A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression and identification). Concepts are introduced with lectures and on-line problems, and then mastered during weekly labs. In lab, students model, design, test and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g. optimizing thrust-driven positioners or stabilizing magnetic levitators). Students in the graduate version complete additional problems and labs.

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.

Integrated overview of the biophysics of cells from prokaryotes to neurons, with a focus on mass transport and electrical signal generation across cell membrane. First third of course focuses on mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Second third focuses on electrical properties of cells: ion transport to action potential generation and propagation in electrically excitable cells. Synaptic transmission. Electrical properties interpreted via kinetic and molecular properties of single voltage-gated ion channels. Final third focuses on biophysics of synaptic transmission and introduction to neural computing. Laboratory and computer exercises illustrate the concepts. Students taking graduate version complete different assignments.

Develops and applies scaling laws and the methods of continuum mechanics to biomechanical phenomena over a range of length scales. Topics include structure of tissues and the molecular basis for macroscopic properties; chemical and electrical effects on mechanical behavior; cell mechanics, motility and adhesion; biomembranes; biomolecular mechanics and molecular motors. Experimental methods for probing structures at the tissue, cellular, and molecular levels. Students taking graduate version complete additional assignments.

Provides an intense project-based learning experience around the design of medical devices with foci ranging from mechanical to electro mechanical to electronics. Projects motivated by real-world clinical challenges provided by sponsors and clinicians who also help mentor teams. Covers the design process, project management, and fundamentals of mechanical and electrical circuit and sensor design. Students work in small teams to execute a substantial term project, with emphasis placed upon developing creative designs — via a deterministic design process — that are developed and optimized using analytical techniques. Includes mandatory lab. Instruction and practice in written and oral communication provided. Students taking graduate version complete additional assignments. Enrollment limited.

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.

Concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Covers means for decoupling goals from strategy, mechanisms for implementing additive data-directed invocation, work with partially-specified entities, and how to manage multiple viewpoints. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. 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.

Introduction to the design and analysis of algorithms for geometric problems, in low- and high-dimensional spaces. Algorithms: convex hulls, polygon triangulation, Delaunay triangulation, motion planning, pattern matching. Geometric data structures: point location, Voronoi diagrams, Binary Space Partitions. Geometric problems in higher dimensions: linear programming, closest pair problems. High-dimensional nearest neighbor search and low-distortion embeddings between metric spaces. Geometric algorithms for massive data sets: external memory and streaming algorithms. Geometric optimization.

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.

Explores topics around matrix multiplication (MM) and its use in the design of graph algorithms. Focuses on problems such as transitive closure, shortest paths, graph matching, and other classical graph problems. Explores fast approximation algorithms when MM techniques are too expensive.

Current research topics in computational complexity theory. Nondeterministic, alternating, probabilistic, and parallel computation models. Boolean circuits. Complexity classes and complete sets. The polynomial-time hierarchy. Interactive proof systems. Relativization. Definitions of randomness. Pseudo-randomness and derandomizations. Interactive proof systems and probabilistically checkable proofs.

The power and sources of randomness in computation. Connections and applications to computational complexity, computational learning theory, cryptography and combinatorics. Topics include: probabilistic proofs, uniform generation and approximate counting, Fourier analysis of Boolean functions, computational learning theory, expander graphs, pseudorandom generators, derandomization.

Covers advanced applications of cryptography, implementation of cryptographic primitives, and cryptanalysis. Topics may include: proof systems; zero knowledge; secret sharing; multiparty computation; fully homomorphic encryption; electronic voting; design of block ciphers and hash functions; elliptic-curve and lattice-based cryptosystems; and algorithms for collision-finding, discrete-log, and factoring. Assignments include a final group project. Topics may vary from year to year.

In-depth exploration of recent results in cryptography.

Design and implementation of secure computer systems. Lectures cover attacks that compromise security as well as techniques for achieving security, based on recent research papers. Topics include operating system security, privilege separation, capabilities, language-based security, cryptographic network protocols, trusted hardware, and security in web applications and mobile phones. Labs involve implementing and compromising a web application that sandboxes arbitrary code, and a group final project.

Topics related to the engineering and design of database systems, including data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel and heterogeneous databases; adaptive databases; trigger systems; pub-sub systems; semi structured data and XML querying. Lecture and readings from original research papers. Semester-long project and paper. Students taking graduate version complete different assignments. Enrollment may be limited.

Abstractions and implementation techniques for engineering distributed systems: remote procedure call, threads and locking, client/server, peer-to-peer, consistency, fault tolerance, and security. Readings from current literature. Individual laboratory assignments culminate in the construction of a fault-tolerant and scalable storage. Experience with programming and debugging is expected. Enrollment limited.

Introduction to the design and implementation of large-scale digital systems using hardware description languages and high-level synthesis tools in conjunction with standard commercial electronic design automation (EDA) tools. Emphasizes modular and robust designs, reusable modules, correctness by construction, architectural exploration, meeting area and timing constraints, and developing functional field-programmable gate array (FPGA) prototypes. Extensive use of CAD tools in weekly labs serve as preparation for a multi-person design project on multi-million gate FPGAs. Enrollment may be limited.

Introduction to parallel and multicore computer architecture and programming. Topics include the design and implementation of multicore processors; networking, video, continuum, particle and graph applications for multicores; communication and synchronization algorithms and mechanisms; locality in parallel computations; computational models, including shared memory, streams, message passing, and data parallel; multicore mechanisms for synchronization, cache coherence, and multithreading. Performance evaluation of multicores; compilation and runtime systems for parallel computing. Substantial project required.

Introduction to the design and implementation of hardware architectures for efficient processing of deep learning algorithms and tensor algebra in AI systems. Topics include basics of deep learning, optimization principles for programmable platforms, design principles of accelerator architectures, co-optimization of algorithms and hardware (including sparsity) and use of advanced technologies (including memristors and optical computing). Includes labs involving modeling and analysis of hardware architectures, architecting deep learning inference systems, and an open-ended design project. Students taking graduate version complete additional assignments.

Introduction to basic concepts, principles, and implementation issues in the designing of secure hardware systems. Through a mixture of lectures and paper discussions, covers state-of-the-art security attacks and defenses targeting the computer architecture, digital circuits, and physics layers of computer systems. Emphasizes both the conceptual and the practical aspects of security issues in modern hardware systems. Topics include microarchitectural timing side channels, speculative execution attacks, RowHammer, Trusted Execution Environment, physical attacks, hardware support for software security, and verification of digital systems. Students taking graduate version complete additional assignments.

A detailed exposition of the principles involved in designing and optimizing analog and mixed-signal circuits in CMOS technologies. Small-signal and large-signal models. Systemic methodology for device sizing and biasing. Basic circuit building blocks. Operational amplifier design. Principles of switched capacitor networks including switched-capacitor and continuous-time integrated filters. Basic and advanced A/D and D/A converters, delta-sigma modulators, RF and other signal processing circuits. Design projects on op amps and subsystems are a required part of the subject.

The application of electronics to energy conversion and control. Modeling, analysis, and control techniques. Design of power circuits including inverters, rectifiers, and dc-dc converters. Analysis and design of magnetic components and filters. Characteristics of power semiconductor devices. Numerous application examples, such as motion control systems, power supplies, and radio-frequency power amplifiers.

Introduces students to the field of silicon photonics with topics spanning silicon-photonics-based devices, circuits, systems, platforms, and applications. Covers the foundational concepts behind silicon photonics based in electromagnetics, optics, and device physics; the design of silicon-photonics-based devices (including waveguides, couplers, splitters, resonators, antennas, modulators, detectors, and lasers) using both theoretical analysis and numerical simulation tools; the engineering of silicon-photonics-based circuits and systems with a focus on a variety of applications areas (spanning computing, communications, sensing, quantum, and biology); the development of silicon-photonics-based platforms, including fabrication and materials considerations; and the characterization of these silicon-photonics-based devices and systems through hands-on laboratory activities. Students taking graduate version complete additional assignments.

Techniques of nonlinear optics with emphasis on fundamentals for research in optics, photonics, spectroscopy, and ultrafast science. Topics include: electro-optic modulators and devices, sum and difference frequency generation, and parametric conversion. Nonlinear propagation effects in optical fibers including self-phase modulation, pulse compression, solitons, communication, and femtosecond fiber lasers. Review of quantum mechanics, interaction of light with matter, laser gain and operation, density matrix techniques, perturbation theory, diagrammatic methods, nonlinear spectroscopies, ultrafast lasers and measurements. Discussion of research operations and funding and professional development topics. Introduces fundamental methods and techniques needed for independent research in advanced optics and photonics, but useful in many other engineering and physics disciplines.

Examines quantum computation and quantum information. Topics include quantum circuits, the quantum Fourier transform and search algorithms, the quantum operations formalism, quantum error correction, Calderbank-Shor-Steane and stabilizer codes, fault tolerant quantum computation, quantum data compression, quantum entanglement, capacity of quantum channels, and quantum cryptography and the proof of its security. Prior knowledge of quantum mechanics required.

Introduction to techniques and current state of the art in solid state quantum information processing devices, with a focus on superconducting quantum bits. Topics include the basics of applied superconductivity, Josephson junction, qubit design and simulation, interactions with microwave photons, qubit control and decoherence mitigation in the presence of noise, measurement, error detection/correction, and a survey of other solid-state qubit modalities. Exposes students to both fundamentals and the research state-of-art.

Classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Crystal lattices, electronic energy band structures, phonon dispersion relations, effective mass theorem, semiclassical equations of motion, electron scattering and semiconductor optical properties. Band structure and transport properties of selected semiconductors. Connection of quantum theory of solids with quasi-Fermi levels and Boltzmann transport used in device modeling.

Focuses on the physics of the interaction of photons with semiconductor materials. Uses the band theory of solids to calculate the absorption and gain of semiconductor media; and uses rate equation formalism to develop the concepts of laser threshold, population inversion, and modulation response. Presents theory and design for photodetectors, solar cells, modulators, amplifiers, and lasers. Introduces noise models for semiconductor devices, and applications of optoelectronic devices to fiber optic communications.

Describes current techniques used to analyze and fabricate nanometer-length-scale structures and devices. Emphasizes imaging and patterning of nanostructures, including fundamentals of optical, electron (scanning, transmission, and tunneling), and atomic-force microscopy; optical, electron, ion, and nanoimprint lithography, templated self-assembly, and resist technology. Surveys substrate characterization and preparation, facilities, and metrology requirements for nanolithography. Addresses nanodevice processing methods, such as liquid and plasma etching, lift-off, electroplating, and ion-implant. Discusses applications in nanoelectronics, nanomaterials, and nanophotonics.

Introduces models, theories, and algorithms key to digital image processing. Core topics covered include models of image formation, image processing fundamentals, filtering in the spatial and frequency domains, image transforms, and feature extraction. Additional topics include image enhancement, image restoration and reconstruction, compression of images and videos, visual recognition, and the application of machine learning-based approaches to image processing. Includes student-driven term project.

Adaptive and non-adaptive processing of signals received at arrays of sensors. Deterministic beamforming, space-time random processes, optimal and adaptive algorithms, and the sensitivity of algorithm performance to modeling errors and limited data. Methods of improving the robustness of algorithms to modeling errors and limited data are derived. Advanced topics include an introduction to matched field processing and physics-based methods of estimating signal statistics. Homework exercises providing the opportunity to implement and analyze the performance of algorithms in processing data supplied during the course.

Linear, discrete- and continuous-time, multi-input-output systems in control, related areas. Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6.3100.

Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; data-enabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments.

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.

Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexity-based ideas, complexity results, and efficient implementations. Examples from several engineering areas, in particular systems and control applications. Topics include semidefinite programming, resultants/discriminants, hyperbolic polynomials, Groebner bases, quantifier elimination, and sum of squares.

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.

Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging.

Introduces the fundamental and practical aspects of optical network technology, architecture, design and analysis tools and techniques. The treatment of optical networks are from the architecture and system design points of view. Optical hardware technologies are introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. Beyond the Physical Layer, the higher network layers (Media Access Control, Network and Transport Layers) are treated together as integral parts of network design. Performance metrics, analysis and optimization techniques are developed to help guide the creation of high performance complex optical networks.

Introduces the theory of error-correcting codes. Focuses on the essential results in the area, taught from first principles. Special focus on results of asymptotic or algorithmic significance. Principal topics include construction and existence results for error-correcting codes; limitations on the combinatorial performance of error-correcting codes; decoding algorithms; and applications to other areas of mathematics and computer science.

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.

Covers Bayesian modeling and inference at an advanced graduate level. Topics include de Finetti's theorem, decision theory, approximate inference (modern approaches and analysis of Monte Carlo, variational inference, etc.), hierarchical modeling, (continuous and discrete) nonparametric Bayesian approaches, sensitivity and robustness, and evaluation.

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.

Highlights algorithms and paradigms for creating human-robot systems that act intelligently and robustly, by reasoning from models of themselves, their counterparts and their world. Examples include space and undersea explorers, cooperative vehicles, manufacturing robot teams and everyday embedded devices. Themes include architectures for goal-directed systems; decision-theoretic programming and robust execution; state-space programming, activity and path planning; risk-bounded programming and risk-bounded planners; self-monitoring and self-diagnosing systems, and human-robot collaboration. Student teams explore recent advances in cognitive robots through delivery of advanced lectures and final projects, in support of a class-wide grand challenge. Enrollment may be limited.

Provides an in-depth view of the state-of-the-art learning methods for control and the know-how of applying these techniques. Topics span reinforcement learning, self-supervised learning, imitation learning, model-based learning, and advanced deep learning architectures, and specific machine learning challenges unique to building sensorimotor systems. Discusses how to identify if learning-based control can help solve a particular problem, how to formulate the problem in the learning framework, and what algorithm to use. Applications of algorithms in robotics, logistics, recommendation systems, playing games, and other control domains covered. Instruction involves two lectures a week, practical experience through exercises, discussion of current research directions, and a group project.

Covers nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on computational methods. Topics include the nonlinear dynamics of robotic manipulators, applied optimal and robust control and motion planning. Discussions include examples from biology and applications to legged locomotion, compliant manipulation, underwater robots, and flying machines.

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 computational aspects of computer-aided design and manufacturing. Explores relevant methods in the context of additive manufacturing (e.g., 3D printing). Topics include computer graphics (geometry modeling, solid modeling, procedural modeling), physically-based simulation (kinematics, finite element method), 3D scanning/geometry processing, and an overview of 3D fabrication methods. Exposes students to the latest research in computational fabrication. Students taking graduate version complete additional assignments.

Implementation and evaluation of intelligent multi-modal user interfaces, taught from a combination of hands-on exercises and papers from the original literature. Topics include basic technologies for handling speech, vision, pen-based interaction, and other modalities, as well as various techniques for combining modalities. Substantial readings and a term project, where students build a program that illustrates one or more of the themes of the course.

Interactive visualization provides a means of making sense of a world awash in data. Covers the techniques and algorithms for creating effective visualizations, using principles from graphic design, perceptual psychology, and cognitive science. Short assignments build familiarity with the data analysis and visualization design process, and a final project provides experience designing, implementing, and deploying an explanatory narrative visualization or visual analysis tool to address a concrete challenge.

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 rapidly developing field of spoken language processing including automatic speech recognition. Topics include acoustic theory of speech production, acoustic-phonetics, signal representation, acoustic and language modeling, search, hidden Markov modeling, neural networks models, end-to-end deep learning models, and other machine learning techniques applied to speech and language processing topics. Lecture material intersperses theory with practice. Includes problem sets, laboratory exercises, and open-ended term project.

Explores the relationship between the computer representation and acquisition of knowledge and the structure of human language, its acquisition, and hypotheses about its differentiating uniqueness. Emphasizes development of analytical skills necessary to judge the computational implications of grammatical formalisms and their role in connecting human intelligence to computational intelligence. Uses concrete examples to illustrate particular computational issues in this area.

Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments.

Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. Students taking graduate version complete additional assignments.

Applies analysis of signals and noise in linear systems, sampling, and Fourier properties to magnetic resonance (MR) imaging acquisition and reconstruction. Provides adequate foundation for MR physics to enable study of RF excitation design, efficient Fourier sampling, parallel encoding, reconstruction of non-uniformly sampled data, and the impact of hardware imperfections on reconstruction performance. Surveys active areas of MR research. Assignments include Matlab-based work with real data. Includes visit to a scan site for human MR studies.

Drawing on the latest research in psychology, evolutionary biology, neuroscience, and artificial intelligence, as well as in behavioral and mainstream financial economics, provides new perspectives and insights into the role that human behavior plays in the business environment and the dynamics of financial markets and institutions. Incorporates practical applications from several industries including finance, insurance, biotechnology, pharmaceuticals, and government policy. Students apply ideas from this perspective to formulate original hypotheses regarding new career opportunities and disruptive technologies in their industry of choice. Enrollment may be limited; preference to Sloan graduate students.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Building on core material in 6.C51, emphasizes the design and operation of sustainable systems. Students learn to leverage heterogeneous data from urban services, cities, and the environment, and apply machine learning methods to evaluate and/or improve sustainability solutions. Provides case studies from various domains, such as transportation and mobility, energy and water resources, environment monitoring, infrastructure sensing and control, climate adaptation, and disaster resilience. Projects focus on using machine learning to identify new insights or decisions to help engineer sustainability in societal-scale systems. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject 6.C51.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Building on core material in 6.C51, explores applications of machine learning techniques to solve problems in modern finance. Provides an introduction to financial models that balance risk and reward, along with machine learning tools to uncover and analyze financial regularities. Applications include valuation, credit analysis, proprietary trading and hedge-fund strategies, portfolio management, market structure, risk management and stress testing, natural language processing, and personal finance. Students cannot receive credit without completion of 6.C51.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Building on core material in 6.C51, encourages open-ended exploration of the increasingly topical intersection between artificial intelligence and the physical sciences. Uses energy and information, and their respective optimality conditions, to define supervised and unsupervised learning algorithms as well as ordinary and partial differential equations. Subsequently, physical systems with complex constitutive relationships are drawn from elasticity, biophysics, fluid mechanics, hydrodynamics, acoustics, and electromagnetics to illustrate how machine learning-inspired optimization can approximate solutions to forward and inverse problems in these domains. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject 6.C51.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Building on core material in 6.C51, provides an introduction to the use of machine learning to solve problems arising in the science and engineering of biology, chemistry, and materials. Equips students to design and implement machine learning approaches to challenges such as analysis of omics (genomics, transcriptomics, proteomics, etc.), microscopy, spectroscopy, or crystallography data and design of new molecules and materials such as drugs, catalysts, polymer, alloys, ceramics, and proteins. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject 6.C51.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Focuses on in-depth modeling of engineering tasks as machine learning problems. Emphasizes framing, method design, and interpretation of results. In comparison to broader co-requisite 6.C01/6.C51, this project oriented subject consists of deep dives into select technical areas or engineering tasks involving both supervised and exploratory uses of machine learning. Deep dives into technical areas such robustness, interpretability, fairness; engineering tasks such as recommender systems, performance optimization, automated design. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject 6.C51. Enrollment may be limited.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Introduces machine learning as a tool to understand natural biological systems, with an evolving emphasis on problems in molecular and cellular biology that are being actively advanced using machine learning. Students design, implement, and interpret machine learning approaches to aid in predicting protein structure, probing protein structure/function relationships, and imaging biological systems at scales ranging from the atomic to cellular. Students taking graduate version complete an additional project-based assignment. Students cannot receive credit without completion of the core subject 6.C51.

Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited.

Covers the design, ethical, and technical skills for creating effective visualizations. Short assignments build familiarity with the data analysis and visualization design process. Students participate in hour-long studio reading sessions. A final project provides experience working with real-world big data, provided by external partners, in order to expose and communicate insights about societal issues. Students taking graduate version complete additional assignments.

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.

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. Enrollment limited; priority to Statistics and Data Science minors, and to juniors and seniors.

Provides an introduction to computer vision, covering topics from early vision to mid- and high-level vision, including low-level image analysis, edge detection, image transformations for image synthesis, methods for 3D scene reconstruction, motion analysis and tracking. Additionally, presents basics of machine learning, convolutional neural networks, and transformers in the context of image and video data for object classification, detection, and segmentation.

Concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Covers means for decoupling goals from strategy, mechanisms for implementing additive data-directed invocation, work with partially-specified entities, and how to manage multiple viewpoints. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Students taking graduate version complete additional assignments.

Topics related to the engineering and design of database systems, including data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel and heterogeneous databases; adaptive databases; trigger systems; pub-sub systems; semi structured data and XML querying. Lecture and readings from original research papers. Semester-long project and paper. Students taking graduate version complete different assignments. Enrollment may be limited.

Introduction to the design and implementation of hardware architectures for efficient processing of deep learning algorithms and tensor algebra in AI systems. Topics include basics of deep learning, optimization principles for programmable platforms, design principles of accelerator architectures, co-optimization of algorithms and hardware (including sparsity) and use of advanced technologies (including memristors and optical computing). Includes labs involving modeling and analysis of hardware architectures, architecting deep learning inference systems, and an open-ended design project. Students taking graduate version complete additional assignments.

Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments.

Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. Students taking graduate version complete additional assignments.

Comprehensive survey of molecular, genetic, and cellular aspects of the immune system. Topics include innate and adaptive immunity; cells and organs of the immune system; hematopoiesis; immunoglobulin, T cell receptor, and major histocompatibility complex (MHC) proteins and genes; development and functions of B and T lymphocytes; immune responses to infections and tumors; hypersensitivity, autoimmunity, and immunodeficiencies. Particular attention to the development and function of the immune system as a whole, as studied by modern methods and techniques. Students taking graduate version explore the subject in greater depth, including study of recent primary literature.

Selected topics in biological oceanography.

Advanced problems in biological oceanography with assigned reading and consultation.

Lectures and discussions on physiological and biochemical processes in marine organisms. Topics vary from year to year.

Lectures and discussions on biological oceanography. Topics vary from year to year.

Lectures and discussions on the biology of marine zooplankton. Topics vary from year to year.

Lectures and discussions on the biology of marine benthos. Topics vary from year to year.

Lectures and discussion on the biology of marine phytoplankton. Topics vary from year to year.

Lectures and discussion on molecular biological oceanography. Topics vary from year to year.

Lectures and discussion on the behavioral biology of marine animals. Topics vary from year to year.

Lectures and discussion on the biology of marine prokaryotes. Topics vary from year to year.

Covers the basic models of population growth, demography, population interaction (competition, predation, mutualism), food webs, harvesting, and infectious disease, and the mathematical tools required for their analysis. Because these tools are also basic to the analysis of models in biochemistry, physiology, and behavior, subject also broadly relevant to students whose interests are not limited to ecological problems.

Directed research in biological oceanography not leading to graduate thesis and initiated prior to the qualifying exam.

Directed research in the fields of microbial science and engineering.

For qualified graduate students in the Microbiology graduate program interested in teaching. Classroom or laboratory teaching under the supervision of a faculty member.

Introduces students to faculty participating in the interdepartmental Microbiology graduate program through a series of three lab rotations, which provide broad exposure to microbiology research at MIT. Students select a lab for thesis research by the end of their first year. Given the interdisciplinary nature of the program and the many research programs available, students may be able to work jointly with more than one research advisor. Limited to students in the Microbiology graduate program.

Stresses skills in reading, discussing, and writing scientific papers, with a focus on new findings in the field of aging, including the consequences of immune decline on health, the clearance of senescent cells, and the possibility of immortality by applying epigenetic reprogramming to humans. Culminates in an oral presentation for undergraduate students and a mini-review by graduate students. Students taking graduate version complete additional assignments. 

Detailed analysis of the biochemical mechanisms that control the maintenance, expression, and evolution of prokaryotic and eukaryotic genomes. Topics covered in lecture and readings of relevant literature include: gene regulation, DNA replication, genetic recombination, and mRNA translation. Logic of experimental design and data analysis emphasized. Presentations include both lectures and group discussions of representative papers from the literature. Students taking the graduate version are expected to explore the subject in greater depth.

Eukaryotic genome structure, function, and expression, processing of RNA, and regulation of the cell cycle. Emphasis on the techniques and logic used to address important problems in nuclear cell biology. Lectures on broad topic areas in nuclear cell biology and discussions on representative recent papers.

Comprehensive survey of molecular, genetic, and cellular aspects of the immune system. Topics include innate and adaptive immunity; cells and organs of the immune system; hematopoiesis; immunoglobulin, T cell receptor, and major histocompatibility complex (MHC) proteins and genes; development and functions of B and T lymphocytes; immune responses to infections and tumors; hypersensitivity, autoimmunity, and immunodeficiencies. Particular attention to the development and function of the immune system as a whole, as studied by modern methods and techniques. Students taking graduate version explore the subject in greater depth, including study of recent primary literature.

Investigates the molecular and clinical basis of central nervous system and neuromuscular disorders with particular emphasis on strategies for therapeutic intervention. Considers the in-depth analysis of clinical features, pathological mechanisms, and responses to current therapeutic interventions. Covers neurodegenerative diseases, such as Huntington's disease, Parkinson's disease, Alzheimer's disease, Amyotropic Lateral Schlerosis, Frontal Temporal Dementia, and neuromuscular disorders, such as Myotonic Dystrophy, Facio Scapular Humoral Dystrophy, and Duchenne Muscular Dystrophy.

Focuses on the principles of host-pathogen interactions with an emphasis on infectious diseases of humans. Presents key concepts of pathogenesis through the study of various human pathogens. Includes critical analysis and discussion of assigned readings. Students taking the graduate version are expected to explore the subject in greater depth.

Considers molecular control of neural specification, formation of neuronal connections, construction of neural systems, and the contributions of experience to shaping brain structure and function. Topics include: neural induction and pattern formation, cell lineage and fate determination, neuronal migration, axon guidance, synapse formation and stabilization, activity-dependent development and critical periods, development of behavior. In addition to final exam, analysis and presentation of research papers required for final grade. Students taking graduate version complete additional assignments. Students taking graduate version complete additional readings that will be addressed in their mid-term and final exams.

Seminar examines basic principles of biological regulation of gene expression. Focuses on examples that underpin these principles, as well as those that challenge certain long-held views. Topics covered may include the role of transcription factors, enhancers, DNA modifications, non-coding RNAs, and chromatin structure in the regulation of gene expression and mechanisms for epigenetic inheritance of transcriptional states. Limited to 40.

Introduces students to modern biophysical methods to study biological systems from atomic, to molecular and cellular scales. Includes an in-depth discussion on the techniques that cover the full resolution range, including X-ray crystallography, electron-, and light microscopy. Discusses other common biophysical techniques for macromolecular characterizations. Lectures cover theoretical principles behind the techniques, and students are given practical laboratory exercises using instrumentation available at MIT. Meets with 5.78 when offered concurrently. 

Topics include diverse stem cells, such as muscle, intestine, skin, hair and hematopoietic stem cells, as well as pluripotent stem cells. Topics address cell polarity and cell fate; positional information and patterning of development and regeneration; limb, heart and whole body regeneration; stem cell renewal; progenitor cells in development; responses to wounding; and applications of stem cells in development of therapies. Discussions of papers supplement lectures.

In-depth analysis and discussion of classic and current literature, with an emphasis on the structure, function, and mechanisms of proteins and other biological macromolecules.

Surveys primary literature, focusing on biochemical, biophysical, genetic, and combinatorial approaches for understanding nucleic acids. Topics include the general properties, functions, and structural motifs of DNA and RNA; RNAs as catalysts and as regulators of gene expression; RNA editing and surveillance, and the interaction of nucleic acids with proteins, such as zinc-finger proteins, modification enzymes, aminoacyl-tRNA synthetases and other proteins of the translational machinery. Includes some lectures but is mostly analysis and discussion of current literature in the context of student presentations.

Spanning the fields of biology, chemistry, and engineering, this class introduces students to the principles of chemical biology and the application of chemical and physical methods and reagents to the study and manipulation of biological systems. Topics include nucleic acid structure, recognition, and manipulation; protein folding and stability, and proteostasis; bioorthogonal reactions and activity-based protein profiling; chemical genetics and small-molecule inhibitor screening; fluorescent probes for biological analysis and imaging; and unnatural amino acid mutagenesis. The class will also discuss the logic of dynamic post-translational modification reactions with an emphasis on chemical biology approaches for studying complex processes including glycosylation, phosphorylation, and lipidation. Students taking the graduate version are expected to explore the subject in greater depth.

Seminar covering the key concepts and technological approaches that are used to study and treat human disease. Topics include human genome variation, germline editing, gene therapy, stem cell derived organoids, human-animal chimeras and the application of these approaches to the study and treatment of major diseases.

Advanced seminar involving intensive analysis of historical and current developments in cancer biology. Topics address principles of apoptosis, principles of cancer biology, cancer genetics, cancer cell metabolism, tumor immunology, and therapy. Detailed analysis of research literature, including important reports published in recent years. Enrollment limited.

Examination of the role of neural plasticity during learning and memory of invertebrates and mammals. Detailed critical analysis of the current literature of molecular, cellular, genetic, electrophysiological, and behavioral studies. Student-directed presentations and discussions of original papers supplemented by introductory lectures. Juniors and seniors require instructor's permission.

Covers material in various fields of biology not offered by the regular subjects of instruction.

Covers material in various fields of biology not offered by the regular subjects of instruction.

Covers material in various fields of biology not offered by the regular subjects of instruction.

Covers material in various fields of biology not offered by the regular subjects of instruction.

Examination of the role of neural plasticity during learning and memory of invertebrates and mammals. Detailed critical analysis of the current literature of molecular, cellular, genetic, electrophysiological, and behavioral studies. Student-directed presentations and discussions of original papers supplemented by introductory lectures. Juniors and seniors require instructor's permission.

Covers principles underlying current and future genetic engineering approaches, ranging from single cellular organisms to whole animals. Focuses on development and invention of technologies for engineering biological systems at the genomic level, and applications of engineered biological systems for medical and biotechnological needs, with particular emphasis on genetic manipulation of the nervous system. Design projects by students.

Comprehensive survey of molecular, genetic, and cellular aspects of the immune system. Topics include innate and adaptive immunity; cells and organs of the immune system; hematopoiesis; immunoglobulin, T cell receptor, and major histocompatibility complex (MHC) proteins and genes; development and functions of B and T lymphocytes; immune responses to infections and tumors; hypersensitivity, autoimmunity, and immunodeficiencies. Particular attention to the development and function of the immune system as a whole, as studied by modern methods and techniques. Students taking graduate version explore the subject in greater depth, including study of recent primary literature.

Spanning the fields of biology, chemistry, and engineering, this class introduces students to the principles of chemical biology and the application of chemical and physical methods and reagents to the study and manipulation of biological systems. Topics include nucleic acid structure, recognition, and manipulation; protein folding and stability, and proteostasis; bioorthogonal reactions and activity-based protein profiling; chemical genetics and small-molecule inhibitor screening; fluorescent probes for biological analysis and imaging; and unnatural amino acid mutagenesis. The class will also discuss the logic of dynamic post-translational modification reactions with an emphasis on chemical biology approaches for studying complex processes including glycosylation, phosphorylation, and lipidation. Students taking the graduate version are expected to explore the subject in greater depth.

Explores and illustrates how evolution explains biology, with an emphasis on computational model building for analyzing evolutionary data. Covers key concepts of biological evolution, including adaptive evolution, neutral evolution, evolution of sex, genomic conflict, speciation, phylogeny and comparative methods, life's history, coevolution, human evolution, and evolution of disease.

Spanning the fields of biology, chemistry, and engineering, this class introduces students to the principles of chemical biology and the application of chemical and physical methods and reagents to the study and manipulation of biological systems. Topics include nucleic acid structure, recognition, and manipulation; protein folding and stability, and proteostasis; bioorthogonal reactions and activity-based protein profiling; chemical genetics and small-molecule inhibitor screening; fluorescent probes for biological analysis and imaging; and unnatural amino acid mutagenesis. The class will also discuss the logic of dynamic post-translational modification reactions with an emphasis on chemical biology approaches for studying complex processes including glycosylation, phosphorylation, and lipidation. Students taking the graduate version are expected to explore the subject in greater depth.

Provides a practical introduction to probability and statistics used in modern biology. Topics covered include discrete and continuous probability distributions, statistical modeling, hypothesis testing, independence, conditional probability, multiple test corrections, nonparametric methods, clustering, correlation, linear regression, principal components analysis with applications to high-throughput DNA sequencing, and image data analysis. Homework is in the R programming language, but prior programming experience is not required. Students taking the graduate version are expected to explore the subject in greater depth.

Introduces modern methods in computational biology, focusing on DNA/RNA/protein analysis. Topics include next-generation DNA sequencing and sequencing data analysis, RNA-seq (bulk and single-cell), and protein dynamics. Students taking the graduate version are expected to explore the subject in greater depth.

Comprehensive survey of molecular, genetic, and cellular aspects of the immune system. Topics include innate and adaptive immunity; cells and organs of the immune system; hematopoiesis; immunoglobulin, T cell receptor, and major histocompatibility complex (MHC) proteins and genes; development and functions of B and T lymphocytes; immune responses to infections and tumors; hypersensitivity, autoimmunity, and immunodeficiencies. Particular attention to the development and function of the immune system as a whole, as studied by modern methods and techniques. Students taking graduate version explore the subject in greater depth, including study of recent primary literature.

Provides a comprehensive and intensified understanding of the relevance of the immune system beyond immunity. Focuses on how the immune system intersects with all aspects of body homeostasis/physiology or disease and how the immune system can be manipulated therapeutically. New advances in the intersection of immunology with cancer biology, neurosciences, metabolism, aging, and maternal-fetal immunology or similar explored. Presents new modern methods and techniques applicable beyond immunology. Includes critical analysis and discussion of assigned readings. Students apply principles learned in class to generate a potential research project, presented in a written form. Students taking graduate version complete additional assignments.

Focuses on the principles of host-pathogen interactions with an emphasis on infectious diseases of humans. Presents key concepts of pathogenesis through the study of various human pathogens. Includes critical analysis and discussion of assigned readings. Students taking the graduate version are expected to explore the subject in greater depth.

Covers modern approaches to human diseases and aging, emphasizing the molecular and cellular basis of genetic diseases, infectious diseases, aging, and cancer. Topics include the genetics of simple and complex traits; karyotypic analysis and positional cloning; genetic diagnosis; evolutionary determination of aging, genetic and molecular aspects of aging, HIV/AIDs and other infectious diseases; the roles of oncogenes and tumor suppressors; the interaction between genetics and environment; animal models of human disease, cancer, and aging; and treatment strategies for diseases and aging. Includes a paper describing novel treatment options for a specific disease chosen by each student.

Detailed analysis of the biochemical mechanisms that control the maintenance, expression, and evolution of prokaryotic and eukaryotic genomes. Topics covered in lecture and readings of relevant literature include: gene regulation, DNA replication, genetic recombination, and mRNA translation. Logic of experimental design and data analysis emphasized. Presentations include both lectures and group discussions of representative papers from the literature. Students taking the graduate version are expected to explore the subject in greater depth.

Introduction to the structure and function of the nervous system. Emphasizes the cellular properties of neurons and other excitable cells. Includes the structure and biophysical properties of excitable cells, synaptic transmission, neurochemistry, neurodevelopment, integration of information in simple systems, and detection and information coding during sensory transduction.

Explores and illustrates how evolution explains biology, with an emphasis on computational model building for analyzing evolutionary data. Covers key concepts of biological evolution, including adaptive evolution, neutral evolution, evolution of sex, genomic conflict, speciation, phylogeny and comparative methods, life's history, coevolution, human evolution, and evolution of disease.

Upper-level seminar offering in-depth analysis and engaged discussion of primary literature on the dimensions and phenotypic consequences of variation in human genes, chromosomes, and genomes. Topics include the human genome project; pedigree analysis; mutation and selection; linkage and association studies; medical genetics and disease; sex chromosomes and sex differences; the biology of the germ line; epigenetics, imprinting, and transgenerational inheritance; human origins; and evolutionary and population genetics. Students taking graduate version complete additional assignments. Limited to 20 total for versions meeting together.

Covers biological and bioengineering principles underlying the development and therapeutic use of recombinant proteins and stem cells; glycoengineering of recombinant proteins; normal and pathological signaling by growth factors and their receptors; receptor trafficking; monoclonal antibodies as therapeutics; protein pharmacology and delivery; stem cell-derived tissues as therapeutics; RNA therapeutics; combinatorial protein engineering; and new antitumor drugs.

Considers molecular control of neural specification, formation of neuronal connections, construction of neural systems, and the contributions of experience to shaping brain structure and function. Topics include: neural induction and pattern formation, cell lineage and fate determination, neuronal migration, axon guidance, synapse formation and stabilization, activity-dependent development and critical periods, development of behavior. Students taking graduate version complete additional readings that will be addressed in their mid-term and final exams.

Introduction to the structure and function of the nervous system. Emphasizes the cellular properties of neurons and other excitable cells. Includes the structure and biophysical properties of excitable cells, synaptic transmission, neurochemistry, neurodevelopment, integration of information in simple systems, and detection and information coding during sensory transduction.

Considers molecular control of neural specification, formation of neuronal connections, construction of neural systems, and the contributions of experience to shaping brain structure and function. Topics include: neural induction and pattern formation, cell lineage and fate determination, neuronal migration, axon guidance, synapse formation and stabilization, activity-dependent development and critical periods, development of behavior. Students taking graduate version complete additional readings that will be addressed in their mid-term and final exams.

Covers principles underlying current and future genetic engineering approaches, ranging from single cellular organisms to whole animals. Focuses on development and invention of technologies for engineering biological systems at the genomic level, and applications of engineered biological systems for medical and biotechnological needs, with particular emphasis on genetic manipulation of the nervous system. Design projects by students.

Provides a thorough introduction to the forces driving infectious disease evolution, practical experience with bioinformatics and computational tools, and discussions of current topics relevant to public health. Topics include mechanisms of genome variation in bacteria and viruses, population genetics, outbreak detection and tracking, strategies to impede the evolution of drug resistance, emergence of new disease, and microbiomes and metagenomics. Discusses primary literature and computational assignments. Students taking graduate version complete additional assignments.

Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments.

Detailed analysis of the biochemical mechanisms that control the maintenance, expression, and evolution of prokaryotic and eukaryotic genomes. Topics covered in lecture and readings of relevant literature include: gene regulation, DNA replication, genetic recombination, and mRNA translation. Logic of experimental design and data analysis emphasized. Presentations include both lectures and group discussions of representative papers from the literature. Students taking the graduate version are expected to explore the subject in greater depth.

Eukaryotic genome structure, function, and expression, processing of RNA, and regulation of the cell cycle. Emphasis on the techniques and logic used to address important problems in nuclear cell biology. Lectures on broad topic areas in nuclear cell biology and discussions on representative recent papers.

Provides a thorough introduction to the forces driving infectious disease evolution, practical experience with bioinformatics and computational tools, and discussions of current topics relevant to public health. Topics include mechanisms of genome variation in bacteria and viruses, population genetics, outbreak detection and tracking, strategies to impede the evolution of drug resistance, emergence of new disease, and microbiomes and metagenomics. Discusses primary literature and computational assignments. Students taking graduate version complete additional assignments.

Provides a thorough introduction to the forces driving infectious disease evolution, practical experience with bioinformatics and computational tools, and discussions of current topics relevant to public health. Topics include mechanisms of genome variation in bacteria and viruses, population genetics, outbreak detection and tracking, strategies to impede the evolution of drug resistance, emergence of new disease, and microbiomes and metagenomics. Discusses primary literature and computational assignments. Students taking graduate version complete additional assignments.

Introduction to computational molecular biology with a focus on the basic computational algorithms used to solve problems in practice. Covers classical techniques in the field for solving problems such as genome sequencing, assembly, and search; detecting genome rearrangements; constructing evolutionary trees; analyzing mass spectrometry data; connecting gene expression to cellular function; and machine learning for drug discovery. Prior knowledge of biology is not required. Particular emphasis on problem solving, collaborative learning, theoretical analysis, and practical implementation of algorithms. Students taking graduate version complete additional and more complex assignments.

Explores and illustrates how evolution explains biology, with an emphasis on computational model building for analyzing evolutionary data. Covers key concepts of biological evolution, including adaptive evolution, neutral evolution, evolution of sex, genomic conflict, speciation, phylogeny and comparative methods, life's history, coevolution, human evolution, and evolution of disease.

Provides a practical introduction to probability and statistics used in modern biology. Topics covered include discrete and continuous probability distributions, statistical modeling, hypothesis testing, independence, conditional probability, multiple test corrections, nonparametric methods, clustering, correlation, linear regression, principal components analysis with applications to high-throughput DNA sequencing, and image data analysis. Homework is in the R programming language, but prior programming experience is not required. Students taking the graduate version are expected to explore the subject in greater depth.

Introduces modern methods in computational biology, focusing on DNA/RNA/protein analysis. Topics include next-generation DNA sequencing and sequencing data analysis, RNA-seq (bulk and single-cell), and protein dynamics. Students taking the graduate version are expected to explore the subject in greater depth.

Explores and illustrates how evolution explains biology, with an emphasis on computational model building for analyzing evolutionary data. Covers key concepts of biological evolution, including adaptive evolution, neutral evolution, evolution of sex, genomic conflict, speciation, phylogeny and comparative methods, life's history, coevolution, human evolution, and evolution of disease.

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.

Linear, discrete- and continuous-time, multi-input-output systems in control, related areas. Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6.3100.

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.

Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexity-based ideas, complexity results, and efficient implementations. Examples from several engineering areas, in particular systems and control applications. Topics include semidefinite programming, resultants/discriminants, hyperbolic polynomials, Groebner bases, quantifier elimination, and sum of squares.

Optimization algorithms are central to all of machine learning. Covers a variety of topics in optimization, with a focus on non-convex optimization. Focuses on both classical and cutting-edge results, including foundational topics grounded in convexity, complexity theory of first-order methods, stochastic optimization, as well as recent progress in non-Euclidean optimization, deep learning, and beyond. Prepares students to appreciate a broad spectrum of ideas in OPTML, learning to be not only informed users but also gaining exposure to research questions in the area.

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.

Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging.

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.

Covers Bayesian modeling and inference at an advanced graduate level. Topics include de Finetti's theorem, decision theory, approximate inference (modern approaches and analysis of Monte Carlo, variational inference, etc.), hierarchical modeling, (continuous and discrete) nonparametric Bayesian approaches, sensitivity and robustness, and evaluation.

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.

Provides an in-depth view of the state-of-the-art learning methods for control and the know-how of applying these techniques. Topics span reinforcement learning, self-supervised learning, imitation learning, model-based learning, and advanced deep learning architectures, and specific machine learning challenges unique to building sensorimotor systems. Discusses how to identify if learning-based control can help solve a particular problem, how to formulate the problem in the learning framework, and what algorithm to use. Applications of algorithms in robotics, logistics, recommendation systems, playing games, and other control domains covered. Instruction involves two lectures a week, practical experience through exercises, discussion of current research directions, and a group project.

Covers nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on computational methods. Topics include the nonlinear dynamics of robotic manipulators, applied optimal and robust control and motion planning. Discussions include examples from biology and applications to legged locomotion, compliant manipulation, underwater robots, and flying machines.

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.

Implementation and evaluation of intelligent multi-modal user interfaces, taught from a combination of hands-on exercises and papers from the original literature. Topics include basic technologies for handling speech, vision, pen-based interaction, and other modalities, as well as various techniques for combining modalities. Substantial readings and a term project, where students build a program that illustrates one or more of the themes of the course.

Introduces the rapidly developing field of spoken language processing including automatic speech recognition. Topics include acoustic theory of speech production, acoustic-phonetics, signal representation, acoustic and language modeling, search, hidden Markov modeling, neural networks models, end-to-end deep learning models, and other machine learning techniques applied to speech and language processing topics. Lecture material intersperses theory with practice. Includes problem sets, laboratory exercises, and open-ended term project.

Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments.

Applies analysis of signals and noise in linear systems, sampling, and Fourier properties to magnetic resonance (MR) imaging acquisition and reconstruction. Provides adequate foundation for MR physics to enable study of RF excitation design, efficient Fourier sampling, parallel encoding, reconstruction of non-uniformly sampled data, and the impact of hardware imperfections on reconstruction performance. Surveys active areas of MR research. Assignments include Matlab-based work with real data. Includes visit to a scan site for human MR studies.