Online courses directory (19947)

This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems.

The Workshop on Deliberative Democracy and Dispute Resolution, sponsored by the Program on Negotiation at Harvard Law School and The Flora and William Hewlett Foundation, is a two-day conference that brings together dispute resolution professionals and political theorists in the field of deliberative democracy.

Students work in small collaborative design teams to propose, build, and document a semester-long project focused on mobile applications for cell phones. Additional assignments include creating several small mobile applications such as context-aware mobile media capture and games. Students document their work through a series of written and oral proposals, progress reports, and final reports. This course covers the basics of J2ME and explores mobile imaging and media creation, GPS location, user-centered design, usability testing, and prototyping. Java experience is recommended.

Survey of principles underlying the structure and function of the nervous system, integrating molecular, cellular, and systems approaches. Topics: development of the nervous system and its connections, cell biology or neurons, neurotransmitters and synaptic transmission, sensory systems of the brain, the neuro-endocrine system, the motor system, higher cortical functions, behavioral and cellular analyses of learning and memory. First half of an intensive two-term survey of brain and behavioral studies for first-year graduate students.

Course 12.307 is an undergraduate course intended to illustrate, by means of 'hands on' projects, the basic dynamical and physical principles that govern the general circulation of the atmosphere and ocean and the day to day sequence of weather events.  The course parallels the content of the new undergraduate textbook Atmosphere, Ocean and Climate Dynamics by John Marshall and R. Alan Plumb.

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) 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 subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.

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 provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

This course is conducted as an artificial intelligence programming contest in Java. Students work in teams to program virtual robots to play Battlecode, a real-time strategy game. Optional lectures are provided on topics and programming practices relevant to the game, and students learn and improve their programming skills experientially. The competition culminates in a live Battlecode tournament.

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 is an introduction to copyright law and American law in general. Topics covered include: structure of federal law; basics of legal research; legal citations; how to use LexisNexis®; the 1976 Copyright Act; copyright as applied to music, computers, broadcasting, and education; fair use; Napster®, Grokster®, and Peer-to-Peer file-sharing; Library Access to Music Project; The 1998 Digital Millennium Copyright Act; DVDs and encryption; software licensing; the GNU® General Public License and free software.

This class introduces students to the interdisciplinary nature of 21st-century engineering projects with three threads of learning: a technical toolkit, a social science toolkit, and a methodology for problem-based learning. Students encounter the social, political, economic, and technological challenges of engineering practice by participating in real engineering projects with faculty and industry; this semester's major project focuses on the engineering and economics of solar cells. Student teams will create prototypes and mixed media reports with exercises in project planning, analysis, design, optimization, demonstration, reporting and team building.

This short course provides an introduction to reactor dynamics including subcritical multiplication, critical operation in absence of thermal feedback effects and effects of Xenon, fuel and moderator temperature, etc. Topics include the derivation of point kinetics and dynamic period equations; techniques for reactor control including signal validation, supervisory algorithms, model-based trajectory tracking, and rule-based control; and an overview of light-water reactor startup. Lectures and demonstrations employ computer simulation and the use of the MIT Research Reactor.

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 develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice.

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.