Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.

Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

Introduces students to the basic tools in using data to make informed management decisions. Covers introductory probability, decision analysis, basic statistics, regression, simulation, and linear and nonlinear optimization. Computer spreadsheet exercises and examples drawn from marketing, finance, operations management, and other management functions. Restricted to Sloan Fellows.

Subject covers the analysis, design, implementation, and testing of various forms of digital communication based on group collaboration. Students are encouraged to think about the Web and other new digital interactive media not just in terms of technology but also broader issues such as language (verbal and visual), design, information architecture, communication and community. Students work in small groups on a semester-long project of their choice. Various written and oral presentations document project development.

" This course presents a top-down approach to communications system design. The course will cover communication theory, algorithms and implementation architectures for essential blocks in modern physical-layer communication systems (coders and decoders, filters, multi-tone modulation, synchronization sub-systems). The course is hands-on, with a project component serving as a vehicle for study of different communication techniques, architectures and implementations. This year, the project is focused on WLAN transceivers. At the end of the course, students will have gone through the complete WLAN System-On-a-Chip design process, from communication theory, through algorithm and architecture all the way to the synthesized standard-cell RTL chip representation. "

This course provides an introduction to the technology and policy context of public communications networks, through critical discussion of current issues in communications policy and their historical roots. The course focuses on underlying rationales and models for government involvement and the complex dynamics introduced by co-evolving technologies, industry structure, and public policy objectives. Cases drawn from cellular, fixed-line, and Internet applications include evolution of spectrum policy and current proposals for reform; the migration to broadband and implications for universal service policies; and property rights associated with digital content. The course lays a foundation for thesis research in this domain.

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

This course focuses on the land use-transportation ‰ŰĎinteraction space‰Ű in metropolitan settings. The course aims to develop an understanding of relevant theories and analytical techniques, through the exploration of various cases drawn from different parts of the world. The course begins with an overview of the role of transportation in patterns of urban development and metropolitan growth. It introduces the concept of accessibility and related issues of individual and firm travel demand. Later in the semester, students will explore the influence of the metropolitan built environment on travel behavior and the role of transportation on metropolitan land development. The course will conclude with an examination of the implications of the land use-transportation interaction space for metropolitan futures, and our abilities to forecast them.

This course is offered to graduates and is a project-oriented course to teach new methodologies for designing multi-million-gate CMOS VLSI chips using high-level synthesis tools in conjunction with standard commercial EDA tools. The emphasis is on modular and robust designs, reusable modules, correctness by construction, architectural exploration, and meeting the area, timing, and power constraints within standard cell and FPGA frameworks.

Physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); and optoelectronic devices.

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

Fundamental concepts and results for the compressible flow of gases. Topics include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. Emphasis on physical understanding of the phenomena and basic analytical techniques. 2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. The emphasis will be on physical understanding of the phenomena and basic analytical techniques.

Theory for programmers. Introduction to programming and computability theory based on a term-rewriting, "substitution" model of computation by Scheme programs with side-effects. Computation as algebraic manipulation: provable and valid inequalities for multivariate polynomials. Scheme evaluation as algebraic manipulation and term rewriting theory. Paradoxes from self-application and introduction to formal programming semantics. Undecidability of the Halting Problem for Scheme. Properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences. Introduction to logic for program specification and verification. Hilbert's Tenth Problem. Alternate years. 6.844 is a graduate introduction to programming theory, logic of programming, and computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself. Topics covered include: programming and computability theory based on a term-rewriting, "substitution" model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert's Tenth Problem.

" 6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks ‰ŰÓ logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples. 6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students "hands-on" experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester."

This course is an introduction to computational theories of human cognition. Drawing on formal models from classic and contemporary artificial intelligence, students will explore fundamental issues in human knowledge representation, inductive learning and reasoning. What are the forms that our knowledge of the world takes? What are the inductive principles that allow us to acquire new knowledge from the interaction of prior knowledge with observed data? What kinds of data must be available to human learners, and what kinds of innate knowledge (if any) must they have?

Introduces design as a computational enterprise in which rules are developed to compose and describe architectural and other designs. The class covers topics such as shapes, shape arithmetic, symmetry, spatial relations, shape computations, and shape grammars. It focuses on the application of shape grammars in creative design, and teaches shape grammar fundamentals through in-class, hands-on exercises with abstract shape grammars. The class discusses issues related to practical applications of shape grammars.

Why has it been easier to develop a vaccine to eliminate polio than to control influenza or AIDS? Has there been natural selection for a 'language gene'? Why are there no animals with wheels? When does 'maximizing fitness' lead to evolutionary extinction? How are sex and parasites related? Why don't snakes eat grass? Why don't we have eyes in the back of our heads? How does modern genomics illustrate and challenge the field? This course analyzes evolution from a computational, modeling, and engineering perspective. The course has extensive hands-on laboratory exercises in model-building and analyzing evolutionary data.

Study and discussion of computational approaches and algorithms for contemporary problems in functional genomics. Topics include DNA chip design, experimental data normalization, expression data representation standards, proteomics, gene clustering, self-organizing maps, Boolean networks, statistical graph models, Bayesian network models, continuous dynamic models, statistical metrics for model validation, model elaboration, experiment planning, and the computational complexity of functional genomics problems.

Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.