#nUnderactuated Robotics
#dNonlinear dynamics and control of underactuated mechanical systems,with an emphasis on machine learning methods. Topics include nonlinear dynamics of passive robots (walkers,swimmers,flyers),motion planning,partial feedback linearization,energy-shaping control,analytical optimal control,reinforcement learning/approximate optimal control,and the influence of mechanical design on control. Discussions include examples from biology and applications to legged locomotion,compliant manipulation,underwater robots,and flying machines.
#iRussell Tedrake
#t2010,spring


#nUnderactuated Robotics
#dNonlinear dynamics and control of underactuated mechanical systems,with an emphasis on machine learning methods. Topics include nonlinear dynamics of passive robots (walkers,swimmers,flyers),motion planning,partial feedback linearization,energy-shaping control,analytical optimal control,reinforcement learning/approximate optimal control,and the influence of mechanical design on control. Discussions include examples from biology and applications to legged locomotion,compliant manipulation,underwater robots,and flying machines.
#iRussell Tedrake
#t2009,spring


#nDynamic Programming and Stochastic Control
#dSequential decision-making via dynamic programming. Unified approach to optimal control of stochastic dynamic systems and Markovian decision problems. Applications in linear-quadratic control,inventory control,resource allocation,scheduling,and control of queues. Optimal decision making under perfect and imperfect state information. Certainty equivalent,open loop-feedback control,rollout,and other suboptimal control methods. Infinite horizon problems: discounted,stochastic shortest path,average cost,and semi-Markov models. Value and policy iteration. Approximations and neurodynamic programming.
#iD. P. Bertsekas
#t2009,fall


#nDynamic Programming and Stochastic Control
#dSequential decision-making via dynamic programming. Unified approach to optimal control of stochastic dynamic systems and Markovian decision problems. Applications in linear-quadratic control,inventory control,resource allocation,scheduling,and control of queues. Optimal decision making under perfect and imperfect state information. Certainty equivalent,open loop-feedback control,rollout,and other suboptimal control methods. Infinite horizon problems: discounted,stochastic shortest path,average cost,and semi-Markov models. Value and policy iteration. Approximations and neurodynamic programming.
#iD. P. Bertsekas
#t2008,fall


#nDynamic Systems and Control
#dLinear,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.
#iM. A. Dahleh,A. Megretski,G. C. Verghese
#t2009,fall


#nDynamic Systems and Control
#dLinear,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.
#iM. A. Dahleh,A. Megretski,G. C. Verghese
#t2008,fall


#nAdvanced Linear Control Systems
#dIntroduction to uncertain multivariable control systems,plus modeling assumptions and objectives. Stability of linear time invariant systems,coprime factorization,parametrization of all stabilizing compensators. Design using H2,H L1 -optimization. Stability and performance robustness in the presence of structured uncertainty. Special topics.
#iM. A. Dahleh,A. Megretski
#t2009,fall


#nDynamics of Nonlinear Systems
#dIntroduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration,contraction mapping theorem,and Bellman-Gronwall lemma. Stability of equilibria by Lyapunovs first and second methods. Feedback linearization. Application to nonlinear circuits and control systems.
#iJ. L. Wyatt,Jr.,A. Megretski,M. Dahleh
#t2009,fall


#nMultivariable Control Systems
#dComputer-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. 6 Engineering Design Points.
#iA. Megretski
#t2010,spring


#nIntroduction to Mathematical
#dIntroduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method,duality theory,sensitivity analysis,network flow problems,decomposition,integer programming,interior point algorithms for linear programming,and introduction to combinatorial optimization and NP-completeness.
#iJ. N. Tsitsiklis,D. Bertsimas
#t2009,fall


#nIntroduction to Mathematical
#dIntroduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method,duality theory,sensitivity analysis,network flow problems,decomposition,integer programming,interior point algorithms for linear programming,and introduction to combinatorial optimization and NP-completeness.
#iJ. N. Tsitsiklis,D. Bertsimas
#t2008,fall


#nNonlinear Programming
#dA unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient,conjugate direction,Newton,and quasi-Newton methods. Constrained optimization methods include feasible directions,projection,interior point,and Lagrange multiplier methods. Convex analysis,Lagrangian relaxation,nondifferentiable optimization,and applications in integer programming. Comprehensive treatment of optimality conditions,Lagrange multiplier theory,and duality theory. Applications drawn from control,communications,power systems,and resource allocation problems.
#iR. M. Freund,D. P. Bertsekas,G. Perakis
#t2010,spring


#nNonlinear Programming
#dA unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient,conjugate direction,Newton,and quasi-Newton methods. Constrained optimization methods include feasible directions,projection,interior point,and Lagrange multiplier methods. Convex analysis,Lagrangian relaxation,nondifferentiable optimization,and applications in integer programming. Comprehensive treatment of optimality conditions,Lagrange multiplier theory,and duality theory. Applications drawn from control,communications,power systems,and resource allocation problems.
#iR. M. Freund,D. P. Bertsekas,G. Perakis
#t2009,spring


#nConvex Analysis and Optimization
#dCore analytical issues of continuous optimization,duality,and saddle point theory,and development using a handful of unifying principles that can be easily visualized and readily understood. Discusses in detail the mathematical theory of convex sets and functions which are the basis for an intuitive,highly visual,geometrical approach to the subject. Convex optimization algorithms focus on large-scale problems,drawn from several types of applications,such as resource allocation and machine learning. Includes batch and incremental subgradient,cutting plane,proximal,and bundle methods.
#iD. P. Bertsekas
#t2010,spring


#nConvex Analysis and Optimization
#dCore analytical issues of continuous optimization,duality,and saddle point theory,and development using a handful of unifying principles that can be easily visualized and readily understood. Discusses in detail the mathematical theory of convex sets and functions which are the basis for an intuitive,highly visual,geometrical approach to the subject. Convex optimization algorithms focus on large-scale problems,drawn from several types of applications,such as resource allocation and machine learning. Includes batch and incremental subgradient,cutting plane,proximal,and bundle methods.
#iD. P. Bertsekas
#t2009,fall


#nGame Theory with Engineering Applications
#dIntroduction 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.
#iA. Ozdaglar
#t2010,spring


#nGame Theory with Engineering Applications
#dIntroduction 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.
#iA. Ozdaglar
#t2009,spring


#nOptimization Methods
#dIntroduces the principal algorithms for linear,network,discrete,nonlinear,dynamic optimization and optimal control. Emphasis on methodology and the underlying mathematical structures. Topics include the simplex method,network flow methods,branch and bound and cutting plane methods for discrete optimization,optimality conditions for nonlinear optimization,interior point methods for convex optimization,Newton's method,heuristic methods,and dynamic programming and optimal control methods. 
#iD. Bertsimas,P. Parrilo
#t2009,fall


#nOptimization Methods
#dIntroduces the principal algorithms for linear,network,discrete,nonlinear,dynamic optimization and optimal control. Emphasis on methodology and the underlying mathematical structures. Topics include the simplex method,network flow methods,branch and bound and cutting plane methods for discrete optimization,optimality conditions for nonlinear optimization,interior point methods for convex optimization,Newton's method,heuristic methods,and dynamic programming and optimal control methods. 
#iD. Bertsimas,P. Parrilo
#t2008,fall


#nAlgebraic Techniques and Semidefinite Optimization
#dTheory 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.
#iP. Parrilo
#t2010,spring


#nDiscrete Stochastic Processes
#dReview of probability and laws of large numbers,Poisson counting process and renewal processes,Markov chains (including Markov decision theory),branching processes,birth-death processes,and semi-Markov processes,continuous-time Markov chains and reversibility,random walks,martingales,and large deviations,applications from queueing,communication,control,and operations research.
#iR. G. Gallager,J. L. Wyatt
#t2010,spring


#nDiscrete Stochastic Processes
#dReview of probability and laws of large numbers,Poisson counting process and renewal processes,Markov chains (including Markov decision theory),branching processes,birth-death processes,and semi-Markov processes,continuous-time Markov chains and reversibility,random walks,martingales,and large deviations,applications from queueing,communication,control,and operations research.
#iR. G. Gallager,J. L. Wyatt
#t2009,spring


#nData-Communication Networks
#dModeling of the control processes in conventional and high-speed data communication networks. Develops and utilizes elementary concepts from queueing theory,algorithms,linear and nonlinear programming to study the problems of line and network protocols,distributed algorithms,quasi-static and dynamic routing,congestion control,deadlock prevention. Treats local and wide-area networks,and high-speed electronic and optical networks.
#iD. P. Bertsekas,E. Modiano
#t2008,fall


#nQueues: Theory and Applications
#dModeling and analysis of queueing systems,with applications in communications,manufacturing,computers,call centers,service industries and transportation. Topics include birth-death processes and simple Markovian queues,networks of queues and product form networks,single and multi-server queues,multi-class queueing networks,fluid models,adversarial queueing networks,heavy-traffic theory and diffusion approximations. Covers state of the art results which lead to research opportunities. 
#iD. Bertsimas,D. Gamarnik,J. N. Tsitsiklis
#t2010,spring


#nAdvanced Stochastic Processes
#dAnalysis and modeling of stochastic processes. Topics include measure theoretic probability,martingales,filtration,and stopping theorems,elements of large deviations theory,Brownian motion and reflected Brownian motion,stochastic integration and Ito calculus,functional limit theorems. Applications to finance theory,insurance,queueing and inventory models
#iD. Gamarnik,D. Shah
#t2008,fall


#nNetwork Algorithms
#dModern theory of networks from the algorithmic perspective with emphasis on the foundations in terms of modeling,performance analysis,and design. Topics include algorithmic questions arising in the context of scheduling,routing and congestion control in a communication network,information processing and data fusion in peer-to-peer,sensor and social networks,and efficient data storage/retrieval in a distributed storage network.
#iD. Shah
#t2008,fall


#nSeminar in Systems,Communications,and Control Research
#dAdvanced topics in systems,communications,control,optimization,and signal processing. Topics selected according to student and instructor interest. See instructor for specific topics to be offered in a particular term.
#iS. K. Mitter
#t2009,fall


#nSeminar in Systems,Communications,and Control Research
#dAdvanced topics in systems,communications,control,optimization,and signal processing. Topics selected according to student and instructor interest. See instructor for specific topics to be offered in a particular term.
#iS. K. Mitter
#t2010,spring


#nSeminar in Systems,Communications,and Control Research
#dAdvanced topics in systems,communications,control,optimization,and signal processing. Topics selected according to student and instructor interest. See instructor for specific topics to be offered in a particular term.
#iS. K. Mitter
#t2009,spring


#nSeminar in Systems,Communications,and Control Research
#dAdvanced topics in systems,communications,control,optimization,and signal processing. Topics selected according to student and instructor interest. See instructor for specific topics to be offered in a particular term.
#iS. K. Mitter
#t2008,fall


#nSolid-State Circuits
#dAnalysis 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. The charge-control model. Introduction to operational-amplifier design and application. Some previous laboratory experience assumed. 4 Engineering Design Points.
#iJ. K. Roberge,H. S. Lee
#t2009,fall


#nSolid-State Circuits
#dAnalysis 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. The charge-control model. Introduction to operational-amplifier design and application. Some previous laboratory experience assumed. 4 Engineering Design Points.
#iJ. K. Roberge,H. S. Lee
#t2008,fall


#nLogistical and Transportation Planning Methods
#dQuantitative techniques of operations research with emphasis on applications in transportation systems analysis (urban,air,ocean,highway,and pickup and delivery systems) and in the planning and design of logistically oriented urban service systems (e.g.,fire and police departments,emergency medical services,and emergency repair services). Unified study of functions of random variables,geometrical probability,multi-server queuing theory,spatial location theory,network analysis and graph theory,and relevant methods of simulation. Computer exercises and discussions of implementation difficulties. 
#iR. C. Larson,A. R. Odoni,A. I. Barnett,J. B. Orlin
#t2009,fall


#nLogistical and Transportation Planning Methods
#dQuantitative techniques of operations research with emphasis on applications in transportation systems analysis (urban,air,ocean,highway,and pickup and delivery systems) and in the planning and design of logistically oriented urban service systems (e.g.,fire and police departments,emergency medical services,and emergency repair services). Unified study of functions of random variables,geometrical probability,multi-server queuing theory,spatial location theory,network analysis and graph theory,and relevant methods of simulation. Computer exercises and discussions of implementation difficulties. 
#iR. C. Larson,A. R. Odoni,A. I. Barnett,J. B. Orlin
#t2008,fall


#nFeedback Systems
#dIntroduction to design of feedback systems. Properties and advantages of feedback systems. Time-domain and frequency-domain performance measures. Stability and degree of stability. Nyquist criterion. Frequency-domain design. Root locus method. Compensation techniques. Application to a wide variety of physical systems. Some previous laboratory experience with electronic systems is assumed
#iJ. K. Roberge
#t2010,spring


#nFeedback Systems
#dIntroduction to design of feedback systems. Properties and advantages of feedback systems. Time-domain and frequency-domain performance measures. Stability and degree of stability. Nyquist criterion. Frequency-domain design. Root locus method. Compensation techniques. Application to a wide variety of physical systems. Some previous laboratory experience with electronic systems is assumed
#iJ. K. Roberge
#t2009,spring


#nAdvanced Circuit Techniques
#dFollowing a brief classroom discussion of relevant principles,each student completes the paper design of several advanced circuits such as multiplexers,sample-and-holds,gain-controlled amplifiers,analog multipliers,digital-to-analog or analog-to-digital converters,and power amplifiers. One of each students designs is presented to the class,and one may be built and evaluated. Associated laboratory emphasizing the use of modern analog building blocks. Enrollment limited. 12 Engineering Design Points.
#iJ. K. Roberge
#t2009,fall


#nPower Electronics
#dThe 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. 6 Engineering Design Points.
#iJ. G. Kassakian,D. Perreault
#t2010,spring


#nPower Electronics
#dThe 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. 6 Engineering Design Points.
#iJ. G. Kassakian,D. Perreault
#t2009,spring


#nIntroduction to Numerical Simulation
#dIntroduction to computational techniques for the simulation of a large variety of engineering and engineered systems. Applications drawn from aerospace,mechanical,electrical,and chemical engineering,biology,and materials science. Topics: mathematical formulations,network problems,sparse direct and iterative matrix solution techniques,Newton methods for nonlinear problems,discretization methods for ordinary,time-periodic and partial differential equations,fast methods for partial differential equations and integral equations,techniques for model order reduction of dynamical systems and approaches for molecular dynamics.
#iL. Daniel,J. K. White
#t2009,fall


#nIntroduction to Numerical Simulation
#dIntroduction to computational techniques for the simulation of a large variety of engineering and engineered systems. Applications drawn from aerospace,mechanical,electrical,and chemical engineering,biology,and materials science. Topics: mathematical formulations,network problems,sparse direct and iterative matrix solution techniques,Newton methods for nonlinear problems,discretization methods for ordinary,time-periodic and partial differential equations,fast methods for partial differential equations and integral equations,techniques for model order reduction of dynamical systems and approaches for molecular dynamics.
#iL. Daniel,J. K. White
#t2008,fall


#nParallel Computing
#dAdvanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra,N-body problems,and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with emphasis on understanding the realities and myths of what is possible on the world's fastest machines. Programming languages include MPI and Star-P with MATLAB and Python. 
#iA. Edelman
#t2010,spring


#nParallel Computing
#dAdvanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra,N-body problems,and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with emphasis on understanding the realities and myths of what is possible on the world's fastest machines. Programming languages include MPI and Star-P with MATLAB and Python. 
#iA. Edelman,J. K. White
#t2009,spring


#nWavelets,Approximation,and Compression
#dHilbert space formulation of continuous-time and discrete-time signals,sampling,orthogonal and biorthogonal signal expansions,uncertainty principles and the time-frequency plane,two-channel filter banks,iterated filter banks,discrete wavelet transforms,multiresolution analysis,wavelet bases,regularity,approximation properties,and nonlinear approximation,basics of quantization and source coding,compression,denoising,and other image processing using wavelets. Advanced topics from the current research literature.
#iV. K. Goyal
#t2009,spring


#nIntroduction to Numerical Methods
#dAdvanced introduction to numerical linear algebra and related numerical methods. Topics include direct and iterative methods for linear systems,eigenvalue decompositions and QR/SVD factorizations,stability and accuracy of numerical algorithms,the IEEE floating point standard,sparse and structured matrices,preconditioning,linear algebra software. Problem sets require some knowledge of MATLAB. 
#iS. G. Johnson
#t2009,fall


#nIntroduction to Numerical Methods
#dAdvanced introduction to numerical linear algebra and related numerical methods. Topics include direct and iterative methods for linear systems,eigenvalue decompositions and QR/SVD factorizations,stability and accuracy of numerical algorithms,the IEEE floating point standard,sparse and structured matrices,preconditioning,linear algebra software. Problem sets require some knowledge of MATLAB. 
#iS. G. Johnson
#t2008,fall


#nNumerical Methods for Partial Differential Equations
#dCovers 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. 
#iJ. Peraire,A. T. Patera,J. K. White
#t2009,fall


#nNumerical Methods for Partial Differential Equations
#dCovers 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. 
#iJ. Peraire,A. T. Patera,J. K. White
#t2008,fall


#nDiscrete-Time Signal Processing
#dRepresentation,analysis,and design of discrete time signals and systems. Discrete-time processing of continuous-time signals. Decimation,interpolation,and sampling rate conversion. Flowgraph structures for DT systems. Time- and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform,FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms,Cepstral analysis,various applications.
#iA. V. Oppenheim,V. K. Goyal
#t2009,fall


#nDiscrete-Time Signal Processing
#dRepresentation,analysis,and design of discrete time signals and systems. Discrete-time processing of continuous-time signals. Decimation,interpolation,and sampling rate conversion. Flowgraph structures for DT systems. Time- and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform,FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms,Cepstral analysis,various applications.
#iA. V. Oppenheim,V. K. Goyal
#t2008,fall


#nDigital Image Processing
#dDigital 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.
#iJ. S. Lim
#t2009,spring


#nAutomatic Speech Recognition
#dGraduate-level introduction to automatic speech recognition. Provide fundamental background in acoustic theory of speech production,properties of speech sounds,signal representation,acoustic modeling,pattern classification,search algorithms,stochastic modeling techniques (including hidden Markov modeling),and language modeling. Advanced topics include finite-state transducer formulation for speech recognition,system robustness and adaptation,audio-visual integration for speech processing,and speech understanding. Hands-on experience gained through laboratory exercises and a term project. 4 Engineering Design Points.
#iV. W. Zue,J. R. Glass
#t2009,spring


#nAnalysis and Design of Digital Integrated Circuits
#dDevice 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. 4 Engineering Design Points.
#iA. P. Chandrakasan
#t2009,fall


#nAnalysis and Design of Digital Integrated Circuits
#dDevice 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. 4 Engineering Design Points.
#iA. P. Chandrakasan
#t2008,fall


#nComplex Digital Systems Design
#dIntroduction to the design and implementation of large-scale digital systems using CMOS VLSI: technology and scaling,VLSI implementation styles- full custom to FPGAs,design flows and associated EDA tools,design verification,design for fabrication testing,hardware description languages (Verilog & Bluespec),power,area and delay optimizations,clocking schemes,power distribution and dissipation,I/O and packaging. Extensive use of CAD tools in weekly labs as preparation for a multi-person design project on multi-million gate FPGAs. Enrollment may be limited. 12 Engineering Design Points.
#iArvind
#t2010,spring


#nComplex Digital Systems Design
#dIntroduction to the design and implementation of large-scale digital systems using CMOS VLSI: technology and scaling,VLSI implementation styles- full custom to FPGAs,design flows and associated EDA tools,design verification,design for fabrication testing,hardware description languages (Verilog & Bluespec),power,area and delay optimizations,clocking schemes,power distribution and dissipation,I/O and packaging. Extensive use of CAD tools in weekly labs as preparation for a multi-person design project on multi-million gate FPGAs. Enrollment may be limited. 12 Engineering Design Points.
#iArvind
#t2009,spring


#nLow Power Analog VLSI
#dComprehensive introduction to analog microelectronic design including ultra-low-power,ultra-low-noise,and feedback circuits. Device physics of the MOS transistor,including subthreshold operation and scaling to nanometer processes. VLSI chip layout and design. Transconductance amplifiers and filters,imagers,microphone circuits,current-mode circuits,analog-to-digital converters,biologically inspired circuits and systems,energy-harvesting circuits,basic electrochemistry and battery operation. Electrical modeling of non-electrical systems. System examples vary from year to year and include biomedical systems,micromechanical systems (MEMS),RF systems,sensory systems,and learning systems. The class project involves a complete design of a VLSI chip,including layout,verification,design-rule checking,and SPICE simulation. 8 Engineering Design Points.
#iR. Sarpeshkar
#t2009,fall


#nLow Power Analog VLSI
#dComprehensive introduction to analog microelectronic design including ultra-low-power,ultra-low-noise,and feedback circuits. Device physics of the MOS transistor,including subthreshold operation and scaling to nanometer processes. VLSI chip layout and design. Transconductance amplifiers and filters,imagers,microphone circuits,current-mode circuits,analog-to-digital converters,biologically inspired circuits and systems,energy-harvesting circuits,basic electrochemistry and battery operation. Electrical modeling of non-electrical systems. System examples vary from year to year and include biomedical systems,micromechanical systems (MEMS),RF systems,sensory systems,and learning systems. The class project involves a complete design of a VLSI chip,including layout,verification,design-rule checking,and SPICE simulation. 8 Engineering Design Points.
#iR. Sarpeshkar
#t2008,fall


#nApplied Probability
#dAn introduction to probability theory,and the modeling and analysis of probabilistic systems. Sample space,probabilistic models,conditional probability. Discrete and continuous random variables. Transform techniques. Bernoulli and Poisson processes. Markov processes. Limit theorems and elements of statistical inference. Meets with graduate subject 6.431,but assignments differ.
#iD. P. Bertsekas,J. N. Tsitsiklis
#t2009,fall


#nApplied Probability
#dAn introduction to probability theory,and the modeling and analysis of probabilistic systems. Sample space,probabilistic models,conditional probability. Discrete and continuous random variables. Transform techniques. Bernoulli and Poisson processes. Markov processes. Limit theorems and elements of statistical inference. Meets with graduate subject 6.431,but assignments differ.
#iD. P. Bertsekas,J. N. Tsitsiklis
#t2010,spring


#nApplied Probability
#dAn introduction to probability theory,and the modeling and analysis of probabilistic systems. Sample space,probabilistic models,conditional probability. Discrete and continuous random variables. Transform techniques. Bernoulli and Poisson processes. Markov processes. Limit theorems and elements of statistical inference. Meets with graduate subject 6.431,but assignments differ.
#iD. P. Bertsekas,J. N. Tsitsiklis
#t2008,fall


#nApplied Probability
#dAn introduction to probability theory,and the modeling and analysis of probabilistic systems. Sample space,probabilistic models,conditional probability. Discrete and continuous random variables. Transform techniques. Bernoulli and Poisson processes. Markov processes. Limit theorems and elements of statistical inference. Meets with graduate subject 6.431,but assignments differ.
#iD. P. Bertsekas,J. N. Tsitsiklis
#t2009,spring


#nStatistics for Engineers and Scientists
#dProvides a rigorous introduction to fundamentals of statistics motivated by engineering applications and emphasizing the informed use of modern statistical software. Topics include sufficient statistics,exponential families,estimation,hypothesis testing,measures of performance,and notion of optimality.
#iM. Win,J. N. Tsitsiklis
#t2009,fall


#nSystem Identification
#dMathematical models of systems from observations of their behavior. Time series,state-space,and input-output models. Model structures,parametrization,and identifiability. Non-parametric methods. Prediction error methods for parameter estimation,convergence,consistency,andasymptotic distribution. Relations to maximum likelihood estimation. Recursive estimation,relation to Kalman filters,structure determination,order estimation,Akaike criterion,and bounded but unknown noise models. Robustness and practical issues.
#iM. A. Dahleh,S. K. Mitter
#t2010,spring


#nInference and Information
#dIntroduction 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.
#iP. Golland,A. S. Willsky,G. W. Wornell
#t2010,spring


#nInference and Information
#dIntroduction 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.
#iP. Golland,A. S. Willsky,G. W. Wornell
#t2009,spring


#nFundamentals of Probability
#dIntroduction 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.
#iJ. N. Tsitsiklis,D. Bertsimas
#t2009,fall


#nFundamentals of Probability
#dIntroduction 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.
#iJ. N. Tsitsiklis,D. Bertsimas
#t2008,fall


#nAlgorithms for Inference
#dIntroduction to models and algorithms for efficient estimation and inference. Linear estimation via inner product spaces,Karhunen-Loeve expansions,Cholesky decompositions. Linear state-space models,Kalman filtering,RTS algorithm. Non-linear extensions and particle filtering. Autoregressive modeling and linear prediction,RLS and Levinson algorithms. Hidden Markov models,forward-backward,Viterbi,and Baum-Welch algorithms. Introduction to graphical models and belief propagation,sum-product,min-sum,and junction tree algorithms. Selected special topics such as variational methods and mean field theory.
#iP. Golland,G. W. Wornell,W. T. Freeman
#t2009,fall


#nAlgorithms for Estimation and Inference
#dIntroduction to models and algorithms for efficient estimation and inference. Linear estimation via inner product spaces,Karhunen-Loeve expansions,Cholesky decompositions. Linear state-space models,Kalman filtering,RTS algorithm. Asymptotics,non-linear extensions and particle filtering. Autoregressive modeling and linear predition,RLS and Levinson algorithms. Hidden Markov models,forward-backward,Viterbi,and Baum-Welch algorithms. Introduction to graphical models and belief propagation,sum-product,min-sum,and junction tree algorithms. Selected special topics such as variational methods and mean field theory.
#iP. Golland,A. S. Willsky,G. W. Wornell
#t2008,fall


#nEssential Coding Theory
#dIntroduces 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.
#iM. Sudan
#t2010,spring


#nInformation Theory
#dIntroduction to the quantitative theory of information and its applications to reliable,efficient communication systems. Mathematical definition and properties of information and its operational meanings. Basics of large deviations and its use in information theory,coding theory,and statistics. Source coding theorem and noisy channel coding theorem,error exponents,the source-channel separation theorem,multiple access channels,broadcast channels. Readings from the literature in these topics.
#iM. Medard,L. Zheng
#t2010,spring


#nInformation Theory
#dIntroduction to the quantitative theory of information and its applications to reliable,efficient communication systems. Mathematical definition and properties of information and its operational meanings. Basics of large deviations and its use in information theory,coding theory,and statistics. Source coding theorem and noisy channel coding theorem,error exponents,the source-channel separation theorem,multiple access channels,broadcast channels. Readings from the literature in these topics.
#iM. Medard,L. Zheng
#t2009,spring


#nOptical Networks
#dIntroduces 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 introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. In addition to the Physical Layer,the higher network layers (Media Access Control,Network and Transport Layers) are considered 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.
#iV. W. S. Chan
#t2010,spring


#nOptical Networks
#dIntroduces 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 introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. In addition to the Physical Layer,the higher network layers (Media Access Control,Network and Transport Layers) are considered 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.
#iV. W. S. Chan
#t2009,spring


#nQuantum Information Science
#dSubject examines quantum computation and quantum information. Topics include quantum circuits,quantum Fourier transform and search algorithms,physical implementations,the quantum operations formalism,quantum error correction,stabilizer and Calderbank-Shor-Steans codes,fault tolerant quantum computation,quantum data compression,entanglement,capacity of quantum channels,and proof of the security of quantum cryptography. Prior knowledge of quantum mechanics is required. 
#iP. Shor
#t2010,spring


#nQuantum Information Science
#dSubject examines quantum computation and quantum information. Topics include quantum circuits,quantum Fourier transform and search algorithms,physical implementations,the quantum operations formalism,quantum error correction,stabilizer and Calderbank-Shor-Steans codes,fault tolerant quantum computation,quantum data compression,entanglement,capacity of quantum channels,and proof of the security of quantum cryptography. Prior knowledge of quantum mechanics is required. 
#iP. Shor
#t2009,spring


#nPrinciples of Digital Communications II
#dCoding for the AWGN channel,the gap to capacity,binary block and convolutional codes,finite fields and Reed-Solomon codes,trellis representations,codes on graphs and iterative decoding,capacity-approaching codes,lattice and trellis codes.
#iG. D. Forney
#t2008,fall


#nPrinciples of Digital Communication I
#dCommunication 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.
#iR. G. Gallager,L. Zheng
#2008,fall


#nPrinciples of Digital Communication I
#dCommunication 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.
#iR. G. Gallager,L. Zheng
#2009,fall


#nQuantitative Physiology: Organ Transport Systems
#dApplication 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. 
#iR. G. Mark,C. M. Stultz
#t2010,spring


#nQuantitative Physiology: Organ Transport Systems
#dApplication 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. 
#iR. G. Mark,C. M. Stultz
#t2009,spring


#nQuantitative Physiology: Cells and Tissues
#d
#iD. M. Freeman,J. Han
#2008,fall


#nPrinciples of Wireless Communication
#dIntroduction 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.
#iG. W. Wornell,L. Zheng
#t2008,fall


#nPrinciples of Wireless Communication
#dIntroduction 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.
#iG. W. Wornell,L. Zheng
#t2009,fall


#nQuantum Optical Communication
#dQuantum 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.
#iJ. H. Shapiro
#t2008,fall


#nGraduate Seminar in Area I
#dStudent-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. Enrollment limited to 12.
#iL. Zheng,D. Shah
#t2009,fall


#nGraduate Seminar in Area I
#dStudent-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. Enrollment limited to 12.
#iL. Zheng,D. Shah
#t2008,fall


#nSonar,Radar,and Seismic Signal Processing
#dSignal processing used in sonar,radar,and geophysical data analysis. Active sonar and radar systems: matched filters and ambiguity functions,signal design of range/doppler resolution,second moment characterizations of random processes with correlation functions and power density spectra,deconvolution,spectral estimation by Fourier techniques and adaptive methods,beam forming. 
#iN. C. Makris,J. C. Preisig,Woods Hole Staff
#t2008,fall


#nAdaptive Array Processing
#dSpace-time random processes,beamforming,directivity,sensitivity and white noise gain metrics. Classical pattern shaping,2-D arrays,deterministic design for sidelobe control and nulling. Adaptive array processing,design of large arrays and the snapshot limit problem,directional spectra estimation,sample matrix inversion (SMI) and recursive algorithms,synthetic aperture arrays,space-time adaptive systems,direction of arrival (DOA) algorithms,matched field processing and back propagation methods for range dependent environments. Applications in radar,sonar,communications and seismic array systems.
#iJ. Preisig
#t2009,fall


#nCellular Biophysics
#dIntegrated overview of the biophysics of cells from prokaryotes to neurons,with a focus on mass transport and electrical signal generation across cell membrane. First half of course focuses on mass transport through membranes: diffusion,osmosis,chemically mediated,and active transport. Second half focuses on electrical properties of cells: ion transport to action potentials in electrically excitable cells. Electrical properties interpreted via kinetic and molecular properties of single voltage-gated ion channels. Laboratory and computer exercises illustrate the concepts. Provides instruction in written and oral communication. Students taking graduate version complete different assignments. Preference to juniors and seniors. 
#iD. M. Freeman,J. Han
#t2009,fall


#nLaboratory on the Physiology,Acoustics,and Perception of Speech
#dExperimental 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. 4 Engineering Design Points.
#iL. D. Braida,S. Shattuck-Hufnagel
#t2009,fall


#nAcoustics of Speech and Hearing
#dProvides background for understanding how the acoustics and mechanics of the speech production and auditory systems define what sounds we are capable of producing and what sounds we can sense. Particular focus on the acoustic cues used in determining the direction of a sound source,the mechanisms involved in speech production,the mechanisms used by the auditory system to transduce and analyze sounds,and sound perception (absolute detection,discrimination,masking,and auditory frequency selectivity). 4 Engineering Design Points.
#iL. D. Braida,S. S. Ghosh,J. J. Rosowski,C. Shera
#t2009,fall


#nAcoustics of Speech and Hearing
#dProvides background for understanding how the acoustics and mechanics of the speech production and auditory systems define what sounds we are capable of producing and what sounds we can sense. Particular focus on the acoustic cues used in determining the direction of a sound source,the mechanisms involved in speech production,the mechanisms used by the auditory system to transduce and analyze sounds,and sound perception (absolute detection,discrimination,masking,and auditory frequency selectivity). 4 Engineering Design Points.
#iL. D. Braida,S. S. Ghosh,J. J. Rosowski,C. Shera
#t2008,fall


#nMolecular,Cellular,and Tissue Biomechanics
#dDevelops 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. 
#iA. J. Grodzinsky,M. Bathe
#t2010,spring



#nMolecular,Cellular,and Tissue Biomechanics
#dDevelops 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. 
#iA. J. Grodzinsky,P. Doyle
#t2009,spring


#nSpeech Communication
#dSurvey of human speech communication with special emphasis on the sound patterns of natural languages. Acoustic theory of speech production,physiologic and acoustic descriptions of phonetic features,prosody,speech perception,speech respiration,and speech motor control. Applications to recognition and generation of speech by machine and to speech disorders.
#iL. D. Braida,R. E. Hillman,S. Shattuck-Hufnagel
#t2010,spring


#nSpeech Communication
#dSurvey of human speech communication with special emphasis on the sound patterns of natural languages. Acoustic theory of speech production,physiologic and acoustic descriptions of phonetic features,prosody,speech perception,speech respiration,and speech motor control. Applications to recognition and generation of speech by machine and to speech disorders.
#iL. D. Braida,R. E. Hillman,S. Shattuck-Hufnagel
#t2009,spring


#nThe Lexicon and Its Features
#dOverview of features that distinguish sound categories in languages of the world. Theories that relate these categories to their acoustic and articulatory correlates,both universally and in particular languages. Models of word recognition by listeners. A variety of perspectives on these issues,drawn from electrical engineering and computer science,linguistics and cognitive science. 
#iD. Gow,D. Steriade,S. Shattuck-Hufnagel
#t2010,spring


#nFoundations of Algorithms and Computational Techniques in Systems Biology
#dDescribes and illustrates computational approaches to solving problems in systems biology. A series of case studies demonstrates 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.
#iB. Tidor,J. K. White
#t2010,spring


#nData Acquisition and Image Reconstruction in MRI
#dApplies 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.
#iE. Adalsteinsson
#t2009,fall


#nBiomedical Signal and Image Processing
#dFundamentals 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. 6 Engineering Design Points. 
#iJ. Greenberg,E. Adalsteinsson,W. Wells,G. Clifford
#t2010,spring


#nBiomedical Signal and Image Processing
#dFundamentals 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. 6 Engineering Design Points. 
#iJ. Greenberg,E. Adalsteinsson,W. Wells,G. Clifford
#t2009,spring


#nSignal Processing by the Auditory System: Perception
#dStudies 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.
#iL. D. Braida
#t2008,fall


#nFields,Forces,and Flows in Biological Systems
#dMolecular 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. 
#iA. J. Grodzinsky,D. Lauffenburger
#t2009,fall


#nFields,Forces,and Flows in Biological Systems
#dMolecular 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. 
#iA. J. Grodzinsky,D. Lauffenburger
#t2008,fall


#nMolecular Simulations
#dIntroduction to the basic concepts underlying dynamical simulations of proteins and nucleic acids. Basic definitions of components that form biological systems used to develop physical models that describe the dynamics of biomolecules. Topics include classical statistical thermodynamics for calculation of macroscopic observables,normal-mode analyses of protein dynamics,and thermodynamic perturbation theory. Emphasizes actual techniques and algorithms used for such calculations. Prior knowledge of biochemistry is not required. Students taking the graduate version complete an additional project.
#iC. M. Stultz
#t2008,fall


#nElectromagnetics
#dExplores 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 Maxwells equations,waves,radiation,and diffraction,coupling to media and structures,guided and unguided waves,modal expansions,resonance,acoustic analogs,and forces,power,and energy. Students taking graduate version complete different assignments. Meets with 6.013 in fall term only.
#iD. H. Staelin,E. P. Ippen,M. Zahn
#t2009,fall


#nElectromagnetics
#dExplores 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 Maxwells equations,waves,radiation,and diffraction,coupling to media and structures,guided and unguided waves,modal expansions,resonance,acoustic analogs,and forces,power,and energy. Students taking graduate version complete different assignments. Meets with 6.013 in fall term only.
#iD. H. Staelin,E. P. Ippen,M. Zahn
#t2008,fall


#nIntroduction to Particle Accelerators
#dPrinciples of acceleration: beam properties,linear accelerators,synchrotrons,and storage rings. Accelerator technologies: radio frequency cavities,bending and focusing magnets,beam diagnostics. Particle beam optics and dynamics. Special topics: measures of accelerators performance in science,medicine and industry,synchrotron radiation sources,free electron lasers,high-energy colliders,and accelerators for radiation therapy. 
#iW. Barletta
#t2010,spring


#nFundamentals of Photonics
#dFundamentals of optical and opto-electronic phenomena and devices: topics include electromagnetic waves in media and at interfaces,interference,Gaussian beams,resonators,waveguides,and integrated optics. Quantum electronics: topics include thermal radiation,photo detection,quantum mechanics,light-matter interaction,quantum theory of light. Lasers: topics include gas,solid-state and semiconductor lasers,laser dynamics,Q-switching and mode-locking. 
#iF. Kaertner
#t2010,spring


#nFundamentals of Photonics
#dFundamentals of optical and opto-electronic phenomena and devices: topics include electromagnetic waves in media and at interfaces,interference,Gaussian beams,resonators,waveguides,and integrated optics. Quantum electronics: topics include thermal radiation,photo detection,quantum mechanics,light-matter interaction,quantum theory of light. Lasers: topics include gas,solid-state and semiconductor lasers,laser dynamics,Q-switching and mode-locking. 
#iF. Kaertner
#t2009,spring


#nOptics and Photonics
#dIntroduction to fundamental concepts and techniques of optics,photonics,and fiber optics. Review of Maxwells 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.
#iJ. G. Fujimoto
#t2009,fall


#nOptics and Photonics
#dIntroduction to fundamental concepts and techniques of optics,photonics,and fiber optics. Review of Maxwells 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.
#iJ. G. Fujimoto
#t2008,fall


#nIntroduction to Plasma Physics I
#dIntroduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Elementary plasma concepts,plasma characterization. Motion of charged particles in magnetic fields. Coulomb collisions,relaxation times,transport processes. Two-fluid hydrodynamic and MHD descriptions. Plasma confinement by magnetic fields,simple equilibrium and stability analysis. Wave propagation in a magnetic field,application to RF plasma heating. Introduction to kinetic theory,Vlasov,Boltzmann and Fokker-Planck equations,relation of fluid and kinetic descriptions. Electron and ion acoustic plasma waves,Landau damping.
#iJ. Egedal-Pedersen
#t2009,fall


#nIntroduction to Plasma Physics I
#dIntroduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Elementary plasma concepts,plasma characterization. Motion of charged particles in magnetic fields. Coulomb collisions,relaxation times,transport processes. Two-fluid hydrodynamic and MHD descriptions. Plasma confinement by magnetic fields,simple equilibrium and stability analysis. Wave propagation in a magnetic field,application to RF plasma heating. Introduction to kinetic theory,Vlasov,Boltzmann and Fokker-Planck equations,relation of fluid and kinetic descriptions. Electron and ion acoustic plasma waves,Landau damping.
#iJ. Egedal-Pedersen
#t2008,fall


#nContinuum Electromechanics
#dLaws,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.
#iM. Zahn
#t2008,fall


#nUltrafast Optics
#dDetailed exposition of the principles involved in ultrashort pulse generation,propagation,and characterization. Linear and nonlinear pulse shaping processes are discussed. Optical solitons,pulse compression. Laser principles: Single- and multimode-laser dynamics,Q-switching and mode-locking: active and passive model-locking mechanisms. Noise in mode-locked lasers and its limitations imposed on measurements. Laser amplifiers. Optical parametric amplifiers and oscillators. Applications in research and industry,such as various pump-probe techniques,optical imaging,frequency metrology,High Harmonic Generation,Attosecond pulse generation.
#iF. X. Kaertner
#t2008,fall


#nOptical Signals,Devices,and Systems
#dPrinciples 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.
#iC. Warde
#t2009,fall


#nOptical Signals,Devices,and Systems
#dPrinciples 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.
#iC. Warde
#t2008,fall


#nNonlinear Optics
#dTechniques of nonlinear optics with emphasis on fundamentals for optics and photonics research and engineering. 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,density matrix techniques,nonlinear spectroscopies and femtosecond optics.
#iE. P. Ippen,J. G. Fujimoto
#t2010,spring


#nNonlinear Optics
#dTechniques of nonlinear optics with emphasis on fundamentals for optics and photonics research and engineering. 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,density matrix techniques,nonlinear spectroscopies and femtosecond optics.
#iE. P. Ippen,J. G. Fujimoto
#t2009,spring


#nElectromagnetic Fields,Forces,and Motion
#dElectric and magnetic quasistatic forms of Maxwells 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.
#iM. Zahn,J. H. Lang
#t2010,spring


#nElectromagnetic Fields,Forces,and Motion
#dElectric and magnetic quasistatic forms of Maxwells 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.
#iM. Zahn,J. H. Lang
#t2009,spring


#nSeminar in Electric Power Systems
#dPlanning and operation of modern electric power systems. Content varies with current interests of instructor and class,emphasis on engineering aspects,but economic issues may be examined. Core topics include overview of power system structure and operation,representation of components,including transmission lines,transformers,generating plants,loads,power flow analysis,dynamics and control of multimachine systems,steady-state and transient stability,system protection,economic dispatch,mobil and isolated power systems,computation and simulation.
#iJ. L. Kirtley,Jr.
#t2010,spring


#nIntroduction to Numerical Simulation in Electrical Engineering
#dSelection of a simulation model and physical approximations. Solution of nonlinear coupled PDEs in 1-D through finite difference and finite element methods,Newtons method,and variants. Finite difference and finite element methods in 2-D and sparse matrix methods emphasizing conjugate gradient algorithms. Semiconductor devices used as primary examples,additional examples drawn from E&M modeling,nonlinear pulse propagation,and laser physics.
#iP. L. Hagelstein
#t2010,spring


#nElectric Machines
#dTreatment of electromechanical transducers,rotating and linear electric machines. Lumped-parameter electromechanics. Power flow using Poyntings 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.
#iJ. L. Kirtley,Jr.
#t2009,fall


#nIntroduction to Electric Power Systems
#dElectric 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. 6 Engineering Design Points. 
#iJ. L. Kirtley,Jr.
#t2009,spring


#nProgramming Languages
#dPrinciples of functional,imperative,and logic programming languages. Meta-circular interpreters,semantics (operational and denotational),type systems (polymorphism,inference,and abstract types),object oriented programming,modules,and multiprocessing. Case studies of contemporary programming languages. Programming experience and background in language implementation required.
#iD. K. Gifford
#t2009,fall


#nProgramming Languages
#dPrinciples of functional,imperative,and logic programming languages. Meta-circular interpreters,semantics (operational and denotational),type systems (polymorphism,inference,and abstract types),object oriented programming,modules,and multiprocessing. Case studies of contemporary programming languages. Programming experience and background in language implementation required.
#iD. K. Gifford
#t2008,fall


#nComputer System Architecture
#dEmphasizes the relationship among technology,hardware organization,and programming systems in the evolution of computer architecture. Pipelined,out-of-order,and speculative execution. Superscalar,VLIW,vector,and multithreaded processors. Virtual memory and exception handling. I/O and memory systems. Parallel computers,message passing and shared memory systems. Memory models,synchronization,and cache coherence protocols. Embedded computers. Assumes an undergraduate knowledge of computer systems. 4 Engineering Design Points.
#iArvind
#t2009,fall


#nComputer System Architecture
#dEmphasizes the relationship among technology,hardware organization,and programming systems in the evolution of computer architecture. Pipelined,out-of-order,and speculative execution. Superscalar,VLIW,vector,and multithreaded processors. Virtual memory and exception handling. I/O and memory systems. Parallel computers,message passing and shared memory systems. Memory models,synchronization,and cache coherence protocols. Embedded computers. Assumes an undergraduate knowledge of computer systems. 4 Engineering Design Points.
#iArvind
#t2008,fall


#nMultithreaded Parallelism: Languages and Compilers
#dLanguages and compilers to exploit multithreaded parallelism. Implicit parallel programming using functional languages and their extensions. Higher-order functions,non-strictness,and polymorphism. Explicit parallel programming and nondeterminism. The lambda calculus and its variants. Term rewriting and operational semantics. Compiling multithreaded code for symmetric multiprocessors and clusters. Static analysis and compiler optimizations. 4 Engineering Design Points.
#iArvind
#t2009,fall


#nOperating System Engineering
#dFundamental 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. 6 Engineering Design Points.
#iM. F. Kaashoek
#t2009,fall


#nOperating System Engineering
#dFundamental 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. 6 Engineering Design Points.
#iM. F. Kaashoek
#t2008,fall


#nDistributed Computer Systems Engineering
#dAbstractions 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. 6 Engineering Design Points.
#iR. T. Morris,M. F. Kaashoek
#t2010,spring


#nDistributed Computer Systems Engineering
#dAbstractions 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. 6 Engineering Design Points.
#iR. T. Morris,M. F. Kaashoek
#t2009,spring


#nTechniques in Artificial Intelligence
#dA graduate-level introduction to artificial intelligence. Topics include representation and inference in first-order logic,modern deterministic and decision-theoretic planning techniques,basic supervised learning methods,and Bayesian network inference and learning.
#iL. Kaelbling
#t2010,spring


#nTechniques in Artificial Intelligence
#dA graduate-level introduction to artificial intelligence. Topics include representation and inference in first-order logic,modern deterministic and decision-theoretic planning techniques,basic supervised learning methods,and Bayesian network inference and learning.
#iL. Kaelbling
#t2009,spring


#nPrinciples of Computer Systems
#dAn 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.
#iB. W. Lampson
#t2009,spring


#nComputer Networks
#dTopics on the engineering and analysis of network protocols and architecture,including architectural principles for designing heterogeneous networks,transport protocols,internet routing foundations and practice,router design,congestion control and network resource management,wireless networks,network security,naming,overlay and peer-to-peer networks. Readings from original research papers and Internet RFCs. Semester-long project and paper. Enrollment may be limited. 4 Engineering Design Points.
#iH. Balakrishnan
#t2010,spring


#nComputer Networks
#dTopics on the engineering and analysis of network protocols and architecture,including architectural principles for designing heterogeneous networks,transport protocols,internet routing foundations and practice,router design,congestion control and network resource management,wireless networks,network security,naming,overlay and peer-to-peer networks. Readings from original research papers and Internet RFCs. Semester-long project and paper. Enrollment may be limited. 4 Engineering Design Points.
#iH. Balakrishnan
#t2009,spring


#nUser Interface Design and Implementation
#dDesign,implementation,and evaluation of human-computer interfaces. Human capabilities,including the human information processing model,perception,Fittss Law,memory,attention,and color vision,task analysis,user-centered design,design principles,low-fidelity prototyping,heuristic evaluation,formative evaluation,controlled experiments,model-view-controller,input models,output models,constraints,layout,animation,and automatic user interface generation. Readings from current literature,assignments related to research topics and experiment design and analysis,and substantial,semester-long group programming project. Students taking the graduate version complete different assignments. 6 Engineering Design Points.
#iR. C. Miller
#t2010,spring


#nUser Interface Design and Implementation
#dDesign,implementation,and evaluation of human-computer interfaces. Human capabilities,including the human information processing model,perception,Fittss Law,memory,attention,and color vision,task analysis,user-centered design,design principles,low-fidelity prototyping,heuristic evaluation,formative evaluation,controlled experiments,model-view-controller,input models,output models,constraints,layout,animation,and automatic user interface generation. Readings from current literature,assignments related to research topics and experiment design and analysis,and substantial,semester-long group programming project. Students taking the graduate version complete different assignments. 6 Engineering Design Points.
#iR. C. Miller
#t2009,spring


#nDatabase Systems
#dTopics 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. 4 Engineering Design Points.
#iS. R. Madden
#t2009,fall


#nDatabase Systems
#dTopics 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. 4 Engineering Design Points.
#iS. R. Madden
#t2008,fall


#nTheory of Computation
#dA more extensive and theoretical treatment of the material in 6.045J/18.400J,emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems,reducibility,recursive function theory. Time and space measures on computation,completeness,hierarchy theorems,inherently complex problems,oracles,probabilistic computation,and interactive proof systems. 
#iM. Sipser
#t2009,fall


#nTheory of Computation
#dA more extensive and theoretical treatment of the material in 6.045J/18.400J,emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems,reducibility,recursive function theory. Time and space measures on computation,completeness,hierarchy theorems,inherently complex problems,oracles,probabilistic computation,and interactive proof systems. 
#iM. Sipser
#t2008,fall


#nAdvanced Computer Graphics
#dA graduate level course investigates computational problems in rendering,animation,and geometric modeling. The course draws on advanced techniques from computational geometry,applied mathematics,statistics,scientific computing and other. Substantial programming experience required.
#iF. P. Durand
#t2010,spring


#nAdvanced Computer Graphics
#dA graduate level course investigates computational problems in rendering,animation,and geometric modeling. The course draws on advanced techniques from computational geometry,applied mathematics,statistics,scientific computing and other. Substantial programming experience required.
#iF. P. Durand
#t2009,spring


#nAdvanced Topics in Computer Graphics
#dIn-depth study of an active research topic in computer graphics. Topics change each term. Readings from the literature,student presentations,short assignments,and a programming project.
#iF. P. Durand
#t2008,fall


#nThe Human Intelligence Enterprise
#dMeets with undergraduate subject 6.803. Intended,in part,to prepare students for MEng thesis work in the Artificial Intelligence concentration. Requires completion of supplementary exercises and a substantial term project. Enrollment limited.
#iP. H. Winston
#t2010,spring


#nThe Human Intelligence Enterprise
#dMeets with undergraduate subject 6.803. Intended,in part,to prepare students for MEng thesis work in the Artificial Intelligence concentration. Requires completion of supplementary exercises and a substantial term project. Enrollment limited.
#iP. H. Winston
#t2009,spring


#nCognitive Robotics
#dAlgorithms and paradigms for creating a wide range of robotic systems that act intelligently and robustly,by reasoning extensively from models of themselves and their world. Examples range from autonomous Mars explorers and cooperative air vehicles,to everyday embedded devices. Topics include deduction and search in real-time,temporal,decision-theoretic and contingency planning,dynamic execution and re-planning,reasoning about hidden state and failures,reasoning under uncertainty,path planning,mapping and localization,and cooperative and distributed robotics. 
#iB. C. Williams
#t2009,spring


#nIntelligent Multimodal User Interfaces
#dImplementation and evaluation of intelligent multi-modal user interfaces,taught from a combination of hands-on exercises and papers from the original literature. Topics include basic technologies for handling speech,vision,pen-based interaction,and other modalities,as well as various techniques for combining modalities. Substantial readings and a term project,where students build an interface to illustrate one or more themes of the course. 8 Engineering Design Points.
#iR. Davis
#t2010,spring


#nIntelligent Multimodal User Interfaces
#dImplementation and evaluation of intelligent multi-modal user interfaces,taught from a combination of hands-on exercises and papers from the original literature. Topics include basic technologies for handling speech,vision,pen-based interaction,and other modalities,as well as various techniques for combining modalities. Substantial readings and a term project,where students build an interface to illustrate one or more themes of the course. 8 Engineering Design Points.
#iR. Davis
#t2009,spring


#nAdvanced Complexity Theory 
#dCurrent research topics in computational complexity theory. Nondeterministic,alternating,probabilistic,and parallel computation models. Boolean circuits. Complexity classes and complete sets. The polynomial-time hierarchy. Interactive proof systems. Relativization. Definitions of randomness. Pseudo-randomness and derandomizations. Interactive proof systems and probabilistically checkable proofs. 
#iM. Sudan,M. Sipser 
#t2009,spring


#nRandomness and Computation 
#dThe power and sources of randomness in computation. Connections and applications to computational complexity,computational learning theory,cryptography and combinatorics. Topics include: probabilistic proofs,uniform generation and approximate counting,Fourier analysis of Boolean functions,computational learning theory,expander graphs,pseudorandom generators,derandomization. 
#iR. Rubinfeld 
#t2010,spring


#nRandomness and Computation
#dTheory for programmers. Introduction to programming and computability theory based on a substitution model of computation by Scheme programs with side effects. Computation as algebraic manipulation: provable and valid inequalities for multivariate polynomials. Scheme evaluation as algebraic manipulation and term rewriting. Paradoxes from self-application and introduction to formal programming semantics. Undecidability of the Halting Problem for Scheme. Properties of recursively enumerable sets,leading to Incompleteness theorems for Scheme equivalences. Introduction to logic for program specification and verification. Hilberts tenth problem.
#iA. R. Meyer
#2009,spring


#nParallel Computing 
#dIntroduction 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. 4 Engineering Design Points. 
#iA. Agarwal 
#t2010,spring


#nParallel Computing 
#dIntroduction 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. 4 Engineering Design Points. 
#iA. Agarwal 
#t2009,spring


#nGeometric Computing 
#dIntroduction to the design and analysis of algorithms for geometric problems,in low and high dimensional spaces. Algorithms: convex hulls,polygon triangulation,Delaunay triangulation,motion planning,pattern matching. Geometric data structures: point location,Voronoi diagrams,Binary Space Partitions. Geometric problems in higher dimensions: linear programming,closest pair problems. High dimensional nearest neighbor search and low-distortion embeddings between metric spaces. Geometric algorithms for massive data sets: external memory and streaming algorithms. Geometric optimization. 
#iP. Indyk 
#t2010,spring


#nParallel Computing 
#dIntroduction 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. 4 Engineering Design Points. 
#iA. Agarwal 
#t2009,spring


#nAdvanced Data Structures 
#dMore advanced and powerful data structures for answering several queries on the same data. Such structures are crucial in particular for designing efficient algorithms. Dictionaries,hashing,search trees. Self-adjusting data structures,linear search,splay trees,dynamic optimality. Integer data structures,word RAM. Predecessor problem,van Emde Boas priority queues,y-fast trees,fusion trees. Lower bounds,cell-probe model,round elimination. Dynamic graphs,link-cut trees,dynamic connectivity. Strings,text indexing,suffix arrays,suffix trees. Static data structures,compact arrays,rank and select. Succinct data structures,tree encodings,implicit data structures. External-memory and cache-oblivious data structures,B-trees,buffer trees,tree layout,ordered-file maintenance. Temporal data structures,persistence,retroactivity. 
#iE. D. Demaine 
#t2010,spring


#nDistributed Algorithms 
#dDesign and analysis of concurrent algorithms,emphasizing those suitable for use in distributed networks. Process synchronization,allocation of computational resources,distributed consensus,distributed graph algorithms,election of a leader in a network,distributed termination,deadlock detection,concurrency control,communication,and clock synchronization. Special consideration given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation. 
#iN. A. Lynch 
#t2009,fall


#nAdvanced Algorithms 
#dFirst-year graduate subject in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design,analysis,and implementation. Surveys a variety of computational models and the algorithms for them. Data structures,network flows,linear programming,computational geometry,approximation algorithms,online algorithms,parallel algorithms,external memory,streaming algorithms. 
#iD. R. Karger 
#t2009,fall


#nAdvanced Algorithms 
#dFirst-year graduate subject in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design,analysis,and implementation. Surveys a variety of computational models and the algorithms for them. Data structures,network flows,linear programming,computational geometry,approximation algorithms,online algorithms,parallel algorithms,external memory,streaming algorithms. 
#iD. R. Karger 
#t2008,fall


#nNetwork Optimization 
#dNetwork models for industrial logistics systems,transportation systems,communication systems,and other applications. Emphasizes a rigorous treatment of algorithms and their efficiency. Algorithms for shortest paths,maximum flows,minimum cost flows,traffic equilibrium,and network design. Implementation issues. 
#iA. S. Schulz 
#t2009,spring


#nRandomized Algorithms 
#dStudies how randomization can be used to make algorithms simpler and more efficient via random sampling,random selection of witnesses,symmetry breaking,and Markov chains. Models of randomized computation. Data structures: hash tables,and skip lists. Graph algorithms: minimum spanning trees,shortest paths,and minimum cuts. Geometric algorithms: convex hulls,linear programming in fixed or arbitrary dimension. Approximate counting,parallel algorithms,online algorithms,derandomization techniques,and tools for probabilistic analysis of algorithms. 
#iD. R. Karger 
#t2009,spring


#nNetwork and Computer Security 
#dTechniques for achieving security in multi-user computer systems and distributed computer systems. Topics: physical security,discretionary and mandatory access control,biometrics,information-flow models of security,covert channels,elementary cryptography,public-key cryptography,logic of authentication,electronic cash,viruses,firewalls,electronic voting,risk assessment,secure web browsers. 
#iR. L. Rivest 
#t2010,spring


#nNetwork and Computer Security 
#dTechniques for achieving security in multi-user computer systems and distributed computer systems. Topics: physical security,discretionary and mandatory access control,biometrics,information-flow models of security,covert channels,elementary cryptography,public-key cryptography,logic of authentication,electronic cash,viruses,firewalls,electronic voting,risk assessment,secure web browsers. 
#iR. L. Rivest 
#t2009,spring


#nInteger Programming and Combinatorial Optimization 
#dIn-depth treatment of the modern theory of integer programming and combinatorial optimization,emphasizing geometry,duality and algorithms. Topics include formulating problems in integer variables,enhancement of formulations,ideal formulations,integer programming duality,linear and semidefinite relaxations,lattices and their applications,the geometry of integer programming,primal methods,cutting plane methods,connections with algebraic geometry,computational complexity,approximation algorithms,heuristic and enumerative algorithms,mixed integer programming and solutions of large scale problems. 
#iD. J. Bertsimas,A. S. Schulz 
#t2009,fall


#nNatural Language and the Computer Representation of Knowledge 
#dRelationship between computer representation of knowledge and the structure of natural language. Emphasizes development of the analytical skills necessary to judge the computational implications of grammatical formalisms,and uses concrete examples to illustrate particular computational issues. Efficient parsing algorithms for context-free grammars,augmented transition network grammars. Question answering systems. Extensive laboratory work on building natural language processing systems. 8 Engineering Design Points. 
#iR. C. Berwick 
#t2010,spring


#nNatural Language and the Computer Representation of Knowledge 
#dRelationship between computer representation of knowledge and the structure of natural language. Emphasizes development of the analytical skills necessary to judge the computational implications of grammatical formalisms,and uses concrete examples to illustrate particular computational issues. Efficient parsing algorithms for context-free grammars,augmented transition network grammars. Question answering systems. Extensive laboratory work on building natural language processing systems. 8 Engineering Design Points. 
#iR. C. Berwick 
#t2009,spring


#nAdvanced Natural Language Processing 
#dGraduate introduction to natural language processing,the study of human language from a computational perspective. Syntactic,semantic and discourse processing models. Emphasis on machine learning or corpus-based methods and algorithms. Use of these methods and models in applications including syntactic parsing,information extraction,statistical machine translation,dialogue systems,and summarization. 
R. A. Barzilay,M. J. Collins 
#t2009,fall


#nAdvanced Natural Language Processing 
#dGraduate introduction to natural language processing,the study of human language from a computational perspective. Syntactic,semantic and discourse processing models. Emphasis on machine learning or corpus-based methods and algorithms. Use of these methods and models in applications including syntactic parsing,information extraction,statistical machine translation,dialogue systems,and summarization. 
R. A. Barzilay,M. J. Collins 
#t2008,fall


#nAdvanced Computational Photography 
#dRequires the completion of additional advanced homework assignments and presentation of a research paper. See subject description under 6.815. 
#iF. P. Durand,W. T. Freeman 
#t2010,spring


#nAdvanced Computational Photography 
#dRequires the completion of additional advanced homework assignments and presentation of a research paper. See subject description under 6.815. 
#iF. P. Durand,W. T. Freeman 
#t2009,spring


#nMachine Vision 
#dIntensive introduction to the process of generating a symbolic description of the environment from an image. Students expected to attend the 6.801 lectures as well as occasional seminar meetings on special topics. Material presented in 6.801 is supplemented by reading from the literature. Students required to prepare a paper analyzing research in a selected area. 
#iB. K. P. Horn 
#t2009,fall


#nMachine Vision 
#dIntensive introduction to the process of generating a symbolic description of the environment from an image. Students expected to attend the 6.801 lectures as well as occasional seminar meetings on special topics. Material presented in 6.801 is supplemented by reading from the literature. Students required to prepare a paper analyzing research in a selected area. 
#iB. K. P. Horn 
#t2008,fall


#nMachine Learning 
#dPrinciples,techniques,and algorithms in machine learning from the point of view of statistical inference,representation,generalization,and model selection,and methods such as linear/additive models,active learning,boosting,support vector machines,hidden Markov models,and Bayesian networks. 
#iT. Jaakkola,L. P. Kaelbling,M. J. Collins 
#t2009,fall


#nMachine Learning 
#dPrinciples,techniques,and algorithms in machine learning from the point of view of statistical inference,representation,generalization,and model selection,and methods such as linear/additive models,active learning,boosting,support vector machines,hidden Markov models,and Bayesian networks. 
#iT. Jaakkola,L. P. Kaelbling,M. J. Collins 
#t2008,fall


#nThe Society of Mind 
#dIntroduction to a theory that tries to explain how minds are made from collections of simpler processes. Treats such aspects of thinking as vision,language,learning,reasoning,memory,consciousness,ideals,emotions,and personality. Incorporates ideas from psychology,artificial intelligence,and computer science to resolve theoretical issues such as wholes vs. parts,structural vs. functional descriptions,declarative vs. procedural representations,symbolic vs. connectionist models,and logical vs. common-sense theories of learning. Enrollment limited. 
#iM. Minsky 
#t2010,spring


#nThe Society of Mind 
#dIntroduction to a theory that tries to explain how minds are made from collections of simpler processes. Treats such aspects of thinking as vision,language,learning,reasoning,memory,consciousness,ideals,emotions,and personality. Incorporates ideas from psychology,artificial intelligence,and computer science to resolve theoretical issues such as wholes vs. parts,structural vs. functional descriptions,declarative vs. procedural representations,symbolic vs. connectionist models,and logical vs. common-sense theories of learning. Enrollment limited. 
#iM. Minsky 
#t2009,spring


#nAdvances in Computer Vision 
#dAdvanced topics in computer vision with a focus on the use of machine learning techniques and applications in graphics and human-computer interface. Topics include image representations,texture models,structure-from-motion algorithms,Bayesian techniques,object and scene recognition,tracking,shape modeling,and image databases. Applications may include face recognition,multimodal interaction,interactive systems,cinematic special effects,and photorealistic rendering. Covers topics complementary to 6.801/6.866,these subjects may be taken in sequence. 
#iW. T. Freeman,A. Torralba 
#t2010,spring


#nAdvances in Computer Vision 
#dAdvanced topics in computer vision with a focus on the use of machine learning techniques and applications in graphics and human-computer interface. Topics include image representations,texture models,structure-from-motion algorithms,Bayesian techniques,object and scene recognition,tracking,shape modeling,and image databases. Applications may include face recognition,multimodal interaction,interactive systems,cinematic special effects,and photorealistic rendering. Covers topics complementary to 6.801/6.866,these subjects may be taken in sequence. 
#iT. Darrell,W. T. Freeman 
#t2009,spring


#nAdvanced Topics in Computer Vision 
#dSeminar exploring advanced research topics in the field of computer vision,focus varies with lecturer. Typically structured around discussion of assigned research papers and presentations by students. Example research areas explored in this seminar include learning in vision,computational imaging techniques,multimodal human-computer interaction,biomedical imaging,representation and estimation methods used in modern computer vision. 
#iW. T. Freeman,P. Golland,B. K. P. Horn,A. Torralba 
#t2010,spring


#nAdvanced Topics in Computer Vision 
#dSeminar exploring advanced research topics in the field of computer vision,focus varies with lecturer. Typically structured around discussion of assigned research papers and presentations by students. Example research areas explored in this seminar include learning in vision,computational imaging techniques,multimodal human-computer interaction,biomedical imaging,representation and estimation methods used in modern computer vision. 
#iW. T. Freeman,P. Golland,B. K. P. Horn,A. Torralba 
#t2008,fall


#nBiomedical Computing 
#dAnalyzes computational needs of clinical medicine,reviews systems and approaches that have been used to support those needs,and the relationship between clinical data and gene and protein measurements. Topics: the nature of clinical data,architecture and design of healthcare information systems,privacy and security issues,medical expert systems,introduction to bioinformatics. Case studies and guest lectures describe contemporary systems and research projects. Term project using large clinical and genomic data sets integrates classroom topics. 6 Engineering Design Points. 
#iP. Szolovits,I. Kohane,L. Ohno-Machado 
#t2009,fall


#nBiomedical Computing 
#dAnalyzes computational needs of clinical medicine,reviews systems and approaches that have been used to support those needs,and the relationship between clinical data and gene and protein measurements. Topics: the nature of clinical data,architecture and design of healthcare information systems,privacy and security issues,medical expert systems,introduction to bioinformatics. Case studies and guest lectures describe contemporary systems and research projects. Term project using large clinical and genomic data sets integrates classroom topics. 6 Engineering Design Points. 
#iP. Szolovits,I. Kohane,L. Ohno-Machado 
#t2008,fall


#nBiomedical Decision Support 
#dPresents the main concepts of decision analysis,artificial intelligence,and predictive model construction and evaluation in the specific context of medical applications. Emphasizes the advantages and disadvantages of using these methods in real-world systems. Technical focus on decision analysis,knowledge-based systems (qualitative and quantitative),learning systems (including logistic regression,classification trees,neural networks),and techniques to evaluate the performance of such systems. Students produce a final project using the methods learned in the subject,based on actual clinical data. Required for students in the master's program in medical informatics,but open to other graduate students and advanced undergraduates. 
#iR. Lacson,S. Vinterbo 
#t2009,fall


#nBiomedical Decision Support 
#dPresents the main concepts of decision analysis,artificial intelligence,and predictive model construction and evaluation in the specific context of medical applications. Emphasizes the advantages and disadvantages of using these methods in real-world systems. Technical focus on decision analysis,knowledge-based systems (qualitative and quantitative),learning systems (including logistic regression,classification trees,neural networks),and techniques to evaluate the performance of such systems. Students produce a final project using the methods learned in the subject,based on actual clinical data. Required for students in the master's program in medical informatics,but open to other graduate students and advanced undergraduates. 
#iR. Lacson,S. Vinterbo 
#t2008,fall


#nComputational Systems Biology 
#dComputational approaches and algorithms for contemporary problems in systems biology,with a focus on models of biological systems,including regulatory network discovery and validation. Topics include (1) genotypes,regulatory factor binding and motif discovery,whole genome RNA expression,(2) Regulatory networks: discovery,validation,data integration,protein-protein interactions,signaling,whole genome chromatin immunoprecipitation analysis,(3) Experimental design: model validation,interpretation of interventions. Computational methods discussed include directed and undirected graphical models such as Bayesian networks,factor graphs,Dirichlet processes,and topic models. Multidisciplinary team oriented final research project. 
#iD. K. Gifford,T. S. Jaakkola 
#t2010,spring


#nComputational Systems Biology 
#dComputational approaches and algorithms for contemporary problems in systems biology,with a focus on models of biological systems,including regulatory network discovery and validation. Topics include (1) genotypes,regulatory factor binding and motif discovery,whole genome RNA expression,(2) Regulatory networks: discovery,validation,data integration,protein-protein interactions,signaling,whole genome chromatin immunoprecipitation analysis,(3) Experimental design: model validation,interpretation of interventions. Computational methods discussed include directed and undirected graphical models such as Bayesian networks,factor graphs,Dirichlet processes,and topic models. Multidisciplinary team oriented final research project. 
#iD. K. Gifford,T. S. Jaakkola 
#t2009,spring


#nCryptography and Cryptanalysis 
#dA rigorous introduction to modern cryptography. Emphasis on the fundamental cryptographic primitives of public-key encryption,digital signatures,pseudo-random number generation,and basic protocols and their computational complexity requirements. 
#iS. Goldwasser,S. Micali 
#t2010,spring


#nCryptography and Cryptanalysis 
#dA rigorous introduction to modern cryptography. Emphasis on the fundamental cryptographic primitives of public-key encryption,digital signatures,pseudo-random number generation,and basic protocols and their computational complexity requirements. 
#iS. Goldwasser,S. Micali 
#t2009,spring


#nAdvanced Topics in Cryptography 
#dRecent results in cryptography,interactive proofs,and cryptographic game theory. Lectures by instructor,invited speakers,and students. 
#iS. Goldwasser,S. Micali 
#t2008,fall


#nComputational Evolutionary Biology 
#dExplores and illustrates theory underlying computational approaches to solving problems in evolutionary biology. Begins with components of evolutionary theory and inferential logic of evolution by natural selection. Emphasizes development of analytical skills needed to judge the computational and algorithmic implications and requirements of evolutionary models. Examples drawn from current research in evolutionary biology: whole-genome species comparison,phylogenetic tree construction,molecular evolution,homology and development,optimization and evolvability,heritability,disease evolution,detecting selection in human populations,and evolution of language. Extensive laboratory exercises in model-building and analyzing evolutionary data. Graduate version requires a more substantial final project and completion of additional laboratory assignments. 4 Engineering Design Points. 
#iR. C. Berwick 
#t2009,fall


#nAdvanced Computational Biology: Genomes,Networks,Evolution 
#dSee description for 6.047. Additionally examines recent publications in the areas covered,with research-style assignments. A more substantial final project is expected,which can lead to a thesis and publication. 
#iM. Kellis 
#t2009,fall


#nAdvanced Computational Biology: Genomes,Networks,Evolution 
#dSee description for 6.047. Additionally examines recent publications in the areas covered,with research-style assignments. A more substantial final project is expected,which can lead to a thesis and publication. 
#iM. Kellis 
#t2008,fall


#nSpecial Subjects in Computer Science 1
#dOpportunity for group study of advanced subjects related to Computer Science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2009,fall


#nSpecial Subjects in Computer Science 1
#dOpportunity for group study of advanced subjects related to Computer Science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2010,spring


#nSpecial Subjects in Computer Science 
#dOpportunity for group study of advanced subjects related to Computer Science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iG. V. Verghese 
#t2008,fall


#nSpecial Subjects in Computer Science 
#dOpportunity for group study of advanced subjects related to Computer Science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iG. V. Verghese 
#t2009,spring


#nSpecial Subjects in Computer Science 2
#dOpportunity for group study of advanced subjects related to computer science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2009,fall


#nSpecial Subjects in Computer Science 3
#dOpportunity for group study of advanced subjects related to computer science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2009,fall


#nSpecial Subjects in Computer Science 2
#dOpportunity for group study of advanced subjects related to computer science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2010,spring


#nSpecial Subjects in Computer Science 3
#dOpportunity for group study of advanced subjects related to computer science not otherwise included in curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2010,spring


#nEngineering Risk-Benefit Analysis 
#dEmphasis on three methodologies pertaining to decision making in the presence of uncertainty: reliability and probabilistic risk assessment (RPRA),decision analysis (DA),and cost-benefit analysis (CBA). Risks of particular interest are those associated with large engineering projects such as the development of new products,the building,maintenance and operation of nuclear reactors and space systems. Presents and interprets some of the frameworks helpful for balancing risks and benefits in the situations that typically involve human safety,potential environmental effects,and large financial and technological uncertainties. Review of elementary probability theory and statistics included. 
#iG. E. Apostolakis 
#t2009,spring


#nLarge-scale Symbolic Systems 
#dConcepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers,computer-algebra systems,deductive systems,and some artificial intelligence applications. Means for decoupling goals from strategy. Mechanisms for implementing additive data-directed invocation. Work with partially-specified entities. Manage multiple viewpoints. Topics include combinators,generic operations,pattern matching,pattern-directed invocation,rule systems,backtracking,dependencies,indeterminacy,memoization,constraint propagation,and incremental refinement. Comparable programming experience required. 
#iG. J. Sussman 
#t2010,spring


#nLarge-scale Symbolic Systems 
#dConcepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers,computer-algebra systems,deductive systems,and some artificial intelligence applications. Means for decoupling goals from strategy. Mechanisms for implementing additive data-directed invocation. Work with partially-specified entities. Manage multiple viewpoints. Topics include combinators,generic operations,pattern matching,pattern-directed invocation,rule systems,backtracking,dependencies,indeterminacy,memoization,constraint propagation,and incremental refinement. Comparable programming experience required. 
#iG. J. Sussman 
#t2009,spring


#nClassical Mechanics: A Computational Approach 
#dClassical mechanics in a computational framework,Lagrangian formulation,action,variational principles,and Hamilton's principle. Conserved quantities,Hamiltonian formulation,surfaces of section,chaos,and Liouville's theorem. Poincare integral invariants,Poincare-Birkhoff and KAM theorems. Invariant curves and cantori. Nonlinear resonances,resonance overlap and transition to chaos. Symplectic integration. Adiabatic invariants. Applications to simple physical systems and solar system dynamics. Extensive use of computation to capture methods,for simulation,and for symbolic analysis. Programming experience required. Students taking the graduate version complete additional assignments. 
#iJ. Wisdom,G. J. Sussman 
#t2009,fall


#nClassical Mechanics: A Computational Approach 
#dClassical mechanics in a computational framework,Lagrangian formulation,action,variational principles,and Hamilton's principle. Conserved quantities,Hamiltonian formulation,surfaces of section,chaos,and Liouville's theorem. Poincare integral invariants,Poincare-Birkhoff and KAM theorems. Invariant curves and cantori. Nonlinear resonances,resonance overlap and transition to chaos. Symplectic integration. Adiabatic invariants. Applications to simple physical systems and solar system dynamics. Extensive use of computation to capture methods,for simulation,and for symbolic analysis. Programming experience required. Students taking the graduate version complete additional assignments. 
#iJ. Wisdom,G. J. Sussman 
#t2008,fall


#nGraduate VI-A Internship 1
#dProvides academic credit for a graduate assignment of graduate VI-A students at companies affiliated with the department's VI-A internship program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2009,fall


#nGraduate VI-A Internship 1
#dProvides academic credit for a graduate assignment of graduate VI-A students at companies affiliated with the department's VI-A internship program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2010,spring


#nGraduate VI-A Internship 1
#dProvides academic credit for a graduate assignment of graduate VI-A students at companies affiliated with the department's VI-A internship program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2010,summer


#nGraduate VI-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the department's VI-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2009,fall


#nGraduate VI-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the department's VI-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2010,spring


#nGraduate VI-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the department's VI-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the VI-A internship program. 
#iM. Zahn 
#t2010,summer


#nGraduate 6-A Internship 1
#dProvides academic credit for a graduate assignment of graduate 6-A students at companies affiliated with the departments 6-A internship program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2008,fall


#nGraduate 6-A Internship 1
#dProvides academic credit for a graduate assignment of graduate 6-A students at companies affiliated with the departments 6-A internship program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2009,spring


#nGraduate 6-A Internship 1
#dProvides academic credit for a graduate assignment of graduate 6-A students at companies affiliated with the departments 6-A internship program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2009,summer


#nGraduate 6-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the departments 6-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2008,fall


#nGraduate 6-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the departments 6-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2008,fall


#nGraduate 6-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the departments 6-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2009,spring


#nGraduate 6-A Internship 2
#dProvides academic credit for graduate students who require an additional term at the company to complete the graduate assignment of the departments 6-A internship program. This academic credit is for registration purposes only and cannot be used toward fulfilling the requirements of any degree program. Enrollment limited to graduate students participating in the 6-A internship program.
#iM. Zahn
#t2009,summer


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,fall 


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,spring


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,summer


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2009,fall


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2010,spring


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2010,summer


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2008,fall 


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,spring


#nIntroductory Research in Electrical Engineering and Computer Science 1
#dEnrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM,EE,ECS,PhD,or ScD thesis. Opportunity to become involved in graduate research,under guidance of a staff member,on a problem of mutual interest to student and supervisor. Individual programs subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,summer


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2008,fall


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2009,spring


#nIntroduction to Research in Electrical Engineering and Computer Science 2
#dSeminar on topics related to research leading to an SM,EE,ECS,PhD,or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. 
#iT. P. Orlando 
#t2009,summer


#nSpecial Studies in Electrical Engineering and Computer Science 1 
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando 
#t2009,fall


#nSpecial Studies in Electrical Engineering and Computer Science 1
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,spring


#nSpecial Studies in Electrical Engineering and Computer Science 1
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,Sumer


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando 
#t2009,fall


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,spring


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2010,summer


#nSpecial Subjects in Electrical Engineering and Computer Science 
#dOpportunity for group study of advanced subjects related to Electrical Engineering and Computer Science not otherwise included in curriculum. Offerings initiated by members of EECS faculty on an ad hoc basis,subject to departmental approval. 
#iD. M. Freeman 
#t2010,fall


#nSpecial Subjects in Electrical Engineering and Computer Science 
#dOpportunity for group study of advanced subjects related to Electrical Engineering and Computer Science not otherwise included in curriculum. Offerings initiated by members of EECS faculty on an ad hoc basis,subject to departmental approval. 
#iD. M. Freeman 
#t2010,spring


#nSpecial Studies in Electrical Engineering and Computer Science 1 
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando 
#t2008,fall


#nSpecial Studies in Electrical Engineering and Computer Science 1
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,spring


#nSpecial Studies in Electrical Engineering and Computer Science 1
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving individual study (under supervision of a faculty member) concerning topics of mutual interest to student and supervisor,but may,when appropriate,be used for small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,Sumer


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando 
#t2008,fall


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,spring


#nSpecial Studies in Electrical Engineering and Computer Science 2
#dOpportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. 
#iT. P. Orlando
#t2009,summer


#nSpecial Subjects in Electrical Engineering and Computer Science 
#dOpportunity for group study of advanced subjects related to Electrical Engineering and Computer Science not otherwise included in curriculum. Offerings initiated by members of EECS faculty on an ad hoc basis,subject to departmental approval. 
#iG. C. Verghese 
#t2008,fall


#nSpecial Subjects in Electrical Engineering and Computer Science 
#dOpportunity for group study of advanced subjects related to Electrical Engineering and Computer Science not otherwise included in curriculum. Offerings initiated by members of EECS faculty on an ad hoc basis,subject to departmental approval. 
#iG. C. Verghese 
#t2009,spring


#nTeaching Electrical Engineering and Computer Science 1
#dFor qualified students interested in gaining teaching experience. Classroom,tutorial,or laboratory teaching under the supervision of a faculty member. Enrollment limited by availability of suitable teaching assignments. 
#iD. M. Freeman 
#t2009,fall


#nTeaching Electrical Engineering and Computer Science 1
#dFor qualified students interested in gaining teaching experience. Classroom,tutorial,or laboratory teaching under the supervision of a faculty member. Enrollment limited by availability of suitable teaching assignments. 
#iD. M. Freeman 
#t2010,spring


#nTeaching Electrical Engineering and Computer Science 2
#dFor Teaching Assistants in Electrical Engineering and Computer Science,in cases where teaching assignment is approved for academic credit by the department. 
#iD. M. Freeman 
#t2009,fall


#nTeaching Electrical Engineering and Computer Science 2
#dFor Teaching Assistants in Electrical Engineering and Computer Science,in cases where teaching assignment is approved for academic credit by the department. 
#iD. M. Freeman 
#t2010,spring


#nTeaching College-Level Science and Engineering 
#dParticipatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include: theories of adult learning,course development,promoting active learning,problem solving,and critical thinking in students,communicating with a diverse student body,using educational technology to further learning,lecturing,creating effective tests and assignments,and assessment and evaluation. Students research and present a relevant topic of particular interest. Subject is appropriate for both novices and those with teaching experience. 
#iL. Breslow 
#t2010,spring


#nSpecial Subjects in Electrical Engineering 
#dOpportunity for group study of advanced subjects related to electrical engineering outside of the curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2009,fall


#nSpecial Subjects in Electrical Engineering 
#dOpportunity for group study of advanced subjects related to electrical engineering outside of the curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iD. M. Freeman 
#t2010,spring


#nTeaching Electrical Engineering and Computer Science 1
#dFor qualified students interested in gaining teaching experience. Classroom,tutorial,or laboratory teaching under the supervision of a faculty member. Enrollment limited by availability of suitable teaching assignments. 
#iG. C. Verghese 
#t2008,fall


#nTeaching Electrical Engineering and Computer Science 1
#dFor qualified students interested in gaining teaching experience. Classroom,tutorial,or laboratory teaching under the supervision of a faculty member. Enrollment limited by availability of suitable teaching assignments. 
#iG. C. Verghese
#t2009,spring


#nTeaching Electrical Engineering and Computer Science 2
#dFor Teaching Assistants in Electrical Engineering and Computer Science,in cases where teaching assignment is approved for academic credit by the department. 
#iG. C. Verghese 
#t2008,fall


#nTeaching Electrical Engineering and Computer Science 2
#dFor Teaching Assistants in Electrical Engineering and Computer Science,in cases where teaching assignment is approved for academic credit by the department. 
#iG. C. Verghese
#t2009,spring


#nTeaching College-Level Science and Engineering 
#dParticipatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include: theories of adult learning,course development,promoting active learning,problem solving,and critical thinking in students,communicating with a diverse student body,using educational technology to further learning,lecturing,creating effective tests and assignments,and assessment and evaluation. Students research and present a relevant topic of particular interest. Subject is appropriate for both novices and those with teaching experience. 
#iL. Breslow 
#t2009,spring


#nSpecial Subjects in Electrical Engineering 
#dOpportunity for group study of advanced subjects related to electrical engineering outside of the curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iG. C. Verghese
#t2008,fall


#nSpecial Subjects in Electrical Engineering 
#dOpportunity for group study of advanced subjects related to electrical engineering outside of the curriculum. Offerings initiated by members of the EECS faculty on an ad hoc basis,subject to department approval. 
#iG. C. Verghese 
#t2009,spring


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iC. J. Terman 
#t2009,fall


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iC. J. Terman 
#t2010,spring


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iC. J. Terman 
#t2010,summer


#nPractical Experience in EECS 
#dFor Course 6 students in the SM/PhD track who seek practical off-campus research experiences or internships in electrical engineering or computer science. Before enrolling,students must have a firm employment offer from a company or organization and secure a research supervisor within EECS. Employers required to document the work accomplished. Research proposals subject to departmental approval,consult departmental Graduate Office. 
#iT. P. Orlando 
#t2009,fall


#nPractical Experience in EECS 
#dFor Course 6 students in the SM/PhD track who seek practical off-campus research experiences or internships in electrical engineering or computer science. Before enrolling,students must have a firm employment offer from a company or organization and secure a research supervisor within EECS. Employers required to document the work accomplished. Research proposals subject to departmental approval,consult departmental Graduate Office. 
#iT. P. Orlando 
#t2010,spring


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iA. C. Smith 
#t2008,fall


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iA. C. Smith 
#t2009,spring


#nResearch in Electrical Engineering and Computer Science 
#dFor EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science,in cases where the assigned research is approved for academic credit by the department. Hours arranged with research supervisor. 
#iA. C. Smith
#t2009,summer


#nPractical Experience in EECS 
#dFor Course 6 students in the SM/PhD track who seek practical off-campus research experiences or internships in electrical engineering or computer science. Before enrolling,students must have a firm employment offer from a company or organization and secure a research supervisor within EECS. Employers required to document the work accomplished. Research proposals subject to departmental approval,consult departmental Graduate Office. 
#iT. P. Orlando 
#t2008,fall


#nPractical Experience in EECS 
#dFor Course 6 students in the SM/PhD track who seek practical off-campus research experiences or internships in electrical engineering or computer science. Before enrolling,students must have a firm employment offer from a company or organization and secure a research supervisor within EECS. Employers required to document the work accomplished. Research proposals subject to departmental approval,consult departmental Graduate Office. 
#iT. P. Orlando 
#t2009,spring


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2009,fall


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2010,spring


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2010,summer


#nMaster of Engineering Program Thesis 
#dProgram of research leading to the writing of an MEng thesis,to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng students who have been admitted to the MEng program. 
#iC. J. Terman 
#t2009,fall


#nMaster of Engineering Program Thesis 
#dProgram of research leading to the writing of an MEng thesis,to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng students who have been admitted to the MEng program. 
#iC. J. Terman 
#t2010,spring


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2008,fall


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2009,spring


#nGraduate Thesis 
#dProgram of research leading to the writing of an SM,EE,ECS,PhD,or ScD thesis,to be arranged by the student and an appropriate MIT faculty member. 
#iT. P. Orlando 
#t2009,summer


#nMaster of Engineering Program Thesis 
#dProgram of research leading to the writing of an MEng thesis,to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng students who have been admitted to the MEng program. 
#iA. C. Smith
#t2008,fall


#nMaster of Engineering Program Thesis 
#dProgram of research leading to the writing of an MEng thesis,to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng students who have been admitted to the MEng program. 
#iA. C. Smith 
#t2009,spring


#nMaster of Engineering Program Thesis 
#dProgram of research leading to the writing of an MEng thesis,to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng students who have been admitted to the MEng program. 
#iA. C. Smith
#t2009,summer

