A general introduction to manifolds and Lie groups. The role of Lie groups in mathematics and physics. The exponential mapping. Correspondence with Lie algebras. Homogeneous spaces and transformation groups. Adjoint representation. Covering groups. Automorphism groups. Invariant differential forms and cohomology of Lie groups and homogeneous spaces. 18.101 recommended but not required. DThis course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

Organization of synaptic connectivity as the basis of neural computation and learning. Single and multilayer perceptrons. Dynamical theories of recurrent networks: amplifiers, attractors, and hybrid computation. Backpropagation and Hebbian learning. Models of perception, motor control, memory, and neural development. Alternate years.

This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This class was originally listed in Course 13 (Ocean Engineering) as 13.002J.

An introduction to the results and techniques of observations of the ocean in the context of its physical properties and dynamical constraints. Emphasis on large-scale steady circulation and the time-dependent processes that contribute to it. Includes the physical setting of the ocean, atmospheric forcing, application of conservation laws, description of wind-driven and thermohaline circulation, eddy processes, and interpretive techniques.

This course is an introduction to the fundamental aspects of science and engineering necessary for exploring, observing, and utilizing the oceans. Hands-on projects focus on instrumentation in the marine environment and the design of ocean observatories for ocean monitoring and exploration. Topics include acoustics, sound speed and refraction, sounds generated by ships and marine animals, sonar systems and their principles of operation, hydrostatic behavior of floating and submerged bodies geared towards ocean vehicle design, stability of ocean vessels, and the application of instrumentation and electronics in the marine environment. Students work with sensor systems and deploy them in the field to gather and analyze real world data.

" This course, which spans a third of a semester, provides students with experienceĺĘusing techniques employed in synthetic organic chemistry. It alsoĺĘintroduces them to the exciting research area of catalytic chiral catalysis. This class is part of the new laboratory curriculum in the MIT Department of Chemistry. Undergraduate Research-Inspired Experimental Chemistry Alternatives (URIECA) introduces students to cutting edge research topics in a modular format."

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

The plasma state dominates the visible universe, and is important in fields as diverse as Astrophysics and Controlled Fusion. Plasma is often referred to as "the fourth state of matter." This course introduces the study of the nature and behavior of plasma. A variety of models to describe plasma behavior are presented.

" This course is an introduction to software engineering, using the Java™ programming language. It covers concepts useful to 6.005. Students will learn the fundamentals of Java. The focus is on developing high quality, working software that solves real problems. The course is designed for students with some programming experience, but if you have none and are motivated you will do fine. Students who have taken 6.005 should not take this course. Each class is composed of one hour of lecture and one hour of assisted lab work. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month."

" This graduate level course presents a basic study in seismology and the utilization of seismic waves for the study of Earth's interior. It introduces techniques necessary for understanding of elastic wave propagation in layered media."

This course is an introduction to Java programming and software engineering. It is designed for those who have little or no programming experience in Java and covers concepts useful to 6.005. The focus is on developing high quality, working software that solves real problems. Students will learn the fundamentals of Java, and how to use 3rd party libraries to get more done with less work. Each session includes one hour of lecture and one hour of assisted lab work. Short labs are assigned with each lecture. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.

This section of Introduction to Technical Communication deals with ethical issues associated with the design, use, and propagation of technology. At virtually all stages of development and use, any technology can carry with it ethical dilemmas for both creators and users. Of particular interest is how such dilemmas are resolved (or complicated) according to how effectively they are communicated to stakeholders.

Frameworks and Models for Technology and Policy students explore perspectives in the policy process -- agenda setting, problem definition, framing the terms of debate, formulation and analysis of options, implementation and evaluation of policy outcomes using frameworks including economics and markets, law, and business and management. Methods include cost/benefit analysis, probabilistic risk assessment, and system dynamics. Exercises for Technology and Policy students include developing skills to work on the interface between technology and societal issues; simulation exercises; case studies; and group projects that illustrate issues involving multiple stakeholders with different value structures, high levels of uncertainty, multiple levels of complexity; and value trade-offs that are characteristic of engineering systems. Emphasis on negotiation, team building and group dynamics, and management of multiple actors and leadership. This course explores perspectives in the policy process - agenda setting, problem definition, framing the terms of debate, formulation and analysis of options, implementation and evaluation of policy outcomes using frameworks including economics and markets, law, and business and management. Methods include cost/benefit analysis, probabilistic risk assessment, and system dynamics. Exercises include developing skills to work on the interface between technology and societal issues; simulation exercises; case studies; and group projects that illustrate issues involving multiple stakeholders with different value structures, high levels of uncertainty, multiple levels of complexity; and value trade-offs that are characteristic of engineering systems. Emphasis on negotiation, team building and group dynamics, and management of multiple actors and leadership.

Introduces topology, covering topics fundamental to modern analysis and geometry. Topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems, the Tychonoff theorem.

First term of a three-term laboratory subject sequence for Course V majors. Experimental work emphasizes development of fundamental laboratory skills and techniques: volumetric and colorimetric analysis; nuclear magnetic resonance; preparation, purification, and characterization of chemical substances; and data analysis.

Lectures and labs on digital logic, flipflops, PALs, counters, timing, synchronization, finite-state machines, and microprogrammed systems prepare students for the design and implementation of a final project of their choice: games, music, digital filters, graphics, etc. Extensive use of VHDL for describing and implementing digital logic designs. Possible use of lab report for Phase II of the Writing Requirement. Six extra units possible via registration for 6.905 after project proposal.

Fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications to: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. Approximation methods: WKB method, variational principle, and perturbation theory.

" This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles."

This course focuses on introducing the language, libraries, tools and concepts of Java®. The course is specifically targeted at students who intend to take 6.170 in the following term and feel they would struggle because they lack the necessary background. Topics include: Object-oriented programming, primitives, arrays, objects, inheritance, interfaces, polymorphism, hashing, data structures, collections, nested classes, floating point precision, defensive programming, and depth first search algorithm.