The program is described in more detail under Interdisciplinary Graduate Programs. The month Leaders for Global Operations LGO program combines graduate degrees in engineering and management for those with previous postgraduate work experience and strong undergraduate degrees in a technical field.
During the two-year program, students complete a six-month internship at one of LGO's partner companies, where they conduct research that forms the basis of a dual-degree thesis. After graduation, alumni lead strategic initiatives in high-tech, operations, and manufacturing companies.
The System Design and Management SDM program is a partnership among industry, government, and the university for educating technically grounded leaders of 21st-century enterprises. Jointly sponsored by the School of Engineering and the Sloan School of Management, it is MIT's first degree program to be offered with a distance learning option in addition to a full-time in-residence option.
The Master of Science in Technology and Policy is an engineering research degree with a strong focus on the role of technology in policy analysis and formulation. The Technology and Policy Program TPP curriculum provides a solid grounding in technology and policy by combining advanced subjects in the student's chosen technical field with courses in economics, politics, quantitative methods, and social science. Many students combine TPP's curriculum with complementary subjects to obtain dual degrees in TPP and either a specialized branch of engineering or an applied social science such as political science or urban studies and planning.
See the program description under the Institute for Data, Systems, and Society. Prereq: None U Fall, Spring; first half of term units. Introduction to computer science and programming for students with little or no programming experience. Students develop skills to program and use computational techniques to solve problems.
Topics include the notion of computation, Python, simple algorithms and data structures, testing and debugging, and algorithmic complexity. Combination of 6. Final given in the seventh week of the term. Prereq: 6. Provides an introduction to using computation to understand real-world phenomena. Topics include plotting, stochastic programs, probability and statistics, random walks, Monte Carlo simulations, modeling data, optimization problems, and clustering.
Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Bell, W. Grimson, J. Fundamentals of linear systems and abstraction modeling through lumped electronic circuits. Linear networks involving independent and dependent sources, resistors, capacitors and inductors. Extensions to include nonlinear resistors, switches, transistors, operational amplifiers and transducers.
Dynamics of first- and second-order networks; design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers. Lang, T. Palacios, D. Perreault, J. 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. Provides an introduction to the design of digital systems and computer architecture.
Emphasizes expressing all hardware designs in a high-level hardware language and synthesizing the designs. Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.
Institute LAB. Introduces probabilistic modeling for problems of inference and machine learning from data, emphasizing analytical and computational aspects. Distributions, marginalization, conditioning, and structure, including graphical and neural network representations.
Belief propagation, decision-making, classification, estimation, and prediction. Sampling methods and analysis. Introduces asymptotic analysis and information measures. Computational laboratory component explores the concepts introduced in class in the context of contemporary applications.
Students design inference algorithms, investigate their behavior on real data, and discuss experimental results. Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design.
Boning, A. Chlipala, S. Devadas, A. An integrated introduction to electrical engineering and computer science, taught using substantial laboratory experiments with mobile robots. Key issues in the design of engineered artifacts operating in the natural world: measuring and modeling system behaviors; assessing errors in sensors and effectors; specifying tasks; designing solutions based on analytical and computational models; planning, executing, and evaluating experimental tests of performance; refining models and designs.
Issues addressed in the context of computer programs, control systems, probabilistic inference problems, circuits and transducers, which all play important roles in achieving robust operation of a large variety of engineered systems. Freeman, A. Hartz, L. Kaelbling, T. Covers signals, systems and inference in communication, control and signal processing.
Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization.
Least-mean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters. Studies interaction between materials, semiconductor physics, electronic devices, and computing systems. Develops intuition of how transistors operate.
Topics range from introductory semiconductor physics to modern state-of-the-art nano-scale devices. Considers how innovations in devices have driven historical progress in computing, and explores ideas for further improvements in devices and computing. Students apply material to understand how building improved computing systems requires knowledge of devices, and how making the correct device requires knowledge of computing systems.
Includes a design project for practical application of concepts, and labs for experience building silicon transistors and devices. Akinwande, J. Kong, T. Palacios, M. Analysis and design of modern applications that employ electromagnetic phenomena for signals and power transmission in RF, microwaves, optical and wireless communication systems. Fundamentals include dynamic solutions for Maxwell's equations; electromagnetic power and energy, waves in media, metallic and dielectric waveguides, radiation, and diffraction; resonance; filters; and acoustic analogs.
Lab activities range from building to testing of devices and systems e. Students work in teams on self-proposed maker-style design projects with a focus on fostering creativity, teamwork, and debugging skills.
Subject meets with 6. Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators.
Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors.
Extensive use of engineering examples. Students taking graduate version complete additional assignments. Studies key concepts, systems, and algorithms to reliably communicate data in settings ranging from the cellular phone network and the Internet to deep space. Weekly laboratory experiments explore these areas in depth. Topics presented in three modules - bits, signals, and packets - spanning the multiple layers of a communication system.
Bits module includes information, entropy, data compression algorithms, and error correction with block and convolutional codes. Signals module includes modeling physical channels and noise, signal design, filtering and detection, modulation, and frequency-division multiplexing.
Packets module includes switching and queuing principles, media access control, routing protocols, and data transport protocols. Same subject as 2. Integrated overview of the biophysics of cells from prokaryotes to neurons, with a focus on mass transport and electrical signal generation across cell membrane.
First third of course focuses on mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Second third focuses on electrical properties of cells: ion transport to action potential generation and propagation in electrically excitable cells. Synaptic transmission. Electrical properties interpreted via kinetic and molecular properties of single voltage-gated ion channels. Final third focuses on biophysics of synaptic transmission and introduction to neural computing.
Laboratory and computer exercises illustrate the concepts. Students taking graduate version complete different assignments. Preference to juniors and seniors. Application of the principles of energy and mass flow to major human organ systems. Anatomical, physiological and clinical features of the cardiovascular, respiratory and renal systems.
Mechanisms of regulation and homeostasis. Systems, features and devices that are most illuminated by the methods of physical sciences and engineering models. Required laboratory work includes animal studies. See description under subject See description under subject 2. Enrollment limited. Slocum, G. Hom, E. Roche, N. Same subject as HST. Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine.
Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling.
Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs.
Greenberg, E. Adalsteinsson, W. Explores biomedical signals generated from electrocardiograms, glucose detectors or ultrasound images, and magnetic resonance images. Topics include physical characterization and modeling of systems in the time and frequency domains; analog and digital signals and noise; basic machine learning including decision trees, clustering, and classification; and introductory machine vision. Labs designed to strengthen background in signal processing and machine learning.
Students design and run structured experiments, and develop and test procedures through further experimentation. Introduces fundamental principles and techniques of software development: how to write software that is safe from bugs, easy to understand, and ready for change. Topics include specifications and invariants; testing, test-case generation, and coverage; abstract data types and representation independence; design patterns for object-oriented programming; concurrent programming, including message passing and shared memory concurrency, and defending against races and deadlock; and functional programming with immutable data and higher-order functions.
Includes weekly programming exercises and larger group programming projects. Topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, operating systems; performance, networks; naming; security and privacy; fault-tolerant systems, atomicity and coordination of concurrent activities, and recovery; impact of computer systems on society.
Case studies of working systems and readings from the current literature provide comparisons and contrasts. Includes a single, semester-long design project. Students engage in extensive written communication exercises. Introduces representations, methods, and architectures used to build applications and to account for human intelligence from a computational point of view. Covers applications of rule chaining, constraint propagation, constrained search, inheritance, statistical inference, and other problem-solving paradigms.
Also addresses applications of identification trees, neural nets, genetic algorithms, support-vector machines, boosting, and other learning paradigms. Considers what separates human intelligence from that of other animals. Analyzes issues associated with the implementation of higher-level programming languages.
Fundamental concepts, functions, and structures of compilers. The interaction of theory and practice. Using tools in building software. Includes a multi-person project on compiler design and implementation. Introduces principles, algorithms, and applications of machine learning from the point of view of modeling and prediction; formulation of learning problems; representation, over-fitting, generalization; clustering, classification, probabilistic modeling; and methods such as support vector machines, hidden Markov models, and neural networks.
Meets with 6. Recommended prerequisites: 6. Boning, P. Jaillet, L. Studies the structure and interpretation of computer programs which transcend specific programming languages.
Demonstrates thought patterns for computer science using Scheme. Includes weekly programming projects. REST Credit cannot also be received for An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems.
Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Bresler, P. Jaillet, J. Same subject as Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.
Mathematical introduction to the theory of computing. Rigorously explores what kinds of tasks can be efficiently solved with computers by way of finite automata, circuits, Turing machines, and communication complexity, introducing students to some major open problems in mathematics. Builds skills in classifying computational tasks in terms of their difficulty.
Discusses other fundamental issues in computing, including the Halting Problem, the Church-Turing Thesis, the P versus NP problem, and the power of randomness. Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths.
Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. Covers the algorithmic and machine learning foundations of computational biology, combining theory with practice. Principles of algorithm design, influential problems and techniques, and analysis of large-scale biological datasets.
Topics include a genomes: sequence analysis, gene finding, RNA folding, genome alignment and assembly, database search; b networks: gene expression analysis, regulatory motifs, biological network analysis; c evolution: comparative genomics, phylogenetics, genome duplication, genome rearrangements, evolutionary theory.
These are coupled with fundamental algorithmic techniques including: dynamic programming, hashing, Gibbs sampling, expectation maximization, hidden Markov models, stochastic context-free grammars, graph clustering, dimensionality reduction, Bayesian networks. Same subject as 7. See description under subject 7.
Students must provide their own laptop and software. Introduces fundamental concepts for 6. Students engage in problem solving, using Mathematica and MATLAB software extensively to help visualize processing in the time frequency domains. Electric circuit theory with application to power handling electric circuits. Modeling and behavior of electromechanical devices, including magnetic circuits, motors, and generators. Operational fundamentals of synchronous. Interconnection of generators and motors with electric power transmission and distribution circuits.
Power generation, including alternative and sustainable sources. Incorporation of energy storage in power systems. Same subject as EC. Intuition-based introduction to electronics, electronic components and test equipment such as oscilloscopes, meters voltage, resistance inductance, capacitance, etc.
Emphasizes individual instruction and development of skills, such as soldering, assembly, and troubleshooting. Students design, build, and keep a small electronics project to put their new knowledge into practice.
Intended for students with little or no previous background in electronics. Same subject as CMS. See description under subject CMS. Limited to Tan, S. Verrilli, R. Eberhardt, A. Introduction to embedded systems in the context of connected devices, wearables, and the "Internet of Things" IoT.
Topics include microcontrollers, energy utilization, algorithmic efficiency, interfacing with sensors, networking, cryptography, and local versus distributed computation. Students design, make, and program an Internet-connected wearable or handheld device. In the final project, student teams design and demo their own server-connected IoT system. Enrollment limited; preference to first- and second-year students.
Mueller, J. Steinmeyer, J. Prereq: None U Fall Units arranged. Prereq: Permission of instructor U Fall Not offered regularly; consult department Units arranged Can be repeated for credit. Prereq: Permission of instructor U Fall; second half of term Not offered regularly; consult department Units arranged Can be repeated for credit. Individual experimental work related to electrical engineering and computer science.
Student must make arrangements with a project supervisor and file a proposal endorsed by the supervisor. Departmental approval required. Written report to be submitted upon completion of work. Consult Department Undergraduate Office. Experimental laboratory explores the design, construction, and debugging of analog electronic circuits.
Lectures and laboratory projects in the first half of the course investigate the performance characteristics of semiconductor devices diodes, BJTs, and MOSFETs and functional analog building blocks, including single-stage amplifiers, op amps, small audio amplifier, filters, converters, sensor circuits, and medical electronics ECG, pulse-oximetry.
Projects involve design, implementation, and presentation in an environment similar to that of industry engineering design teams. Instruction and practice in written and oral communication provided. Opportunity to simulate real-world problems and solutions that involve tradeoffs and the use of engineering judgment. Investigates digital systems with a focus on FPGAs.
Lectures and labs cover logic, flip flops, counters, timing, synchronization, finite-state machines, digital signal processing, as well as more advanced topics such as communication protocols and modern sensors. Prepares students for the design and implementation of a final project of their choice: games, music, digital filters, wireless communications, video, or graphics. Steinmeyer, G. Hom, A. Introduces analysis and design of embedded systems.
Microcontrollers provide adaptation, flexibility, and real-time control. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station e. Includes a sequence of assigned projects, followed by a final project of the student's choice, emphasizing creativity and uniqueness.
Provides instruction in written and oral communication. To satisfy the independent inquiry component of this subject, students expand the scope of their laboratory project. Students taking independent inquiry version 6.
Introduces basic electrical engineering concepts, components, and laboratory techniques. Covers analog integrated circuits, power supplies, and digital circuits. Lab exercises provide practical experience in constructing projects using multi-meters, oscilloscopes, logic analyzers, and other tools. Includes a project in which students build a circuit to display their own EKG.
Enrollment limited; preference to Course 20 majors and minors. Boyden, M. Jonas, S. Nagle, P. So, S. Wasserman, M. Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating.
Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Presents concepts, principles, and algorithmic foundations for robots and autonomous vehicles operating in the physical world. Topics include sensing, kinematics and dynamics, state estimation, computer vision, perception, learning, control, motion planning, and embedded system development.
Students design and implement advanced algorithms on complex robotic platforms capable of agile autonomous navigation and real-time interaction with the physical word. Students engage in extensive written and oral communication exercises. Autonomous robotics contest emphasizing technical AI, vision, mapping and navigation from a robot-mounted camera.
Teams should have members with varying engineering, programming and mechanical backgrounds. Culminates with a robot competition at the end of IAP. Artificial Intelligence programming contest in Java. Student teams program virtual robots to play Battlecode, a real-time strategy game.
Competition culminates in a live BattleCode tournament. Assumes basic knowledge of programming. Student teams learn to design and build functional and user-friendly web applications.
All teams are eligible to enter a competition where sites are judged by industry experts. Beginners and experienced web programmers welcome, but some previous programming experience is recommended. Student teams design and build an Android application based on a given theme. Lectures and labs led by experienced students and leading industry experts, covering the basics of Android development, concepts and tools to help participants build great apps.
Contest culminates with a public presentation in front of a judging panel comprised of professional developers and MIT faculty. Prizes awarded. Introduction to iOS game design and development for students already familiar with object-oriented programming. Provides a set of basic tools Objective-C and Cocos2D and exposure to real-world issues in game design. Working in small teams, students complete a final project in which they create their own iPhone game.
At the end of IAP, teams present their games in competition for prizes awarded by a judging panel of gaming experts. Same subject as 3. Includes lectures and laboratory sessions on processing techniques: wet and dry etching, chemical and physical deposition, lithography, thermal processes, packaging, and device and materials characterization. Homework uses process simulation tools to build intuition about higher order effects. Emphasizes interrelationships between material properties and processing, device structure, and the electrical, mechanical, optical, chemical or biological behavior of devices.
Students fabricate solar cells, and a choice of MEMS cantilevers or microfluidic mixers. Students formulate their own device idea, either based on cantilevers or mixers, then implement and test their designs in the lab. Institute LAB Credit cannot also be received for 6. Lectures, laboratory exercises and projects on optical signal generation, transmission, detection, storage, processing and display.
Topics include polarization properties of light; reflection and refraction; coherence and interference; Fraunhofer and Fresnel diffraction; holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; display technologies; optical waveguides and fiber-optic communication systems; photodetectors.
Students may use this subject to find an advanced undergraduate project. Students engage in extensive oral and written communication exercises. Recommended prerequisite: 8. Application of electronic flash sources to measurement and photography. First half covers fundamentals of photography and electronic flashes, including experiments on application of electronic flash to photography, stroboscopy, motion analysis, and high-speed videography. Students write four extensive lab reports.
In the second half, students work in small groups to select, design, and execute independent projects in measurement or photography that apply learned techniques. Project planning and execution skills are discussed and developed over the term. Provides design-focused instruction on how to build software applications. Design topics include classic human-computer interaction HCI design tactics need finding, heuristic evaluation, prototyping, user testing , conceptual design modeling and evaluating constituent concepts , abstract data modeling, and visual design.
Implementation topics include functional programming in Javascript, reactive front-ends, web services, and databases.
Students work in teams on term-long projects in which they construct applications of social value. Project-based introduction to building efficient, high-performance and scalable software systems. Topics include performance analysis, algorithmic techniques for high performance, instruction-level optimizations, vectorization, cache and memory hierarchy optimization, and parallel programming.
Illustrates a constructive as opposed to a descriptive approach to computer architecture. Topics include combinational and pipelined arithmetic-logic units ALU , in-order pipelined microarchitectures, branch prediction, blocking and unblocking caches, interrupts, virtual memory support, cache coherence and multicore architectures.
Labs in a modern Hardware Design Language HDL illustrate various aspects of microprocessor design, culminating in a term project in which students present a multicore design running on an FPGA board. Build autonomous poker players and aquire the knowledge of the game of poker. Showcase decision making skills, apply concepts in mathematics, computer science and economics. Provides instruction in programming, game theory, probability and statistics and machine learning. Concludes with a final competition and prizes.
Covers the fundamentals of Java, helping students develop intuition about object-oriented programming. Focuses on developing working software that solves real problems. Designed for students with little or no programming experience.
Concepts covered useful to 6. Students complete daily assignments, a small-scale individual project, and a mandatory online diagnostic test. Prereq: None U Spring Not offered regularly; consult department units. Introduces the methods used to measure human auditory abilities. Discusses auditory function, principles of psychoacoustic measurement, models for psychoacoustic performance, and experimental techniques.
Project topics: absolute and differential auditory sensitivity, operating characteristics of human observers, span of auditory judgment, adaptive measurement procedures, and scaling sensory magnitudes. Knowledge of probability helpful. Same subject as 21M. See description under subject 21M. Laboratory subject that covers content not offered in the regular curriculum.
Research project for those EECS students whose curriculum requires a senior project. To be arranged by the student and an appropriate MIT faculty member. Students who register for this subject must consult the department undergraduate office. Students engage in extensive written communications exercises. Instruction in effective undergraduate research, including choosing and developing a research topic, surveying previous work and publications, research topics in EECS and the School of Engineering, industry best practices, design for robustness, technical presentation, authorship and collaboration, and ethics.
Students engage in extensive written and oral communication exercises, in the context of an approved advanced research project. A total of 12 units of credit is awarded for completion of the fall and subsequent spring term offerings.
Prereq: None U Fall, Spring units. Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.
Introduces the principal algorithms for linear, network, discrete, robust, nonlinear, and dynamic optimization. Emphasizes 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. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details.
Prereq: Dynamic programming as a unifying framework for sequential decision-making under uncertainty, Markov decision problems, and stochastic control.
Perfect and imperfect state information models. Finite horizon and infinite horizon problems, including discounted and average cost formulations. Value and policy iteration. Suboptimal methods. Approximate dynamic programming for large-scale problems, and reinforcement learning. Applications and examples drawn from diverse domains. While an analysis prerequisite is not required, mathematical maturity is necessary. Linear, discrete- and continuous-time, multi-input-output systems in control, related areas.
Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators.
Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6. Same subject as IDS. See description under subject IDS. Computer-aided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness trade-offs. Model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; nonlinear effects.
Prereq: Permission of instructor G Spring Not offered regularly; consult department units Can be repeated for credit. Advanced study of topics in control. Specific focus varies from year to year. Prereq: Permission of instructor G Fall, Spring Not offered regularly; consult department units Can be repeated for credit.
Advanced study of topics in numerical methods. Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas.
Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; robust optimization; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness.
Unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, sub-gradient and first-order methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods.
Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions and Lagrange multipliers. Geometric approach to duality theory.
Applications drawn from control, communications, machine learning, and resource allocation problems. Emphasis on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notion in different environments. Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexity-based ideas, complexity results, and efficient implementations.
Examples from several engineering areas, in particular systems and control applications. Advanced study of topics in communications. Review of probability and laws of large numbers; Poisson counting process and renewal processes; Markov chains including Markov decision theory , branching processes, birth-death processes, and semi-Markov processes; continuous-time Markov chains and reversibility; random walks, martingales, and large deviations; applications from queueing, communication, control, and operations research.
Provides an introduction to 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. Bresler, D. Gamarnik, E. Mossel, Y. 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. 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. Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor BJT and metal oxide semiconductor MOS technologies.
Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references, and translinear circuits. Provides practical experience through various lab exercises, including a broadband amplifier design and characterization. Learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from classical analytical techniques to modern computational strategies.
Students apply concepts introduced in lectures and online assignments to design labs that include discussion-based checkoffs. In lab, students use circuits, sensors, actuators, and a microcontroller to design, build and test controllers for, e. Hands-on introduction to the design and construction of power electronic circuits and motor drives.
Laboratory exercises shared with 6. Basic electric machines introduced including DC, induction, and permanent magnet motors, with drive considerations.
Students taking graduate version complete additional assignments and an extended final project. Prereq: Permission of instructor G Fall Not offered regularly; consult department units Can be repeated for credit.
Advanced study of topics in circuits. Consult department for details. The application of electronics to energy conversion and control. Modeling, analysis, and control techniques. Design of power circuits including inverters, rectifiers, and dc-dc converters.
Analysis and design of magnetic components and filters. Characteristics of power semiconductor devices. Numerous application examples, such as motion control systems, power supplies, and radio-frequency power amplifiers. Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socio-economical systems.
Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations e. Students develop their own models and simulators for self-proposed applications, with an emphasis on creativity, teamwork, and communication.
Prior basic linear algebra and programming e. Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion.
Noise shaping. Flowgraph structures for DT systems. Parametric signal modeling, linear prediction, and lattice filters. Spectral analysis, time-frequency analysis, relation to filter banks. Multirate signal processing, perfect reconstruction filter banks, and connection to wavelets.
Digital images as two-dimensional signals. Digital signal processing theories used for digital image processing, including one-dimensional and two-dimensional convolution, Fourier transform, discrete Fourier transform, and discrete cosine transform.
Image processing basics. Image enhancement. Image restoration. Image coding and compression. Video processing including video coding and compression.
Additional topics in image and video processing. Introduces the rapidly developing field of spoken language processing including automatic speech recognition. Topics include acoustic theory of speech production, acoustic-phonetics, signal representation, acoustic and language modeling, search, hidden Markov modeling, neural networks models, end-to-end deep learning models, and other machine learning techniques applied to speech and language processing topics.
Lecture material intersperses theory with practice. Includes problem sets, laboratory exercises, and opened-ended term project. Advanced study of topics in signals and systems. Device and circuit level optimization of digital building blocks. Circuit design styles for logic, arithmetic, and sequential blocks.
Estimation and minimization of energy consumption. Interconnect models and parasitics, device sizing and logical effort, timing issues clock skew and jitter , and active clock distribution techniques. Memory architectures, circuits sense amplifiers , and devices. Testing of integrated circuits.
Extensive custom and standard cell layout and simulation in design projects and software labs. Introduction to the design and implementation of large-scale digital systems using hardware description languages and high-level synthesis tools in conjunction with standard commercial electronic design automation EDA tools. Emphasizes modular and robust designs, reusable modules, correctness by construction, architectural exploration, meeting area and timing constraints, and developing functional field-programmable gate array FPGA prototypes.
Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment.
Topics include learning of distributions, hypothesis testing including multiple comparison procedures , linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Recommended prerequisite: Polyanskiy, D.
Shah, J. Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches.
Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated.
Students cannot receive credit without simultaneous completion of a 6-unit disciplinary module. Using typical engineering examples, the text provides readers with an understanding of recent developments in DOBC as well as the tools required to make the most of this promising approach to disturbance-attenuation.
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