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6.1820[J] | Mobile and Sensor Computing | Focuses on "Internet of Things" (IoT) systems and technologies, sensing, computing, and communication. Explores fundamental design and implementation issues in the engineering of mobile and sensor computing systems. Topics include battery-free sensors, seeing through wall, robotic sensors, vital sign sensors (breathing, heartbeats, emotions), sensing in cars and autonomous vehicles, subsea IoT, sensor security, positioning technologies (including GPS and indoor WiFi), inertial sensing (accelerometers, gyroscopes, inertial measurement units, dead-reckoning), embedded and distributed system architectures, sensing with radio signals, sensing with microphones and cameras, wireless sensor networks, embedded and distributed system architectures, mobile libraries and APIs to sensors, and application case studies. Includes readings from research literature, as well as laboratory assignments and a significant term project. | true | Spring | Undergraduate | 3-0-9 | 6.1800 or permission of instructor | MAS.453[J] | false | false | false | False | False | False |
6.1850 | Computer Systems and Society | Explores the impact of computer systems on individual humans, society, and the environment. Examines large- and small-scale power structures that stem from low-level technical design decisions, the consequences of those structures on society, and how they can limit or provide access to certain technologies. Students learn to assess design decisions within an ethical framework and consider the impact of their decisions on non-users. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Possible topics include the implications of hierarchical designs (e.g., DNS) for scale; how layered models influence what parts of a network have the power to take certain actions; and the environmental impact of proof-of-work-based systems such as Bitcoin. Enrollment may be limited. | true | Fall | Undergraduate | 3-0-9 | 6.1800 | null | false | false | false | False | False | False |
6.5810 | Operating System Engineering | Fundamental design and implementation issues in the engineering of operating systems. Lectures based on the study of a symmetric multiprocessor version of UNIX version 6 and research papers. Topics include virtual memory; file system; threads; context switches; kernels; interrupts; system calls; interprocess communication; coordination, and interaction between software and hardware. Individual laboratory assignments accumulate in the construction of a minimal operating system (for an x86-based personal computer) that implements the basic operating system abstractions and a shell. Knowledge of programming in the C language is a prerequisite. | true | Fall | Graduate | 3-6-3 | 6.1020 and (6.1800 or 6.1810) | null | false | false | false | False | False | False |
6.5820 | Computer Networks | Topics on the engineering and analysis of network protocols and architecture, including architectural principles for designing heterogeneous networks; transport protocols; Internet routing; router design; congestion control and network resource management; wireless networks; network security; naming; overlay and peer-to-peer networks. Readings from original research papers. Semester-long project and paper. | true | Fall | Graduate | 4-0-8 | 6.1800 or permission of instructor | null | false | false | false | False | False | False |
6.5830 | Database Systems | 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. | true | Fall | Graduate | 3-0-9 | ((6.1210 or 6.1220) and (6.1800 or 6.1810)) or permission of instructor | null | false | false | false | False | False | False |
6.5831 | Database Systems | 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. | true | Fall | Undergraduate | 3-0-9 | ((6.1210 or 6.1220) and (6.1800 or 6.1810)) or permission of instructor | null | false | false | false | False | False | False |
6.5840 | Distributed Computer Systems Engineering | 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 network file system. Programming experience with C/C++ required. Enrollment limited. | true | Spring | Graduate | 3-0-9 | 6.1800, 6.1810, or permission of instructor | null | false | false | false | False | False | False |
6.5850 | Principles of Computer Systems | Introduction to the basic principles of computer systems with emphasis on the use of rigorous techniques as an aid to understanding and building modern computing systems. Particular attention paid to concurrent and distributed systems. Topics include: specification and verification, concurrent algorithms, synchronization, naming, Networking, replication techniques (including distributed cache management), and principles and algorithms for achieving reliability. | true | Fall | Graduate | 3-0-9 | Permission of instructor | null | false | false | false | False | False | False |
6.1903 | Introduction to Low-level Programming in C and Assembly | Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions. | true | Spring | Undergraduate | 2-2-2 | 6.100A | null | false | false | false | False | False | False |
6.1904 | Introduction to Low-level Programming in C and Assembly | Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions. | true | Spring | Undergraduate | 2-2-2 | 6.100A | null | false | false | false | False | False | False |
6.1910 | Computation Structures | Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems. | true | Fall, Spring | Undergraduate | 4-0-8 | Physics II (GIR), 6.100A, and (Coreq: 6.1903 or 6.1904); or permission of instructor | null | false | false | true | False | False | False |
6.1920 | Constructive Computer Architecture | Illustrates a constructive (as opposed to a descriptive) approach to computer architecture. Topics include combinational and pipelined arithmetic-logic units (ALU), in-order pipelined microarchitectures, branch prediction, blocking and unblocking caches, interrupts, virtual memory support, cache coherence and multicore architectures. Labs in a modern Hardware Design Language (HDL) illustrate various aspects of microprocessor design, culminating in a term project in which students present a multicore design running on an FPGA board. | true | Spring | Undergraduate | 3-8-1 | 6.1910 | null | false | false | false | False | False | False |
6.5900 | Computer System Architecture | Introduction to the principles underlying modern computer architecture. Emphasizes the relationship among technology, hardware organization, and programming systems in the evolution of computer architecture. Topics include pipelined, out-of-order, and speculative execution; caches, virtual memory and exception handling, superscalar, very long instruction word (VLIW), vector, and multithreaded processors; on-chip networks, memory models, synchronization, and cache coherence protocols for multiprocessors. | true | Fall | Graduate | 4-0-8 | 6.1910 | null | false | false | false | False | False | False |
6.5910 | Complex Digital Systems Design | 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. | true | Spring | Graduate | 5-5-2 | 6.1910 | null | false | false | false | False | False | False |
6.5920 | Parallel Computing | 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. | true | Spring | Graduate | 3-0-9 | 6.1910 or permission of instructor | null | false | false | false | False | False | False |
6.5930 | Hardware Architecture for Deep Learning | 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. | true | Spring | Graduate | 3-3-6 | 6.1910 and (6.3000 or 6.3900) | null | false | false | false | False | False | False |
6.5931 | Hardware Architecture for Deep Learning | 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. | true | Spring | Undergraduate | 3-3-6 | 6.1910 and (6.3000 or 6.3900) | null | false | false | false | False | False | False |
6.5940 | TinyML and Efficient Deep Learning Computing | Introduces efficient deep learning computing techniques that enable powerful deep learning applications on resource-constrained devices. Topics include model compression, pruning, quantization, neural architecture search, distributed training, data/model parallellism, gradient compression, on-device fine-tuning. It also introduces application-specific acceleration techniques for video recognition, point cloud, and generative AI (diffusion model, LLM). Students will get hands-on experience accelerating deep learning applications with an open-ended design project. | true | Fall | Graduate | 3-0-9 | 6.1910 and 6.3900 | null | false | false | false | False | False | False |
6.5950 | Secure Hardware Design | 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. | true | Spring | Graduate | 3-0-9 | 6.1910 | null | false | false | false | False | False | False |
6.5951 | Secure Hardware Design | 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. | true | Spring | Undergraduate | 3-0-9 | 6.1910 | null | false | false | false | False | False | False |
6.2000 | Electrical Circuits: Modeling and Design of Physical Systems | Fundamentals of linear systems, and abstraction modeling of multi-physics lumped and distributed systems using lumped electrical circuits. Linear networks involving independent and dependent sources, resistors, capacitors, and inductors. Extensions to include operational amplifiers and transducers. Dynamics of first- and second-order networks; analysis and design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers. | true | Fall, Spring | Undergraduate | 3-2-7 | Physics II (GIR) | null | false | false | true | False | False | False |
6.2020[J] | Electronics Project Laboratory | Intuition-based introduction to electronics, electronic components, and test equipment such as oscilloscopes, multimeters, and signal generators. Key components studied and used are op-amps, comparators, bi-polar transistors, and diodes (including LEDs). Students design, build, and debug small electronics projects (often featuring sound and light) to put their new knowledge into practice. Upon completing the class, students can take home a kit of components. Intended for students with little or no previous background in electronics. Enrollment may be limited. | true | Fall, Spring | Undergraduate | 1-2-3 | null | EC.120[J] | false | false | false | False | False | False |
6.2030 | Electronics First Laboratory | Practical introduction to the design and construction of electronic circuits for information processing and control. Laboratory exercises include activities such as the construction of oscillators for a simple musical instrument, a laser audio communicator, a countdown timer, an audio amplifier, and a feedback-controlled solid-state lighting system for daylight energy conservation. Introduces basic electrical components including resistors, capacitors, and inductors; basic assembly techniques for electronics include breadboarding and soldering; and programmable system-on-chip electronics and C programming language. Enrollment limited. | true | Spring | Undergraduate | 4-4-4 | None. Coreq: Physics II (GIR) | null | false | false | false | False | False | False |
6.2040 | Analog Electronics Laboratory | Experimental laboratory explores the design, construction, and debugging of analog electronic circuits. Lectures and laboratory projects in the first half of the course investigate the performance characteristics of semiconductor devices (diodes, BJTs, and MOSFETs) and functional analog building blocks, including single-stage amplifiers, op amps, small audio amplifier, filters, converters, sensor circuits, and medical electronics (ECG, pulse-oximetry). Projects involve design, implementation, and presentation in an environment similar to that of industry engineering design teams. Instruction and practice in written and oral communication provided. Opportunity to simulate real-world problems and solutions that involve tradeoffs and the use of engineering judgment. | true | Spring | Undergraduate | 2-9-1 | 6.2000 | null | true | false | false | False | False | False |
6.2050 | Digital Systems Laboratory | Lab-intensive subject that investigates digital systems with a focus on FPGAs. Lectures and labs cover logic, flip flops, counters, timing, synchronization, finite-state machines, digital signal processing, communication protocols, and modern sensors. Prepares students for the design and implementation of a large-scale final project of their choice: games, music, digital filters, wireless communications, video, or graphics. Extensive use of System/Verilog for describing and implementing and verifying digital logic designs. | true | Fall | Undergraduate | 3-7-2 | 6.1910 or permission of instructor | null | true | false | false | False | False | False |
6.2060 | Microcomputer Project Laboratory | Introduces analysis and design of embedded systems. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station (e.g., a CAT scan), and a simple calculator. Presents a wide range of basic tools, including software and development tools, programmable system on chip, peripheral components such as A/D converters, communication schemes, signal processing techniques, closed-loop digital feedback control, interface and power electronics, and modeling of electromechanical systems. Includes a sequence of assigned projects, followed by a final project of the student's choice, emphasizing creativity and uniqueness. Provides instruction in written and oral communication. To satisfy the independent inquiry component of this subject, students expand the scope of their laboratory project. Enrollment limited. | true | Spring | Undergraduate | 3-6-3 | 6.1910, 6.2000, or 6.3000 | null | true | false | false | False | False | False |
6.2061 | Microcomputer Project Laboratory - Independent Inquiry | Introduces analysis and design of embedded systems. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station (e.g., a CAT scan), and a simple calculator. Presents a wide range of basic tools, including software and development tools, programmable system on chip, peripheral components such as A/D converters, communication schemes, signal processing techniques, closed-loop digital feedback control, interface and power electronics, and modeling of electromechanical systems. Includes a sequence of assigned projects, followed by a final project of the student's choice, emphasizing creativity and uniqueness. Provides instruction in written and oral communication. Students taking independent inquiry version 6.2061 expand the scope of their laboratory project. Enrollment limited. | true | Spring | Undergraduate | 3-9-3 | 6.1910, 6.2000, or 6.3000 | null | false | false | false | False | False | False |
6.2080 | Semiconductor Electronic Circuits | Provides an introduction to basic circuit design, starting from basic semiconductor devices such as diodes and transistors, large and small signal models and analysis, to circuits such as basic amplifier and opamp circuits. Labs give students access to CAD/EDA tools to design, analyze, and layout analog circuits. At the end of the term, students have their chip design fabricated using a 22nm FinFET CMOS process. | true | Spring | Undergraduate | 3-2-7 | 6.2000 | null | false | false | false | False | False | False |
6.2090 | Solid-State Circuits | Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor (BJT) and metal oxide semiconductor (MOS) technologies. Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references. Covers topics such as noise, linearity and stability. Homework and labs give students access to CAD/EDA tools to design and analyze analog circuits. Provides practical experience through lab exercises, including a broadband amplifier design and characterization. Students taking graduate version complete additional assignments. | true | Fall | Undergraduate | 3-2-7 | 6.2040, 6.2080, or permission of instructor | null | false | false | false | False | False | False |
6.2092 | Solid-State Circuits | Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor (BJT) and metal oxide semiconductor (MOS) technologies. Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references. Covers topics such as noise, linearity and stability. Homework and labs give students access to CAD/EDA tools to design and analyze analog circuits. Provides practical experience through lab exercises, including a broadband amplifier design and characterization. Students taking graduate version complete additional assignments. | true | Fall | Graduate | 3-2-7 | 6.2040, 6.2080, or permission of instructor | null | false | false | false | False | False | False |
6.6000 | CMOS Analog and Mixed-Signal Circuit Design | 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. | true | Spring | Graduate | 3-0-9 | 6.2090 | null | false | false | false | False | False | False |
6.6010 | Analysis and Design of Digital Integrated Circuits | Device and circuit level optimization of digital building blocks. Circuit design styles for logic, arithmetic, and sequential blocks. Estimation and minimization of energy consumption. Interconnect models and parasitics, device sizing and logical effort, timing issues (clock skew and jitter), and active clock distribution techniques. Memory architectures, circuits (sense amplifiers), and devices. Evaluation of how design choices affect tradeoffs across key metrics including energy consumption, speed, robustness, and cost. Extensive use of modern design flow and EDA/CAD tools for the analysis and design of digital building blocks and digital VLSI design for labs and design projects | true | Fall | Graduate | 3-3-6 | 6.1910 and (6.2080 or 6.2500) | null | false | false | false | False | False | False |
6.6020 | High-Frequency Integrated Circuits | Principles and techniques of high-speed integrated circuits used in wireless/wireline data links and remote sensing. On-chip passive component design of inductors, capacitors, and antennas. Analysis of distributed effects, such as transmission line modeling, S-parameters, and Smith chart. Transceiver architectures and circuit blocks, which include low-noise amplifiers, mixers, voltage-controlled oscillators, power amplifiers, and frequency dividers. Involves IC/EM simulation and laboratory projects. | true | Fall | Graduate | 3-3-6 | 6.2080 | null | false | false | false | False | False | False |
6.2200 | Electric Energy Systems | Analysis and design of modern energy conversion and delivery systems. Develops a solid foundation in electromagnetic phenomena with a focus on electrical energy distribution, electro-mechanical energy conversion (motors and generators), and electrical-to-electrical energy conversion (DC-DC, DC-AC power conversion). Students apply the material covered to consider critical challenges associated with global energy systems, with particular examples related to the electrification of transport and decarbonization of the grid. | true | Fall | Undergraduate | 4-0-8 | 6.2000 | null | false | false | false | False | False | False |
6.2210 | Electromagnetic Fields, Forces and Motion | Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators. Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors. Extensive use of engineering examples. Students taking graduate version complete additional assignments. | true | Fall | Undergraduate | 4-0-8 | Physics II (GIR) and 18.03 | null | false | false | false | False | False | False |
6.2220 | Power Electronics Laboratory | Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Provides instruction in written and oral communication. Students taking independent inquiry version 6.2221 expand the scope of their laboratory project. | true | Fall | Undergraduate | 3-6-3 | 6.2000 or 6.3100 | null | true | false | false | False | False | False |
6.2221 | Power Electronics Laboratory - Independent Inquiry | Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Provides instruction in written and oral communication. To satisfy the independent inquiry component of this subject, students expand the scope of their laboratory project. | true | Fall | Undergraduate | 3-9-3 | 6.2000 or 6.3000 | null | false | false | false | False | False | False |
6.2222 | Power Electronics Laboratory | Hands-on introduction to the design and construction of power electronic circuits and motor drives. Laboratory exercises (shared with 6.131 and 6.1311) include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced including DC, induction, and permanent magnet motors, with drive considerations. Students taking graduate version complete additional assignments and an extended final project. | true | Fall | Graduate | 3-9-3 | Permission of instructor | null | false | false | false | False | False | False |
6.6210 | Electromagnetic Fields, Forces and Motion | Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators. Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors. Extensive use of engineering examples. Students taking graduate version complete additional assignments. | true | Fall | Graduate | 4-0-8 | Physics II (GIR) and 18.03 | null | false | false | false | False | False | False |
6.6220 | Power Electronics | 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. | true | Spring | Graduate | 3-0-9 | 6.2500 | null | false | false | false | False | False | False |
6.6280 | Electric Machines | Treatment of electromechanical transducers, rotating and linear electric machines. Lumped-parameter electromechanics. Power flow using Poynting's theorem, force estimation using the Maxwell stress tensor and Principle of virtual work. Development of analytical techniques for predicting device characteristics: energy conversion density, efficiency; and of system interaction characteristics: regulation, stability, controllability, and response. Use of electric machines in drive systems. Problems taken from current research. | true | Fall | Graduate | 3-0-9 | 6.2200, 6.690, or permission of instructor | null | false | false | false | False | False | False |
6.2300 | Electromagnetics Waves and Applications | Analysis and design of modern applications that employ electromagnetic phenomena for signals and power transmission in RF, microwaves, optical and wireless communication systems. Fundamentals include dynamic solutions for Maxwell's equations; electromagnetic power and energy, waves in media, metallic and dielectric waveguides, radiation, and diffraction; resonance; filters; and acoustic analogs. Lab activities range from building to testing of devices and systems (e.g., antenna arrays, radars, dielectric waveguides). Students work in teams on self-proposed maker-style design projects with a focus on fostering creativity, teamwork, and debugging skills. 6.2000 and 6.3000 are recommended but not required. | true | Spring | Undergraduate | 3-5-4 | Calculus II (GIR) and Physics II (GIR) | null | false | false | false | False | False | False |
6.2320 | Silicon Photonics (New) | 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, displays, and biophotonics); the development of silicon-photonics-based platforms, including fabrication and materials considerations; and the characterization of these silicon-photonics-based devices and systems through laboratory demonstrations and projects. Students taking graduate version complete additional assignments. | true | Spring | Undergraduate | 3-0-9 | 6.2300 or 8.07 | null | false | false | false | False | False | False |
6.2370 | Modern Optics Project Laboratory | Lectures, laboratory exercises and projects on optical signal generation, transmission, detection, storage, processing and display. Topics include polarization properties of light; reflection and refraction; coherence and interference; Fraunhofer and Fresnel diffraction; holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; display technologies; optical waveguides and fiber-optic communication systems; photodetectors. Students may use this subject to find an advanced undergraduate project. Students engage in extensive oral and written communication exercises. Recommended prerequisite: 8.03. | true | Fall | Undergraduate | 3-5-4 | 6.3000 | null | true | false | false | False | False | False |
6.2400 | Introduction to Quantum Systems Engineering | Introduction to the quantum mechanics needed to engineer quantum systems for computation, communication, and sensing. Topics include: motivation for quantum engineering, qubits and quantum gates, rules of quantum mechanics, mathematical background, quantum electrical circuits and other physical quantum systems, harmonic and anharmonic oscillators, measurement, the Schrödinger equation, noise, entanglement, benchmarking, quantum communication, and quantum algorithms. No prior experience with quantum mechanics is assumed. | true | Fall | Undergraduate | 4-2-6 | 6.2300 and (18.06 or 18.C06) | null | false | false | false | False | False | False |
6.2410 | Quantum Engineering Platforms | Provides practical knowledge and quantum engineering experience with several physical platforms for quantum computation, communication, and sensing, including photonics, superconducting qubits, and trapped ions. Labs include both a hardware component -- to gain experience with challenges, design, and non-idealities -- and a cloud component to run algorithms on state of the art commercial systems. Use entangled photons to communicate securely (quantum key distribution). Run quantum algorithms on trapped ion and superconducting quantum computers. | true | Spring | Undergraduate | 1-5-6 | 6.2400, 6.6400, 18.435, or (8.04 and 8.05) | null | false | false | false | False | False | False |
6.6300 | Electromagnetics | Explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; modal expansions; resonance; acoustic analogs; and forces, power, and energy. | true | Fall | Graduate | 4-0-8 | Physics II (GIR) and 6.3000 | null | false | false | false | False | False | False |
6.6310 | Optics and Photonics | Introduction to fundamental concepts and techniques of optics, photonics, and fiber optics, aimed at developing skills for independent research. Topics include: Review of Maxwell's equations, light propagation, reflection and transmission, dielectric mirrors and filters. Scattering matrices, interferometers, and interferometric measurement. Fresnel and Fraunhoffer diffraction theory. Lenses, optical imaging systems, and software design tools. Gaussian beams, propagation and resonator design. Optical waveguides, optical fibers and photonic devices for encoding and detection. Discussion of research operations / funding and professional development topics. The course reviews and introduces mathematical methods and techniques, which are fundamental in optics and photonics, but also useful in many other engineering specialties. | true | Fall | Graduate | 3-0-9 | 6.2300 or 8.03 | null | false | false | false | False | False | False |
6.6320 | Silicon Photonics (New) | 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, displays, and biophotonics); the development of silicon-photonics-based platforms, including fabrication and materials considerations; and the characterization of these silicon-photonics-based devices and systems through laboratory demonstrations and projects. Students taking graduate version complete additional assignments. | true | Spring | Graduate | 3-0-9 | 6.2300 or 8.07 | null | false | false | false | False | False | False |
6.6330 | Fundamentals of Photonics | Covers the fundamentals of optics and the interaction of light and matter, leading to devices such as light emitting diodes, optical amplifiers, and lasers. Topics include classical ray, wave, beam, and Fourier optics; Maxwell's electromagnetic waves; resonators; quantum theory of photons; light-matter interaction; laser amplification; lasers; and semiconductors optoelectronics. Students taking graduate version complete additional assignments. | true | Fall | Graduate | 3-0-9 | 2.71, 6.2300, or 8.07 | null | false | false | false | False | False | False |
6.6331 | Fundamentals of Photonics | Covers the fundamentals of optics and the interaction of light and matter, leading to devices such as light emitting diodes, optical amplifiers, and lasers. Topics include classical ray, wave, beam, and Fourier optics; Maxwell's electromagnetic waves; resonators; quantum theory of photons; light-matter interaction; laser amplification; lasers; and semiconductors optoelectronics. Students taking graduate version complete additional assignments. | true | Fall | Undergraduate | 3-0-9 | 2.71, 6.2300, or 8.07 | null | false | false | false | False | False | False |
6.6340[J] | Nonlinear Optics | 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. | true | Spring | Graduate | 3-0-9 | 6.2300 or 8.03 | 8.431[J] | false | false | false | False | False | False |
6.6370 | Optical Imaging Devices, and Systems | Principles of operation and applications of optical imaging devices and systems (includes optical signal generation, transmission, detection, storage, processing and display). Topics include review of the basic properties of electromagnetic waves; coherence and interference; diffraction and holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; spatial light modulators and displays; near-eye and projection displays, holographic and other 3-D display schemes, photodetectors; 2-D and 3-D optical storage technologies; adaptive optical systems; role of optics in next-generation computers. Requires a research paper on a specific contemporary optical imaging topic. Recommended prerequisite: 8.03. | true | Fall | Graduate | 3-0-9 | 6.3000 | null | false | false | false | False | False | False |
6.6400 | Applied Quantum and Statistical Physics | Elementary quantum mechanics and statistical physics. Introduces applied quantum physics. Emphasizes experimental basis for quantum mechanics. Applies Schrodinger's equation to the free particle, tunneling, the harmonic oscillator, and hydrogen atom. Variational methods. Elementary statistical physics; Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions. Simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and more. Some familiarity with continuous time Fourier transforms recommended. | true | Fall | Graduate | 4-0-8 | 18.06 | null | false | false | false | False | False | False |
6.6410[J] | Quantum Computation | Provides an introduction to the theory and practice of quantum computation. Topics covered: physics of information processing; quantum algorithms including the factoring algorithm and Grover's search algorithm; quantum error correction; quantum communication and cryptography. Knowledge of quantum mechanics helpful but not required. | true | Fall | Graduate | 3-0-9 | 8.05, 18.06, 18.700, 18.701, or 18.C06 | 2.111[J], 8.370[J], 18.435[J] | false | false | false | False | False | False |
6.6420[J] | Quantum Information Science | 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. | true | Spring | Graduate | 3-0-9 | 18.435 | 8.371[J], 18.436[J] | false | false | false | False | False | False |
6.2500[J] | Nanoelectronics and Computing Systems | Studies interaction between materials, semiconductor physics, electronic devices, and computing systems. Develops intuition of how transistors operate. Topics range from introductory semiconductor physics to modern state-of-the-art nano-scale devices. Considers how innovations in devices have driven historical progress in computing, and explores ideas for further improvements in devices and computing. Students apply material to understand how building improved computing systems requires knowledge of devices, and how making the correct device requires knowledge of computing systems. Includes a design project for practical application of concepts, and labs for experience building silicon transistors and devices. | true | Spring | Undergraduate | 4-0-8 | 6.2000 | 3.158[J] | false | false | false | False | False | False |
6.2530 | Introduction to Nanoelectronics | Transistors at the nanoscale. Quantization, wavefunctions, and Schrodinger's equation. Introduction to electronic properties of molecules, carbon nanotubes, and crystals. Energy band formation and the origin of metals, insulators and semiconductors. Ballistic transport, Ohm's law, ballistic versus traditional MOSFETs, fundamental limits to computation. | true | Fall | Undergraduate | 4-0-8 | 6.3000 | null | false | false | false | False | False | False |
6.2532 | Nanoelectronics | Meets with undergraduate subject 6.2530, but requires the completion of additional/different homework assignments and or projects. See subject description under 6.2530. | true | Fall | Graduate | 4-0-8 | 6.3000 | null | false | false | false | False | False | False |
6.2540 | Nanotechnology: From Atoms to Systems | Introduces the fundamentals of applied quantum mechanics, materials science, and fabrication skills needed to design, engineer, and build emerging nanodevices with diverse applications in energy, memory, display, communications, and sensing. Focuses on the application and outlines the full progression from the fundamentals to the implemented device and functional technology. Closely integrates lectures with design-oriented laboratory modules. | true | Fall | Undergraduate | 2-3-7 | Physics II (GIR) | null | false | false | false | False | False | False |
6.2600[J] | Micro/Nano Processing Technology | Introduces the theory and technology of micro/nano fabrication. Includes lectures and laboratory sessions on processing techniques: wet and dry etching, chemical and physical deposition, lithography, thermal processes, packaging, and device and materials characterization. Homework uses process simulation tools to build intuition about higher order effects. Emphasizes interrelationships between material properties and processing, device structure, and the electrical, mechanical, optical, chemical or biological behavior of devices. Students fabricate solar cells, and a choice of MEMS cantilevers or microfluidic mixers. Students formulate their own device idea, either based on cantilevers or mixers, then implement and test their designs in the lab. Students engage in extensive written and oral communication exercises. Course provides background for research work related to micro/nano fabrication. Enrollment limited. | true | Spring | Undergraduate | 3-4-5 | Calculus II (GIR), Chemistry (GIR), Physics II (GIR), or permission of instructor | 3.155[J] | false | false | false | False | False | False |
6.6500[J] | Integrated Microelectronic Devices | Covers physics of microelectronic semiconductor devices for integrated circuit applications. Topics include semiconductor fundamentals, p-n junction, metal-oxide semiconductor structure, metal-semiconductor junction, MOS field-effect transistor, and bipolar junction transistor. Emphasizes physical understanding of device operation through energy band diagrams and short-channel MOSFET device design and modern device scaling. Familiarity with MATLAB recommended. | true | Fall | Graduate | 4-0-8 | 3.42 or 6.2500 | 3.43[J] | false | false | false | False | False | False |
6.6510 | Physics for Solid-State Applications | 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. | true | Spring | Graduate | 5-0-7 | 6.2300 and 6.6400 | null | false | false | false | False | False | False |
6.6520 | Semiconductor Optoelectronics: Theory and Design | 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. | false | Spring | Graduate | 3-0-9 | 6.2500 and 6.6400 | null | false | false | false | False | False | False |
6.6530 | Physics of Solids | Continuation of 6.730 emphasizing applications-related physical issues in solids. Topics include: electronic structure and energy band diagrams of semiconductors, metals, and insulators; Fermi surfaces; dynamics of electrons under electric and magnetic fields; classical diffusive transport phenomena such as electrical and thermal conduction and thermoelectric phenomena; quantum transport in tunneling and ballistic devices; optical properties of metals, semiconductors, and insulators; impurities and excitons; photon-lattice interactions; Kramers-Kronig relations; optoelectronic devices based on interband and intersubband transitions; magnetic properties of solids; exchange energy and magnetic ordering; magneto-oscillatory phenomena; quantum Hall effect; superconducting phenomena and simple models. | true | Fall | Graduate | 4-0-8 | 6.6510 or 8.231 | null | false | false | false | False | False | False |
6.6600[J] | Nanostructure Fabrication | 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. | true | Spring | Graduate | 4-0-8 | 2.710, 6.2370, 6.2600, or permission of instructor | 2.391[J] | false | false | false | False | False | False |
6.6630[J] | Control of Manufacturing Processes | Statistical modeling and control in manufacturing processes. Use of experimental design and response surface modeling to understand manufacturing process physics. Defect and parametric yield modeling and optimization. Forms of process control, including statistical process control, run by run and adaptive control, and real-time feedback control. Application contexts include semiconductor manufacturing, conventional metal and polymer processing, and emerging micro-nano manufacturing processes. | true | Fall | Graduate | 3-0-9 | 2.008, 6.2600, or 6.3700 | 2.830[J] | false | false | false | False | False | False |
6.3000 | Signal Processing | Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design. | true | Fall, Spring | Undergraduate | 6-0-6 | 6.100A and 18.03 | null | false | false | true | False | False | False |
6.3010 | Signals, Systems and Inference | Covers signals, systems and inference in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization. Least-mean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters. | true | Spring | Undergraduate | 4-0-8 | 6.3000 and (6.3700, 6.3800, or 18.05) | null | false | false | false | False | False | False |
6.3020[J] | Fundamentals of Music Processing | Analyzes recorded music in digital audio form using advanced signal processing and optimization techniques to understand higher-level musical meaning. Covers fundamental tools like windowing, feature extraction, discrete and short-time Fourier transforms, chromagrams, and onset detection. Addresses analysis methods including dynamic time warping, dynamic programming, self-similarity matrices, and matrix factorization. Explores a variety of applications, such as event classification, audio alignment, chord recognition, structural analysis, tempo and beat tracking, content-based audio retrieval, and audio decomposition. Students taking graduate version complete different assignments. | true | Fall | Undergraduate | 3-0-9 | 6.3000 and 21M.051 | 21M.387[J] | false | false | false | False | Arts | False |
6.7000 | Discrete-Time Signal Processing | Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion. Noise shaping. Flowgraph structures for DT systems. IIR and FIR filter design techniques. Parametric signal modeling, linear prediction, and lattice filters. Discrete Fourier transform, DFT computation, and FFT algorithms. Spectral analysis, time-frequency analysis, relation to filter banks. Multirate signal processing, perfect reconstruction filter banks, and connection to wavelets. | true | Fall | Graduate | 4-0-8 | 6.3010 | null | false | false | false | False | False | False |
6.7010 | Digital Image Processing | 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. | true | Spring | Graduate | 3-0-9 | 6.3000 and 6.3700 | null | false | false | false | False | False | False |
6.7020 | Array Processing | 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. | true | Fall | Graduate | 3-2-7 | 6.7000 and (2.687 or (6.3010 and 18.06)) | null | false | false | false | False | False | False |
6.3100 | Dynamical System Modeling and Control Design | 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 online 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 taking graduate version complete additional problems and labs. | true | Fall, Spring | Undergraduate | 4-4-4 | Physics II (GIR) and (18.06 or 18.C06) | null | true | false | false | False | False | False |
6.3102 | Dynamical System Modeling and Control Design | 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. | true | Fall, Spring | Graduate | 4-4-4 | Physics II (GIR) and (18.06 or 18.C06) | null | false | false | false | False | False | False |
6.7100[J] | Dynamic Systems and Control | 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. | true | Spring | Graduate | 4-0-8 | 6.3000 and 18.06 | 16.338[J] | false | false | false | False | False | False |
6.7110 | Multivariable Control Systems | Computer-aided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness trade-offs. Model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; nonlinear effects. Computer-aided (MATLAB) design homework using models of physical processes. | true | Fall | Graduate | 3-0-9 | 6.7100 or 16.31 | null | false | false | false | False | False | False |
6.7120 | Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems | 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. | true | Fall | Undergraduate | 4-0-8 | 6.2200, (6.2000 and 6.3100), or permission of instructor | null | false | false | false | False | False | False |
6.7121 | Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems | 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. | true | Fall | Graduate | 4-0-8 | 6.2200, (6.2000 and 6.3100), or permission of instructor | null | false | false | false | False | False | False |
6.3260[J] | Networks | Highlights common principles that permeate the functioning of diverse technological, economic and social networks. Utilizes three sets of tools for analyzing networks -- random graph models, optimization, and game theory -- to study informational and learning cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; control and use of energy networks; and biological networks. Students taking graduate version complete additional assignments. | true | Spring | Undergraduate | 4-0-8 | 6.3700 or 14.30 | 14.15[J] | false | false | false | False | Social Sciences | False |
6.7210[J] | Introduction to Mathematical Programming | Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; robust optimization; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness. | true | Fall | Graduate | 4-0-8 | 18.06 | 15.081[J] | false | false | false | False | False | False |
6.7220[J] | Nonlinear Optimization | 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. | true | Spring | Graduate | 4-0-8 | 18.06 and (18.100A, 18.100B, or 18.100Q) | 15.084[J] | false | false | false | False | False | False |
6.7230[J] | Algebraic Techniques and Semidefinite Optimization | 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. | true | Spring | Graduate | 3-0-9 | 6.7210 or 15.093 | 18.456[J] | false | false | false | False | False | False |
6.7240 | Game Theory with Engineering Applications | Introduction to fundamentals of game theory and mechanism design with motivations for each topic drawn from engineering applications (including distributed control of wireline/wireless communication networks, transportation networks, pricing). Emphasis on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notion in different environments. Topics include normal form games, supermodular games, dynamic games, repeated games, games with incomplete/imperfect information, mechanism design, cooperative game theory, and network games. | true | Fall | Graduate | 4-0-8 | 6.3702 | null | false | false | false | False | False | False |
6.7250 | Optimization for Machine Learning | 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. | true | Spring | Graduate | 3-0-9 | 6.3900 and 18.06 | null | false | false | false | False | False | False |
6.7260 | Network Science and Models | 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. | true | Spring | Graduate | 3-0-9 | 6.3702 and 18.06 | null | false | false | false | False | False | False |
6.7300[J] | Introduction to Modeling and Simulation | Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socio-economical systems. Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations (e.g., automatic assembly of constitutive and conservation principles); linear system solvers (sparse and iterative); nonlinear solvers (Newton and homotopy); ordinary, time-periodic and partial differential equation solvers; and model order reduction. Students develop their own models and simulators for self-proposed applications, with an emphasis on creativity, teamwork, and communication. Prior basic linear algebra required and at least one numerical programming language (e.g., MATLAB, Julia, Python, etc.) helpful. | true | Fall | Graduate | 3-6-3 | 18.03 or 18.06 | 2.096[J], 16.910[J] | false | false | false | False | False | False |
6.7310[J] | Introduction to Numerical Methods | Advanced introduction to numerical analysis: accuracy and efficiency of numerical algorithms. In-depth coverage of sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems). Floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) may also be surveyed. Final project involves some programming. | false | Spring | Graduate | 3-0-9 | 18.06, 18.700, or 18.701 | 18.335[J] | false | false | false | False | False | False |
6.7320[J] | Parallel Computing and Scientific Machine Learning | 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. | true | Spring | Graduate | 3-0-9 | 18.06, 18.700, or 18.701 | 18.337[J] | false | false | false | False | False | False |
6.7330[J] | Numerical Methods for Partial Differential Equations | Covers the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential and integral equations. Topics include mathematical formulations; finite difference, finite volume, finite element, and boundary element discretization methods; and direct and iterative solution techniques. The methodologies described form the foundation for computational approaches to engineering systems involving heat transfer, solid mechanics, fluid dynamics, and electromagnetics. Computer assignments requiring programming. | true | Fall | Graduate | 3-0-9 | 18.03 or 18.06 | 2.097[J], 16.920[J] | false | false | false | False | False | False |
6.7340[J] | Fast Methods for Partial Differential and Integral Equations | 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. | true | Fall, Spring | Graduate | 3-0-9 | 6.7300, 16.920, 18.085, 18.335, or permission of instructor | 18.336[J] | false | false | false | False | False | False |
6.3400 | Introduction to EECS via Communication Networks | Studies key concepts, systems, and algorithms to reliably communicate data in settings ranging from the cellular phone network and the Internet to deep space. Weekly laboratory experiments explore these areas in depth. Topics presented in three modules - bits, signals, and packets - spanning the multiple layers of a communication system. Bits module includes information, entropy, data compression algorithms, and error correction with block and convolutional codes. Signals module includes modeling physical channels and noise, signal design, filtering and detection, modulation, and frequency-division multiplexing. Packets module includes switching and queuing principles, media access control, routing protocols, and data transport protocols. | true | Fall | Undergraduate | 4-4-4 | 6.100A | null | true | false | false | False | False | False |
6.7410 | Principles of Digital Communication | Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. | true | Fall | Graduate | 3-0-9 | (6.3000 or 6.3102) and (6.3700, 6.3800, or 18.05) | null | false | false | false | False | False | False |
6.7411 | Principles of Digital Communication | Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. | true | Fall | Undergraduate | 3-0-9 | (6.3000, 6.3100, or 6.3400) and (6.3700, 6.3800, or 18.05) | null | false | false | false | False | False | False |
6.7420 | Heterogeneous Networks: Architecture, Transport, Proctocols, and Management | Introduction to modern heterogeneous networks and the provision of heterogeneous services. Architectural principles, analysis, algorithmic techniques, performance analysis, and existing designs are developed and applied to understand current problems in network design and architecture. Begins with basic principles of networking. Emphasizes development of mathematical and algorithmic tools; applies them to understanding network layer design from the performance and scalability viewpoint. Concludes with network management and control, including the architecture and performance analysis of interconnected heterogeneous networks. Provides background and insight to understand current network literature and to perform research on networks with the aid of network design projects. | true | Fall | Graduate | 4-0-8 | 6.1200 or 6.3700 | null | false | false | false | False | False | False |
6.7430 | Optical Networks | 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. | true | Spring | Graduate | 3-0-9 | 6.1200 or 6.3700 | null | false | false | false | False | False | False |
6.7440 | Principles of Wireless Communication | Introduction to design, analysis, and fundamental limits of wireless transmission systems. Wireless channel and system models; fading and diversity; resource management and power control; multiple-antenna and MIMO systems; space-time codes and decoding algorithms; multiple-access techniques and multiuser detection; broadcast codes and precoding; cellular and ad-hoc network topologies; OFDM and ultrawideband systems; architectural issues. | true | Fall | Graduate | 3-0-9 | 6.7410 | null | false | false | false | False | False | False |
6.7450[J] | Data-Communication Networks | Provides an introduction to data networks with an analytic perspective, using wireless networks, satellite networks, optical networks, the internet and data centers as primary applications. Presents basic tools for modeling and performance analysis. Draws upon concepts from stochastic processes, queuing theory, and optimization. | true | Fall | Graduate | 3-0-9 | 6.3700 or 18.204 | 16.37[J] | false | false | false | False | False | False |
6.7460 | Essential Coding Theory | 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. | true | Spring | Graduate | 3-0-9 | 6.1210 and 6.1400 | null | false | false | false | False | False | False |
6.7470 | Information Theory | Mathematical definitions of information measures, convexity, continuity, and variational properties. Lossless source coding; variable-length and block compression; Slepian-Wolf theorem; ergodic sources and Shannon-McMillan theorem. Hypothesis testing, large deviations and I-projection. Fundamental limits of block coding for noisy channels: capacity, dispersion, finite blocklength bounds. Coding with feedback. Joint source-channel problem. Rate-distortion theory, vector quantizers. Advanced topics include Gelfand-Pinsker problem, multiple access channels, broadcast channels (depending on available time). | true | Fall | Graduate | 3-0-9 | 6.3700 | null | false | false | false | False | False | False |
Subsets and Splits