Common Ground Subjects

Teaches students from a range of majors to translate a problem into a machine learning (ML) formulation and find appropriate tools for solving it. Students enroll in two 6-unit modules — starting with the common “hub” module (6.C01 or 6.C51), which covers ML fundamentals, and followed by a discipline-specific “spoke” module that builds on the core material.

Examines applications of artificial intelligence and machine learning to climate change mitigation, adaptation, and monitoring. Introduces the physical science of climate change, data-driven modeling and observation, and approaches for decision-making in domains such as climate modeling, biodiversity, and energy systems.

Includes common (‘merged’) lectures on climate fundamentals followed by domain-specific sections (‘forks’) focusing on advanced methods such as physics-informed learning, data assimilation, and uncertainty quantification. Within each ‘fork’, students present, critique, and lead discussions of current research papers and develop a written research proposal applying machine learning methods to the track’s focus area. ‘Merged’ sessions later in the term synthesize lessons and foster exchange across domains. Both graduate and undergraduate students are encouraged to register.

Provides a comprehensive introduction to computational tools and systems approaches for addressing sustainability challenges in ecosystems, climate, transportation urban systems, and energy systems (including decarbonization). Using dynamical systems models, optimization techniques, and data-driven approaches, students explore how to analyze and design sustainable systems, balance physical, environmental, and economic considerations, and make decisions under uncertainty. Computational projects focus on real-world case studies. Students taking graduate version complete additional assignments.

Introduction to Earth observation satellites and modern computational tools for environmental monitoring. Covers a range of sensing modalities and resolutions, including multispectral, hyperspectral, thermal, radar, and lidar measurements from sub-meter to kilometer scales. Overview of remote sensing applications to the land (vegetation, soil, flooding, human development) and atmosphere (air pollution, greenhouse gases, weather). Analysis techniques include spectral image interpretation, time series analysis, inverse methods, and machine learning. Assignments require students to use cloud computing tools including Google Earth Engine.

Artificial Intelligence holds great promise to enhance digital productivity, physical interactions, overall well-being, and the human experience. To enable the true impact of AI, these systems will need to be grounded in many real-world data modalities, from language-only systems to holistically integrating vision, audio, sensors, medical data, music, art, smell, taste, and more. This course introduces the principles of multimodal AI that can process many modalities at once, such as connecting language and images, music and art, sensing and actuation, and more.

We will cover AI methods to:

1. Represent and fuse heterogeneous and interconnected data sources
2. Align data across different views
3. Reason over multiple steps with many modalities
4. Generate new multimodal content
5. Transfer knowledge from high-resource to low-resource data
6. Quantify the principles of multimodal AI for safe, ethical, and human-aligned deployment

Covers same fundamental concepts as 18.06 Linear Algebra with a view toward modeling, computation, and applications. Integrates geometric, algebraic, and computational viewpoints. Satisfies a General Institute Requirement (REST).

Unified introduction to linear algebra and optimization, their interconnections, and applications throughout science and engineering. Topics include: vectors, matrices, eigenvalues, singular values, least-squares, convex optimization, linear/quadratic programming, gradient descent, Newton’s method. Viewpoint will emphasize conceptual, geometric, and computational aspects. Applications from many domains, including networks, signal processing, and machine learning.

Provides an accessible overview of modern quantitative methods for causal inference: testing whether an action causes an outcome to occur. Makes heavy use of applied, real-data examples using Python or R and drawn from the participating domains (economics, political science, business, public policy, etc.). Covers topics including potential outcomes, causal graphs, randomized controlled trials, observational studies, instrumental variable estimation, and a contrast with machine learning techniques. Seeks to provide an intuitive understanding of the core concepts and techniques to help students produce and consume evidence of causal claims.

Satisfies requirements in the 6-3, 6-4, 15-1, 15-2, and 17 degree programs.

Provides an introduction to computational principles that underlie autonomous robots and vehicles. Topics include planning on state-space graphs, estimation of probabilistic belief state, formulating constraint programs, and reinforcement learning of optimal decision-making policies.

Introduction to the methods and applications of optimization. Topics include linear optimization, duality, non-linear optimization, integer optimization, and optimization under uncertainty. Instruction provided in modeling techniques to address problems arising in practice, mathematical theory to understand the structure of optimization problems, computational algorithms to solve complex optimization problems, and practical applications. Covers several examples and in-depth case studies based on real-world data to showcase impactful applications of optimization across management and engineering. Computational exercises based on the Julia-based programming language JuMP. Includes a term project. Basic competency in computational programming and linear algebra recommended. Students taking graduate version complete additional assignments. This subject was previously listed as 6.7201.

Follows the same pedagogy as 6.100B Introduction to Computational Thinking and Data Science, including Python, but is set in the context of computational science and engineering and uses applications from across science and engineering including dynamics, mechanics, robotics, heat transfer, climate science, chemistry, biology, aerospace and others.

This course provides an introduction to computational algorithms for understanding of scientific phenomena and designing of engineering systems. Topics include: computational algorithms to simulate time-dependent phenomena; optimize and control applications from science and engineering; and quantify uncertainty in problems involving randomness, including an introduction to probability and statistics.

Credit cannot also be received for 6.100B. Can be combined with 6.100A Introduction to Computer Science Programming in Python for REST credit.

Basic numerical methods, including curve fitting, root finding, numerical differential equations, and floating-point arithmetic. Emphasizes the complementary concerns of accuracy and computational cost. Foundational half-term subject to prepare for additional study of more specialized numerical methods.

Core Module: Interdisciplinary Numerical Methods

• Offered under: 16.C21, 18.C21
• Term: Spring (first half)
• Prerequisite: 18.03, 18.06
• Instructors: Steven G. Johnson (Mathematics), Youssef Marzouk (AeroAstro)

Specialized Modules

This class will cover an extensive range of topics that relate to sound and vibration analysis, focusing on computational tools needed to process such data, and exploring applications in various disciplines. Material covered will include basic signal processing, vibration and acoustical simulations and measurements, machine learning audio, microphone and speaker arrays, signal enhancement and restoration, and psychoacoustics. Applications will be drawn from fields including music, phonetics, mechanical and electrical engineering, architecture, medicine, and more. Students taking the graduate version will complete additional assignments.

Focuses on algorithms and techniques for writing and using modern technical software in a job, lab, or research group environment that may consist of interdisciplinary teams, where performance may be critical, and where the software needs to be flexible and adaptable. Topics include automatic differentiation, matrix calculus, scientific machine learning, parallel and GPU computing, and performance optimization with introductory applications to climate science, economics, agent-based modeling, and other areas. Labs and projects focus on performant, readable, composable algorithms and software. Programming will be in Julia. Expects students have some familiarity with Python, Matlab, or R. No Julia experience necessary.

Counts as an elective for CEE students, an advanced subject (18.100 and higher) for Math students, an advanced elective for EECS students, and a computation restricted elective for NSE students. AeroAstro students can petition department to count this class as a professional subject in the computing area.

Contemporary understanding of imaging is essentially computational: it involves encoding onto a form of radiation the information about a physical object, transferring the radiation through the imaging system, converting it to a digital signal, and finally computationally decoding the object information and presenting it to the user. This class introduces a unified formulation of computational imaging systems in the form of a three-round “learning spiral:” in the first two rounds of the spiral, the instructors describe the physical and algorithmic parts in two exemplary imaging systems; in the third round, students conduct themselves in the context of the class project on an imaging system of their choice.

The undergraduate and graduate versions share lectures but have different recitations. Includes optional “clinics” throughout the term to even out background knowledge of linear algebra, optimization, and computational imaging-related programming best practices for students of diverse disciplinary backgrounds.

Did you know that your mindset can add up to seven years to your life? Or that only five percent of leaders know the secret to motivating their teams? Or that time pressure decreases your creative problem solving by 45 percent? Thriving in life, work, and school isn’t a mystery — it’s within your grasp. Research shows that nearly half of your well-being is shaped by your daily choices.

In Hack Yourself, you’ll learn how to design those choices, building a toolkit of over 60 sustainable positive habits. You’ll apply a data science approach to how you live and lead — using tools from generative AI to vibe coding to statistical analysis to validate and personalize positive psychology practices, while also applying the same data methods across domains from leadership to innovation. Instruction and practice in oral and written communication provided. Students complete a group project in the last ¼ of the course.

This class proposes that the study of sound and movement practices can inform how we build and envision computational systems, focusing particularly on our relationship to AIs. This course explores computational and humanistic approaches to alignment; tuning AI systems while exploring our capacities for expression. We introduce students to a range of movement and music practices in improvisation and somatics, and include motion capture technologies, critical interaction design, generative modeling, and algorithms for interpretability and learning through human feedback. We explore metaphoric, material, and process based synchronicity across learning systems.

The world is awash with increasing amounts of data, and we must keep afloat with our relatively constant perceptual and cognitive abilities. Visualization provides one means of combating information overload, as a well-designed visual encoding can supplant cognitive calculations with simpler perceptual inferences and improve comprehension, memory, and decision-making. Moreover, visual representations may help engage more diverse audiences in the process of analytic thinking.

Teaches an end-to-end user-centric design process focusing on developing humane (usable, joyful, whimsical) frontend user experiences for generative AI, grounded in anthropology.

Topics include understanding human context (e.g., through observation, interviews, and user testing), qualitative data analysis, principles of effective and expressive visual and interaction design, frontend web application implementation, and user testing and ethical audits. Enrollment is limited.

Explores how to design machine learning and AI algorithms that enhance human decision-making and tackle real-world societal challenges. Combines statistical ML frameworks with behavioral economics, focusing on applications in areas such as education, finance, economic mobility, and policy. Emphasizes identifying high-impact problems and building effective, reliable solutions. Students taking the graduate version will complete additional assignments.

AI is radically transforming society, with big changes in the economy, education, health care, government, and criminal justice. How can we ensure that these changes are ethical and beneficial? This Common Ground course explores issues like AI alignment, fairness and bias in algorithmic decision-making, monoculture and homogeneity in AI systems, privacy and data protection, digital surveillance, and LLM ‘model specs’ and ‘constitutions’, among others. It will combine tools and methods from computer science and philosophy to rigorously analyze difficult ethical challenges involved in the development and deployment of AI and computing.

How can we design artificial systems to be rational agents, capable of learning about the world and pursuing goals in sensible ways? And what can AI research, where computational and memory limitations are front and center, tell us about human rationality?

This course presents theories of “ideal” rationality while observing the ways in which they demand things (e.g., instantaneous probability updating and logical omniscience) which are unattainable by humans and intractable for computational systems. Topics include Bayesian probability, the relation between belief and probability, expected utility theory, sequential decision-making under uncertainty, belief and goal inference, and multi-agent settings.

Explores moral, political, and computational foundations of AI alignment. Draws on political theory and computer science to consider how individual and collective values are elicited and embedded in AI.

Topics include bureaucracy-based versus AI-based decision rules; the concept of values; fairness and welfare objectives; pluralism and democratic input; and how well technical elicitation methods can capture considered judgments. Activities include seminar discussion, periodic problem sets, short response papers, and a course research project.

Scientists are increasingly turning to machine learning challenges, or competitions that require participants to build and evaluate machine learning models over a given period of time to solve a problem. The Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard organizes global machine learning challenges to leverage machine learning for solving key biomedical problems and to help prioritize what experiments biologists could run next – creating the next steps in disease diagnostics and treatment.

In this class, students will participate in the Schmidt Center’s machine learning challenge and apply their machine learning skills to help solve a key biomedical problem. Students will learn the basics of genomics and data analysis needed to succeed in the challenge. Top-scoring submissions will be validated in a lab at the Broad Institute, and winners will be eligible for monetary prize