discrete geometry and algorithms underlying the reconfiguration of foldable structures, with applications to robotics, manufacturing, and biology. Linkages made from one-dimensional rods connected by hinges: constructing polynomial curves, characterizing rigidity, characterizing unfoldable versus locked, protein folding. Folding two-dimensional paper (origami): characterizing flat foldability, algorithmic origami design, one-cut magic trick. Unfolding and folding three-dimensional polyhedra: edge unfolding, vertex unfolding, gluings, Alexandrov's Theorem, hinged dissections.

Presents research topics at the interface of computer science and game theory, with an emphasis on algorithms and computational complexity. Explores the types of game-theoretic tools that are applicable to computer systems, the loss in system performance due to the conflicts of interest of users and administrators, and the design of systems whose performance is robust with respect to conflicts of interest inside the system. Algorithmic focus is on algorithms for equilibria, the complexity of equilibria and fixed points, algorithmic tools in mechanism design, learning in games, and the price of anarchy.

Introduces the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Static models of random graphs, preferential attachment, and other graph evolution models. Epidemic propagation, opinion dynamics, social learning, and inference in networks. Applications drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks.

Introduction to scientific machine learning with an emphasis on developing scalable differentiable programs. Covers scientific computing topics (numerical differential equations, dense and sparse linear algebra, Fourier transformations, parallelization of large-scale scientific simulation) simultaneously with modern data science (machine learning, deep neural networks, automatic differentiation), focusing on the emerging techniques at the connection between these areas, such as neural differential equations and physics-informed deep learning. Provides direct experience with the modern realities of optimizing code performance for supercomputers, GPUs, and multicores in a high-level language.

Review of probability and laws of large numbers; Poisson counting process and renewal processes; Markov chains (including Markov decision theory), branching processes, birth-death processes, and semi-Markov processes; continuous-time Markov chains and reversibility; random walks, martingales, and large deviations; applications from queueing, communication, control, and operations research.

Provides an introduction to tools used for probabilistic reasoning in the context of discrete systems and processes. Tools such as the probabilistic method, first and second moment method, martingales, concentration and correlation inequalities, theory of random graphs, weak convergence, random walks and Brownian motion, branching processes, Markov chains, Markov random fields, correlation decay method, isoperimetry, coupling, influences and other basic tools of modern research in probability will be presented. Algorithmic aspects and connections to statistics and machine learning will be emphasized.

Introduction to principles of Bayesian and non-Bayesian statistical inference and its information theoretic foundations. Hypothesis testing and parameter estimation, sufficient statistics, exponential families. Loss functions, information measures, model capacity, and information geometry. Variational inference and EM algorithm; MCMC and other Monte Carlo methods. Asymptotic analysis and large deviations theory; universal inference and learning. Selected topics such as representation learning, score-matching, diffusion, and nonparametric statistics.

Introduces students to machine learning in healthcare, including the nature of clinical data and the use of machine learning for risk stratification, disease progression modeling, precision medicine, diagnosis, subtype discovery, and improving clinical workflows. Topics include causality, interpretability, algorithmic fairness, time-series analysis, graphical models, deep learning and transfer learning. Guest lectures by clinicians from the Boston area, and projects with real clinical data, emphasize subtleties of working with clinical data and translating machine learning into clinical practice.

Dynamic programming as a unifying framework for sequential decision-making under uncertainty, Markov decision problems, and stochastic control. Perfect and imperfect state information models. Finite horizon and infinite horizon problems, including discounted and average cost formulations. Value and policy iteration. Suboptimal methods. Approximate dynamic programming for large-scale problems, and reinforcement learning. Applications and examples drawn from diverse domains. While an analysis prerequisite is not required, mathematical maturity is necessary.

Advanced topics in computer vision focusing on geometry in computer vision, including image formation, representation theory for vision, classic multi-view geometry, multi-view geometry in the age of deep learning, differentiable rendering, neural scene representations, correspondence estimation, optical flow computation, and point tracking. Topics include generative modeling and representation learning including image and video generation, guidance in diffusion models, conditional probabilistic models, as well as representation learning in the form of contrastive and masking-based methods. Explores the intersection of robotics and computer vision with "vision for embodied agents," investigating the role of vision for decision-making, planning and control.

Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems.

Introduces the theoretical and empirical literature of behavioral economics. Examines important and systematic departures from the standard models in economics by incorporating insights from psychology and other social sciences. Covers theory and evidence on time, risk, and social preferences; beliefs and learning; emotions; limited attention; and frames, defaults, and nudges. Studies applications to many different areas, such as credit card debt, procrastination, retirement savings, addiction, portfolio choice, poverty, labor supply, happiness, and government policy. Students participate in surveys and experiments in class, review evidence from lab experiments, examine how the results can be integrated into models, and test models using field and lab data. Students taking graduate version complete additional assignments.

Covers modern applications of game theory where incomplete information plays an important role. Applications include bargaining, auctions, global games, market design, information design, and network economics. Students taking graduate version complete additional assignments.

Provides a rigorous, but not overly technical introduction to the economic theory of organization together with a varying set of applications. Addresses incentives, control, relationships, decision processes, and organizational culture and performance. Introduces selected fundamentals of game theory. Students taking graduate version complete additional assignments.

Provides a rigorous, but not overly technical introduction to the economic theory of organization together with a varying set of applications. Addresses incentives, control, relationships, decision processes, and organizational culture and performance. Introduces selected fundamentals of game theory. Students taking graduate version complete additional assignments.

Introduces the theoretical and empirical literature of behavioral economics. Examines important and systematic departures from the standard models in economics by incorporating insights from psychology and other social sciences. Covers theory and evidence on time, risk, and social preferences; beliefs and learning; emotions; limited attention; and frames, defaults, and nudges. Studies applications to many different areas, such as credit card debt, procrastination, retirement savings, addiction, portfolio choice, poverty, labor supply, happiness, and government policy. Students participate in surveys and experiments in class, review evidence from lab experiments, examine how the results can be integrated into models, and test models using field and lab data.  Students taking graduate version complete additional assignments.

Examines "psychology appreciation" for economics students. Aims to enhance knowledge and intuition about psychological processes in areas relevant to economics. Increases understanding of psychology as an experimental discipline, with its own distinct rules and style of argument. Topics include self-knowledge, cognitive dissonance, self-deception, emotions, social norms, self-control, learning, mental accounting, memory, individual and group behavior, and some personality and psycho-analytic models. Within each of these topics, we showcase effective and central experiments and discuss their role in the development of psychological theory. Term paper required.

Covers modern applications of game theory where incomplete information plays an important role. Applications include bargaining, auctions, global games, market design, information design, and network economics. Students taking graduate version complete additional assignments.

Analyzes the current debate over the rise of monopolies, the strategic behavior and performance of firms in imperfectly competitive markets, and the role of competition policy. Topics include monopoly power; pricing, product choice, and innovation decisions by firms in oligopoly markets; static and dynamic measurement of market performance; and incentives in organizations. Requires regular participation in class discussion and teamwork in a competitive strategy game. Students taking graduate version complete additional assignments.

Uses theoretical economic models and empirical evidence to help understand the past and likely future impacts that digitization has had on legacy markets and institutions. These models help frame class discussions on e-commerce, search, online advertising, traditional and social media, privacy, platform design, and distance learning, among other topics. Students  complete a project, and those taking the graduate version have additional assignments.

Provides an applied treatment of modern causal inference with high-dimensional data, focusing on empirical economic problems encountered in academic research and the tech industry. Formulates problems in the languages of structural equation modeling and potential outcomes. Presents state-of-the-art approaches for inference on causal and structural parameters, including de-biased machine learning, synthetic control methods, and reinforcement learning. Introduces tools from machine learning and deep learning developed for prediction purposes, and discusses how to adapt them to learn causal parameters. Emphasizes the applied and practical perspectives. Requires knowledge of mathematical statistics and regression analysis and programming experience in R or Python.

Introduces students to key concepts and recent advances in environmental economics, and explores their application to environmental policy questions. Topics include market efficiency and market failure, methods for valuing the benefits of environmental quality, the proper role of government in the regulation of the environment, environmental policy design and implementation challenges. Also considers international aspects of environmental policy including the economics of climate change, trade and the environment and environmental challenges in developing countries. Students taking graduate version complete additional assignments.

Analyzes business and public policy issues in energy markets and in the environmental markets to which they are closely tied. Examines the economic determinants of industry structure and evolution of competition among firms in these industries. Investigates successful and unsuccessful strategies for entering new markets and competing in existing markets. Industries studied include oil, natural gas, coal, electricity, and transportation. Topics include climate change and environmental policy, the role of speculation in energy markets, the political economy of energy policies, and market power and antitrust. Two team-based simulation games, representing the world oil market and a deregulated electricity market, act to cement the concepts covered in lecture. Students taking graduate version complete additional assignments. Limited to 60.

Provides an introduction to the labor market, how it functions, and the important role it plays in people's lives. Topics include supply and demand, minimum wages, labor market effects of social insurance and welfare programs, the collective bargaining relationship, discrimination, human capital, and unemployment. Completion of or concurrent enrollment in 14.03 or 14.04, and 14.32 recommended. Students taking graduate version complete additional assignments.

Explores the relationship between political institutions and economic development, covering key theoretical issues as well as recent empirical evidence. Topics include colonialism and its legacy, voting, vote buying, media, social media, corruption, and war. Discusses not just what we know on these topics, but how we know it, covering how to craft a good empirical study or field experiment and how to discriminate between reliable and unreliable statistical evidence. Some basic familiarity with probability and/or statistics is useful for this class. Students taking graduate version complete additional assignments.

Examines how industrial development and international trade have brought about rapid growth and large-scale reductions in poverty for some developing countries, while globalization has simply increased inequality and brought little growth for others. Also considers why, in yet other developing countries, firms remain small-scale and have not integrated with global supply chains. Draws on both theoretical models and empirical evidence to better understand the reasons for these very different experiences and implications for policy. Students taking graduate version complete additional assignments.

Analyzes business and public policy issues in energy markets and in the environmental markets to which they are closely tied. Examines the economic determinants of industry structure and evolution of competition among firms in these industries. Investigates successful and unsuccessful strategies for entering new markets and competing in existing markets. Industries studied include oil, natural gas, coal, electricity, and transportation. Topics include climate change and environmental policy, the role of speculation in energy markets, the political economy of energy policies, and market power and antitrust. Two team-based simulation games, representing the world oil market and a deregulated electricity market, act to cement the concepts covered in lecture. Students taking graduate version complete additional assignments. Limited to 60.

Examines "psychology appreciation" for economics students. Aims to enhance knowledge and intuition about psychological processes in areas relevant to economics. Increases understanding of psychology as an experimental discipline, with its own distinct rules and style of argument. Topics include self-knowledge, cognitive dissonance, self-deception, emotions, social norms, self-control, learning, mental accounting, memory, individual and group behavior, and some personality and psycho-analytic models. Within each of these topics, we showcase effective and central experiments and discuss their role in the development of psychological theory. Term paper required.