Home  Subject Search  Help  Symbols Help  PreReg Help  Final Exam Schedule  
Course 6: Electrical Engineering and Computer Science 
  6.10/6.50    6.20/6.60    6.30/6.70    6.40/6.80    6.90/6.ZZ   
Signal Processing6.3000 Signal Processing
(, )
Prereq: 6.100A and 18.03 Units: 606 Lecture: TR2 (3270) Lab: TR4 (4370) Recitation: TR3 (4370) +final Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design. J. Kong No textbook information available 6.3010 Signals, Systems and Inference
()
Prereq: 6.3000 and (6.3700, 6.3800, or 18.05) Units: 408 Covers signals, systems and inference in communication, control and signal processing. Topics include inputoutput and statespace models of linear systems driven by deterministic and random signals; time and transformdomain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization. Leastmean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters. Staff 6.3020[J] Fundamentals of Music Processing
()
(Same subject as 21M.387[J]) (Subject meets with 21M.587) Prereq: 6.3000 and 21M.051 Units: 309 URL: https://mta.mit.edu/music/classschedule Lecture: TR12.30 (4270) Analyzes recorded music in digital audio form using advanced signal processing and optimization techniques to understand higherlevel musical meaning. Covers fundamental tools like windowing, feature extraction, discrete and shorttime Fourier transforms, chromagrams, and onset detection. Addresses analysis methods including dynamic time warping, dynamic programming, selfsimilarity matrices, and matrix factorization. Explores a variety of applications, such as event classification, audio alignment, chord recognition, structural analysis, tempo and beat tracking, contentbased audio retrieval, and audio decomposition. Students taking graduate version complete different assignments. E. Egozy Textbooks (Fall 2024) 6.7000 DiscreteTime Signal Processing
()
Prereq: 6.3010 Units: 408 Lecture: TR1112.30 (34303) Recitation: F1 (34301) or F2 (34301) Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion. Noise shaping. Flowgraph structures for DT systems. IIR and FIR filter design techniques. Parametric signal modeling, linear prediction, and lattice filters. Discrete Fourier transform, DFT computation, and FFT algorithms. Spectral analysis, timefrequency analysis, relation to filter banks. Multirate signal processing, perfect reconstruction filter banks, and connection to wavelets. J. Ward No textbook information available 6.7010 Digital Image Processing
()
Prereq: 6.3000 and 6.3700 Units: 309 Introduces models, theories, and algorithms key to digital image processing. Core topics covered include models of image formation, image processing fundamentals, filtering in the spatial and frequency domains, image transforms, and feature extraction. Additional topics include image enhancement, image restoration and reconstruction, compression of images and videos, visual recognition, and the application of machine learningbased approaches to image processing. Includes studentdriven term project. Y. Rachlin, J. S. Lim 6.7020 Array Processing
()
Prereq: 6.7000 and (2.687 or (6.3010 and 18.06)) Units: 327 Adaptive and nonadaptive processing of signals received at arrays of sensors. Deterministic beamforming, spacetime random processes, optimal and adaptive algorithms, and the sensitivity of algorithm performance to modeling errors and limited data. Methods of improving the robustness of algorithms to modeling errors and limited data are derived. Advanced topics include an introduction to matched field processing and physicsbased methods of estimating signal statistics. Homework exercises providing the opportunity to implement and analyze the performance of algorithms in processing data supplied during the course. Staff Control6.3100 Dynamical System Modeling and Control Design
(, )
(Subject meets with 6.3102) Prereq: Physics II (GIR) and (18.06 or 18.C06) Units: 444 First lecture (9/4) meets in. Lecture: MW3 (2190) Lab: F101 (38545) or F25 (38545) A learnbydesign introduction to modeling and control of discrete and continuoustime systems, from intuitionbuilding analytical techniques to more computational and datacentric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, rootloci, leadlag, phase margin); computational strategies (statespace, eigenplacement, LQR); and datacentric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrustdriven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs. D. Freeman No textbook information available 6.3102 Dynamical System Modeling and Control Design
(, )
(Subject meets with 6.3100) Prereq: Physics II (GIR) and (18.06 or 18.C06) Units: 444 First lecture (9/4) meets in. Lecture: MW3 (2190) Lab: F101 (38545) or F25 (38545) A learnbydesign introduction to modeling and control of discrete and continuoustime systems, from intuitionbuilding analytical techniques to more computational and datacentric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, rootloci, leadlag, phase margin); computational strategies (statespace, eigenplacement, LQR); and datacentric approaches (state estimation, regression and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g. optimizing thrustdriven positioners or stabilizing magnetic levitators). Students in the graduate version complete additional problems and labs. D. M. Freeman No textbook information available 6.7100[J] Dynamic Systems and Control
()
(Same subject as 16.338[J]) Prereq: 6.3000 and 18.06 Units: 408 Linear, discrete and continuoustime, multiinputoutput systems in control, related areas. Least squares and matrix perturbation problems. Statespace 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 observerbased compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6.3100. Staff 6.7110 Multivariable Control Systems
()Not offered regularly; consult department Prereq: 6.7100 or 16.31 Units: 309 Computeraided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness tradeoffs. Modelbased compensators; Qparameterization; illposed optimization problems; dynamic augmentation; linearquadratic optimization of controllers; Hinfinity controller design; Musynthesis; model and compensator simplification; nonlinear effects. Computeraided (MATLAB) design homework using models of physical processes. A. Megretski 6.7120 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems
()
(Subject meets with 6.7121) Prereq: 6.2200, (6.2000 and 6.3100), or permission of instructor Units: 408 Lecture: MW10.3012 (26322) Recitation: R11 (26314) Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; dataenabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. M. Ilic No textbook information available 6.7121 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems
()
(Subject meets with 6.7120) Prereq: 6.2200, (6.2000 and 6.3100), or permission of instructor Units: 408 Lecture: MW10.3012 (26322) Recitation: R11 (26314) Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; dataenabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. M. Ilic No textbook information available Optimization & Engineering Mathematics6.3260[J] Networks
()
(Same subject as 14.15[J]) (Subject meets with 14.150) Prereq: 6.3700 or 14.30 Units: 408 Highlights common principles that permeate the functioning of diverse technological, economic and social networks. Utilizes three sets of tools for analyzing networks  random graph models, optimization, and game theory  to study informational and learning cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; control and use of energy networks; and biological networks. Students taking graduate version complete additional assignments. A. Wolitzky 6.7210[J] Introduction to Mathematical Programming
()
(Same subject as 15.081[J]) Prereq: 18.06 Units: 408 Lecture: TR12.30 (E52164) Recitation: F12 (2105) +final Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; robust optimization; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NPcompleteness. P. Jaillet Textbooks (Fall 2024) 6.7220[J] Nonlinear Optimization
()
(Same subject as 15.084[J]) Prereq: 18.06 and (18.100A, 18.100B, or 18.100Q) Units: 408 Unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, subgradient and firstorder methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions and Lagrange multipliers. Geometric approach to duality theory. Applications drawn from control, communications, machine learning, and resource allocation problems. Staff 6.7230[J] Algebraic Techniques and Semidefinite Optimization
()
(Same subject as 18.456[J]) Prereq: 6.7210 or 15.093 Units: 309 Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexitybased 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. Staff 6.7240 Game Theory with Engineering Applications
()Not offered regularly; consult department Prereq: 6.3702 Units: 408 Introduction to fundamentals of game theory and mechanism design with motivations for each topic drawn from engineering applications (including distributed control of wireline/wireless communication networks, transportation networks, pricing). Emphasis on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notion in different environments. Topics include normal form games, supermodular games, dynamic games, repeated games, games with incomplete/imperfect information, mechanism design, cooperative game theory, and network games. A. Ozdaglar 6.7250 Optimization for Machine Learning
()Not offered regularly; consult department Prereq: 6.3900 and 18.06 Units: 309 Optimization algorithms are central to all of machine learning. Covers a variety of topics in optimization, with a focus on nonconvex optimization. Focuses on both classical and cuttingedge results, including foundational topics grounded in convexity, complexity theory of firstorder methods, stochastic optimization, as well as recent progress in nonEuclidean optimization, deep learning, and beyond. Prepares students to appreciate a broad spectrum of ideas in OPTML, learning to be not only informed users but also gaining exposure to research questions in the area. Staff 6.7260 Network Science and Models
()
Prereq: 6.3702 and 18.06 Units: 309 Introduces the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Static models of random graphs, preferential attachment, and other graph evolution models. Epidemic propagation, opinion dynamics, social learning, and inference in networks. Applications drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks. P. Jaillet 6.7300[J] Introduction to Modeling and Simulation
()
(Same subject as 2.096[J], 16.910[J]) Prereq: 18.03 or 18.06 Units: 363 Lecture: MW12.30 (32155) Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socioeconomical systems. Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations (e.g., automatic assembly of constitutive and conservation principles); linear system solvers (sparse and iterative); nonlinear solvers (Newton and homotopy); ordinary, timeperiodic and partial differential equation solvers; and model order reduction. Students develop their own models and simulators for selfproposed applications, with an emphasis on creativity, teamwork, and communication. Prior basic linear algebra required and at least one numerical programming language (e.g., MATLAB, Julia, Python, etc.) helpful. L. Daniel No required or recommended textbooks 6.7310[J] Introduction to Numerical Methods
()
(Same subject as 18.335[J]) Prereq: 18.06, 18.700, or 18.701 Units: 309 Advanced introduction to numerical analysis: accuracy and efficiency of numerical algorithms. Indepth coverage of sparsematrix/iterative and densematrix algorithms in numerical linear algebra (for linear systems and eigenproblems). Floatingpoint arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) may also be surveyed. Final project involves some programming. Staff 6.7320[J] Parallel Computing and Scientific Machine Learning
()
(Same subject as 18.337[J]) Prereq: 18.06, 18.700, or 18.701 Units: 309 Introduction to scientific machine learning with an emphasis on developing scalable differentiable programs. Covers scientific computing topics (numerical differential equations, dense and sparse linear algebra, Fourier transformations, parallelization of largescale scientific simulation) simultaneously with modern data science (machine learning, deep neural networks, automatic differentiation), focusing on the emerging techniques at the connection between these areas, such as neural differential equations and physicsinformed deep learning. Provides direct experience with the modern realities of optimizing code performance for supercomputers, GPUs, and multicores in a highlevel language. Staff 6.7330[J] Numerical Methods for Partial Differential Equations
()
(Same subject as 2.097[J], 16.920[J]) Prereq: 18.03 or 18.06 Units: 309 Lecture: MW9.3011 (37212) Covers the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential and integral equations. Topics include mathematical formulations; finite difference, finite volume, finite element, and boundary element discretization methods; and direct and iterative solution techniques. The methodologies described form the foundation for computational approaches to engineering systems involving heat transfer, solid mechanics, fluid dynamics, and electromagnetics. Computer assignments requiring programming. J. Peraire No textbook information available 6.7340[J] Fast Methods for Partial Differential and Integral Equations
(, )
(Same subject as 18.336[J]) Prereq: 6.7300, 16.920, 18.085, 18.335, or permission of instructor Units: 309 Unified introduction to the theory and practice of modern, near lineartime, numerical methods for largescale partialdifferential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterflybased methods; multiresolution approaches, such as multigrid algorithms and hierarchical lowrank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging. Staff Communications6.3400 Introduction to EECS via Communication Networks
() Not offered regularly; consult department Prereq: 6.100A Units: 444 Studies key concepts, systems, and algorithms to reliably communicate data in settings ranging from the cellular phone network and the Internet to deep space. Weekly laboratory experiments explore these areas in depth. Topics presented in three modules  bits, signals, and packets  spanning the multiple layers of a communication system. Bits module includes information, entropy, data compression algorithms, and error correction with block and convolutional codes. Signals module includes modeling physical channels and noise, signal design, filtering and detection, modulation, and frequencydivision multiplexing. Packets module includes switching and queuing principles, media access control, routing protocols, and data transport protocols. Staff 6.7410 Principles of Digital Communication
()Not offered regularly; consult department (Subject meets with 6.7411) Prereq: (6.3000 or 6.3102) and (6.3700, 6.3800, or 18.05) Units: 309 Subject Cancelled Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systemslevel view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; inclass time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. V. Chan 6.7411 Principles of Digital Communication
()
(Subject meets with 6.7410) Prereq: (6.3000, 6.3100, or 6.3400) and (6.3700, 6.3800, or 18.05) Units: 309 Subject Cancelled Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systemslevel view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; inclass time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. M. Medard 6.7420 Heterogeneous Networks: Architecture, Transport, Proctocols, and Management
()Not offered regularly; consult department Prereq: 6.1200 or 6.3700 Units: 408 Subject Cancelled Introduction to modern heterogeneous networks and the provision of heterogeneous services. Architectural principles, analysis, algorithmic techniques, performance analysis, and existing designs are developed and applied to understand current problems in network design and architecture. Begins with basic principles of networking. Emphasizes development of mathematical and algorithmic tools; applies them to understanding network layer design from the performance and scalability viewpoint. Concludes with network management and control, including the architecture and performance analysis of interconnected heterogeneous networks. Provides background and insight to understand current network literature and to perform research on networks with the aid of network design projects. V. W. S. Chan, R. G. Gallager 6.7430 Optical Networks
()Not offered regularly; consult department Prereq: 6.1200 or 6.3700 Units: 309 Introduces the fundamental and practical aspects of optical network technology, architecture, design and analysis tools and techniques. The treatment of optical networks are from the architecture and system design points of view. Optical hardware technologies are introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. Beyond the Physical Layer, the higher network layers (Media Access Control, Network and Transport Layers) are treated together as integral parts of network design. Performance metrics, analysis and optimization techniques are developed to help guide the creation of high performance complex optical networks. Staff 6.7440 Principles of Wireless Communication
()Not offered regularly; consult department Prereq: 6.7410 Units: 309 Introduction to design, analysis, and fundamental limits of wireless transmission systems. Wireless channel and system models; fading and diversity; resource management and power control; multipleantenna and MIMO systems; spacetime codes and decoding algorithms; multipleaccess techniques and multiuser detection; broadcast codes and precoding; cellular and adhoc network topologies; OFDM and ultrawideband systems; architectural issues. G. W. Wornell, L. Zheng 6.7450[J] DataCommunication Networks
()
(Same subject as 16.37[J]) Prereq: 6.3700 or 18.204 Units: 309 Subject Cancelled Provides an introduction to data networks with an analytic perspective, using wireless networks, satellite networks, optical networks, the internet and data centers as primary applications. Presents basic tools for modeling and performance analysis. Draws upon concepts from stochastic processes, queuing theory, and optimization. E. Modiano 6.7460 Essential Coding Theory
()Not offered regularly; consult department Prereq: 6.1210 and 6.1400 Units: 309 Introduces the theory of errorcorrecting 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 errorcorrecting codes; limitations on the combinatorial performance of errorcorrecting codes; decoding algorithms; and applications to other areas of mathematics and computer science. Staff 6.7470 Information Theory
()
Prereq: 6.3700 Units: 309 Credit cannot also be received for 6.7480 Subject Cancelled Mathematical definitions of information measures, convexity, continuity, and variational properties. Lossless source coding; variablelength and block compression; SlepianWolf theorem; ergodic sources and ShannonMcMillan theorem. Hypothesis testing, large deviations and Iprojection. Fundamental limits of block coding for noisy channels: capacity, dispersion, finite blocklength bounds. Coding with feedback. Joint sourcechannel problem. Ratedistortion theory, vector quantizers. Advanced topics include GelfandPinsker problem, multiple access channels, broadcast channels (depending on available time). M. Medard, L. Zheng 6.7480 Information Theory: From Coding to Learning
()

  6.10/6.50    6.20/6.60    6.30/6.70    6.40/6.80    6.90/6.ZZ   