Electronics, Computers, and Systems
6.301 Solid-State Circuits

( )
Prereq: 6.012
Units: 3-2-7
URL: http://web.mit.edu/6.301/www/
Lecture: TR1-2.30 (32-124)
Analysis and design of transistor circuits, based directly on the semiconductor physics and transistor circuit models developed in 6.012. High-frequency and low-frequency design calculations and simulation of multistage transistor circuits. Trans-linear circuits. Introduction to operational-amplifier design and application. Some previous laboratory experience assumed.
H. S. Lee Textbooks (Fall 2016)
6.302 Feedback System Design

( )
(Subject meets with 6.320)
Prereq: 6.003, 2.003, or 16.002
Units: 4-2-6
URL: http://web.mit.edu/6.302/www/
Learn-by-design introduction to continuous and discrete-time system modeling and feedback control. Topics include performance metrics; time- and frequency-domain model extraction and classical control; and basic state-space control. Students apply the control concepts in weekly labs and in a midterm project. Labs involve designing circuits and software, and using sensors and a high-performance microcontroller, to address control problems, such as positioning a motor- or propeller-actuated robot arm, reducing distortion in a PWM-based audio amplifier, eliminating field crosstalk for a magnetic-resonance imager, stabilizing magnetic levitation, balancing a two-wheel vehicle. Students taking graduate version complete additional assignments and an extra lab on observer-based state-space control. Intended for students who have previous laboratory experience with electronic systems.
J. D. Steinmeyer, J. K. White
6.320 Feedback System Design
(New)

( )
(Subject meets with 6.302)
Prereq: 6.003, 2.004, 2.04A, or 16.002
Units: 4-2-6
Learn-by-design introduction to continuous and discrete-time system modeling and feedback control. Topics include performance metrics; time- and frequency-domain model extraction and classical control; and basic state-space control. Students apply the control concepts in weekly labs and in a midterm project. Labs involve designing circuits and software, and using sensors and a high-performance microcontroller, to address control problems, such as positioning a motor- or propeller-actuated robot arm, reducing distortion in a PWM-based audio amplifier, eliminating field crosstalk for a magnetic-resonance imager, stabilizing magnetic levitation, balancing a two-wheel vehicle. Students taking graduate version complete additional assignments and an extra lab on observer-based state-space control. Intended for students who have previous laboratory experience with electronic systems. students taking graduate version complete additional assignments.
J. D. Steinmeyer, J. K. White
6.332, 6.333 Advanced Topics in Circuits

( , )  Not offered regularly; consult department
Prereq: Permission of instructor
Units: 3-0-9
6.332: URL: https://www.eecs.mit.edu//academics-admissions/academic-information/subject-updates-st-2013?shib-logout=1
Advanced study of topics in circuits. Specific focus varies from year to year. Consult department for details.
Consult Department
6.334 Power Electronics

( )
Prereq: 6.012
Units: 3-0-9
URL: http://web.mit.edu/course/6/6.334/
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.
D. J. Perreault
6.335[J] Fast Methods for Partial Differential and Integral Equations

( )
(Same subject as 18.336[J])
Prereq: 6.336, 16.920, 18.085, 18.335, or permission of instructor
Units: 3-0-9
Lecture: MW9.30-11 (2-146)
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.
C. Perez No required or recommended textbooks
6.336[J] Introduction to Numerical Simulation

( )
(Same subject as 2.096[J], 16.910[J])
Prereq: 18.03 or 18.06
Units: 3-3-6
Lecture: MW1-2.30 (32-141)
Introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical engineering, biology, and materials science. Topics include mathematical formulations (techniques for automatic assembly of mathematical problems from physics' principles); sparse, direct and iterative solution techniques for linear systems; Newton and Homotopy methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations; accelerated methods for integral equations; techniques for automatic generation of compact dynamical system models and model order reduction.
L. Daniel, J. K. White No required or recommended textbooks
6.337[J] Introduction to Numerical Methods

( )
(Same subject as 18.335[J])
Prereq: 18.06, 18.700, or 18.701
Units: 3-0-9
URL: http://math.mit.edu/classes/18.335
Advanced introduction to numerical analysis. Surveys major topics that arise at various levels of solving classic numerical problems, such as systems of linear equations, eigenvalue equations, and least squares problems. Specific topics include matrix factorizations (QR, SVD, LU, Cholesky); direct and iterative methods to solve linear systems (Gaussian elimination, Krylov subspace methods); numerical algorithms to solve eigenvalue equations (Rayleigh quotient iteration, inverse iteration, QR algorithm); conditioning of problems and stability of algorithms; and floating point arithmetic.
W. Shin
6.338[J] Parallel Computing

( )
(Same subject as 18.337[J])
Prereq: 18.06, 18.700, or 18.701
Units: 3-0-9
URL: http://beowulf.csail.mit.edu/18.337/index.html
Lecture: MW2-3.30 (4-237)
Interdisciplinary introduction to computing with Julia. Covers scientific computing and data analysis problems. Combines knowledge from computer science and computational science illustrating Julia's new approach to scientific computing. Sample scientific computing topics include dense and sparse linear algebra, Fourier transforms, data handling, and N-body problems. Provides direct experience with programming traditional-style supercomputing as well as working with modern cloud computing stacks.
A. Edelman No textbook information available
6.339[J] Numerical Methods for Partial Differential Equations

( )
(Same subject as 2.097[J], 16.920[J])
Prereq: 18.03 or 18.06
Units: 3-0-9
Lecture: MW9.30-11 (4-163)
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.
Q. Wang, J. K. White No textbook information available
6.341 Discrete-Time Signal Processing

( )
Prereq: 6.011
Units: 4-0-8
URL: http://web.mit.edu/6.341/www/
Lecture: TR11-12.30 (32-124) Recitation: F11 (4-145) or F2 (4-145) +final
Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion. Noise shaping. Flowgraph structures for DT systems. Lattice filters. Time- and frequency-domain design techniques for IIR and FIR filters. Parametric signal modeling, linear prediction, and the relation to lattice filters. Discrete Fourier transform (DFT). Computation of the DFT including FFT algorithms. Short-time Fourier analysis and relation to filter banks. Multirate techniques. Perfect reconstruction filter banks and their relation to wavelets.
A. V. Oppenheim, J. Ward Textbooks (Fall 2016)
6.344 Digital Image Processing

( )
Prereq: 6.003, 6.041B
Units: 3-0-9
Digital images as two-dimensional signals. Digital signal processing theories used for digital image processing, including one-dimensional and two-dimensional convolution, Fourier transform, discrete Fourier transform, and discrete cosine transform. Image processing basics. Image enhancement. Image restoration. Image coding and compression. Video processing including video coding and compression. Additional topics including digital high-definition television systems.
J. S. Lim
6.345[J] Automatic Speech Recognition

 ( )
(Same subject as HST.728[J])
Prereq: 6.011, 6.036
Units: 3-1-8
URL: http://courses.csail.mit.edu/6.345/
Introduces the rapidly developing fields of automatic speech recognition and spoken language processing. Topics include acoustic theory of speech production, acoustic-phonetics, signal representation, acoustic and language modeling, search, hidden Markov modeling, deep neural networks, system robustness, adaptation, and other related speech processing topics. Lecture material intersperses theory with practice. Includes problem sets, laboratory exercises, and opened-ended term project.
V. W. Zue, J. R. Glass
6.347, 6.348 Advanced Topics in Signals and Systems

( , )  Not offered regularly; consult department
Prereq: Permission of instructor
Units: 3-0-9
6.348: URL: http://www.eecs.mit.edu/academics-admissions/academic-information/subject-updates-ft-2014
Advanced study of topics in signals and systems. Specific focus varies from year to year.
Consult Department
6.374 Analysis and Design of Digital Integrated Circuits

( )
Prereq: 6.012, 6.004
Units: 3-3-6
Lecture: TR11-12.30 (34-302) Lab: TBA
Device and circuit level optimization of digital building blocks. MOS device models including Deep Sub-Micron effects. 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. Testing of integrated circuits. Extensive custom and standard cell layout and simulation in design projects and software labs.
V. Sze, A. P. Chandrakasan Textbooks (Fall 2016)
6.375 Complex Digital Systems Design

 ( )
Prereq: 6.004
Units: 5-5-2
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.
Arvind
Probabilistic Systems and Communication
6.431A Introduction to Probability I
(New)

( , ); first half of term
(Subject meets with 6.041A)
Prereq: Calculus II (GIR)
Units: 2-0-4
Ends Oct 21. Lecture: MW12 (34-101) Recitation: TR11 (24-121) or TR12 (24-121) or TR1 (24-121) or TR2 (24-121)
Provides an introduction to probability theory and the modeling and analysis of probabilistic systems. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation. Limit Theorems. Students taking graduate version complete additional assignments.
P. Jaillet, J. N. Tsitsiklis No textbook information available
6.431B Introduction to Probability II
(New)

( , ); second half of term
(Subject meets with 6.041B)
Prereq: 6.431A
Units: 2-0-4
Begins Oct 24. Lecture: MW12 (34-101) Recitation: TR11 (24-121) or TR12 (24-121) or TR1 (24-121) or TR2 (24-121) +final
Further topics in probability. Bayesian estimation and hypothesis testing. Elements of statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.
P. Jaillet, J. N. Tsitsiklis No textbook information available
6.434[J] Statistics for Engineers and Scientists

( )
(Same subject as 16.391[J])
Prereq: Calculus II (GIR), 18.06, 6.431B, or permission of instructor
Units: 3-0-9
Lecture: MW1-2.30 (8-205)
Rigorous introduction to fundamentals of statistics motivated by engineering applications. Topics include exponential families, order statistics, sufficient statistics, estimation theory, hypothesis testing, measures of performance, notions of optimality, analysis of variance (ANOVA), simple linear regression, and selected topics.
M. Win, J. N. Tsitsiklis No textbook information available
6.436[J] Fundamentals of Probability

( )
(Same subject as 15.085[J])
Prereq: Calculus II (GIR)
Units: 4-0-8
Lecture: MW2.30-4 (E51-345) Recitation: F2 (66-144) +final
Introduction to probability theory. Probability spaces and measures. Discrete and continuous random variables. Conditioning and independence. Multivariate normal distribution. Abstract integration, expectation, and related convergence results. Moment generating and characteristic functions. Bernoulli and Poisson process. Finite-state Markov chains. Convergence notions and their relations. Limit theorems. Familiarity with elementary notions in probability and real analysis is desirable.
J. N. Tsitsiklis, D. Gamarnik Textbooks (Fall 2016)
6.437 Inference and Information

( )
Prereq: 6.008, 6.041B, or 6.436
Units: 4-0-8
Introduction to principles of Bayesian and non-Bayesian statistical inference. Hypothesis testing and parameter estimation, sufficient statistics; exponential families. EM agorithm. Log-loss inference criterion, entropy and model capacity. Kullback-Leibler distance and information geometry. Asymptotic analysis and large deviations theory. Model order estimation; nonparametric statistics. Computational issues and approximation techniques; Monte Carlo methods. Selected special topics such as universal prediction and compression.
P. Golland, G. W. Wornell
6.438 Algorithms for Inference

( )
Prereq: 6.008, 6.041B, or 6.436; 18.06
Units: 4-0-8
Lecture: TR9.30-11 (4-370) Recitation: F10 (8-119) or F11 (8-119) +final
Introduction to statistical inference with probabilistic graphical models. Directed and undirected graphical models, and factor graphs, over discrete and Gaussian distributions; hidden Markov models, linear dynamical systems. Sum-product and junction tree algorithms; forward-backward algorithm, Kalman filtering and smoothing. Min-sum and Viterbi algorithms. Variational methods, mean-field theory, and loopy belief propagation. Particle methods and filtering. Building graphical models from data, including parameter estimation and structure learning; Baum-Welch and Chow-Liu algorithms. Selected special topics.
P. Golland, G. W. Wornell, D. Shah No textbook information available
6.440 Essential Coding Theory

 ( )
Prereq: 6.006, 6.045
Units: 3-0-9
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.
Staff
6.441 Information Theory

( )
Prereq: 6.041B
Units: 3-0-9
URL: http://web.mit.edu/6.441/www/
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).
M. Medard, Y. Polyanskiy, L. Zheng
6.442 Optical Networks

 ( )
Prereq: 6.041B or 6.042
Units: 3-0-9
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.
V. W. S. Chan
6.443[J] Quantum Information Science

( )
(Same subject as 8.371[J], 18.436[J])
Prereq: 18.435
Units: 3-0-9
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.
I. Chuang
6.450 Principles of Digital Communication

( )
Prereq: 6.011
Units: 3-0-9
Lecture: MW9.30-11 (36-155) +final
Communication sources and channels; data compression; entropy and the AEP; Lempel-Ziv universal coding; scalar and vector quantization; L2 waveforms; signal space and its representation by sampling and other expansions; aliasing; the Nyquist criterion; PAM and QAM modulation; Gaussian noise and random processes; detection and optimal receivers; fading channels and wireless communication; introduction to communication system design.
M. Medard, L. Zheng Textbooks (Fall 2016)
6.452 Principles of Wireless Communication

 ( )
Prereq: 6.450
Units: 3-0-9
Subject Cancelled
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.
G. W. Wornell, L. Zheng
6.453 Quantum Optical Communication

( )
Prereq: 6.011, 18.06
Units: 3-0-9
Lecture: TR1-2.30 (8-205)
Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection. Second-order nonlinear optics: phasematched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and polarization entanglement. Quantum systems theory: optimum binary detection; quantum precision measurements; quantum cryptography; and quantum teleportation.
J. H. Shapiro No required or recommended textbooks
6.454 Graduate Seminar in Area I

 ( )
Prereq: Permission of instructor
Units: 2-0-4
URL: http://web.mit.edu/6.454/www/
Student-run advanced graduate seminar with focus on topics in communications, control, signal processing, optimization. Participants give presentations outside of their own research to expose colleagues to topics not covered in the usual curriculum. Recent topics have included compressed sensing, MDL principle, communication complexity, linear programming decoding, biology in EECS, distributed hypothesis testing, algorithms for random satisfaction problems, and cryptogaphy. Open to advanced students from all areas of EECS. Limited to 12.
L. Zheng, D. Shah
6.456 Array Processing

 ( )
Prereq: 6.341; 2.687, or 6.011 and 18.06
Units: 3-2-7
Subject Cancelled
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.
Staff
Bioelectrical Engineering
6.503 Foundations of Algorithms and Computational Techniques in Systems Biology

 ( )
(Subject meets with 6.581[J], 20.482[J])
Prereq: 6.021, 6.034, 6.046, 6.336, 18.417, or permission of instructor
Units: 3-0-9
Illustrates computational approaches to solving problems in systems biology. Uses a series of case studies to demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. Covers several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology. Students taking graduate version complete additional assignments.
B. Tidor, J. K. White
6.521[J] Cellular Neurophysiology

( )
(Same subject as 2.794[J], 20.470[J], HST.541[J]) (Subject meets with 2.791[J], 6.021[J], 20.370[J])
Prereq: Physics II (GIR); 18.03; 2.005, 6.002, 6.003, 6.071, 10.301, 20.110, or permission of instructor
Units: 5-2-5
Lecture: MWF10 (32-144) Lab: TBA Recitation: T12 (34-303) or T4 (34-302) +final
Meets with undergraduate subject 6.021J. Requires the completion of more advanced home problems and/or an additional project.
J. Han, T. Heldt Textbooks (Fall 2016)
6.522[J] Quantitative Physiology: Organ Transport Systems

( )
(Same subject as 2.796[J]) (Subject meets with 2.792[J], 6.022[J], HST.542[J])
Prereq: 2.006 or 6.013; 6.021
Units: 4-2-6
Application of the principles of energy and mass flow to major human organ systems. Mechanisms of regulation and homeostasis. Anatomical, physiological and pathophysiological features of the cardiovascular, respiratory and renal systems. Systems, features and devices that are most illuminated by the methods of physical sciences. Laboratory work includes some animal studies. Students taking graduate version complete additional assignments. Application of the principles of energy and mass flow to major human organ systems. Mechanisms of regulation and homeostasis. Anatomical, physiological and pathophysiological features of the cardiovascular, respiratory and renal systems. Systems, features and devices that are most illuminated by the methods of physical sciences. Laboratory work includes some animal studies. Students taking graduate version complete additional assignments.
T. Heldt, R. G. Mark, C. M. Stultz
6.524[J] Molecular, Cellular, and Tissue Biomechanics

( )
(Same subject as 2.798[J], 3.971[J], 10.537[J], 20.410[J])
Prereq: Biology (GIR); 2.002, 2.006, 6.013, 10.301, or 10.302
Units: 3-0-9
Lecture: TR10.30-12 (2-143)
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.
R. D. Kamm, K. J. Van Vliet No textbook information available
6.525[J] Medical Device Design

( )
(Same subject as 2.75[J], HST.552[J]) (Subject meets with 2.750[J], 6.025[J])
Prereq: 2.72, 6.101, 6.111, 6.115, 22.071, or permission of instructor
Units: 3-0-9
Lecture: MW1-2.30 (3-270)
Application of mechanical and electrical engineering fundamentals to the design of medical devices that address clinical needs. Students work in small teams on a major project to translate a clinical challenge into a proof-of-concept prototype device. Students conduct user analysis, develop design specifications, and follow a structured process to cultivate creative designs and apply analytical techniques to optimize them. They deepen their understanding of art and intellectual property by researching prior representations. Develops practical skills in prototyping and testing as well as project management. Includes lectures, problem sets and exams that focus on design fundamentals. Instruction and practice in written and oral communication provided. Students taking graduate version complete additional assignments. Enrollment limited.
A. H. Slocum, G. Hom No required or recommended textbooks
6.542[J] Laboratory on the Physiology, Acoustics, and Perception of Speech

 ( )
(Same subject as 24.966[J], HST.712[J])
Prereq: Permission of instructor
Units: 2-2-8
Experimental investigations of speech processes. Topics: measurement of articulatory movements; measurements of pressures and airflows in speech production; computer-aided waveform analysis and spectral analysis of speech; synthesis of speech; perception and discrimination of speechlike sounds; speech prosody; models for speech recognition; speech development; and other topics. Recommended prerequisites: 6.002 or 18.03.
L. D. Braida, S. Shattuck-Hufnagel
6.544, 6.545 Advanced Topics in BioEECS

( , )  Not offered regularly; consult department
Prereq: Permission of instructor
Units: 3-0-9
Advanced study of topics in BioEECS. Specific focus varies from year to year. Consult department for details.
Consult Department
6.552[J] Signal Processing by the Auditory System: Perception

 ( )
(Same subject as HST.716[J])
Prereq: 6.003; 6.041B or 6.431B; or permission of instructor
Units: 3-0-9
Subject Cancelled
Studies information processing performance of the human auditory system in relation to current physiological knowledge. Examines mathematical models for the quantification of auditory-based behavior and the relation between behavior and peripheral physiology, reflecting the tono-topic organization and stochastic responses of the auditory system. Mathematical models of psychophysical relations, incorporating quantitative knowledge of physiological transformations by the peripheral auditory system.
L. D. Braida
6.555[J] Biomedical Signal and Image Processing

( )
(Same subject as 16.456[J], HST.582[J])
Prereq: 6.003, 2.004, 16.004, or 18.085
Units: 3-4-5
URL: http://web.mit.edu/6.555/www/
Fundamentals of digital signal processing with particular emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for data acquisition, imaging, filtering, and feature extraction. Laboratory projects provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging.
J. Greenberg, E. Adalsteinsson, W. Wells
6.556[J] Data Acquisition and Image Reconstruction in MRI

( )
(Same subject as HST.580[J])
Prereq: 6.011
Units: 3-0-9
Lecture: TR11-12.30 (1-150)
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.
E. Adalsteinsson No textbook information available
6.557[J] Biomolecular Feedback Systems

( )
(Same subject as 2.18[J]) (Subject meets with 2.180[J], 6.027[J])
Prereq: 18.03, Biology (GIR), or permission of instructor
Units: 3-0-9
Comprehensive introduction to dynamics and control of biomolecular systems with emphasis on design/analysis techniques from control theory. Provides a review of biology concepts, regulation mechanisms, and models. Covers basic enabling technologies, engineering principles for designing biological functions, modular design techniques, and design limitations. Students taking graduate version complete additional assignments.
D. Del Vecchio, R. Weiss
6.561[J] Fields, Forces, and Flows in Biological Systems

( )
(Same subject as 2.795[J], 10.539[J], 20.430[J])
Prereq: 6.013, 2.005, 10.302, or permission of instructor
Units: 3-0-9
Lecture: MW1-2.30 (32-124)
Molecular diffusion, diffusion-reaction, conduction, convection in biological systems; fields in heterogeneous media; electrical double layers; Maxwell stress tensor, electrical forces in physiological systems. Fluid and solid continua: equations of motion useful for porous, hydrated biological tissues. Case studies of membrane transport, electrode interfaces, electrical, mechanical, and chemical transduction in tissues, convective-diffusion/reaction, electrophoretic, electroosmotic flows in tissues/MEMs, and ECG. Electromechanical and physicochemical interactions in cells and biomaterials; musculoskeletal, cardiovascular, and other biological and clinical examples.
M. Bathe, A. J. Grodzinsky Textbooks (Fall 2016)
6.580[J] Principles of Synthetic Biology

( )
(Same subject as 20.305[J]) (Subject meets with 6.589[J], 20.405[J])
Prereq: None
Units: 3-0-9
Lecture: TR11-12.30 (9-057) +final
Introduces the basics of synthetic biology, including quantitative cellular network characterization and modeling. Considers the discovery and genetic factoring of useful cellular activities into reusable functions for design. Emphasizes the principles of biomolecular system design and diagnosis of designed systems. Illustrates cutting-edge applications in synthetic biology and enhances skills in analysis and design of synthetic biological applications. Students taking graduate version complete additional assignments.
R. Weiss No textbook information available
6.581[J] Foundations of Algorithms and Computational Techniques in Systems Biology

 ( )
(Same subject as 20.482[J]) (Subject meets with 6.503)
Prereq: 6.021, 6.034, 6.046, 6.336, 18.417, or permission of instructor
Units: 3-0-9
Illustrates computational approaches to solving problems in systems biology. Uses a series of case studies to demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. Covers several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology. Students taking graduate version complete additional assignments.
B. Tidor, J. K. White
6.589[J] Principles of Synthetic Biology

( )
(Same subject as 20.405[J]) (Subject meets with 6.580[J], 20.305[J])
Prereq: None
Units: 3-0-9
Lecture: TR11-12.30 (9-057) +final
Introduces the basics of synthetic biology, including quantitative cellular network characterization and modeling. Considers the discovery and genetic factoring of useful cellular activities into reusable functions for design. Emphasizes the principles of biomolecular system design and diagnosis of designed systems. Illustrates cutting-edge applications in synthetic biology and enhances skills in analysis and design of synthetic biological applications. Students taking graduate version complete additional assignments.
R. Weiss No textbook information available
Electrodynamics
6.602 Fundamentals of Photonics

 ( )
(Subject meets with 6.621)
Prereq: 2.71, 6.013, or 8.07
Units: 3-0-9
Subject Cancelled
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.
D. R. Englund
6.621 Fundamentals of Photonics

 ( )
(Subject meets with 6.602)
Prereq: 2.71, 6.013, or 8.07
Units: 3-0-9
Subject Cancelled
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.
D. R. Englund
6.630 Electromagnetics

( )
Prereq: 6.003 or 6.007
Units: 4-0-8
URL: http://cetaweb.mit.edu/6.630/
Lecture: WF2.30-4 (32-144)
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.
L. Daniel, M. R. Watts Textbooks (Fall 2016)
6.631 Optics and Photonics

( )
Prereq: 6.013 or 8.07
Units: 3-0-9
Lecture: MW3-4.30 (36-372) +final
Introduction to fundamental concepts and techniques of optics, photonics, and fiber optics. Review of Maxwell's equations, light propagation, and reflection from dielectrics mirrors and filters. Interferometers, filters, and optical imaging systems. Fresnel and Fraunhoffer diffraction theory. Propagation of Gaussian beams and laser resonator design. Optical waveguides and optical fibers. Optical waveguide and photonic devices.
J. G. Fujimoto Textbooks (Fall 2016)
6.632 Electromagnetic Wave Theory

 ( )
Prereq: 6.013, 6.630, or 8.07
Units: 3-0-9
Solutions to Maxwell equations and physical interpretation. Topics include waves in media, equivalence principle, duality and complementarity, Huygens' principle, Fresnel and Fraunhofer diffraction, radiation and dyadic Green's functions, scattering, metamaterials, and plasmonics, mode theory, dielectric waveguides, and resonators. Examples deal with limiting cases of electromagnetic theory, multi-port elements, filters and antennas. Discusses current topics in microwave and photonic devices.
M. R. Watts
6.634[J] Nonlinear Optics

( )
(Same subject as 8.431[J])
Prereq: 6.013 or 8.07
Units: 3-0-9
Techniques of nonlinear optics with emphasis on fundamentals for research and engineering in optics, photonics, and spectroscopy. Electro optic modulators, harmonic generation, and frequency conversion devices. Nonlinear effects in optical fibers including self-phase modulation, nonlinear wave propagation, and solitons. Interaction of light with matter, laser operation, density matrix techniques, nonlinear spectroscopies, and femtosecond optics.
J. G. Fujimoto
6.637 Optical Signals, Devices, and Systems

( )
(Subject meets with 6.161)
Prereq: 6.003
Units: 3-0-9
Lecture: TR2.30-4 (34-304) Lab: TBA
Principles of operation and applications of devices and systems for 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; optical waveguides and fiber-optic communication systems; photodetectors; 2-D and 3-D optical storage technologies; adaptive optical systems; role of optics in next-generation computers. Student research paper on a specific contemporary topic required. Recommended prerequisites: 6.007 or 8.03.
C. Warde No textbook information available
6.641 Electromagnetic Fields, Forces, and Motion

 ( )
Prereq: 6.013
Units: 4-0-8
Electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Electromagnetic forces, force densities, and stress tensors, including magnetization and polarization. Thermodynamics of electromagnetic fields, equations of motion, and energy conservation. Applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.
J. H. Lang
6.642 Continuum Electromechanics

 ( )
Prereq: 6.641 or permission of instructor
Units: 4-0-8
Laws, approximations, and relations of continuum mechanics. Mechanical and electromechanical transfer relations. Statics and dynamics of electromechanical systems having a static equilibrium. Electromechanical flows. Field coupling with thermal and molecular diffusion. Electrokinetics. Streaming interactions. Application to materials processing, magnetohydrodynamic and electrohydrodynamic pumps and generators, ferrohydrodynamics, physiochemical systems, heat transfer, continuum feedback control, electron beam devices, and plasma dynamics.
Staff
6.644, 6.645 Advanced Topics in Applied Physics

 ( )
Prereq: Permission of instructor
Units: 3-0-9
6.645 Cancelled
Advanced study of topics in applied physics. Specific focus varies from year to year. Consult department for details.
Consult Department
6.685 Electric Machines

 ( )
Prereq: 6.061 or 6.690; or permission of instructor
Units: 3-0-9
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.
J. L. Kirtley, Jr.
6.690 Introduction to Electric Power Systems

 ( )
(Subject meets with 6.061)
Prereq: 6.002, 6.013
Units: 3-0-9
Electric circuit theory with application to power handling electric circuits. Modeling and behavior of electromechanical devices, including magnetic circuits, motors, and generators. Operational fundamentals of synchronous, induction and DC machinery. Interconnection of generators and motors with electric power transmission and distribution circuits. Power generation, including alternative and sustainable sources. Students taking graduate version complete additional assignments.
J. L. Kirtley, Jr.
6.695[J] Engineering, Economics and Regulation of the Electric Power Sector

( )
(Same subject as 15.032[J], IDS.505[J])
Prereq: Permission of instructor
Units: 3-0-9
Provides an in-depth and interdisciplinary look at electric power systems, focusing on regulation as the link among engineering, economic, legal, and environmental viewpoints. Topics include electricity markets, incentive regulation of network utilities, retail competition, tariff design, distributed generation, rural electrification, multinational electricity markets, environmental impacts, future of utilities and strategic sustainability issues under both traditional and competitive regulatory frameworks. Background in policy, microeconomics, or engineering desirable.
C. Vergara
Solid-State Materials and Devices
6.701 Introduction to Nanoelectronics

 ( )
(Subject meets with 6.719)
Prereq: 6.003
Units: 4-0-8
Subject Cancelled
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.
M. A. Baldo
6.717[J] Design and Fabrication of Microelectromechanical Systems

 ( )
(Same subject as 2.374[J]) (Subject meets with 2.372[J], 6.777[J])
Prereq: 6.003 or 2.003, Physics II (GIR); or permission of instructor
Units: 3-0-9
Provides an introduction to microsystem design. Covers material properties, microfabrication technologies, structural behavior, sensing methods, electromechanical actuation, thermal actuation and control, multi-domain modeling, noise, and microsystem packaging. Applies microsystem modeling, and manufacturing principles to the design and analysis a variety of microscale sensors and actuators (e.g., optical MEMS, bioMEMS, and inertial sensors). Emphasizes modeling and simulation in the design process. Students taking the graduate version complete additional assignments.
Staff
6.719 Nanoelectronics

 ( )
(Subject meets with 6.701)
Prereq: 6.003
Units: 4-0-8
Subject Cancelled
Meets with undergraduate subject 6.701, but requires the completion of additional/different homework assignments and or projects. See subject description under 6.701.
M. A. Baldo
6.720[J] Integrated Microelectronic Devices

( )
(Same subject as 3.43[J])
Prereq: 6.012 or 3.42
Units: 4-0-8
Lecture: MWRF10 (66-144) +final
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. Studies modern nanoscale devices, including electrostatic scaling, materials beyond Si, carrier transport from the diffusive to the ballistic regime. Emphasizes physical understanding of device operation through energy band diagrams and short-channel MOSFET device design. Includes device modeling exercises. Familiarity with MATLAB required. 2 Engineering Design Points.
D. A. Antoniadis, J. A. del Alamo, H. L. Tuller No textbook information available
6.728 Applied Quantum and Statistical Physics

( )
Prereq: 6.003, 18.06
Units: 4-0-8
Lecture: WF11-12.30 (26-328) Recitation: M11 (26-328) +final
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.
P. L. Hagelstein Textbooks (Fall 2016)
6.730 Physics for Solid-State Applications

( )
Prereq: 6.013, 6.728
Units: 5-0-7
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.
Q. Hu, R. Ram
6.731 Semiconductor Optoelectronics: Theory and Design

 ( )
Prereq: 6.728, 6.012
Units: 3-0-9
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.
R. J. Ram
6.732 Physics of Solids

( )
Prereq: 6.730 or 8.231
Units: 4-0-8
Lecture: MWF11 (34-303) Recitation: F10 (34-303)
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.
Q. Hu No textbook information available
6.735, 6.736 Advanced Topics in Materials, Devices, and Nanotechnology

( , )  Not offered regularly; consult department
Prereq: Permission of instructor
Units: 3-0-9
Advanced study of topics in materials, devices, and nanotechnology. Specific focus varies from year to year.
Consult Department
6.774 Physics of Microfabrication: Front End Processing

( ) Not offered regularly; consult department
Prereq: 6.152
Units: 3-0-9
Presents advanced physical models and practical aspects of front-end microfabrication processes, such as oxidation, diffusion, ion implantation, chemical vapor deposition, atomic layer deposition, etching, and epitaxy. Covers topics relevant to CMOS, bipolar, and optoelectronic device fabrication, including high k gate dielectrics, gate etching, implant-damage enhanced diffusion, advanced metrology, stress effects on oxidation, non-planar and nanowire device fabrication, SiGe and fabrication of process-induced strained Si. Exposure to CMOS process integration concepts, and impacts of processing on device characteristics. Students use modern process simulation tools.
J. L. Hoyt, L. R. Reif
6.775 CMOS Analog and Mixed-Signal Circuit Design

( )
Prereq: 6.301
Units: 3-0-9
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. Large signal considerations. 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. 4 Engineering Design Points.
H. S. Lee
6.776 High Speed Communication Circuits

 ( )
Prereq: 6.301
Units: 3-3-6
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.
R. Han
6.777[J] Design and Fabrication of Microelectromechanical Systems

 ( )
(Same subject as 2.372[J]) (Subject meets with 2.374[J], 6.717[J])
Prereq: 6.003 or 2.003, Physics II (GIR); or permission of instructor
Units: 3-0-9
Provides an introduction to microsystem design. Covers material properties, microfabrication technologies, structural behavior, sensing methods, electromechanical actuation, thermal actuation and control, multi-domain modeling, noise, and microsystem packaging. Applies microsystem modeling, and manufacturing principles to the design and analysis a variety of microscale sensors and actuators (e.g., optical MEMS, bioMEMS, and inertial sensors). Emphasizes modeling and simulation in the design process. Students taking the graduate version complete additional assignments. 4 Engineering Design Points.
Staff
6.780[J] Control of Manufacturing Processes

( )
(Same subject as 2.830[J])
Prereq: 2.008, 6.041B, 6.152, or 15.064
Units: 3-0-9
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.
D. E. Hardt, D. S. Boning
6.781[J] Nanostructure Fabrication

( )
(Same subject as 2.391[J])
Prereq: 6.152, 6.161, or 2.710; or permission of instructor
Units: 4-0-8
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.
K. K. Berggren
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