In-depth treatment of the modern theory of integer programming and combinatorial optimization, emphasizing geometry, duality, and algorithms. Topics include formulating problems in integer variables, enhancement of formulations, ideal formulations, integer programming duality, linear and semidefinite relaxations, lattices and their applications, the geometry of integer programming, primal methods, cutting plane methods, connections with algebraic geometry, computational complexity, approximation algorithms, heuristic and enumerative algorithms, mixed integer programming and solutions of large-scale problems.

The course examines urban transportation policymaking and planning, its relationship to social and environmental justice and the influences of politics, governance structures and human and institutional behavior. Through the lens of history and current events the course explores the pathway that led to today’s legacy infrastructure, legacy policies (and legacy thinking), how attitudes are influenced, and how change happens. The course will examine the tensions and potential synergies among transportation policy values of individual mobility, access, system efficiency and “sustainability”. Traditional planning methods will be assessed with a critical eye, and through that process students will learn how to approach transportation planning in a way that responds to contemporary needs and values, with an emphasis on transport justice.
Planning and policymaking will be discussed in relation to recent pandemic effects, which bring
an unprecedented level of uncertainty and complexity to the policy context. Among other
topics to be explored: the roles of the federal, state, and local government; analysis of current trends and pattern breaks; transport sector decarbonization; land use, placemaking, and sustainable mobility networks; the role of “mobility as a service”, and the implications of disruptive technology on personal mobility.

Introduces the principal algorithms for linear, network, discrete, robust, nonlinear, and dynamic optimization. Emphasizes methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details.

Seminar dissects ten transportation studies from head to toe to illustrate how research ideas are initiated, framed, analyzed, evidenced, written, presented, criticized, revised, extended, and published, quoted and applied. Students design and execute their own transportation research.

Survey of the latest transportation research offered by 12 MIT faculty each presenting their ongoing research. Students are required to attend the classes, read the assigned articles, and write a brief reflection memo.

This summer’s extreme weather and the just-released IPCC report have brought renewed attention to the urgent need to drive global carbon dioxide emissions to zero by 2050. Transportation is the single largest source of those emissions in the United States, and a major source globally. What combination of policy, technology, behavior change, and investment is best positioned to accelerate the decarbonization of urban mobility? A new course from MIT Mobility Initiative and DUSP Prof. Jinhua Zhao and transportation & climate change professional Andrew Salzberg will grapple with this question, drawing from the latest research and industry trends.

This course is designed for students who aspire to shape the future of mobility. The course explores technological, behavioral, policy and systems-wide frameworks for innovation in transportation systems, complemented with case studies across the mobility spectrum, from autonomous vehicles to urban air mobility to last-mile sidewalk robots. Students will interact with a series of guest lecturers from CEOs and other business and government executives who are actively reshaping the future of mobility.

Explores deep learning (DL) methods for urban mobility applications. Covers concepts of algorithmic prediction, interpretability, causality, and fairness in the context of urban mobility system design and policy making. Topics include demand prediction at both individual and aggregate levels, decision making with and without uncertainty, vehicle and ride sharing, built environment and travel behavior, traffic prediction and control, maps and information provision, and multimodal system design. Students learn intuitions and methods in DNN, CNN, RNN and reinforcement learning, build hands-on models using real-world datasets, and design and implement group projects. At the intersection of machine learning methods and urban mobility applications, the course seeks to reconcile the tension between generic-purpose models and domain-specific knowledge. Furthermore, the course envisions and critically reflects on how machine learning methods shape transportation research and mobility industry, and examines the potentials and pitfalls of their applications in urban mobility business and policies.

Overview of the global airline industry, focusing on recent industry performance, current issues and challenges for the future. Fundamentals of airline industry structure, airline economics, operations planning, safety, labor relations, airports and air traffic control, marketing, and competitive strategies, with an emphasis on the interrelationships among major industry stakeholders. Recent research findings of the MIT Global Airline Industry Program are showcased, including the impacts of congestion and delays, evolution of information technologies, changing human resource management practices, and competitive effects of new entrant airlines. Taught by faculty participants of the Global Airline Industry Program.

Development Ventures is an exploratory Fall semester elective Action Lab on founding, financing, and building entrepreneurial ventures targeting developing countries, emerging markets, and underserved consumers everywhere.

Particular emphasis is placed on transformative innovations and exponentially scalable business models that can enable or accelerate major positive social change throughout the world.

More advanced version of 15.071 introduces core methods of business analytics, their algorithmic implementations and their applications to various domains of management and public policy. Spans descriptive analytics (e.g., clustering, dimensionality reduction), predictive analytics (e.g., linear/logistic regression, classification and regression trees, random forests, boosting deep learning) and prescriptive analytics (e.g., optimization). Presents analytics algorithms, and their implementations in data science. Includes case studies in e-commerce, transportation, energy, healthcare, social media, sports, the internet, and beyond. Uses the R and Julia programming languages. Includes team projects. Preference to Sloan Master of Business Analytics students.

Principles, techniques, and algorithms in machine learning from the point of view of statistical inference; representation, generalization, and model selection; and methods such as linear/additive models, active learning, boosting, support vector machines, non-parametric Bayesian methods, hidden Markov models, Bayesian networks, and convolutional and recurrent neural networks. Recommended prerequisite: 6.036 or other previous experience in machine learning.

Unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, sub-gradient and first-order methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions and Lagrange multipliers. Geometric approach to duality theory. Applications drawn from control, communications, machine learning, and resource allocation problems.

Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness.

Introduces modern robust optimization, including theory, applications, and computation. Presents formulations and their connection to probability, information and risk theory for conic optimization (linear, second-order, and semidefinite cones) and integer optimization. Application domains include analysis and optimization of stochastic networks, optimal mechanism design, network information theory, transportation, pattern classification, structural and engineering design, and financial engineering. Students formulate and solve a problem aligned with their interests in a final project.

Introduces regression and other tools for causal inference and descriptive analysis in empirical economics. Topics include analysis of randomized experiments, instrumental variables methods and regression discontinuity designs, differences-in-differences estimation, and regress with time series data. Develops the skills needed to conduct — and critique — empirical studies in economics and related fields. Empirical applications are drawn from published examples and frontier research. Familiarity with statistical programming languages is helpful. Students taking graduate version complete an empirical project leading to a short paper. Limited to 70 total for versions meeting together.

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.

This subject counts as a Control concentration subject. Reinforcement learning (RL) as a methodology for approximately solving sequential decision-making under uncertainty, with foundations in optimal control and machine learning. Finite horizon and infinite horizon dynamic programming, focusing on discounted Markov decision processes. Value and policy iteration. Monte Carlo, temporal differences, Q-learning, and stochastic approximation. Approximate dynamic programming, including value-based methods and policy space methods. Special topics at the boundary of theory and practice in RL. Applications and examples drawn from diverse domains. While an analysis prerequisite is not required, mathematical maturity is necessary. Enrollment limited

Practical-oriented subject that builds upon theory and methods and culminates in extended application. Covers methods to identify, value, and implement flexibility in design (real options). Topics include definition of uncertainties, simulation of performance for scenarios, screening models to identify desirable flexibility, decision analysis, and multidimensional economic evaluation. Students demonstrate proficiency through an extended application to a system design of their choice. Complements research or thesis projects. Meets with IDS.333 first half of term. Enrollment limited.

Introduces principles, algorithms, and applications of machine learning from the point of view of modeling and prediction; formulation of learning problems; representation, over-fitting, generalization; classification, regression, reinforcement learning; and methods such as linear classifiers, feed-forward, convolutional, and recurrent networks. Students taking graduate version complete different assignments. Meets with 6.036 when offered concurrently. Recommended prerequisites: 18.06 and 6.006. Enrollment limited; no listeners.

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.

Extends the computing and geographic information systems (GIS) skills developed in 11.520 to include spatial data management in client/server environments and advanced GIS techniques. First half covers the content of 11.523, introducing database management concepts, SQL (Structured Query Language), and enterprise-class database management software. Second half explores advanced features and the customization features of GIS software that perform analyses for decision support that go beyond basic thematic mapping. Includes the half-term GIS project of 11.524 that studies a real-world planning issue.

Introduction to data mining, data science, and machine learning, methods that assist in recognizing patterns, developing models and predictive analytics, and making intelligent use of massive amounts of data collected via the internet, e-commerce, electronic banking, pointof-sale devices, bar-code readers, medical databases, and other sources. Topics include logistic regression, association rules, treestructured classification and regression, cluster analysis, discriminant analysis, and neural network methods. Presents examples of successful applications in credit ratings, fraud detection, marketing, customer relationship management, investments, and synthetic clinical trials. Introduces data-mining software focusing on R. Term project required. Meets with 15.062 when offered concurrently. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details.

Students will gain experience processing, visualizing, and analyzing urban mobility data, with special emphasis on models and performance metrics tailored to scheduled, fixed-route transit services. The evolution of urban public transportation modes and services, as well as interaction with emerging on-demand services, will be covered. Instructors and guest lecturers from industry will discuss both methods for data collection and analysis, as well as organizational, policy, and governance constraints on transit planning. In assignments, students will practice using spatial database, data visualization, network analysis, and other software to shape recommendations for transit that effectively meets the future needs of cities.

A vigorous use of probabilistic models to approximate real-life situations in Finance, Operations Management, Economics, and Operations Research. Emphasis on how to develop a suitable probabilistic model in a given setting and, merging probability with statistics, and on how to validate a proposed model against empirical evidence. Extensive treatment of Monte Carlo simulation for modeling random processes when analytic solutions are unattainable.

Focuses on the ways economics and politics influence the fate of energy technologies, business models, and policies around the world. Extends fundamental concepts in the social sciences to case studies and simulations that illustrate how corporate, government, and individual decisions shape energy and environmental outcomes. In a final project, students apply the concepts in order to assess the prospects for an energy innovation to scale and advance sustainability goals in a particular regional market. Recommended prerequisite: 14.01. Meets with 15.219 when offered concurrently. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Preference to juniors, seniors, and Energy Minors.

Theory and application of probabilistic techniques for autonomous mobile robotics. Topics include probabilistic state estimation and decision making for mobile robots; stochastic representations of the environment; dynamic models and sensor models for mobile robots; algorithms for mapping and localization; planning and control in the presence of uncertainty; cooperative operation of multiple mobile robots; mobile sensor networks; application to autonomous marine (underwater and floating), ground, and air vehicles.

Covers energy and environmental market organization and regulation. Explores economic challenges and solutions to transforming energy markets to be more efficient, accessible, affordable, and sustainable. Applies core economic concepts - consumer choice, firm profit maximization, and strategic behavior - to understand when energy and environmental markets work well and when they fail. They also conduct data-driven economic analysis on the trade-offs of real and proposed policy interventions. Topics include renewable generation sources for electricity, energy access in emerging markets, efficiency programs and fuel efficiency standards, transitioning transportation to alternative fuels, measuring damages and adaptation to climate change, and the effect of energy and environmental policy on innovation.

Reviews the contributions of energy systems to global greenhouse gas emissions, and the levers for reducing those emissions. Lectures and projects focus on evaluating energy systems against climate policy goals, using performance metrics such as cost, carbon intensity, and others. Student projects explore pathways for realizing emissions reduction scenarios. Projects address the climate change mitigation potential of energy technologies, technological and behavioral change trajectories, and technology and policy portfolios.

Introduces concepts of supply chain design and planning with a focus on supply chains for products destined to improve quality of life in developing countries. Topics include demand estimation, process analysis and improvement, facility location and capacity planning, inventory management, and supply chain coordination. Also covers issues specific to emerging markets, such as sustainable supply chains, choice of distribution channels, and how to account for the value-adding role of a supply chain. Students conduct D-Lab-based projects on supply chain design or improvement. Students taking graduate version will complete additional assignments.

Students design an autonomous vehicle system to satisfy stated performance goals. Emphasizes both hardware and software components of the design and implementation. Entails application of fundamental principles and design engineering in both individual and group efforts. Practice in written and oral communication provided. Students showcase the final design to the public at the end of the term.

Covers the mathematical foundations and state-of-the-art implementations of algorithms for vision-based navigation of autonomous vehicles (e.g., mobile robots, self-driving cars, drones). Topics include geometric control, 3D vision, visual-inertial navigation, place recognition, and simultaneous localization and mapping. Provides students with a rigorous but pragmatic overview of differential geometry and optimization on manifolds and knowledge of the fundamentals of 2-view and multi-view geometric vision for real-time motion estimation, calibration, localization, and mapping. The theoretical foundations are complemented with hands-on labs based on state-of-the-art mini race car and drone platforms. Culminates in a critical review of recent advances in the field and a team project aimed at advancing the state-of-the-art.

Explores specific challenges of urban last-mile B2C and B2B distribution in both industrialized and emerging economies. Develops an in-depth understanding of the perspectives, roles, and decisions of all relevant stakeholder groups, from consumers, to private sector decision makers, to public policy makers. Discussion of the most relevant traditional and the most promising innovating operating models for urban last-mile distribution. Introduces applications of the essential quantitative methods for the strategic design and tactical planning of urban last-mile distribution systems, including optimization and simulation. Covers basic facility location problems, network design problems, single- and multi-echelon vehicle routing problems, as well as associated approximation techniques.

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.

Provides an introduction to complex networks, their structure, and function, with examples from engineering, applied mathematics and social sciences. Topics include spectral graph theory, notions of centrality, random graph models, contagion phenomena, cascades and diffusion, and opinion dynamics.

Topics on the engineering and analysis of network protocols and architecture, including architectural principles for designing heterogeneous networks; transport protocols; Internet routing; router design; congestion control and network resource management; wireless networks; network security; naming; overlay and peer-to-peer networks. Readings from original research papers.

Presents concepts, principles, and algorithmic foundations for robots and autonomous vehicles operating in the physical world. Topics include sensing, kinematics and dynamics, state estimation, computer vision, perception, learning, control, motion planning, and embedded system development. Students design and implement advanced algorithms on complex robotic platforms capable of agile autonomous navigation and real-time interaction with the physical word. Students engage in extensive written and oral communication exercises.

Focuses on architectural and mobility interventions that respond to changing patterns of living, working, and transport. Emphasizes mass-customized housing, autonomous parking, charging infrastructure, and shared-use networks of lightweight electric vehicles (LEVs). Students work in small teams and are lead by researchers from the Changing Places group. Projects focus on the application of these ideas to case study cities and may include travel. Invited guests from academia and industry participate. Repeatable for credit with permission of instructor.

Design of an atmospheric flight vehicle to satisfy stated performance, stability, and control requirements. Emphasizes individual initiative, application of fundamental principles, and the compromises inherent in the engineering design process. Includes instruction and practice in written and oral communication, through team presentations and a written final report. Course 16 students are expected to complete two professional or concentration subjects from the departmental program before taking this capstone.

Presents a unified view of advanced quantitative analysis and optimization techniques applied to the air transportation sector. Considers the problem of operating and managing the aviation sector from the perspectives of the system operators (e.g., the FAA), the airlines, and the resultant impacts on the end-users (the passengers). Explores models and optimization approaches to system-level problems, airline schedule planning problems, and airline management challenges.