Course 06

COURSE 6 E L E C T R I C A L E N G I N E E R I N G A N D CO M P U T E R S C I E N C E
98 2 0 1 4 – 2 0 1 5
BA S I C U N D E R G R A D UAT E
S U B J EC TS
6.0001 Introduction to Computer Science
Programming in Python (New)
Prereq: None
U (Fall, Spring; first half of term)
2-3-1
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 6.0001 and 6.0002 counts as
REST subject.
J. V. Guttag
6.0002 Introduction to Computational
Thinking and Data Science (New)
Prereq: 6.0001 or permission of instructor
U (Fall, Spring; second half of term)
2-3-1
Provides an introduction to using computa-tion
to understand real-world phenomena.
Topics include plotting, stochastic programs,
probability and statistics, random walks,
Monte Carlo simulations, modeling data,
optimization problems, and clustering.
Combination of 6.0001 and 6.0002 counts as
REST subject.
J. V. Guttag
6.01 Introduction to EECS I
Prereq: None. Coreq: Physics II (GIR)
U (Fall, Spring)
2-4-6 1/2 Institute LAB
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 solu-tions
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. 6 Engineering Design
Points.
D. M. Freeman, A. Hartz, L. P. Kaelbling,
T. Lozano-Perez
6.02 Introduction to EECS II
Prereq: 6.01; 18.03 or 18.06
U (Fall, Spring)
4-4-4 1/2 Institute LAB
Credit cannot also be received for 6.S02
Explores communication signals, systems and
networks. Substantial laboratory experiments
illustrate the role of abstraction and modularity
in engineering design. Students gain practical
experience in building reliable systems using
imperfect components; selecting appropriate
design metrics; choosing effective representa-tions
for information; and evaluating tradeoffs
in complex systems. Topics include physical
characterization and modeling of transmission
systems in the time and frequency domains;
analog and digital signaling; coding; detect-ing
and correcting errors; relating information
transmission rate to signal power, bandwidth
and noise; and engineering of packet-switched
networks. 6 Engineering Design Points.
H. Balakrishnan, G. C. Verghese, J. K. White
6.07J Projects in Microscale Engineering for the
Life Sciences
(Same subject as HST.410J)
Prereq: None
U (Spring)
2-4-3
See description under subject HST.410J.
D. Freeman, M. Gray, A. Aranyosi
6.002 Circuits and Electronics
Prereq: 18.03; Physics II (GIR) or 6.01
U (Fall, Spring)
4-1-7 REST
Fundamentals of the lumped circuit abstraction.
Resistive elements and networks, independent
and dependent sources, switches and MOS
devices, digital abstraction, amplifiers, and
energy storage elements. Dynamics of first- and
second-order networks; design in the time and
frequency domains; analog and digital circuits
and applications. Design exercises. Occasional
laboratory. 4 Engineering Design Points.
A. Agarwal, J. del Alamo, J. H. Lang,
D. J. Perreault
6.003 Signals and Systems
Prereq: 6.02
U (Fall, Spring)
5-0-7
Presents the fundamentals of signal and
system analysis. Topics include discrete-time
and continuous-time signals, Fourier series
and transforms, Laplace and Z transforms, and
analysis of linear, time-invariant systems. Ap-plications
drawn broadly from engineering and
physics, including audio and image processing,
communications, and automatic control.
4 Engineering Design Points.
D. M. Freeman, Q. Hu, J. S. Lim
6.004 Computation Structures
Prereq: Physics II (GIR)
U (Fall, Spring)
4-0-8
Introduces architecture of digital systems,
emphasizing structural principles common
to a wide range of technologies. Multilevel
implementation strategies; definition of new
primitives (e.g., gates, instructions, procedures,
and processes) and their mechanization using
lower-level elements. Analysis of potential
concurrency; precedence constraints and per-formance
measures; pipelined and multidimen-sional
systems. Instruction set design issues;
architectural support for contemporary software
structures. 4 Engineering Design Points.
S. A. Ward, C. J. Terman
6.005 Elements of Software Construction
Prereq: 6.01; Coreq: 6.042
U (Fall, Spring)
4-0-8 REST
Introduces fundamental principles and tech-niques
of software development, i.e., how to
write software that is safe from bugs, easy to un-derstand,
and ready for change. Topics include
specifications and invariants; testing, test-case
generation, and coverage; state machines;
abstract data types and representation inde-pendence;
design patterns for object-oriented

99
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 0 0 0 1 t o 6 . 0 2 3 J
programming; concurrent programming, includ-ing
message passing and shared concurrency,
and defending against races and deadlock; and
functional programming with immutable data
and higher-order functions. Includes weekly pro-gramming
exercises and two substantial group
projects. 12 Engineering Design Points.
D. N. Jackson, R. C. Miller
6.006 Introduction to Algorithms
Prereq: 6.01, 6.042
U (Fall, Spring)
4-0-8
Introduction to mathematical modeling of
computational problems, as well as common
algorithms, algorithmic paradigms, and data
structures used to solve these problems. Empha-sizes
the relationship between algorithms and
programming, and introduces basic performance
measures and analysis techniques for these
problems.
R. L. Rivest, S. Devadas
6.007 Electromagnetic Energy: From Motors to
Solar Cells
Prereq: Physics II (GIR) or 6.01; 18.03
U (Fall, Spring)
5-1-6
Discusses applications of electromagnetic and
equivalent quantum mechanical principles to
classical and modern devices. Covers energy
conversion and power flow in both macroscopic
and quantum-scale electrical and electrome-chanical
systems, including electric motors and
generators, electric circuit elements, quantum
tunneling structures and instruments. Studies
photons as waves and particles and their inter-action
with matter in optoelectronic devices,
including solar cells and displays.
V. Bulovic, R. J. Ram
6.008 Introduction to Inference (New)
U (Fall)
4-0-8
Introduces probabilistic modeling for problems
of inference and machine learning from data,
emphasizing analytical and computational as-pects.
Distributions, marginalization, condition-ing,
and structure; graphical representations.
Belief propagation, decision-making, classifica-tion,
estimation, and prediction. Sampling meth-ods
and analysis. Also provides introduction to
asymptotic analysis and information measures,
and applications. 4 Engineering Design Points.
P. Golland, G. W. Wornell
6.011 Introduction to Communication, Control,
and Signal Processing
Prereq: 6.003; 6.041 or 18.440
U (Spring)
4-0-8
Covers signals, systems and inference in com-munication,
control and signal processing. Top-ics
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, cor-relation
functions, power spectra, spectral fac-torization.
Least-mean square error estimation;
Wiener filtering. Hypothesis testing; detection;
matched filters.
A. V. Oppenheim, G. C. Verghese
6.012 Microelectronic Devices and Circuits
Prereq: 6.002
U (Fall, Spring)
4-0-8
Microelectronic device modeling, and basic
microelectronic circuit analysis and design.
Physical electronics of semiconductor junction
and MOS devices. Relating terminal behavior to
internal physical processes, developing circuit
models, and understanding the uses and limita-tions
of different models. Use of incremental and
large-signal techniques to analyze and design
transistor circuits, with examples chosen from
digital circuits, linear amplifiers, and other
integrated circuits. Design project. 4 Engineer-ing
Design Points.
A. I. Akinwande, D. A. Antoniadis, J. Kong,
C. G. Sodini
6.013 Electromagnetics and Applications
Prereq: 6.007
U (Spring)
4-0-8
Credit cannot also be received for 6.630
Analysis and design of modern applications that
employ electromagnetic phenomena, including
signal and power transmission in guided com-munication
systems and wireless and optical
communications. Fundamentals include dynamic
solutions to Maxwell's equations; electromag-netic
power and energy, waves in media, guided
waves, radiation, and diffraction; coupling to
media and structures; resonance; and acoustic
analogs.
L. Daniel, M. R. Watts
6.021J Cellular Biophysics and Neurophysiology
(Same subject as 2.791J, 20.370J)
(Subject meets with 2.794J, 6.521J, 20.470J,
HST.541J)
Prereq: Physics II (GIR); 18.03; 2.005, 6.002,
6.003, 6.071, 10.301, 20.110, 20.111, or
permission of instructor
U (Fall)
5-2-5
Integrated overview of the biophysics of cells
from prokaryotes to neurons, with a focus on
mass transport and electrical signal genera-tion
across cell membrane. First half of course
focuses on mass transport through membranes:
diffusion, osmosis, chemically mediated, and
active transport. Second half focuses on electri-cal
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 gradu-ate
version complete different assignments.
Preference to juniors and seniors. 4 Engineering
Design Points.
J. Han, T. Heldt, J. Voldman
6.022J Quantitative Systems Physiology
(Same subject as 2.792J, 20.371J, HST.542J)
(Subject meets with 2.796J, 6.522J, 20.471J)
Prereq: Physics II (GIR), 18.03, or permission of
instructor
U (Spring)
4-2-6
Application of the principles of energy and mass
flow to major human organ systems. Mecha-nisms
of regulation and homeostasis. Ana-tomical,
physiological and pathophysiological
features of the cardiovascular, respiratory and
renal systems. Systems, features and devices
that are most illuminated by the methods of
physical sciences. Laboratory work includes
some animal studies. Students taking graduate
version complete additional assignments. 2
Engineering Design Points.
T. Heldt, R. G. Mark, C. M. Stultz
6.023J Fields, Forces and Flows in Biological
Systems
Prereq: Physics II (GIR); 2.005, 6.021, 20.320, or
U (Spring)
4-0-8
See description under subject 20.330J.
J. Han, S. Manalis

100
2 0 1 4 – 2 0 1 5 E L E C T R I C A L E N G I N E E R I N G A N D C O M P U T E R S C I E N C E
6.024J Molecular, Cellular, and Tissue
Biomechanics
(Same subject as 2.797J, 3.053J, 20.310J)
Prereq: 2.370 or 2.772J; 18.03 or 3.016; Biology
(GIR)
U (Spring)
4-0-8
R. D. Kamm, A. J. Grodzinsky, K. Van Vliet
6.025J Medical Device Design
(Same subject as 2.750J)
(Subject meets with 2.75J, 6.525J)
Prereq: 2.72, 6.071, 6.115, or permission of
instructor
U (Fall)
4-0-8
A. H. Slocum, C. G. Sodini
6.033 Computer System Engineering
Prereq: 6.004, 6.02
U (Spring)
5-1-6
Topics on the engineering of computer soft-ware
and hardware systems: techniques for
controlling complexity; strong modularity using
client-server design, operating systems; perfor-mance,
networks; naming; security and privacy;
fault-tolerant systems, atomicity and coordi-nation
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. Two design projects. Students engage
in extensive written communication exercises.
Enrollment may be limited. 4 Engineering Design
Points.
M. F. Kaashoek, H. Balakrishnan
6.034 Artificial Intelligence
Prereq: 6.01
U (Fall)
5-3-4
Introduces representations, techniques, and
architectures used to build applied systems and
to account for intelligence from a computational
point of view. Applications of rule chaining,
heuristic search, constraint propagation, con-strained
search, inheritance, and other problem-solving
paradigms. Applications of identification
trees, neural nets, genetic algorithms, and
other learning paradigms. Speculations on the
contributions of human vision and language
systems to human intelligence. 4 Engineering
Design Points.
P. H. Winston
6.035 Computer Language Engineering
Prereq: 6.004 and 6.005
U (Fall)
4-4-4
Analyzes issues associated with the implemen-tation
of higher-level programming languages.
Fundamental concepts, functions, and structures
of compilers. The interaction of theory and prac-tice.
Using tools in building software. Includes
a multi-person project on compiler design and
implementation. 8 Engineering Design Points.
S. P. Amarasinghe
6.036 Introduction to Machine Learning
Prereq: 6.01
U (Spring)
4-0-8
Introduces principles, algorithms, and applica-tions
of machine learning from the point of
view of modeling and prediction; formulation of
learning problems; representation, over-fitting,
generalization; clustering, classification, proba-bilistic
modeling; and methods such as support
vector machines, hidden Markov models, and
Bayesian networks.
R. Barzilay, T. Jaakkola, L. P. Kaelbling
6.037 Structure and Interpretation of Computer
Programs
Prereq: None
U (IAP)
1-0-5 [P/D/F]
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. Enroll-ment
may be limited.
Staff
6.041 Probabilistic Systems Analysis
(Subject meets with 6.431)
Prereq: Calculus II (GIR)
U (Fall, Spring)
4-0-8 REST
An introduction to probability theory, and the
modeling and analysis of probabilistic systems.
Probabilistic models, conditional probability.
Discrete and continuous random variables.
Expectation and conditional expectation. Limit
Theorems. Bernoulli and Poisson processes.
Markov chains. Bayesian estimation and hypoth-esis
testing. Elements of statistical inference.
Meets with graduate subject 6.431, but assign-ments
differ.
D. P. Bertsekas, J. N. Tsitsiklis
6.042J Mathematics for Computer Science
Prereq: Calculus I (GIR)
U (Fall, Spring)
5-0-7 REST
Elementary discrete mathematics for computer
science and engineering. Emphasis on math-ematical
definitions and proofs as well as on
applicable methods. Topics: formal logic nota-tion,
proof methods; induction, well-ordering;
sets, relations; elementary graph theory; integer
congruences; asymptotic notation and growth
of functions; permutations and combinations,
counting principles; discrete probability. Further
selected topics such as: recursive definition and
structural induction; state machines and invari-ants;
recurrences; generating functions.
F. T. Leighton, A. R. Meyer, A. Moitra
6.045J Automata, Computability, and
Complexity
Prereq: 6.042
U (Spring)
4-0-8
Provides an introduction to some of the central
ideas of theoretical computer science, including
circuits, finite automata, Turing machines and
computability, efficient algorithms and reducibil-ity,
the P versus NP problem, NP-completeness,
the power of randomness, cryptography, compu-tational
learning theory, and quantum comput-ing.
Examines the classes of problems that can
and cannot be solved in various computational
models.
S. Aaronson
6.046J Design and Analysis of Algorithms
Prereq: 6.006
U (Fall, Spring)
4-0-8
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; am-ortized
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.
E. Demaine, M. Goemans

101
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 0 2 4 J t o 6 . 0 7 3 J
6.047 Computational Biology: Genomes,
Networks, Evolution
(Subject meets with 6.878J, HST.507J)
Prereq: 6.006, 6.041, Biology (GIR); or
U (Fall)
3-0-9
Covers the algorithmic and machine learning
foundations of computational biology, combin-ing
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, evolution-ary
theory. These are coupled with fundamental
algorithmic techniques including: dynamic pro-gramming,
hashing, Gibbs sampling, expecta-tion
maximization, hidden Markov models, sto-chastic
context-free grammars, graph clustering,
dimensionality reduction, Bayesian networks.
M. Kellis
6.049J Evolutionary Biology: Concepts, Models
and Computation
Prereq: 7.03; 6.0002, 6.01, or permission of
instructor
U (Spring)
3-0-9
R. Berwick, D. Bartel
6.050J Information, Entropy, and Computation
Prereq: Physics I (GIR)
U (Spring)
4-0-5
Explores the ultimate limits to communication
and computation, with an emphasis on the
physical nature of information and information
processing. Topics include information and com-putation,
digital signals, codes, and compres-sion.
Biological representations of information.
Logic circuits, computer architectures, and
algorithmic information. Noise, probability, and
error correction. The concept of entropy applied
to channel capacity and to the second law of
thermodynamics. Reversible and irreversible
operations and the physics of computation.
Quantum computation.
P. Penfield, Jr., S. Lloyd
6.057 Introduction to MATLAB
Prereq: None
U (IAP)
1-0-2 [P/D/F]
Accelerated introduction to MATLAB and its
popular toolboxes. Lectures are interactive, with
students conducting sample MATLAB problems
in real time. Includes problem-based MATLAB
assignments. Students must provide their own
laptop and software. Enrollment limited.
Staff
6.058 Preview of Signals and Systems
Prereq: Calculus II (GIR) or permission of
instructor
U (IAP)
2-2-2 [P/D/F]
Preparation for 6.003 or 6.011, focusing on
several key concepts, including LTI systems,
convolution, CT and DT Fourier series and trans-forms,
filtering, sampling, modulation, Laplace
and z-transforms, and feedback.
Staff
6.061 Introduction to Electric Power Systems
Prereq: 6.002, 6.013
Acad Year 2014–2015: U (Spring)
Acad Year 2015–2016: Not offered
3-0-9
Electric circuit theory with application to
power handling electric circuits. Modeling and
behavior of electromechanical devices, includ-ing
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 sustain-able
sources. Students taking graduate version
complete additional assignments. 6 Engineering
Design Points.
J. L. Kirtley, Jr.
6.S062–6.S064 Special Subject in Electrical
Engineering and Computer Science
Prereq: None
U (Fall, IAP, Spring)
Not offered regularly; consult department
Units arranged
Can be repeated for credit
Basic undergraduate subjects not offered in the
regular curriculum.
Consult Department
6.070J Electronics Project Laboratory
(Same subject as EC.120J)
Prereq: None
U (Fall, Spring)
2-2-2
Intuition-based introduction to electronics,
electronic components and test equipment such
as oscilloscopes, meters (voltage, resistance
inductance, capacitance, etc.), and signal
generators. Emphasizes individual instruction
and development of skills, such as soldering, as-sembly,
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. Enrollment may be limited.
J. Bales
6.071J Electronics, Signals, and Measurement
Prereq: 18.03
U (Spring)
3-3-6 REST
Provides the knowledge necessary for reading
schematics and designing, building, analyzing,
and testing fundamental analog and digital
circuits. Students construct interactive examples
and explore the practical uses of electronics in
engineering and experimental science, including
signals and measurement fundamentals. Uses
state-of-the-art hardware and software for data
acquisition, analysis, and control. Suitable for
students with little or no previous background in
electronics.
A. White
6.072J Introduction to Digital Electronics
(Same subject as EC.110J)
Prereq: None
0-3-3 [P/D/F]
See description under subject EC.110J.
J. Bales
6.073J Creating Video Games
(Same subject as CMS.611J)
Prereq: CMS.608 or 6.01
U (Fall)
3-3-6 HASS-A
See description under subject CMS.611J.
P. Tan, S. Verrilli, O. Macindoe, P. Kaelbling

102
Prereq: Permission of instructor
Units arranged
Units arranged [P/D/F]
Covers subject matter not offered in the regular
curriculum. Consult department to learn of offer-ings
for a particular term.
Consult Department
UNDERGRADUAT E
L A B O R ATO R Y S U B J EC TS
6.100 Electrical Engineering and Computer
Science Project
Prereq: None
U (Fall, Spring, Summer)
Units arranged
Individual experimental work related to electri-cal
engineering and computer science. Student
must make arrangements with a project supervi-sor
and file a proposal endorsed by the supervi-sor.
Departmental approval required. Written
report to be submitted upon completion of work.
A. R. Meyer
6.101 Introductory Analog Electronics
Laboratory
Prereq: 6.002 or 6.071
U (Spring)
2-9-1 Institute LAB
Introductory experimental laboratory explores
the design, construction, and debugging of ana-log
electronic circuits. Lectures and laboratory
projects in the first half of the course investigate
the performance characteristics of semiconduc-tor
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. Engineers
from local companies help students with their
design projects. 12 Engineering Design Points.
G. P. Hom
6.111 Introductory Digital Systems Laboratory
Prereq: 6.002, 6.071, or 16.004
U (Fall)
3-7-2 Institute LAB
Lectures and labs on digital logic, flip flops,
PALs, FPGAs, counters, timing, synchronization,
and finite-state machines prepare students for
the design and implementation of a final project
of their choice: games, music, digital filters,
wireless communications, video, or graphics.
Extensive use of Verilog for describing and
implementating digital logic designs. Students
engage in extensive written and oral communi-cation
exercises. 12 Engineering Design Points.
A. P. Chandrakasan, G. P. Hom
6.115 Microcomputer Project Laboratory
Prereq: 6.002, 6.003, 6.004, or 6.007
U (Spring)
3-6-3 Institute LAB
Introduces the analysis and design of embedded
systems. Microcontrollers provide adaptation,
flexibility, and real-time control. Emphasis
placed on the construction of complete systems,
including a five-axis robot arm, a fluorescent
lamp ballast, a tomographic imaging station
(e.g. a CAT scan), and a simple calculator.
Introduces a wide range of basic tools, including
software and development tools, peripheral
components such as A/D converters, communi-cation
schemes, signal processing techniques,
closed-loop digital feedback control, interface
and power electronics, and modeling of elec-tromechanical
systems. Includes a sequence of
assigned projects, followed by a final project of
the student's choice, emphasizing creativity and
uniqueness. Final project may be expanded to
satisfy a 6.UAP project. Provides instruction in
written and oral communication. 12 Engineering
Design Points.
S. B. Leeb
6.117 Introduction to Electrical Engineering Lab
Skills
Prereq: None
U (IAP)
1-3-2 [P/D/F]
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.
G. P. Hom
6.123J Bioinstrumentation Project Lab
Prereq: Biology (GIR), and 2.004 or 6.003; or
20.309; or permission of instructor
U (Spring)
2-7-3
E. Boyden, M. Jonas, S. F. Nagle, P. So,
S. Wasserman, M. F. Yanik
6.129J Biological Circuit Engineering Laboratory
Prereq: Biology (GIR), Calculus II (GIR)
U (Spring)
2-8-2 Institute LAB
Students assemble individual genes and regula-tory
elements into larger-scale circuits; they
characterize these circuits using quantitative
techniques, including flow cytometry, and model
their results computationally. Emphasizes con-cepts
and techniques to perform independent
synthetic biology research. Discusses current
literature and ongoing research in the field of
synthetic biology. Instruction and practice in
oral and written communication provided. Enroll-ment
limited. 12 Engineering Design Points.
T. Lu, R. Weiss
6.131 Power Electronics Laboratory
Prereq: 6.002, 6.003, or 6.007
U (Fall)
3-6-3 Institute LAB
Introduces the design and construction of power
electronic circuits and motor drives. Labora-tory
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 consider-ations.
Final project may be expanded to serve
as a 6.UAP project, with instructor permission.
Provides instruction in written and oral commu-nication.
S. B. Leeb
6.141J Robotics: Science and Systems I
U (Spring)
2-6-4 Institute LAB
Presents concepts, principles, and algorithms
for sensing and computation related to the

103
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . S 0 7 6 t o 6 . 1 5 2 J
physical world. Topics include motion planning,
geometric reasoning, kinematics and dynam-ics,
state estimation, tracking, map building,
manipulation, human-robot interaction, fault
diagnosis, and embedded system development.
Students specify and design a small-scale yet
complex robot capable of real-time interaction
with the natural world. Students may continue
content in 6.142. Prior knowledge of one or
more of the following areas would be useful:
control (2.004, 6.302, or 16.30); software
(1.00, 6.005, or 16.35); electronics (6.002,
6.070, 6.111, or 6.115); mechanical engineer-ing
(2.007); or independent experience such as
MasLAB, 6.270, or a relevant UROP. Students
engage in extensive written and oral com-munication
exercises. Enrollment limited. 12
N. Roy, D. Rus
6.142J Robotics: Science and Systems II
Acad Year 2015–2016: U (Fall)
2-6-4
Implementation and operation of the embed-ded
system designed in 6.141. Addresses open
research issues such as sustained autonomy,
situational awareness, and human interaction.
Students carry out experiments to assess their
design and deliver a final written report. Prior
knowledge of one or more of the following
areas would be useful: control (2.004, 6.302,
or 16.30), software (1.00, 6.005, or 16.35),
electronics (6.002, 6.070, 6.111, or 6.115),
mechanical engineering (2.007), independent
experience (MasLAB, 6.270, or a UROP). 12
D. Rus, N. Roy
6.145 Autonomous Robot Design Competition
Prereq: None
U (IAP)
1-2-2 [P/D/F]
Teams build an autonomous LEGO robot and
compete for prizes. Provides an opportunity to
explore closed-loop control and artificial intel-ligence,
and apply knowledge of algorithms and
signal processing. Crash course in programming
available to students without experience in
robotics. Enrollment limited.
Staff
6.146 Mobile Autonomous Systems Laboratory:
MASLAB
Prereq: None
U (IAP)
2-2-2 [P/D/F]
Autonomous robotics contest emphasizing tech-nical
AI, vision, mapping and navigation from
a robot-mounted camera. Few restrictions are
placed on materials, sensors, and/or actuators
enabling teams to build robots very creatively.
Teams should have members with varying
engineering, programming and mechanical
backgrounds. Culminates with a robot competi-tion
at the end of IAP. Enrollment limited.
Staff
6.147 The BattleCode Programming Competition
Prereq: None
U (IAP)
3-0-3 [P/D/F]
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 pro-gramming
in Java.
Staff
6.148 Web Programming Competition
U (IAP)
1-0-5 [P/D/F]
Teams compete to build the most functional and
user-friendly website. Competition is judged
by industry experts and includes novice and
advanced divisions. Prizes awarded. Lectures
and workshops cover website basics. Enrollment
limited.
Staff
6.149 Introduction to Programming Using
Python
Prereq: None
U (IAP)
2-2-2 [P/D/F]
Face-paced introduction to Python programming
language for students with little or no program-ming
experience. Covers both function and
object-oriented concepts. Includes weekly lab
exercises and final project. Enrollment limited.
Staff
6.150 Mobile Applications Competition
U (IAP)
2-2-2 [P/D/F]
Student teams design and build an Android ap-plication
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 partici-pants
build great apps. Contest culminates with
a public presentation in front of a judging panel
comprised of professional developers and MIT
faculty. Prizes awarded. Enrollment limited.
Staff
6.151 iOS Game Design and Development
Competition
Prereq: None
U (IAP)
2-2-2 [P/D/F]
Introduction to iOS game design and develop-ment
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 compe-tition
for prizes awarded by a judging panel of
gaming experts. Enrollment limited.
Staff
6.152J Micro/Nano Processing Technology
U (Fall)
3-4-5
Introduces the theory and technology of micro/
nano fabrication. Lectures and laboratory ses-sions
on basic processing techniques such as
vacuum processes, lithography, diffusion, oxida-tion,
and pattern transfer. Students fabricate
MOS capacitors, nanomechanical cantilevers,
and microfluidic mixers. Emphasis on the inter-relationships
between material properties and
processing, device structure, and the electri-cal,
mechanical, optical, chemical or biological
behavior of devices. Provides background for
thesis work in micro/nano fabrication. Students
L. A. Kolodziejski, J. Michel, M. A. Schmidt

104
6.161 Modern Optics Project Laboratory
Prereq: 6.003
U (Fall)
3-5-4 Institute LAB
Lectures, laboratory exercises and projects on
optical signal generation, transmission, detec-tion,
storage, processing and display. Topics
include polarization properties of light; reflec-tion
and refraction; coherence and interference;
Fraunhofer and Fresnel diffraction; holography;
Fourier optics; coherent and incoherent imaging
and signal processing systems; optical proper-ties
of materials; lasers and LEDs; electro-optic
and acousto-optic light modulators; photorefrac-tive
and liquid-crystal light modulation; display
technologies; optical waveguides and fiber-optic
communication systems; photodetectors. Stu-dents
may use this subject to find an advanced
undergraduate project. Students engage in
extensive oral and written communcation exer-cises.
Recommended prerequisites: 6.007 or
8.03. 12 Engineering Design Points.
C. Warde
6.163 Strobe Project Laboratory
Prereq: Physics II (GIR) or permission of
instructor
U (Fall, Spring)
2-8-2 Institute LAB
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 proj-ects
in measurement or photography that apply
learned techniques. Project planning and execu-tion
skills are discussed and developed over
the term. Students engage in extensive written
and oral communication exercises. Enrollment
J. K. Vandiver, J. W. Bales
6.169 Theory and Application of Circuits and
Electronics
Prereq: None. Coreq: 6.002
U (Fall, Spring)
1-1-1
Building on the framework of 6.002, provides a
deeper understanding of the theory and applica-tions
of circuits and electronics.
A. Agarwal, J. del Alamo, J. H. Lang, D. J. Perreault
6.170 Software Studio
Prereq: 6.005, 6.006
U (Fall)
4-0-8
Covers design and implementation of software
systems, using web applications as the plat-form.
Emphasizes the role of conceptual design
in achieving clarity, simplicity, and modularity.
Students complete open-ended individual as-signments
and a major team project. Enrollment
may be limited. 12 Engineering Design Points.
D. N. Jackson
6.172 Performance Engineering of Software
Systems
Prereq: 6.004, 6.005, 6.006
U (Fall)
3-12-3
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. 12 Engineering Design Points.
S. Amarasinghe, C. E. Leiserson
6.175 Constructive Computer Architecture (New)
Prereq: 6.004
U (Fall)
3-8-1
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, block-ing
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. 12 Engineer-ing
Design Points.
Arvind
6.176 Pokerbots Competition
Prereq: None
U (IAP)
2-2-2 [P/D/F]
Build autonomous poker players and aquire the
knowledge of the game of poker. Showcase deci-sion
making skills, apply concepts in mathemat-ics,
computer science and economics. Provides
instruction in programming, game theory,
probability and statistics and machine learning.
Concludes with a final competition and prizes.
Enrollment limited
Staff
6.177 Building Programming Experience in
Python
Prereq: None
U (IAP)
1-4-1 [P/D/F]
Preparation for 6.01 aimed to sharpen skills in
program design, implementation, and debug-ging
in Python. Programming intensive, with one
short structured assignment and a supervised,
but highly individual, mandatory project
presentation. Intended for students with some
elementary programming experience (equivalent
to AP Computer Science). Enrollment limited.
Staff
6.178 Introduction to Software Engineering in
Java
Prereq: None
U (IAP)
1-1-4 [P/D/F]
Covers the fundamentals of Java, helping stu-dents
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 6.005.
Enrollment limited.
Staff
6.179 Introduction to C and C++
Prereq: None
U (IAP)
3-3-0 [P/D/F]
Fast-paced introduction to the C and C++ pro-gramming
languages. Intended for those with ex-perience
in other languages who have never used
C or C++. Students complete daily assignments,
a small-scale individual project, and a mandatory
online diagnostic test. Enrollment limited.
Staff
6.182 Psychoacoustics Project Laboratory
Prereq: None
U (Spring)
3-6-3 Institute LAB
Introduces the methods used to measure human
auditory abilities. Discusses auditory function,
principles of psychoacoustic measurement,
models for psychoacoustic performance, and ex-perimental
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. Students
L. D. Braida

105
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 1 6 1 t o 6 . 2 4 3
6.S183–6.S192 Special Laboratory Subject in
Electrical Engineering and Computer Science
6.S193–6.S198 Special Laboratory Subject in
Electrical Engineering and Computer Science
Units arranged
Laboratory subject that covers content not of-fered
in the regular curriculum. Consult depart-ment
to learn of offerings for a particular term.
D. M. Freeman
SE N I O R P R O J EC TS
6.UAP Undergraduate Advanced Project
Prereq: 6.UAT
U (Fall, IAP, Spring, Summer)
0-6-0
Research project for those students completing
the SB degree, to be arranged by the student
and an appropriate MIT faculty member. Stu-dents
who register for this subject must consult
the department undergraduate office. Students
engage in extensive written communications
exercises.
A. R. Meyer
6.UAR Seminar in Undergraduate Advanced
Research
Prereq: 6.UR
U (Fall, Spring)
1-0-5
Involves choosing and developing a research
topic, surveying previous work and publications,
research topics in EECS, industry best practices,
design for robustness, technical presenta-tion,
authorship and collaboration, and ethics.
Registered students must submit an approved
proposal for an Advanced Research Project
before Add Date. Instruction and practice in oral
and written communication provided. Forms and
instructions are available in the EECS Under-graduate
Office. May be repeated for credit for a
maximum of 12 units.
A. P. Chandrakasan, D. M. Freeman
6.UAT Oral Communication
Prereq: None
U (Fall, Spring)
3-0-3
Instruction in aspects of effective technical oral
presentations through exposure to different
workplace communication skills. As preparation
for the advanced undergraduate project (UAP).
Students develop research topics, identify a re-search
supervisor, and prepare a short research
proposal for an oral presentation.
T. L. Eng
6.URS Undergraduate Research in Electrical
Year-long individual research project arranged
with appropriate faculty member or approved
supervisor. Forms and instructions for the pro-posal
and final report are available in the EECS
Undergraduate Office.
A. R. Meyer
ADVA N CE D U N D E R G R A D UAT E
S U B J EC TS A N D G R A D UAT E
S U B J EC TS BY A R E A
Systems Science and Control
Engineering
6.207J Networks
Prereq: 6.041 or 14.30
U (Spring)
4-0-8 HASS-S
Consult D. Acemoglu, M. Dahleh
6.231 Dynamic Programming and Stochastic
Control
Prereq: 6.041 or 18.313; 18.100
Acad Year 2015–2016: G (Fall)
3-0-9 H-LEVEL Grad Credit
Sequential decision-making via dynamic pro-gramming.
Unified approach to optimal control
of stochastic dynamic systems and Markovian
decision problems. Applications in linear-quadratic
control, inventory control, resource
allocation, scheduling, and planning. Optimal
decision making under perfect and imperfect
state information. Certainty equivalent, open
loop-feedback control, rollout, model predic-tive
control, aggregation, and other suboptimal
control methods. Infinite horizon problems:
discounted, stochastic shortest path, average
cost, and semi-Markov models. Value and policy
iteration. Abstract models in dynamic program-ming.
Approximate/neurodynamic program-ming.
Simulation based methods. Discussion of
current research on the solution of large-scale
problems.
D. P. Bertsekas
6.241J Dynamic Systems and Control
Prereq: 6.003, 18.06
G (Spring)
Linear, discrete- and continuous-time, multi-input-
output systems in control, related areas.
Least squares and matrix perturbation problems.
State-space models, modes, stability, control-lability,
observability, transfer function matrices,
poles and zeros, and minimality. Internal stabil-ity
of interconnected systems, feedback com-pensators,
state feedback, optimal regulation,
observers, and observer-based compensators.
Measures of control performance, robustness is-sues
using singular values of transfer functions.
Introductory ideas on nonlinear systems. Recom-mended
prerequisite: 6.302.
M. A. Dahleh, A. Megretski, E. Frazzoli
6.242 Advanced Linear Control Systems
Prereq: 18.06, 6.241
G (Fall)
Introduction 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 perfor-mance
robustness in the presence of structured
uncertainty.
M. A. Dahleh, A. Megretski
6.243 Dynamics of Nonlinear Systems
Prereq: 6.241; Coreq: 18.100
G (Fall)
Introduction to nonlinear deterministic dynami-cal
systems. Nonlinear ordinary differential equa-tions.
Planar autonomous systems. Fundamental
theory: Picard iteration, contraction mapping
theorem, and Bellman-Gronwall lemma. Stability
of equilibria by Lyapunov's first and second
methods. Feedback linearization. Application to
nonlinear circuits and control systems.
J. L. Wyatt, Jr., A. Megretski, M. Dahleh

106
6.245 Multivariable Control Systems
Prereq: 6.241 or 16.31
Computer-aided design methodologies for
synthesis of multivariable feedback control sys-tems.
Performance and robustness trade-offs.
Model-based compensators; Q-parameteriza-tion;
ill-posed optimization problems; dynamic
augmentation; linear-quadratic optimization of
controllers; H-infinity controller design; Mu-syn-thesis;
model and compensator simplification;
nonlinear effects. Computer-aided (MATLAB)
design homework using models of physical
processes. 6 Engineering Design Points.
A. Megretski
6.246, 6.247 Advanced Topics in Control
G (Fall, Spring)
Advanced study of topics in control. Specific
focus varies from year to year.
Consult Department
6.248, 6.249 Advanced Topics in Numerical
Methods
G (Fall, Spring)
Advanced study of topics in numerical methods.
Specific focus varies from year to year.
Consult Department
6.251J Introduction to Mathematical
Programming
Prereq: 18.06
G (Fall)
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; integer programming;
interior point algorithms for linear programming;
and introduction to combinatorial optimization
and NP-completeness.
J. N. Tsitsiklis, A. Schulz
6.252J Nonlinear Optimization
Prereq: 18.06, 18.100
G (Spring)
Unified analytical and computational approach
to nonlinear optimization problems. Uncon-strained
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, nondifferen-tiable
optimization, and applications in integer
programming. Comprehensive treatment of opti-mality
conditions and Lagrange multipliers. Geo-metric
approach to duality theory. Applications
drawn from control, communications, power
systems, and resource allocation problems.
R. M. Freund, D. P. Bertsekas, G. Perakis
6.253 Convex Analysis and Optimization
Prereq: 18.06, 18.100
G (Spring)
Core analytical issues of continuous optimiza-tion,
duality, and saddle point theory, and
development using a handful of unifying prin-ciples
that can be easily visualized and readily
understood. Discusses in detail the mathemati-cal
theory of convex sets and functions which
are the basis for an intuitive, highly visual, geo-metrical
approach to the subject. Convex optimi-zation
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.
D. P. Bertsekas
6.254 Game Theory with Engineering
Applications
Prereq: 6.041
Introduction to fundamentals of game theory
and mechanism design with motivations for
each topic drawn from engineering applications
(including distributed control of wireline/wire-less
communication networks, transportation
networks, pricing). Emphasis on the foundations
of the theory, mathematical tools, as well as
modeling and the equilibrium notion in differ-ent
environments. Topics include normal form
games, supermodular games, dynamic games,
repeated games, games with incomplete/imper-fect
information, mechanism design, coopera-tive
game theory, and network games.
A. Ozdaglar
6.255J Optimization Methods
Prereq: 18.06
G (Fall)
D. Bertsimas, P. Parrilo
6.256 Algebraic Techniques and Semidefinite
Optimization
Prereq: 6.251 or 6.255
Acad Year 2015–2016: G (Spring)
Theory and computational techniques for optimi-zation
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 implementa-tions.
Examples from several engineering areas,
in particular systems and control applications.
Topics include semidefinite programming,
resultants/discriminants, hyperbolic polynomi-als,
Groebner bases, quantifier elimination, and
sum of squares.
P. Parrilo
6.260, 6.261 Advanced Topics in
Communications
G (Fall, Spring)
Advanced study of topics in communications.
Consult Department
6.262 Discrete Stochastic Processes
Prereq: 6.041, 6.431 or 18.313
G (Spring)
Review of probability and laws of large num-bers;
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 devia-tions;
applications from queueing, communica-tion,
control, and operations research.
R. G. Gallager, J. L. Wyatt

107
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 2 4 5 t o 6 . 3 3 1
6.263J Data-Communication Networks
Prereq: 6.041 or 18.313
Provides an introduction to data networks
with an analytic perspective, using telephone
networks, wireless networks, optical networks,
the Internet and data centers as primary applica-tions.
Presents basic tools for modeling and
performance analysis accompanied by elemen-tary,
meaningful simulations. Develops insights
for large networks by means of simple approxi-mations.
Draws upon concepts from queueing
theory and optimization.
E. Modiano, D. Shah
6.264J Queues: Theory and Applications
Prereq: 6.262
D. Bertsimas, D. Gamarnik, J. N. Tsitsiklis
6.265J Advanced Stochastic Processes
Prereq: 6.431, 15.085J, or 18.100
D. Gamarnik, D. Shah
6.266 Network Algorithms
Prereq: 6.436 or 6.262
Modern 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.
D. Shah
6.267 Heterogeneous Networks: Architecture,
Transport, Proctocols, and Management
Prereq: 6.041 or 6.042
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 under-stand
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 con-trol,
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. 4 Engineering Design
Points.
V. W. S. Chan, R. G. Gallager
6.268 Network Science and Models
Prereq: 6.041, 18.06
Introduces the main mathematical models used
to describe large networks and dynamical pro-cesses
that evolve on networks. Static models
of random graphs, preferential attachment, and
other graph evolution models. Epidemic propa-gation,
opinion dynamics, and social learning.
Applications drawn from social, economic,
natural, and infrastructure networks, as well
as networked decision systems such as sensor
networks.
J. N. Tsitsiklis, P. Jaillet
6.281J Logistical and Transportation Planning
Methods
(Same subject as 1.203J, 15.073J, 16.76J,
ESD.216J)
Prereq: 6.041
G (Fall)
R. C. Larson, A. R. Odoni, A. I. Barnett
6.291 Seminar in Systems, Communications,
and Control Research
G (Fall, Spring)
Units arranged H-LEVEL Grad Credit
Advanced topics in systems, communications,
control, optimization, and signal processing.
Topics selected according to student and instruc-tor
interest. See instructor for specific topics to
be offered in a particular term.
S. K. Mitter
Electronics, Computers, and Systems
6.301 Solid-State Circuits
Prereq: 6.012, 6.003
G (Fall)
3-2-7
Analysis and design of transistor circuits, based
directly on the semiconductor physics and tran-sistor
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 experi-ence
assumed. 4 Engineering Design Points.
H. S. Lee
6.302 Feedback Systems
Prereq: 6.003, 2.003, or 16.004
G (Spring)
4-2-6
Introduction to design of feedback systems.
Properties and advantages of feedback systems.
Time-domain and frequency-domain perfor-mance
measures. Stability and degree of stabil-ity.
Nyquist criterion. Frequency-domain design.
Root locus method. Compensation techniques.
Application to a wide variety of physical sys-tems.
Some previous laboratory experience with
electronic systems is assumed (6.002, 6.071, or
16.04). 4 Engineering Design Points.
Staff
6.331 Advanced Circuit Techniques
Prereq: 6.301, 6.302; permission of instructor
Following 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,

108
digital-to-analog or analog-to-digital converters,
and power amplifiers. One of each student's
designs is presented to the class, and one may
be built and evaluated. Associated laboratory
emphasizing the use of modern analog build-ing
blocks. Enrollment limited. 12 Engineering
Design Points.
Staff
6.332, 6.333 Advanced Topics in Circuits
G (Fall, Spring)
Advanced study of topics in circuits. Specific
focus varies from year to year. Consult depart-ment
for details.
Consult Department
6.334 Power Electronics
Prereq: 6.012
G (Spring)
The application of electronics to energy conver-sion
and control. Modeling, analysis, and control
techniques. Design of power circuits including
inverters, rectifiers, and dc-dc converters. Analy-sis
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.
D. J. Perreault
6.335J Fast Methods for Partial Differential and
Integral Equations
Prereq: 6.336, 16.920, 18.085, 18.335, or
G (Fall)
A. Townsend
6.336J Introduction to Numerical Simulation
Prereq: 18.03 or 18.06
G (Fall)
Introduction 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.
L. Daniel, J. K. White
6.337J Introduction to Numerical Methods
Prereq: 18.03 or 18.034; 18.06, 18.700, or
18.701
G (Spring)
S. G. Johnson
6.338J Parallel Computing
Prereq: 18.06, 18.700, or 18.701
A. Edelman
6.339J Numerical Methods for Partial
Differential Equations
Prereq: 18.03 or 18.06
G (Fall)
Q. Wang, J. K. White
6.341 Discrete-Time Signal Processing
Prereq: 6.011
Representation, analysis, and design of discrete
time signals and systems. Decimation, interpola-tion,
and sampling rate conversion. Noise shap-ing.
Flowgraph structures for DT systems. Lattice
filters. Time- and frequency-domain design
techniques for IIR and FIR filters. Parametric sig-nal
modeling, linear prediction, and the relation
to lattice filters. Discrete Fourier transform (DFT).
Computation of the DFT including FFT algorithms.
Short-time Fourier analysis and relation to filter
banks. Multirate techniques. Perfect reconstruc-tion
filter banks and their relation to wavelets.
Hilbert transforms and cepstral analysis.
A. V. Oppenheim
6.344 Digital Image Processing
Prereq: 6.003, 6.041
G (Spring)
Digital images as two-dimensional signals. Digi-tal
signal processing theories used for digital im-age
processing, including one-dimensional and
two-dimensional convolution, Fourier transform,
discrete Fourier transform, and discrete cosine
transform. Image processing basics. Image en-hancement.
Image restoration. Image coding and
compression. Video processing including video
coding and compression. Additional topics in-cluding
digital high-definition television systems.
J. S. Lim
6.345J Automatic Speech Recognition
Prereq: 6.003, 6.041, or permission of instructor
Introduces the rapidly developing fields of auto-matic
speech recognition and spoken language
processing. Topics include acoustic theory of
speech production and perception, acoustic-phonetics,
signal representation, acoustic and
language modeling, search, hidden Markov
modeling, robustness, adaptation, discrimina-tive
and alternative approaches. Lectures inter-spersed
with theory and applications. Assign-ments
include problems, laboratory exercises,
and a term project. 4 Engineering Design Points.
V. W. Zue, J. R. Glass
6.347, 6.348 Advanced Topics in Signals and
Systems
G (Fall, Spring)
Advanced study of topics in signals and systems.
Consult Department
6.374 Analysis and Design of Digital Integrated
Circuits
Prereq: 6.012, 6.004
G (Fall)
Device and circuit level optimization of digital
building blocks. MOS device models including
Deep Sub-Micron effects. Circuit design styles
for logic, arithmetic, and sequential blocks. Es-timation
and minimization of energy consump-tion.
Interconnect models and parasitics, device
sizing and logical effort, timing issues (clock
skew and jitter), and active clock distribution

109
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 3 3 2 t o 6 . 4 4 0
techniques. Memory architectures, circuits
(sense amplifiers), and devices. Testing of inte-grated
circuits. Extensive custom and standard
cell layout and simulation in design projects and
software labs. 4 Engineering Design Points.
A. P. Chandrakasan, V. Sze, T. Xanthopoulos
6.375 Complex Digital Systems Design
Prereq: 6.004
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. Em-phasizes
modular and robust designs, reusable
modules, correctness by construction, archi-tectural
exploration, meeting area and timing
constraints, and developing functional field-programmable
gate array (FPGA) prototypes.
Extensive use of CAD tools in weekly labs serve
as preparation for a multi-person design project
on multi-million gate FPGAs. Enrollment may be
Arvind
6.376 Bioelectronics
Prereq: 6.301
G (Fall)
Comprehensive introduction to analog micro-electronic
design with an emphasis on ultra-low-power
electronics, biomedical electronics, and
bio-inspired electronics. Device physics of the
MOS transistor, including subthreshold opera-tion
and scaling to nanometer processes. Ultra-low-
noise, RF, sensor, actuator, and feedback
circuits. System examples vary from year to year
and include implantable and noninvasive bio-medical
systems, circuits inspired by neurobiol-ogy
or cell biology, micromechanical systems
(MEMS), and biological sensing and actuating
systems. Class project involves a complete de-sign
of a VLSI chip, including layout, verification,
design-rule checking, and SPICE simulation. 8
R. Sarpeshkar
Probabilistic Systems and
Communication
6.431 Applied Probability
G (Fall, Spring)
4-0-8
Meets with undergraduate subject 6.041.
Requires the completion of additional advanced
home problems.
D. P. Bertsekas, J. N. Tsitsiklis
6.434J Statistics for Engineers and Scientists
Prereq: Calculus II (GIR), 18.06, 6.431, or
Provides a rigorous introduction to fundamen-tals
of statistics motivated by engineering ap-plications
and emphasizing the informed use of
modern statistical software. Topics include suffi-cient
statistics, exponential families, estimation,
hypothesis testing, measures of performance,
and notion of optimality.
M. Win, J. N. Tsitsiklis
6.435 System Identification
Prereq: 6.241, 6.432
Mathematical models of systems from observa-tions
of their behavior. Time series, state-space,
and input-output models. Model structures,
parametrization, and identifiability. Nonpara-metric
methods. Prediction error methods for
parameter estimation, convergence, consis-tency,
andasymptotic distribution. Relations
to maximum likelihood estimation. Recursive
estimation; relation to Kalman filters; structure
determination; order estimation; Akaike crite-rion;
and bounded but unknown noise models.
Robustness and practical issues.
M. A. Dahleh
6.436J Fundamentals of Probability
G (Fall)
Introduction to probability theory. Probability
spaces and measures. Discrete and continuous
random variables. Conditioning and indepen-dence.
Multivariate normal distribution. Abstract
integration, expectation, and related conver-gence
results. Moment generating and charac-teristic
functions. Bernoulli and Poisson process.
Finite-state Markov chains. Convergence notions
and their relations. Limit theorems. Familiarity
with elementary notions in probability and real
analysis is desirable.
J. N. Tsitsiklis, D. Gamarnik
6.437 Inference and Information
Prereq: 6.041 or 6.436
G (Spring)
Introduction to principles of Bayesian and non-
Bayesian statistical inference. Hypothesis test-ing
and parameter estimation, sufficient statis-tics;
exponential families. EM agorithm. Log-loss
inference criterion, entropy and model capacity.
Kullback-Leibler distance and information geom-etry.
Asymptotic analysis and large deviations
theory. Model order estimation; nonparametric
statistics. Computational issues and approxima-tion
techniques; Monte Carlo methods. Selected
special topics such as universal prediction and
compression.
P. Golland, G. W. Wornell
6.438 Algorithms for Inference
Prereq: 6.041 or 6.436; 18.06
G (Fall)
Introduction to statistical inference with proba-bilistic
graphical models. Covers directed and
undirected graphical models, factor graphs, and
Gaussian models; hidden Markov models, linear
dynamical systems.; sum-product and junction
tree algorithms; forward-backward algorithm,
Kalman filtering and smoothing; and min-sum
algorithm and Viterbi algorithm. Presents
variational methods, mean-field theory, and
loopy belief propagation; and particle methods
and filtering. Includes building graphical models
from data; parameter estimation, Baum-Welch
algorithm; structure learning; and selected
special topics.
P. Golland, G. W. Wornell, D. Shah
6.440 Essential Coding Theory
Prereq: 6.006, 6.045
Introduces the theory of error-correcting codes.
Focuses on the essential results in the area,
taught from first principles. Special focus on
results of asymptotic or algorithmic signifi-cance.
Principal topics include construction and
existence results for error-correcting codes;

110
limitations on the combinatorial performance
of error-correcting codes; decoding algorithms;
and applications to other areas of mathematics
and computer science.
M. Sudan, D. Moshkovitz
6.441 Information Theory
Prereq: 6.041
G (Spring)
Mathematical definitions of information mea-sures,
convexity, continuity, and variational
properties. Lossless source coding; variable-length
and block compression; Slepian-Wolf
theorem; ergodic sources and Shannon-
McMillan theorem. Hypothesis testing, large
deviations and I-projection. Fundamental limits
of block coding for noisy channels: capacity,
dispersion, finite blocklength bounds. Coding
with feedback. Joint source-channel problem.
Rate-distortion theory, vector quantizers. Ad-vanced
topics include Gelfand-Pinsker problem,
multiple access channels, broadcast channels
(depending on available time).
M. Medard, Y. Polyanskiy, L. Zheng
6.442 Optical Networks
Prereq: 6.041, 6.042
G (Spring)
Introduces the fundamental and practical as-pects
of optical network technology, architec-ture,
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 transmis-sion
systems and network architectures are
based. Beyond the Physical Layer, the higher
network layers (Media Access Control, Network
and Transport Layers) are treated together as
integral parts of network design. Performance
metrics, analysis and optimization techniques
are developed to help guide the creation of high
performance complex optical networks.
V. W. S. Chan
6.443J Quantum Information Science
Prereq: 18.435
G (Spring, Summer)
Examines quantum computation and quantum
information. Topics include quantum circuits,
the quantum Fourier transform and search
algorithms, the quantum operations formalism,
quantum error correction, Calderbank-Shor-Ste-ane
and stabilizer codes, fault tolerant quantum
computation, quantum data compression,
quantum entanglement, capacity of quantum
channels, and quantum cryptography and the
proof of its security. Prior knowledge of quantum
mechanics required.
Information: P. W. Shor
6.450 Principles of Digital Communication
Prereq: 6.011
G (Fall)
Communication sources and channels; data
compression; entropy and the AEP; Lempel-Ziv
universal coding; scalar and vector quantization;
L2 waveforms; signal space and its representa-tion
by sampling and other expansions; aliasing;
the Nyquist criterion; PAM and QAM modula-tion;
Gaussian noise and random processes;
detection and optimal receivers; fading channels
and wireless communication; introduction to
communication system design.
M. Medard, L. Zheng
6.452 Principles of Wireless Communication
Prereq: 6.450
Introduction to design, analysis, and funda-mental
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 detec-tion;
broadcast codes and precoding; cellular
and ad-hoc network topologies; OFDM and
ultrawideband systems; architectural issues.
G. W. Wornell, L. Zheng
6.453 Quantum Optical Communication
Prereq: 6.011, 18.06
Quantum optics: Dirac notation quantum
mechanics; harmonic oscillator quantization;
number states, coherent states, and squeezed
states; radiation field quantization and quantum
field propagation; P-representation and classi-cal
fields. Linear loss and linear amplification:
commutator preservation and the Uncertainty
Principle; beam splitters; phase-insensitive and
phase-sensitive amplifiers. Quantum photodetec-tion:
direct detection, heterodyne detection, and
homodyne detection. Second-order nonlinear
optics: phasematched interactions; optical para-metric
amplifiers; generation of squeezed states,
photon-twin beams, non-classical fourth-order
interference, and polarization entanglement.
Quantum systems theory: optimum binary detec-tion;
quantum precision measurements; quan-tum
cryptography; and quantum teleportation.
J. H. Shapiro
6.454 Graduate Seminar in Area I
Student-run advanced graduate seminar with
focus on topics in communications, control,
signal processing, optimization. Participants
give presentations outside of their own research
to expose colleagues to topics not covered
in the usual curriculum. Recent topics have
included compressed sensing, MDL principle,
communication complexity, linear programming
decoding, biology in EECS, distributed hypoth-esis
testing, algorithms for random satisfaction
problems, and cryptogaphy. Open to advanced
students from all areas of EECS. Limited to 12.
L. Zheng, D. Shah
6.456 Array Processing
Prereq: 6.341; 2.687, or 6.011 and 18.06
Adaptive and non-adaptive processing of signals
received at arrays of sensors. Deterministic
beamforming, space-time random processes,
optimal and adaptive algorithms, and the sensi-tivity
of algorithm performance to modeling er-rors
and limited data. Methods of improving the
robustness of algorithms to modeling errors and
limited data are derived. Advanced topics in-clude
an introduction to matched field process-ing
and physics-based methods of estimating
signal statistics. Homework exercises providing
the opportunity to implement and analyze the
performance of algorithms in processing data
supplied during the course.
J. Preisig

111
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 4 4 1 t o 6 . 5 5 5 J
Bioelectrical Engineering
6.503 Foundations of Algorithms and
Computational Techniques in Systems Biology
Prereq: 6.021, 6.034, 6.046, 6.336, 18.417, or
Acad Year 2014–2015: U (Spring)
3-0-9
Illustrates computational approaches to solving
problems in systems biology. Uses a series of
case studies to demonstrate how an effective
match between the statement of a biological
problem and the selection of an appropriate al-gorithm
or computational technique can lead to
fundamental advances. Covers several discrete
and numerical algorithms used in simulation,
feature extraction, and optimization for molecu-lar,
network, and systems models in biology.
Students taking graduate version complete
additional assignments.
B. Tidor, J. K. White
6.521J Cellular Biophysics
(Same subject as 2.794J, 20.470J, HST.541J)
(Subject meets with 2.791J, 6.021J, 20.370J)
Prereq: Physics II (GIR); 18.03; 2.005, 6.002,
6.003, 6.071, 10.301, 20.110, or permission of
instructor
G (Fall)
Meets with undergraduate subject 6.021J. Re-quires
the completion of more advanced home
problems and/or an additional project.
D. M. Freeman, J. Han, T. Heldt, J. Voldman,
M. F. Yanik
6.522J Quantitative Physiology: Organ
Transport Systems
HST.542J)
Prereq: 2.006 or 6.013; 6.021
G (Spring)
Application of the principles of energy and mass
flow to major human organ systems. Mecha-nisms
of regulation and homeostasis. Ana-tomical,
physiological and pathophysiological
features of the cardiovascular, respiratory and
renal systems. Systems, features and devices
that are most illuminated by the methods of
physical sciences. Laboratory work includes
some animal studies. Students taking graduate
version complete additional assignments.
T. Heldt, R. G. Mark, C. M. Stultz
6.524J Molecular, Cellular, and Tissue
Biomechanics
20.410J)
Prereq: Biology (GIR); 2.002, 2.006, 6.013,
10.301, or 10.302
G (Fall)
R. D. Kamm, K. Van Vliet
6.525J Medical Device Design
instructor
G (Fall)
A. H. Slocum, C. G. Sodini
6.541J Speech Communication
(Same subject as 24.968J, HST.710J)
G (Spring)
Survey of human speech communication with
special emphasis on the sound patterns of natu-ral
languages. Acoustic theory of speech produc-tion;
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.
Recommended prerequisite: mathematical back-ground
equivalent to 6.003.
L. D. Braida, S. S. Ghosh, R. E. Hillman,
S. Shattuck-Hufnagel
6.542J Laboratory on the Physiology, Acoustics,
and Perception of Speech
Experimental investigations of speech process-es.
Topics: measurement of articulatory move-ments;
measurements of pressures and airflows
in speech production; computer-aided waveform
analysis and spectral analysis of speech; syn-thesis
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.
L. D. Braida, S. Shattuck-Hufnagel
6.544, 6.545 Advanced Topics in BioEECS
G (Fall, Spring)
Advanced study of topics in BioEECS. Specific
focus varies from year to year. Consult depart-ment
for details.
Consult Department
6.551J Acoustics of Speech and Hearing
Prereq: 8.03, 6.003; or permission of instructor
G (Fall)
Provides background for understanding how the
acoustics and mechanics of the speech produc-tion
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 audi-tory
system to transduce and analyze sounds;
and sound perception (absolute detection,
discrimination, masking, and auditory frequency
selectivity). 4 Engineering Design Points.
L. D. Braida, S. S. Ghosh, J. J. Rosowski, C. Shera
6.552J Signal Processing by the Auditory
System: Perception
Prereq: 6.003; 6.041 or 6.431; or permission of
instructor
Studies information processing performance of
the human auditory system in relation to current
physiological knowledge. Examines mathemati-cal
models for the quantification of auditory-based
behavior and the relation between be-havior
and peripheral physiology, reflecting the
tono-topic organization and stochastic responses
of the auditory system. Mathematical models of
psychophysical relations, incorporating quantita-tive
knowledge of physiological transformations
by the peripheral auditory system.
L. D. Braida
6.555J Biomedical Signal and Image Processing
Prereq: 6.003, 2.004, 16.004, or 18.085
G (Spring)
See description under subject HST.582J.
J. Greenberg, E. Adalsteinsson, W. Wells

112
6.556J Data Acquisition and Image
Reconstruction in MRI
Prereq: 6.011
Applies analysis of signals and noise in linear
systems, sampling, and Fourier properties to
magnetic resonance (MR) imaging acquisition
and reconstruction. Provides adequate founda-tion
for MR physics to enable study of RF excita-tion
design, efficient Fourier sampling, parallel
encoding, reconstruction of non-uniformly
sampled data, and the impact of hardware imper-fections
on reconstruction performance. Surveys
active areas of MR research. Assignments include
MATLAB-based work with real data. Includes visit
to a scan site for human MR studies.
E. Adalsteinsson
6.561J Fields, Forces, and Flows in Biological
Systems
HST.544J)
instructor
G (Fall)
M. Bathe, A. J. Grodzinsky, R. D. Kamm
6.580J Principles of Synthetic Biology
Prereq: None
U (Fall)
3-0-9
R. Weiss
6.581J Foundations of Algorithms and
Computational Techniques in Systems Biology
Prereq: 6.021, 6.034, 6.046, 6.336, 7.91,
18.417, or permission of instructor
Illustrates computational approaches to solving
problems in systems biology. Uses a series of
case studies to demonstrate how an effective
match between the statement of a biological
problem and the selection of an appropriate al-gorithm
or computational technique can lead to
fundamental advances. Covers several discrete
and numerical algorithms used in simulation,
feature extraction, and optimization for molecu-lar,
network, and systems models in biology.
Students taking graduate version complete
additional assignments.
B. Tidor, J. K. White
6.589J Principles of Synthetic Biology
Prereq: None
G (Fall)
3-0-9
R. Weiss
Electrodynamics
6.608J Introduction to Particle Accelerators
Prereq: 6.013 or 8.07; permission of instructor
Acad Year 2015–2016: U (Fall, IAP, Spring)
Units arranged
W. Barletta
6.630 Electromagnetics
Prereq: 6.003 or 6.007
Explores electromagnetic phenomena in modern
applications, including wireless and optical com-munications,
circuits, computer interconnects
and peripherals, microwave communications
and radar, antennas, sensors, micro-electrome-chanical
systems, and power generation and
transmission. Fundamentals include quasistatic
and dynamic solutions to Maxwell's equations;
waves, radiation, and diffraction; coupling to
media and structures; guided and unguided
waves; modal expansions; resonance; acoustic
analogs; and forces, power, and energy.
L. Daniel, M. R. Watts
6.631 Optics and Photonics
Prereq: 6.013 or 8.07
G (Fall)
Introduction to fundamental concepts and
techniques of optics, photonics, and fiber optics.
Review of Maxwell's equations, light propaga-tion,
and reflection from dielectrics mirrors and
filters. Interferometers, filters, and optical imag-ing
systems. Fresnel and Fraunhoffer diffraction
theory. Propagation of Gaussian beams and laser
resonator design. Optical waveguides and optical
fibers. Optical waveguide and photonic devices.
J. G. Fujimoto
6.632 Electromagnetic Wave Theory
Prereq: 6.013, 6.630, or 8.07
G (Spring)
Solutions to Maxwell equations and physical
interpretation. Topics include waves in media,
equivalence principle, duality and comple-mentarity,
Huygens’ principle, Fresnel and
Fraunhofer diffraction, radiation and dyadic
Green's functions, scattering, metamateri-als,
and plasmonics, mode theory, dielectric
waveguides, and resonators. Examples deal
with limiting cases of electromagnetic theory,
multi-port elements, filters and antennas. Dis-cusses
current topics in microwave and photonic
devices.
M. R. Watts
6.634J Nonlinear Optics
Prereq: 6.013 or 8.07
G (Spring)
Techniques of nonlinear optics with emphasis
on fundamentals for research and engineering
in optics, photonics, and spectroscopy. Electro
optic modulators, harmonic generation, and
frequency conversion devices. Nonlinear effects
in optical fibers including self-phase modula-tion,
nonlinear wave propagation, and solitons.
Interaction of light with matter, laser operation,
density matrix techniques, nonlinear spectrosco-pies,
and femtosecond optics.
J. G. Fujimoto
6.637 Optical Signals, Devices, and Systems
Prereq: 6.003
G (Fall)
Principles of operation and applications of de-vices
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 proper-ties
of materials; lasers and LEDs; electro-optic
and acousto-optic light modulators; photorefrac-tive
and liquid-crystal light modulation; spatial
light modulators and displays; optical wave-guides
and fiber-optic communication systems;
photodetectors; 2-D and 3-D optical storage

113
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 5 5 6 J t o 6 . 7 1 7 J
technologies; adaptive optical systems; role of
optics in next-generation computers. Student
research paper on a specific contemporary topic
required. Recommended prerequisites: 6.007
or 8.03.
C. Warde
6.641 Electromagnetic Fields, Forces, and
Motion
Prereq: 6.013
G (Fall)
Electric and magnetic quasistatic forms of
Maxwell's equations applied to dielectric,
conduction, and magnetization boundary value
problems. Electromagnetic forces, force densi-ties,
and stress tensors, including magnetiza-tion
and polarization. Thermodynamics of
electromagnetic fields, equations of motion, and
energy conservation. Applications to synchro-nous,
induction, and commutator machines;
sensors and transducers; microelectrome-chanical
systems; propagation and stability of
electromechanical waves; and charge transport
phenomena.
M. Zahn, J. H. Lang
6.642 Continuum Electromechanics
Laws, approximations, and relations of con-tinuum
mechanics. Mechanical and electrome-chanical
transfer relations. Statics and dynamics
of electromechanical systems having a static
equilibrium. Electromechanical flows. Field
coupling with thermal and molecular diffusion.
Electrokinetics. Streaming interactions. Applica-tion
to materials processing, magnetohydro-dynamic
and electrohydrodynamic pumps and
generators, ferrohydrodynamics, physiochemi-cal
systems, heat transfer, continuum feedback
control, electron beam devices, and plasma
dynamics.
M. Zahn
6.644, 6.645 Advanced Topics in Applied
Physics
G (Fall, Spring)
Advanced study of topics in applied physics.
Specific focus varies from year to year. Consult
department for details.
Consult Department
6.651J Introduction to Plasma Physics I
Prereq: 6.013, 8.07, or 22.105; 18.04 or Coreq:
18.075
G (Fall)
A. White
6.652J Introduction to Plasma Physics II
Prereq: 6.651J, 8.613J, or 22.611J
G (Spring)
Staff
6.673 Introduction to Numerical Simulation in
Electrical Engineering
Prereq: 6.012 or 6.013
Selection of a simulation model and physical
approximations. Solution of nonlinear coupled
PDEs in 1-D through finite difference and finite
element methods, Newton's method, and
variants. Finite difference and finite element
methods in 2-D and sparse matrix methods em-phasizing
conjugate gradient algorithms. Semi-conductor
devices used as primary examples;
additional examples drawn from E&M modeling,
nonlinear pulse propagation, and laser physics.
P. L. Hagelstein
6.685 Electric Machines
Prereq: 6.061 or 6.690; or permission of
instructor
Treatment of electromechanical transducers,
rotating and linear electric machines. Lumped-parameter
electromechanics. Power flow using
Poynting's theorem, force estimation using the
Maxwell stress tensor and Principle of virtual
work. Development of analytical techniques
for predicting device characteristics: energy
conversion density, efficiency; and of system
interaction characteristics: regulation, stability,
controllability, and response. Use of electric
machines in drive systems. Problems taken from
current research.
J. L. Kirtley, Jr.
6.690 Introduction to Electric Power Systems
Prereq: 6.002, 6.013
Electric circuit theory with application to
power handling electric circuits. Modeling and
behavior of electromechanical devices, includ-ing
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 sustain-able
sources. Students taking graduate version
complete additional assignments.
J. L. Kirtley, Jr.
6.695J Engineering, Economics and Regulation
of the Electric Power Sector
(Same subject as 15.032J, ESD.162J)
G (Spring)
See description under subject ESD.162J.
I. Perez-Arriaga, C. Knittel
Solid-State Materials and Devices
6.701 Introduction to Nanoelectronics
Prereq: 6.003
U (Fall)
4-0-8
Transistors at the nanoscale. Quantization,
wavefunctions, and Schrodinger's equation. In-troduction
to electronic properties of molecules,
carbon nanotubes, and crystals. Energy band
formation and the origin of metals, insulators
and semiconductors. Ballistic transport, Ohm's
law, ballistic versus traditional MOSFETs, funda-mental
limits to computation.
M. A. Baldo
6.717J Design and Fabrication of
Microelectromechanical Systems
Prereq: 6.003 or 2.003, Physics II (GIR); or
U (Spring)
3-0-9
Provides an introduction to microsystem design.
Covers material properties, microfabrication
technologies, structural behavior, sensing
methods, electromechanical actuation, thermal

114
actuation and control, multi-domain modeling,
noise, and microsystem packaging. Applies
microsystem modeling, and manufacturing
principles to the design and analysis a variety of
microscale sensors and actuators (e.g., optical
MEMS, bioMEMS, and inertial sensors). Empha-sizes
modeling and simulation in the design
process. Students taking the graduate version
Design Points.
D. Weinstein
6.719 Nanoelectronics
Prereq: 6.003
G (Fall)
Meets with undergraduate subject 6.701, but
requires the completion of additional/different
homework assignments and or projects. See
subject description under 6.701.
M. A. Baldo
6.720J Integrated Microelectronic Devices
Prereq: 6.012 or 3.42
G (Fall)
Covers physics of microelectronic semiconductor
devices for silicon integrated circuit applica-tions.
Topics include semiconductor fundamen-tals,
p-n junction, metal-oxide semiconductor
structure, metal-semiconductor junction, MOS
field-effect transistor, and bipolar junction tran-sistor.
Emphasizes physical understanding of
device operation through energy band diagrams
and short-channel MOSFET device design. Out-lines
issues in modern device scaling. Includes
device characterization exercises. 2 Engineering
Design Points.
D. A. Antoniadis, J. A. del Alamo, H. L. Tuller
6.728 Applied Quantum and Statistical Physics
Prereq: 6.003, 18.06
G (Fall)
Elementary quantum mechanics and statistical
physics. Introduces applied quantum physics.
Emphasizes experimental basis for quantum me-chanics.
Applies Schrodinger's equation to the
free particle, tunneling, the harmonic oscillator,
and hydrogen atom. Variational methods. El-ementary
statistical physics; Fermi-Dirac, Bose-
Einstein, and Boltzmann distribution functions.
Simple models for metals, semiconductors, and
devices such as electron microscopes, scanning
tunneling microscope, thermonic emitters,
atomic force microscope, and more.
P. L. Hagelstein, T. P. Orlando, K. K. Berggren
6.730 Physics for Solid-State Applications
Prereq: 6.013, 6.728
G (Spring)
Classical and quantum models of electrons
and lattice vibrations in solids, emphasizing
physical models for elastic properties, electronic
transport, and heat capacity. Crystal lattices,
electronic energy band structures, phonon dis-persion
relatons, effective mass theorem, semi-classical
equations of motion, electron scatter-ing
and semiconductor optical properties. Band
structure and transport properties of selected
semiconductors. Connection of quantum theory
of solids with quasi-Fermi levels and Boltzmann
transport used in device modeling.
T. P. Orlando, R. Ram, Q. Hu
6.731 Semiconductor Optoelectronics: Theory
and Design
Prereq: 6.728, 6.012
Focuses on the physics of the interaction of
photons with semiconductor materials. Uses
the band theory of solids to calculate the ab-sorption
and gain of semiconductor media; and
uses rate equation formalism to develop the
concepts of laser threshold, population inver-sion,
and modulation response. Presents theory
and design for photodetectors, solar cells,
modulators, amplifiers, and lasers. Introduces
noise models for semiconductor devices, and
applications of optoelectronic devices to fiber
optic communications.
R. J. Ram
6.732 Physics of Solids
Prereq: 6.730 or 8.231
G (Fall)
Continuation of 6.730 emphasizing applica-tions-
related physical issues in solids. Topics:
electronic structure and energy band diagrams
of semiconductors, metals, and insulators;
Fermi surfaces; dynamics of electrons; classical
diffusive transport phenomena such as electrical
and thermal conduction and thermoelectric phe-nomena;
quantum transport in tunneling and
ballistic devices; optical properties of metals,
semiconductors, and insulators; photon-lattice
interactions; optical devices based on interband
and intersubband transitions; magnetic proper-ties
of solids; exchange energy and magnetic
ordering; magneto-oscillatory phenomena;
quantum Hall effect; superconducting phenom-ena
and simple models.
Q. Hu
6.735, 6.736 Advanced Topics in Materials,
Devices, and Nanotechnology
G (Fall, Spring)
Advanced study of topics in materials, devices,
and nanotechnology. Specific focus varies from
year to year.
Consult Department
6.763 Applied Superconductivity
Prereq: 6.728
Phenomenological approach to superconductiv-ity,
with emphasis on superconducting electron-ics.
Electrodynamics of superconductors, Lon-don's
model, and flux quantization. Josephson
junctions and superconducting quantum devices
and detectors.Quantized circuits for quantum
computing. Overview of type-II superconductors,
critical magnetic fields, pinning, and microscop-ic
theory of superconductivity.
T. P. Orlando
6.772 Compound Semiconductor and
Heterostructure Devices
Prereq: 6.012
Physics, modeling, and application of compound
semiconductors (primarily III-Vs and Si-Ge)
in high speed electronic, optoelectronic, and
photonic devices and ICs. The materials palette;
energy band and effective mass concepts;
theory and practice of III-V and Si-Ge hetero-junctions,
quantum structures, and strained
layers; metal-semiconductor diodes and field
effect transistors (MESFETs); heterojunction field
effect transistors (HFETs) and bipolar transis-tors
(HBTs); dielectric waveguides and photonic
lattices; LEDs, laser diodes, photodetectors, and
other optoelectronic devices; heterogeneous
integration with Si.
C. G. Fonstad, Jr., T. A. Palacios
6.774 Physics of Microfabrication: Front End
Processing
Prereq: 6.152
G (Fall)
Presents advanced physical models and
practical aspects of front-end microfabrica-tion
processes, such as oxidation, diffusion,

115
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 7 1 9 t o 6 . 8 0 3
ion implantation, chemical vapor deposition,
atomic layer deposition, etching, and epitaxy.
Covers topics relevant to CMOS, bipolar, and
optoelectronic device fabrication, including high
k gate dielectrics, gate etching, implant-damage
enhanced diffusion, advanced metrology, stress
effects on oxidation, non-planar and nanow-ire
device fabrication, SiGe and fabrication of
process-induced strained Si. Exposure to CMOS
process integration concepts, and impacts of
processing on device characteristics. Students
use modern process simulation tools.
J. L. Hoyt, L. R. Reif
6.775 CMOS Analog and Mixed-Signal Circuit
Design
Prereq: 6.301
G (Spring)
A detailed exposition of the principles in-volved
in designing and optimizing analog and
mixed-signal circuits in CMOS technologies.
Small-signal and large-signal models. Systemic
methodology for device sizing and biasing. Basic
circuit building blocks. Operational amplifier de-sign.
Large signal considerations. Principles of
switched capacitor networks including switched-capacitor
and continuous-time integrated filters.
Basic and advanced A/D and D/A converters,
delta-sigma modulators, RF and other signal pro-cessing
circuits. Design projects on op amps and
subsystems are a required part of the subject.
H. S. Lee, C. G. Sodini
6.777J Design and Fabrication of
Microelectromechanical Systems
Prereq: 6.003 or 2.003, Physics II (GIR); or
G (Spring)
Provides an introduction to microsystem design.
Covers material properties, microfabrication
technologies, structural behavior, sensing
methods, electromechanical actuation, thermal
actuation and control, multi-domain modeling,
noise, and microsystem packaging. Applies
microsystem modeling, and manufacturing
principles to the design and analysis a variety of
microscale sensors and actuators (e.g., optical
MEMS, bioMEMS, and inertial sensors). Empha-sizes
modeling and simulation in the design
process. Students taking the graduate version
Design Points.
D. Weinstein
6.780J Control of Manufacturing Processes
Prereq: 2.008, 6.041, 6.152, or 15.064
G (Spring)
D. E. Hardt, D. S. Boning
6.781J Nanostructure Fabrication
Prereq: 6.152, 6.161, or 2.710; or permission of
instructor
G (Spring)
Describes current techniques used in analyz-ing
and fabricating nanometer-length-scale
structures and devices. Covers fundamentals of
optical, electron (scanning, transmission, and
tunneling), and atomic-force microscopy; opti-cal,
electron, ion, and nanoimprint lithography,
templated self-assembly, and resist technology.
Surveys substrate characterization and prepara-tion,
facilities, and metrology requirements
for nanolithography. Nanodevice processing
methods such as liquid and plasma etching,
lift-off, electroplating, and ion-implant are also
presented. Some applications in nanoelectron-ics,
nanomaterials, and nanophotonics are
discussed.
H. I. Smith, G. Barbastathis, K. K. Berggren
6.789 Organic Optoelectronics
Examines optical and electronic processes in
organic molecules and polymers that govern
the behavior of practical organic optoelectronic
devices. Electronic structure of a single organic
molecule is used as a guide to the electronic
behavior of organic aggregate structures.
Emphasis on use of organic thin films in active
organic devices including organic LEDs, solar
cells, photodetectors, transistors, chemical sen-sors,
memory cells, electrochromic devices, as
well as xerography and organic nonlinear optics.
Reaching the ultimate miniaturization limit of
molecular electronics and related nanoscale
patterning techniques of organic materials are
discussed. Laboratory sessions are conducted in
a research laboratory environment with the goal
of exposing students to material deposition and
device testing techniques.
V. Bulovic
Computer Science
6.801 Machine Vision
3-0-9
Deriving a symbolic description of the environ-ment
from an image. Understanding physics of
image formation. Image analysis as an inversion
problem. Binary image processing and filtering
of images as preprocessing steps. Recovering
shape, lightness, orientation, and motion. Using
constraints to reduce the ambiguity. Photo-metric
stereo and extended Gaussian sphere.
Applications to robotics; intelligent interaction
of machines with their environment. Students
taking the graduate version complete different
assignments.
B. K. P. Horn
6.802J Foundations of Computational and
Systems Biology (New)
HST.506J)
Prereq: Biology (GIR), 6.0002 or 6.01; or 7.05;
or permission of instructor
U (Spring)
3-0-9
C. Burge, E. Fraenkel, D. Gifford
6.803 The Human Intelligence Enterprise
U (Spring)
3-0-9
Analyzes seminal work directed at the devel-opment
of a computational understanding of
human intelligence, such as work on learn-ing,
language, vision, event representation,
commonsense reasoning, self reflection, story
understanding, and analogy. Reviews visionary
ideas of Turing, Minsky, and other influential
thinkers. Examines the implications of work on
brain scanning, developmental psychology, and
cognitive psychology. Emphasis on discussion
and analysis of original papers. Students taking
graduate version complete additional assign-ments.
Enrollment limited.
P. H. Winston

116
6.804J Computational Cognitive Science
instructor
U (Fall)
3-0-9
J. Tenenbaum
6.805J Foundations of Information Policy
(Same subject as STS.085J)
(Subject meets with STS.487)
U (Fall)
3-0-9 HASS-S
Studies the growth of computer and commu-nications
technology and the new legal and
ethical challenges that reflect tensions between
individual rights and societal needs. Topics
include computer crime; intellectual property re-strictions
on software; encryption, privacy, and
national security; academic freedom and free
speech. Students meet and question technolo-gists,
activists, law enforcement agents, journal-ists,
and legal experts. Instruction and practice
in oral and written communication provided.
Students taking graduate version complete ad-ditional
assignments. Enrollment limited.
H. Abelson, M. Fischer, D. Weitzner
6.811 Principles and Practice of Assistive
Technology
U (Fall)
3-4-5
Interdisciplinary project-based subject focuses
on the effective practice of assistive and adap-tive
technology for individuals with disabilities.
Lectures cover design methods and problem-solving
strategies; institutional review boards;
human factors; human-machine interfaces; com-munity
perspectives; social and ethical aspects;
and assistive technology for motor, cognitive,
perceptual, and age-related impairments. Prior
knowledge of one or more of the following areas
useful: software; electronics; human-computer
interaction; cognitive science; mechanical engi-neering;
control; or MIT hobby shop, MIT PSC, or
other relevant independent project experience.
R. C. Miller
6.813 User Interface Design and
Implementation
U (Spring)
3-0-9
Examines human-computer interaction in the
context of graphical user interfaces. Covers hu-man
capabilities, design principles, prototyping
techniques, evaluation techniques, and the
implementation of graphical user interfaces.
Includes short programming assignments and
a semester-long group project. Students taking
the graduate version also have readings from
current literature and additional assignments.
Enrollment limited. 6 Engineering Design Points.
R. C. Miller
6.814 Database Systems
instructor
U (Fall)
3-0-9
Topics related to the engineering and design
of database systems, including data mod-els;
database and schema design; schema
normalization and integrity constraints; query
processing; query optimization and cost esti-mation;
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 tak-ing
graduate version complete different assign-ments.
Enrollment may be limited. 4 Engineering
Design Points.
S. R. Madden
6.815 Digital and Computational Photography
Prereq: Calculus II (GIR), 6.01
U (Spring)
3-0-9
Presents fundamentals and applications of hard-ware
and software techniques used in digital and
computational photography, with an emphasis
on software methods. Provides sufficient back-ground
to implement solutions to photographic
challenges and opportunities. Topics include
cameras and image formation, image processing
and image representations, high-dynamic-range
imaging, human visual perception and color,
single view 3-D model reconstruction, morphing,
data-rich photography, super-resolution, and
image-based rendering. Students taking gradu-ate
version complete additional assignments. 6
F. P. Durand, W. T. Freeman
6.816 Multicore Programming
Prereq: 6.006
U (Spring)
4-0-8
Introduces principles and core techniques
for programming multicore machines. Topics
include locking, scalability, concurrent data
structures, multiprocessor scheduling, load
balancing, and state-of-the-art synchroniza-tion
techniques, such as transactional memory.
Includes sequence of programming assignments
on a large multicore machine, culminating with
the design of a highly concurrent "firewall"
application. Students taking graduate version
N. Shavit
6.819 Advances in Computer Vision (New)
Prereq: 6.041 or 6.042; 18.06
U (Fall)
3-0-9
Advanced topics in computer vision with a focus
on the use of machine learning techniques and
applications in graphics and human-computer
interface. Covers image representations, texture
models, structure-from-motion algorithms,
Bayesian techniques, object and scene recogni-tion,
tracking, shape modeling, and image
databases. Applications may include face
recognition, multimodal interaction, interactive
systems, cinematic special effects, and photore-alistic
rendering. Covers topics complementary
to 6.801. Students taking graduate version
W. T. Freeman, A. Torralba
6.820 Foundations of Program Analysis
Prereq: 6.035
Presents major principles and techniques for
program analysis. Includes formal semantics,
type systems and type-based program analysis,
abstract interpretation and model checking and
synthesis. Emphasis on Haskell and Ocaml,
but no prior experience in these languages
is assumed. Student assignments include
implementing of techniques covered in class,
including building simple verifiers.
A. Solar-Lezama

117
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 8 0 4 J t o 6 . 8 3 5
6.823 Computer System Architecture
Prereq: 6.004
G (Spring)
Introduction to the principles underlying modern
computer architecture. Emphasizes the relation-ship
among technology, hardware organization,
and programming systems in the evolution of
computer architecture. Topics include pipe-lined,
out-of-order, and speculative execution;
caches, virtual memory and exception handling,
superscalar, very long instruction word (VLIW),
vector, and multithreaded processors; on-chip
networks, memory models, synchronization, and
cache coherence protocols for multiprocessors.
Arvind, J. S. Emer, D. Sanchez
6.824 Distributed Computer Systems
Engineering
Prereq: 6.033, permission of instructor
G (Spring)
Abstractions and implementation techniques
for engineering distributed systems: remote
procedure call, threads and locking, client/serv-er,
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 Engi-neering
Design Points.
R. T. Morris, M. F. Kaashoek
6.828 Operating System Engineering
Prereq: 6.005, 6.033
G (Fall)
Fundamental design and implementation is-sues
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 commu-nication;
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.
M. F. Kaashoek
6.829 Computer Networks
G (Fall)
Topics on the engineering and analysis of net-work
protocols and architecture, including archi-tectural
principles for designing heterogeneous
networks; transport protocols; internet routing
foundations and practice; router design; conges-tion
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.
H. Balakrishnan
6.830 Database Systems
instructor
G (Fall)
Topics related to the engineering and design
of database systems, including data mod-els;
database and schema design; schema
normalization and integrity constraints; query
processing; query optimization and cost esti-mation;
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 tak-ing
graduate version complete different assign-ments.
Enrollment may be limited. 4 Engineering
Design Points.
S. R. Madden
6.831 User Interface Design and
Implementation
G (Spring)
Examines human-computer interaction in the
context of graphical user interfaces. Covers hu-man
capabilities, design principles, prototyping
techniques, evaluation techniques, and the
implementation of graphical user interfaces.
Includes short programming assignments and
a semester-long group project. Students taking
the graduate version also have readings from
current literature and additional assignments.
Enrollment limited. 6 Engineering Design Points.
R. C. Miller
6.832 Underactuated Robotics
instructor
G (Fall)
Covers nonlinear dynamics and control of under-actuated
mechanical systems, with an emphasis
on computational methods. Topics include
nonlinear dynamics of passive robots (walkers,
swimmers, flyers), motion planning, robust
and optimal control, reinforcement learning/
approximate optimal control, and the influence
of mechanical design on control. Includes ex-amples
from biology and applications to legged
locomotion, compliant manipulation, underwa-ter
robots, and flying machines.
R. Tedrake
6.833 The Human Intelligence Enterprise
Prereq: 6.034
G (Spring)
Analyzes seminal work directed at the devel-opment
of a computational understanding of
human intelligence, such as work on learn-ing,
language, vision, event representation,
commonsense reasoning, self reflection, story
understanding, and analogy. Reviews visionary
ideas of Turing, Minsky, and other influential
thinkers. Examines the implications of work on
brain scanning, developmental psychology, and
cognitive psychology. Emphasis on discussion
and analysis of original papers. Requires the
completion of additional exercises and a sub-stantial
term project. Enrollment limited.
P. H. Winston
6.834J Cognitive Robotics
Prereq: 6.041, 6.042, or 16.09; 16.410, 16.413,
6.034, or 6.825
G (Spring)
B. C. Williams
6.835 Intelligent Multimodal User Interfaces
Implementation 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

118
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.
R. Davis
6.836 Multicore Programming
Prereq: 6.006
G (Spring)
Introduces principles and core techniques
for programming multicore machines. Topics
include locking, scalability, concurrent data
structures, multiprocessor scheduling, load
balancing, and state-of-the-art synchroniza-tion
techniques, such as transactional memory.
Includes sequence of programming assignments
on a large multicore machine, culminating with
the design of a highly concurrent "firewall"
application. Students taking graduate version
N. Shavit
6.837 Computer Graphics
Prereq: Calculus II (GIR), 6.005; or permission of
instructor
3-0-9
Introduction to computer graphics algorithms,
software and hardware. Topics include ray
tracing, the graphics pipeline, transformations,
texture mapping, shadows, sampling, global
illumination, splines, animation and color.
F. P. Durand, W. Matusik
6.838 Advanced Topics in Computer Graphics
Prereq: 6.837
G (Spring)
In-depth study of an active research topic in
computer graphics. Topics change each term.
Readings from the literature, student presenta-tions,
short assignments, and a programming
project.
W. Matusik
6.839 Advanced Computer Graphics
instructor
G (Spring)
A graduate level course investigates compu-tational
problems in rendering, animation,
and geometric modeling. The course draws on
advanced techniques from computational geom-etry,
applied mathematics, statistics, scientific
computing and other. Substantial programming
experience required.
W. Matusik
6.840J Theory of Computation
Prereq: 18.310 or 18.062J
G (Fall)
4-0-8 H-LEVEL Grad Credit H (except for Course
18 students)
M. Sipser
6.841J Advanced Complexity Theory
Prereq: 18.404
D. Moshkovitz
6.842 Randomness and Computation
Prereq: 6.046, 6.840
The power and sources of randomness in
computation. Connections and applications
to computational complexity, computational
learning theory, cryptography and combinator-ics.
Topics include: probabilistic proofs, uniform
generation and approximate counting, Fourier
analysis of Boolean functions, computational
learning theory, expander graphs, pseudoran-dom
generators, derandomization.
R. Rubinfeld
6.845 Quantum Complexity Theory
Prereq: 6.045, 6.840, 18.435
Introduction to quantum computational com-plexity
theory, the study of the fundamental
capabilities and limitations of quantum comput-ers.
Topics include complexity classes, lower
bounds, communication complexity, proofs and
advice, and interactive proof systems in the
quantum world; classical simulation of quantum
circuits. The objective is to bring students to the
research frontier.
S. Aaronson
6.846 Parallel Computing
G (Spring)
Introduction to parallel and multicore computer
architecture and programming. Topics include
the design and implementation of multicore
processors; networking, video, continuum,
particle and graph applications for multicores;
communication and synchronization algorithms
and mechanisms; locality in parallel computa-tions;
computational models, including shared
memory, streams, message passing, and data
parallel; multicore mechanisms for synchroni-zation,
cache coherence, and multithreading.
Performance evaluation of multicores; compila-tion
and runtime systems for parallel comput-ing.
Substantial project required. 4 Engineering
Design Points.
A. Agarwal
6.849 Geometric Folding Algorithms: Linkages,
Origami, Polyhedra
Covers discrete geometry and algorithms under-lying
the reconfiguration of foldable structures,
with applications to robotics, manufacturing,
and biology. Linkages made from one-dimen-sional
rods connected by hinges: constructing
polynomial curves, characterizing rigidity,
characterizing unfoldable versus locked, protein
folding. Folding two-dimensional paper (ori-gami):
characterizing flat foldability, algorithmic
origami design, one-cut magic trick. Unfolding
and folding three-dimensional polyhedra: edge
unfolding, vertex unfolding, gluings, Alexan-drov's
Theorem, hinged dissections.
E. D. Demaine
6.850 Geometric Computing
Prereq: 6.046
Introduction to the design and analysis of algo-rithms
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 dia-grams,
Binary Space Partitions. Geometric prob-lems
in higher dimensions: linear programming,
closest pair problems. High-dimensional nearest
neighbor search and low-distortion embeddings
between metric spaces. Geometric algorithms

119
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 8 3 6 t o 6 . 8 6 3 J
for massive data sets: external memory and
streaming algorithms. Geometric optimization.
P. Indyk
6.851 Advanced Data Structures
Prereq: 6.046
More advanced and powerful data structures for
answering several queries on the same data.
Such structures are crucial in particular for de-signing
efficient algorithms. Dictionaries; hash-ing;
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. Suc-cinct
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.
E. D. Demaine
6.852J Distributed Algorithms
Prereq: 6.046
G (Fall)
Design and analysis of concurrent algorithms,
emphasizing those suitable for use in distribut-ed
networks. Process synchronization, allocation
of computational resources, distributed consen-sus,
distributed graph algorithms, election of
a leader in a network, distributed termination,
deadlock detection, concurrency control, com-munication,
and clock synchronization. Special
consideration given to issues of efficiency and
fault tolerance. Formal models and proof meth-ods
for distributed computation.
N. A. Lynch
6.853 Topics in Algorithmic Game Theory
Prereq: 6.006 or 6.046
G (Fall)
Presents research topics at the interface of com-puter
science and game theory, with an empha-sis
on algorithms and computational complexity.
Explores the types of game-theoretic tools that
are applicable to computer systems, the loss in
system performance due to the conflicts of inter-est
of users and administrators, and the design
of systems whose performance is robust with
respect to conflicts of interest inside the system.
Algorithmic focus is on algorithms for equilibria,
the complexity of equilibria and fixed points,
algorithmic tools in mechanism design, learning
in games, and the price of anarchy.
K. Daskalakis
6.854J Advanced Algorithms
Prereq: 6.041, 6.042, or 18.440; 6.046
G (Fall)
First-year graduate subject in algorithms. Em-phasizes
fundamental algorithms and advanced
methods of algorithmic design, analysis, and
implementation. Surveys a variety of computa-tional
models and the algorithms for them. Data
structures, network flows, linear programming,
computational geometry, approximation algo-rithms,
online algorithms, parallel algorithms,
external memory, streaming algorithms.
D. R. Karger
6.856J Randomized Algorithms
Prereq: 6.854J, 6.041 or 6.042J
Studies how randomization can be used to make
algorithms simpler and more efficient via ran-dom
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.
D. R. Karger
6.857 Network and Computer Security
Prereq: 6.033, 6.042J
G (Spring)
Emphasis on applied cryptography and may
include: basic notion of systems security,
crypotographic hash functions, symmetric cry-potography
(one-time pad, stream ciphers, block
ciphers), cryptanalysis, secret-sharing, authenti-cation
codes, public-key cryptography (encryp-tion,
digital signatures), public-key attacks, web
browser security, biometrics, electronic cash,
viruses, electronic voting, Assignments include a
group final project. Topics may vary year to year.
R. L. Rivest
6.858 Computer Systems Security
Prereq: 6.033, 6.005
G (Fall)
Design and implementation of secure computer
systems. Lectures cover attacks that compro-mise
security as well as techniques for achieving
security, based on recent research papers. Top-ics
include operating system security, privilege
separation, capabilities, language-based secu-rity,
cryptographic network protocols, trusted
hardware, and security in web applications and
mobile phones. Labs involve implementing and
compromising a web application that sandboxes
arbitrary code, and a group final project. 4 Engi-neering
Design Points.
N. B. Zeldovich
6.859J Integer Programming and Combinatorial
Optimization
Prereq: 15.081J or permission of instructor
D. J. Bertsimas, A. S. Schulz
6.863J Natural Language and the Computer
Representation of Knowledge
Prereq: 6.034
Explores the relationship between computer
representation of knowledge and the structure
of natural language. Emphasizes development of
analytical skills necessary to judge the compu-tational
implications of grammatical formalisms,
and uses concrete examples to illustrate par-ticular
computational issues. Efficient parsing
algorithms for context-free grammars; Treebank
grammars and statistical parsing. Question an-swering
systems. Extensive laboratory work on
building natural language processing systems. 8
R. C. Berwick

120
6.864 Advanced Natural Language Processing
Prereq: 6.046J or permission of instructor
G (Fall)
Graduate 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, infor-mation
extraction, statistical machine transla-tion,
dialogue systems, and summarization.
R. A. Barzilay, M. J. Collins
6.865 Advanced Computational Photography
Prereq: Calculus II (GIR), 6.01
G (Spring)
Presents fundamentals and applications of
hardware and software techniques used in
digital and computational photography, with
an emphasis on software methods. Provides
sufficient background to implement solutions
to photographic challenges and opportunities.
Topics include cameras and image formation,
image processing and image representations,
high-dynamic-range imaging, human visual
perception and color, single view 3-D model re-construction,
morphing, data-rich photography,
super-resolution, and image-based rendering.
assignments.
F. P. Durand, W. T. Freeman
6.866 Machine Vision
Intensive introduction to the process of generat-ing
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.
B. K. P. Horn
6.867 Machine Learning
Prereq: 6.041, 18.05, or 18.06
G (Fall)
Principles, techniques, and algorithms in ma-chine
learning from the point of view of statistical
inference; representation, generalization, and
model selection; and methods such as linear/
additive models, active learning, boosting, sup-port
vector machines, non-parametric Bayesian
methods, hidden Markov models, and Bayesian
networks. Recommended prerequisite: 6.036.
T. Jaakkola, L. P. Kaelbling
6.868J The Society of Mind
(Same subject as MAS.731J)
Prereq: Must have read “The Society of Mind”
and “The Emotion Machine”; permission of
instructor
G (Fall)
Introduction 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 personal-ity.
Incorporates ideas from psychology, artificial
intelligence, and computer science to resolve
theoretical issues such as wholes vs. parts,
structural vs. functional descriptions, declara-tive
vs. procedural representations, symbolic vs.
connectionist models, and logical vs. common-sense
theories of learning. Enrollment limited.
M. Minsky
6.869 Advances in Computer Vision
Prereq: 6.041 or 6.042; 18.06
G (Fall)
Advanced topics in computer vision with a focus
on the use of machine learning techniques and
applications in graphics and human-computer
interface. Covers image representations, texture
models, structure-from-motion algorithms,
Bayesian techniques, object and scene recogni-tion,
tracking, shape modeling, and image
databases. Applications may include face
recognition, multimodal interaction, interactive
systems, cinematic special effects, and photore-alistic
rendering. Covers topics complementary
to 6.866. Students taking graduate version
W. T. Freeman, A. Torralba
6.870 Advanced Topics in Computer Vision
Seminar 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 imag-ing,
representation and estimation methods
used in modern computer vision.
W. T. Freeman, P. Golland, B. K. P. Horn,
A. Torralba
6.872J Biomedical Computing
Prereq: 6.034
G (Fall)
Analyzes 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 health-care
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.
G. Alterovitz, P. Szolovits
6.874J Computational Systems Biology
20.390J, 20.490J)
Prereq: Biology (GIR); 18.440 or 6.041
G (Spring)
Presents computational approaches and algo-rithms
for contemporary problems in systems
biology, with a focus on models of biological
systems, including regulatory network discovery
and validation. Topics include genotypes,
regulatory factor binding and motif discovery,
and whole genome RNA expression; regulatory
networks (discovery, validation, data integra-tion,
protein-protein interactions, signaling,
whole genome chromatin immunoprecipitation
analysis); and experimental design (model
validation, interpretation of interventions).
Discusses computational methods, including
directed and undirected graphical models, such
as Bayesian networks, factor graphs, Dirichlet
processes, and topic models. Multidisciplinary
team-oriented final research project.
D. K. Gifford, T. S. Jaakkola

121
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 8 6 4 t o 6 . 9 2 0
6.875J Cryptography and Cryptanalysis
Prereq: 6.046J
G (Spring)
A 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.
S. Goldwasser, S. Micali
6.876J Advanced Topics in Cryptography
Prereq: 6.875
Recent results in cryptography, interactive
proofs, and cryptographic game theory. Lectures
by instructor, invited speakers, and students.
S. Goldwasser, S. Micali
6.878J Advanced Computational Biology:
Genomes, Networks, Evolution
Prereq: 6.006, 6.041, Biology (GIR); or
G (Fall)
See 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.
M. Kellis
6.881–6.884 Advanced Topics in Artificial
Intelligence
G (Fall, Spring)
Advanced study of topics in artificial intelli-gence.
Consult department for details.
Consult Department
6.885–6.888 Advanced Topics in Computer
Systems
G (Fall, IAP, Spring)
Advanced study of topics in computer systems.
Specific focus varies from year to year. Consult
department for details.
Consult Department
6.889–6.893 Advanced Topics in Theoretical
Computer Science
G (Fall, Spring)
Advanced study of topics in theoretical computer
science. Specific focus varies from year to year.
Consult department for details.
Consult Department
6.894–6.896 Advanced Topics in Graphics and
Human-Computer Interfaces
G (Fall, Spring)
Advanced study of topics in graphics and
human-computer interfaces. Specific focus
varies from year to year. Consult department for
details.
Consult Department
6.902J Engineering Innovation and Design
Prereq: None
U (Fall, Spring)
4-0-5
See description under subject ESD.051J.
B. Kotelly
6.903J Patents, Copyrights, and the Law of
Intellectual Property
Prereq: None
U (Spring)
3-0-6
J. A. Meldman, S. M. Bauer
6.905 Large-scale Symbolic Systems (New)
U (Spring)
3-0-9
Concepts 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.
Covers means for decoupling goals from strat-egy,
mechanisms for implementing additive
data-directed invocation, work with partially-specified
entities, and how to manage multiple
viewpoints. Topics include combinators, generic
operations, pattern matching, pattern-directed
invocation, rule systems, backtracking, depen-dencies,
indeterminacy, memoization, constraint
propagation, and incremental refinement.
assignments.
G. J. Sussman
6.910 Independent Study in Electrical
Units arranged
Opportunity for independent study at the under-graduate
level under regular supervision by a
faculty member. Projects require prior approval.
A. R. Meyer
6.920 Practical Work Experience
Prereq: None
0-1-0 [P/D/F]
For Course 6 students participating in curric-ulum-
related off-campus work experiences in
electrical engineering or computer science.
Before enrolling, students must have an employ-ment
offer from a company or organization and
must find an EECS supervisor. Upon completion
of the work the student must submit a letter
from the employer evaluating the work accom-plished,
a substantive final report from the stu-dent,
approved by the MIT supervisor. Subject
to departmental approval. Consult Department
Undergraduate Office for details on procedures
and restrictions.
A. R. Meyer

122
6.921 VI-A Internship
Prereq: None
U (Summer)
0-12-0 [P/D/F]
Provides academic credit for the first assignment
of VI-A undergraduate students at companies
affiliated with the department's VI-A internship
program. Limited to students participating in the
VI-A internship program.
M. Zahn
6.922 Advanced VI-A Internship
Prereq: 6.921
U (Spring, Summer)
0-12-0 [P/D/F]
Provides academic credit for the second as-signment
of VI-A undergraduate students at
companies affiliated with the department's VI-A
internship program. Limited to students partici-pating
in the VI-A internship program.
M. Zahn
6.930 Management in Engineering
Engineering School-Wide Elective Subject
(Offered under: 2.96, 6.930, 10.806, 16.653)
Prereq: None
U (Fall)
3-1-8
See description under subject 2.96.
H. S. Marcus, J.-H. Chun
6.932J Linked Data Ventures
Provides practical experience in the use and
development of semantic web technologies.
Focuses on gaining practical insight from execu-tives
and practitioners who use these technolo-gies
in their companies. Working in multidisci-plinary
teams, students complete a term project
to develop a sustainable prototype. Concludes
with a professional presentation, judged by a
panel of experts, and a technical presentation
to faculty.
T. Berners-Lee, L. Kagal, K. Rae, R. Sturdevant
6.933 Entrepreneurship in Engineering: The
Founder’s Journey
Prereq: None
G (Fall)
4-0-8
Immerses students in the experience of an
engineer who founds a start-up company.
Examines leadership, innovation, and creativity
through the lens of an entrepreneur. Suitable for
students interested in transforming an idea into
a business or other realization for wide-scale
societal impact. Covers critical aspects of vali-dating
ideas and assessing personal attributes
needed to activate and lead a growing organiza-tion.
Teams explore the basics of new venture
creation and experimentation. Emphasizes
personal skills and practical experiences. No
listeners.
C. Chase
6.935J Financial Market Dynamics and Human
Behavior
Prereq: 15.401, 15.414, or 15.415
A. Lo
6.941 Statistics for Research Projects:
Statistical Modeling and Experiment Design
Prereq: None
G (IAP)
2-2-2 [P/D/F]
Practical introduction to data analysis, statistical
modeling, and experimental design, intended to
provide essential skills for conducting research.
Covers basic techniques such as hypothesis-testing
and regression models for both tradition-al
experiments and newer paradignms such as
evaluating simulations. Assignments reinforce
techniques through analyzing sample datasets
and reading case studies. Students with re-search
projects will be encouraged to share their
experiences and project-specific questions.
Staff
6.945 Large-scale Symbolic Systems
G (Spring)
Concepts 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.
Covers means for decoupling goals from strat-egy,
mechanisms for implementing additive
data-directed invocation, work with partially-specified
entities, and how to manage multiple
viewpoints. Topics include combinators, generic
operations, pattern matching, pattern-directed
invocation, rule systems, backtracking, depen-dencies,
indeterminacy, memoization, constraint
propagation, and incremental refinement.
assignments.
G. J. Sussman
6.946J Classical Mechanics: A Computational
Approach
Prereq: Physics I (GIR), 18.03, permission of
instructor
J. Wisdom, G. J. Sussman
6.951 Graduate VI-A Internship
Prereq: 6.921, 6.922, or 6.923
G (Fall, Spring, Summer)
0-12-0 [P/D/F]
Provides academic credit for a graduate assign-ment
of graduate VI-A students at companies
affiliated with the department's VI-A internship
program. Limited to graduate students partici-pating
in the VI-A internship program.
M. Zahn
6.952 Graduate VI-A Internship
Prereq: 6.951
0-12-0 [P/D/F]
Provides 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. Limited
to graduate students participating in the VI-A
internship program.
M. Zahn
6.960 Introductory Research in Electrical
Enrollment 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

123
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . 9 2 1 J t o 6 . S 9 6 7
supervisor. Individual programs subject to ap-proval
of professor in charge.
L. A. Kolodziejski
6.961 Introduction to Research in Electrical
3-0-0
Seminar 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.
L. A. Kolodziejski
6.962 Independent Study in Electrical
Prereq: None
G (Fall, IAP, Spring, Summer)
Units arranged
Opportunity for independent study under regular
supervision by a faculty member. Projects
require prior approval.
L. A. Kolodziejksi
6.980 Teaching Electrical Engineering and
Computer Science
Prereq: None
G (Fall, Spring)
For qualified students interested in gaining
teaching experience. Classroom, tutorial, or
laboratory teaching under the supervision of a
faculty member. Enrollment limited by availabil-ity
of suitable teaching assignments.
H. S. Lee, R. C. Miller
6.981 Teaching Electrical Engineering and
Computer Science
Prereq: None
G (Fall, Spring)
For Teaching Assistants in Electrical Engineering
and Computer Science, in cases where teaching
assignment is approved for academic credit by
the department.
H. S. Lee, R. C. Miller
6.982J Teaching College-Level Science and
Engineering
(Same subject as 1.95J, 5.95J, 7.59J, 8.395J,
18.094J)
Prereq: None
G (Fall)
2-0-2 [P/D/F]
J. Rankin
6.991 Research in Electrical Engineering and
Computer Science
Prereq: None
For EECS MEng students who are Research As-sistants
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.
A. R. Meyer
6.999 Practical Experience in EECS
Prereq: None
G (Fall, Spring)
For Course 6 students in the SM/PhD track who
seek practical off-campus research experiences
or internships in electrical engineering or com-puter
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 sub-ject
to departmental approval; consult depart-mental
Graduate Office.
L. A. Kolodziejski
6.EPE UPOP Engineering Practice Experience
(Offered under: 1.EPE, 2.EPE, 3.EPE, 6.EPE,
10.EPE, 16.EPE, 22.EPE)
Prereq: 2.EPW or permission of instructor
U (Fall, Spring)
0-0-1 [P/D/F]
See description under subject 2.EPE.
Staff
6.EPW UPOP Engineering Practice Workshop
(Offered under: 1.EPW, 2.EPW, 3.EPW, 6.EPW,
10.EPW, 16.EPW, 20.EPW, 22.EPW)
Prereq: None
U (Fall, IAP)
1-0-0 [P/D/F]
See description under subject 2.EPW.
Staff
6.S897–6.S899 Special Subject in Computer
Science
G (Fall, Spring)
Consult Department
curriculum.
Consult Department
6.S963–6.S967 Special Studies: EECS
Prereq: None
Units arranged
Opportunity for study of graduate-level topics
related to electrical engineering and computer
science but not included elsewhere in the cur-riculum.
Registration under this subject normally
used for situations involving small study groups.
Normal registration is for 12 units. Registra-tion
subject to approval of professor in charge.
Consult the department for details.
L. A. Kolodziejski

124
G (Fall, Spring)
Consult Department
6.THG Graduate Thesis
Program 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.
L. A. Kolodziejski
6.THM Master of Engineering Program Thesis
Prereq: 6.UAT
Program 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.
A. R. Meyer
6.UR Undergraduate Research in Electrical
Prereq: None
Individual research project arranged with appro-priate
faculty member or approved supervisor.
Forms and instructions for the proposal and final
report are available in the EECS Undergraduate
Office.
A. R. Meyer
Bachelor of Science in Electrical Science and Engineering/Course 6-1
Bachelor of Science in Electrical Engineering and Computer Science/Course 6-2
Bachelor of Science in Computer Science and Engineering/Course 6-3
General Institute Requirements (GIRs) Subjects
Science Requirement 6
Humanities, Arts, and Social Sciences Requirement 8
Restricted Electives in Science and Technology (REST) Requirement [satisfied by the mathematics
requirement in the Departmental Program] 2
Laboratory Requirement [satisfied by 6.01 and 6.02 together in the Departmental Program] 1
Total GIR Subjects Required for SB Degree 17
Communication Requirement
The program includes a Communication Requirement of 4 subjects:
2 subjects designated as Communication Intensive in Humanities, Arts, and Social Sciences (CI‑H); and
2 subjects designated as Communication Intensive in the Major (CI‑M).
PLUS Departmental Program Units
Subject names below are followed by credit units and by prerequisites, if any (corequisites in italics).
Required Subjects 36
6.01 Introduction to EECS I, 12, 1/2 LAB; Physics II (GIR)
6.02 Introduction to EECS II, 12, 1/2 LAB; 6.01, 18.03*
6.UAT Oral Communication, 6
Plus one of the following:(1)
6.UAP Undergraduate Advanced Project, 6, CI-M; 6.UAT
or
6.UAR Seminar in Undergraduate Advanced Research, 12, CI-M; 6.UR
Restricted Electives 132–144
1. Two mathematics subjects (also satisfies REST requirement):
(a) Either 18.03 or 18.06 (alternatively 18.700)
and
(b) Either 6.041 (alternatively 18.440) or 6.042J. Students in Course 6-1 must select 6.041 (or 18.440);
students in Course 6-3 must select 6.042J.
2. One department laboratory:
One subject selected from the undergraduate laboratory subjects 6.035, 6.101, 6.111, 6.115, 6.123, 6.129, 6.131,
6.141, 6.142, 6.152, 6.161, 6.163, 6.170, 6.172, 6.182, or 6.813; students in Course 6-3 must select a CS laboratory
subject from 6.035, 6.141, 6.170, 6.172, or 6.813. Students in Course 6-1 or 6-2 who take both 6.021J and 6.022J
may use 6.022J to satisfy the department laboratory requirement.
3. Three/four foundation subjects:
(a) Students in Course 6-1 must take three subjects from the EE foundation list: 6.002, 6.003, 6.004, 6.007.
(b) Students in Course 6-3 must take the three subjects in the CS foundation list: 6.004, 6.005, 6.006.
(c) Students in Course 6-2 must take four subjects from the EECS foundation list (6.002–6.007), with two chosen
from the EE foundation list and two from the CS foundation list (6.004 may be counted under either EE or CS).
4. Three header subjects:
(a) Students in Course 6-1 must take three subjects from the EE header list: 6.011, 6.012, 6.013, 6.021J.
(b) Students in Course 6-3 must take the three subjects in the CS header list: 6.033, 6.034, 6.046J.
(c) Students in Course 6-2 must take three subjects from the EECS header list (6.011, 6.012, 6.013, 6.021J,
6.033, 6.034, 6.046J), with at least one chosen from the EE header list and at least one from the CS header list.
5. Two subjects from a departmental list of advanced undergraduate subjects.
To complete the required Communication-Intensive subjects in the major, students must take one of the following
CI‑M subjects as a restricted elective in categories 2 or 4 above by the end of the third year: 6.021J, 6.033, 6.101,
6.111, 6.115, 6.129, 6.131, 6.141J, 6.152J, 6.161, 6.163, 6.173, 6.182, or 6.805. 6.UAT plus 6.UAP, or 6.UAR, typically
constitutes the second CI-M. Students may also take 6.UAT plus a second CI-M undergraduate laboratory subject
(6.101, 6.111, 6.115, 6.131, 6.141J, 6.152J, 6.161, 6.163, 6.182) to fulfill the CI-M component of the Communication
Requirement.
Departmental Program Units That Also Satisfy the GIRs (36)
Unrestricted Electives 48
Total Units Beyond the GIRs Required for SB Degree 180–192
No subject can be counted both as part of the 17-subject GIRs and as part of the 180–192 units required
beyond the GIRs. Every subject in the student’s departmental program will count toward one or the other,
but not both.
Notes
*Alternate prerequisites are listed in the subject descriptions.
(1) See the description of required communication-intensive subjects for information about acceptable substitutions
for the 6.UAT/6.UAP or 6.UAT/6.UAR sequence.
For an explanation of credit units, or hours, please refer to the online help of the MIT Subject Listing & Schedule,
http://student.mit.edu/catalog/index.cgi.

125
C O U R S E 6
2 0 1 4 – 2 0 1 5
s u b j e c t s 6 . S 9 7 4 t o 6 . U R
Master of Engineering in Electrical Engineering and Computer Science/Course 6-P
See Notes on Master of Engineering and Bachelor’s Degree Programs (next page)
Restricted Electives in Science and Technology (REST) Requirement [satisfied by the mathematics
requirement in the Departmental Program] 2
Laboratory Requirement [satisfied by 6.01 and 6.02 together in the Departmental Program] 1
Total GIR Subjects Required for the SB and MEng Degrees 17
2 subjects designated as Communication Intensive in Humanities, Arts, and Social Sciences (CI‑H); and
2 subjects designated as Communication Intensive in the Major (CI‑M).
Subject names below are followed by credit units, and by prerequisites, if any (corequisites in italics).
Required Subjects 60
6.02 Introduction to EECS II, 12, 1/2 LAB; 6.01, 18.03*
or
6.UAP Seminar in Undergraduate Advanced Research, 12, CI-M; 6.UR
6.ThM MEng Program Thesis, 24**
Restricted Electives 198–210
1. Two mathematics subjects (also satisfies REST requirement):
(a) Either 18.03 or 18.06 (alternatively 18.700)
and
(b) Either 6.041 (alternatively 18.440) or 6.042J or both. Students in Course 6-1 for their bachelor’s degree must
select 6.041 (or 18.440); students in Course 6-3 for their bachelor’s degree must select 6.042J.
2. One department laboratory:
One subject selected from the undergraduate laboratory subjects 6.035, 6.101, 6.111, 6.115, 6.123, 6.129, 6.131,
6.141, 6.142, 6.152, 6.161, 6.163, 6.170, 6.172, 6.182 or 6.813; students in Course 6-3 must select a CS laboratory
subject from 6.035, 6.141, 6.170, 6.172, or 6.813. Students in Course 6-1 or 6-2 who take both 6.021J and 6.022J
may use 6.022J to satisfy the department laboratory requirement.
3. Three/four foundation subjects:
(a) Students in Course 6-1 must take three subjects from the EE foundation list: 6.002, 6.003, 6.004, 6.007.
(b) Students in Course 6-3 must take the three subjects in the CS foundation list: 6.004, 6.005, 6.006.
(c) Students in Course 6-2 must take four subjects from the EECS foundation list (6.002-6.007), with two chosen
from the EE foundation list and two from the CS foundation list (6.004 may be counted under either EE or CS).
4. Three header subjects:
(a) Students in Course 6-1 must take three subjects from the EE header list: 6.011, 6.012, 6.013, 6.021J.
(b) Students in Course 6-3 must take the three subjects in the CS header list: 6.033, 6.034, 6.046J.
(c) Students in Course 6-2 must take three subjects from the EECS header list: 6.011, 6.012, 6.013, 6.021J, 6.033,
6.034, 6.046J, with at least one chosen from the EE header list and at least one from the CS header list.
5. Two undergraduate subjects from a departmental list of advanced undergraduate subjects and four graduate
subjects totaling at least 42 units, of which at least 36 units must be offered by EECS. At least three of the five
required EECS subjects must fall within a single concentration field as defined by the department.6. Four H-level
graduate subjects totaling at least 42 units, of which at least 36 units must come from subjects
taken within the department.
6. Two subjects from a restricted departmental list of mathematics, science, and engineering electives.
To complete the required Communication-Intensive subjects in the major, students must take one of the following
CI‑M subjects as a restricted elective in categories 2 or 4 above by the end of the third year: 6.021J, 6.025J, 6.033,
6.101, 6.111, 6.115, 6.129J, 6.131, 6.141J, 6.152J, 6.161, 6.163, 6.182, or 6.805. 6.UAT plus 6.UAP or 6.UAR, typically
constitutes the second CI-M. Students may also take 6.UAT plus a second CI-M undergraduate laboratory subject
(6.101, 6.111, 6.115, 6.129J, 6.131, 6.141J, 6.152J, 6.161, 6.163, 6.182) to fulfill the CI-M component of Communication
Requirement.
Total Units Beyond the GIRs Required for Simultaneous Award of the MEng and SB Degrees 270–282
No subject can be counted both as part of the 17-subject GIRs and as part of the 270–282 units required beyond
the GIRs. Every subject in the student’s departmental program will count toward one or the other, but not both.
Notes
*Alternate prerequisites are listed in the subject description.
**6-PA Program requires performance of thesis at company location.
for the 6.UAT/6.UAP or 6.UAT/6.UAR sequence.

126
Notes on Master of Engineering and Bachelor’s Degree Programs
The Master of Engineering program builds on the bachelor’s degree program selected by the student (6-1, 6-2,
or 6-3), with restricted elective categories 5 and 6 and the MEng thesis (6.ThM).
The graduate subjects required under restricted elective category 5 are selected with departmental review and ap‑proval
to ensure that the combination of these with the two advanced undergraduate subjects includes at least 36
units in a distinct and appropriate area of graduate concentration.
The Master of Engineering in Electrical Engineering and Computer Science is only awarded to students who have
received, or are simultaneously receiving, one of the three bachelor’s degrees. Students who receive the Master
of Engineering degree after having obtained one of the three bachelor’s degrees must fulfill the requirements for
Course 6-P as described above.
For further details on all EECS programs, visit http://www.eecs.mit.edu/acad.html.
For an explanation of credit units, or hours, please refer to the online help in the MIT Subject Listing & Schedule,

127
C O U R S E 6
2 0 1 4 – 2 0 1 5
Bachelor of Science in Computer Science and Molecular Biology/Course 6-7
Restricted Electives in Science and Technology (REST) Requirement [can be satisfied by 6.042,
18.03, or 18.06 in the Departmental Program] 2
Laboratory Requirement [can be satisfied by 7.02 or 20.109 in the Departmental Program] 1
2 subjects designated as Communication Intensive in Humanities, Arts, and Social Sciences (CI-H); and
2 subjects designated as Communication Intensive in the Major (CI-M).
Required Subjects 147–150
1. Mathematics and Introductory
18.03 Differential Equations, 12, REST; Calculus II (GIR)
or
18.06 Linear Algebra, 12, REST; Calculus II (GIR)
6.042J Mathematics for Computer Science, 12, REST; Calculus I (GIR)
2. Chemistry
5.12 Organic Chemistry I, 12, REST; Chemistry (GIR)
5.60 Thermodynamics and Kinetics, 12, REST; Calculus II (GIR), Chemistry (GIR)
or
7.10J Physical Chemistry of Biomolecular Systems, 12; Calculus II (GIR), Chemistry (GIR), Physics I (GIR),
Physics II (GIR)
or
20.110J Thermodynamics of Biomolecular Systems, 12, REST; Calculus II (GIR), Chemistry (GIR)
3. Introductory Laboratory
7.02J Introduction to Experimental Biology and Communication, 18, CI-M, LAB; Biology (GIR)
or
20.109 Laboratory Fundamentals in Biological Engineering, 15, LAB, CI-M; Biology (GIR), Chemistry (GIR),
6.0002, 18.03, 20.110J*
4. Foundational Subjects
Three Computer Science subjects:
6.005 Elements of Software Construction, 12; REST; 6.01, 6.042J
6.006 Introduction to Algorithms, 12; 6.01, 6.042J*
6.046J Design and Analysis of Algorithms, 12; 6.006*
Three Biological Science subjects:
7.03 Genetics, 12, REST; Biology (GIR)
7.06 Cell Biology, 12; 7.03, 7.05
7.05 General Biochemistry, 12, REST; 5.12*
or
5.07J Biological Chemistry I, 12, REST; 5.12
5. Restricted Electives 24
One subject in Computational Biology:
6.047 Computational Biology: Genomes, Networks, Evolution, 12; 6.006, 6.041, Biology (GIR)*
6.503 Foundations of Algorithms and Computational Techniques in Systems Biology, 12; 6.046J*
7.36J Foundations of Computational and Systems Biology, 12; 7.05*
One subject in Biology:
7.20J Human Physiology, 12; 7.05
7.23 Immunology, 12; 7.03*
7.27 Principles of Human Disease, 12; 7.03, 7.05, 7.06
7.28 Molecular Biology, 12; 7.03, 7.05
7.33J Evolutionary Biology: Concepts, Models, and Computation, 12; 7.03, 6.0002*
6. Advanced Undergraduate Project 12
or
No subject can be counted both as part of the 17-subject GIRs and as part of the 198 units required beyond the GIRs.
Every subject in the student’s departmental program will count toward one or the other, but not both.

128
Notes
*Alternate prerequisites and corequisites are listed in the subject description.
for the 6.UAT/6.UAP or6.UAT/6.UAR sequence.
For an explanation of credit units, or hours, please refer to the online help in the MIT Subject Listing & Schedule,

129
C O U R S E 6
2 0 1 4 – 2 0 1 5
Master of Engineering in Computer Science and Molecular Biology/
Course 6-7P
Restricted Electives in Science and Technology (REST) Requirement [can be satisfied by 6.042,
18.03, or 18.06 in the Departmental Program] 2
Laboratory Requirement [can be satisfied by 7.02 in the Departmental Program] 1
2 subjects designated as Communication Intensive in Humanities, Arts, and Social Sciences (CI-H); and
2 subjects designated as Communication Intensive in the Major (CI-M).(1)
Required Subjects 213–216
1. Mathematics and Introductory
18.03 Differential Equations, 12, REST; Calculus II (GIR)
or
18.06 Linear Algebra, 12, REST; Calculus II (GIR)
6.042J Mathematics for Computer Science, 12, REST; Calculus I (GIR)
2. Chemistry
5.12 Organic Chemistry I, 12, REST; Chemistry (GIR)
5.60 Thermodynamics and Kinetics, 12, REST; Calculus II (GIR), Chemistry (GIR)
or
7.10J Physical Chemistry of Biomolecular Systems, 12; Calculus II (GIR), Chemistry (GIR), Physics I (GIR),
Physics II (GIR)
or
20.110J Thermodynamics of Biomolecular Systems, 12, REST; Calculus II (GIR), Chemistry (GIR)
3. Introductory Laboratory
7.02J Introduction to Experimental Biology and Communication, 18, CI-M, LAB; Biology (GIR)
or
20.109 Laboratory Fundamentals in Biological Engineering, 15, LAB, CI-M; Biology (GIR), Chemistry (GIR), 6.0002,
18.03, 20.110J*
4. Foundational Subjects
Three Computer Science subjects:
6.005 Elements of Software Construction, 12; REST; 6.01, 6.042J
6.006 Introduction to Algorithms, 12; 6.01, 6.042J*
6.046J Design and Analysis of Algorithms, 12; 6.006*
Three Biological Science subjects:
7.03 Genetics, 12, REST; Biology (GIR)
7.06 Cell Biology, 12; 7.03, 7.05
7.05 General Biochemistry, 12, REST; 5.12*
or
5.07J Biological Chemistry I, 12, REST; 5.12
5. Restricted Electives 24
One subject in Computational Biology:
6.047 Computational Biology: Genomes, Networks, Evolution, 12; 6.006, 6.041, Biology (GIR)*
6.503 Foundations of Algorithms and Computational Techniques in Systems Biology, 12; 6.046J*
7.36J Foundations of Computational and Systems Biology, 12; 7.05*
One subject in Biology:
7.20J Human Physiology, 12; 7.05
7.23 Immunology, 12; 7.03*
7.27 Principles of Human Disease, 12; 7.03, 7.05, 7.06
7.28 Molecular Biology, 12; 7.03, 7.05
7.33J Evolutionary Biology: Concepts, Models, and Computation, 12; 7.03, 6.0002*
6. Advanced Undergraduate Project 12
or
7. Four graduate subjects totaling at least 42 units, which includes two concentration subjects (approved by the
department) plus a third graduate subject in electrical engineering and computer science and/or biology.
8. Two subjects from a restricted departmental list of math electives.

130
No subject can be counted both as part of the 17-subject GIRs and as part of the 270–282 units required beyond
the GIRs. Every subject in the student’s departmental program will count toward one or the other, but not both.
Notes
* Alternate prerequisites and corequisites are listed in the subject description.
(1) To complete the required Communication-Intensive subjects in the major, students must take 7.02J or 20.109
or 6.UAT/6.UAP by the end of the third year. The second CI-M should be chosen to complete the requirements in
categories 3 and 6 above.
for the 6.UAT/6.UAP or6.UAT/6.UAR sequence.
Notes on Master of Engineering and Bachelor’s Degree Programs
The Master of Engineering program builds on the bachelor’s degree program (6-7), with restricted elective catego‑ries
7 and 8 and the MEng thesis.
The Master of Engineering in Computer Science and Molecular Biology is only awarded to students who have
received, or are simultaneously receiving, the 6-7 bachelor’s degree. Students who receive the Master of
Engineering degree after having obtained the 6-7 bachelor’s degrees must fulfill the requirements for Course
6-7P as described above.
For an explanation of credit units, or hours, please refer to the online help of the MIT Subject Listing & Schedule,

Course 06

More Related Content

What's hot (20)

Viewers also liked (8)

Similar to Course 06 (20)

Course 06