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Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Description

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation. This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research. This course is designed to provide an introduction to a variety of empirical research methods used by political scientists. The primary aims of the course are to make you a more sophisticated consumer of diverse empirical research and to allow you to conduct sophisticated independent work in your junior and senior years. This is not a course in data analysis. Rather, it is a course on how to approach political science research.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available. This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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In this course students examine and critique accounting frameworks, including accounting for the underground economy, multipliers, linkages, and supply chains used to assess employment and environmental impacts and infrastructure investments. They also assess the value of price indices, industrial location and employment measures, and shift-share analyses. Discussions of U.S. and foreign applications and their relation will be featured in the class. In this course students examine and critique accounting frameworks, including accounting for the underground economy, multipliers, linkages, and supply chains used to assess employment and environmental impacts and infrastructure investments. They also assess the value of price indices, industrial location and employment measures, and shift-share analyses. Discussions of U.S. and foreign applications and their relation will be featured in the class.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries. This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered. This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This class explores the creation (and creativity) of the modern scientific and cultural world through study of western Europe in the 17th century, the age of Descartes and Newton, Shakespeare, Rembrandt and Moliere. It compares period thinking to present-day debates about the scientific method, art, religion, and society. This team-taught, interdisciplinary subject draws on a wide range of literary, dramatic, historical, and scientific texts and images, and involves theatrical experimentation as well as reading, writing, researching and conversing. This class explores the creation (and creativity) of the modern scientific and cultural world through study of western Europe in the 17th century, the age of Descartes and Newton, Shakespeare, Rembrandt and Moliere. It compares period thinking to present-day debates about the scientific method, art, religion, and society. This team-taught, interdisciplinary subject draws on a wide range of literary, dramatic, historical, and scientific texts and images, and involves theatrical experimentation as well as reading, writing, researching and conversing.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Offered annually in the spring term, Introduction to Stagecraft is a hands-on course that gets students working with the tools and techniques of theatrical production in a practical way.&#160;It is not a design course but one devoted to artisanship. Among the many remarkable final projects that have been proposed and presented at the end of the course have been a Renaissance hourglass blown in the MIT glass shop and set into a frame turned on our set shop lathe; a four harness loom built by a student who then wove cloth on it; a number of chain mail tunics and coifs; a wide variety of costume and furniture pieces and electrified period lighting fixtures. Offered annually in the spring term, Introduction to Stagecraft is a hands-on course that gets students working with the tools and techniques of theatrical production in a practical way.&#160;It is not a design course but one devoted to artisanship. Among the many remarkable final projects that have been proposed and presented at the end of the course have been a Renaissance hourglass blown in the MIT glass shop and set into a frame turned on our set shop lathe; a four harness loom built by a student who then wove cloth on it; a number of chain mail tunics and coifs; a wide variety of costume and furniture pieces and electrified period lighting fixtures.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Description

Students examine and critique accounting frameworks, including accounting for the underground economy, multipliers, linkages, and supply chains used to assess employment and environmental impacts and infrastructure investments. They also assess the value of price indices, industrial location and employment measures, and shift-share analyses. Discussions of US and foreign applications and their relation will be featured in the class. Students examine and critique accounting frameworks, including accounting for the underground economy, multipliers, linkages, and supply chains used to assess employment and environmental impacts and infrastructure investments. They also assess the value of price indices, industrial location and employment measures, and shift-share analyses. Discussions of US and foreign applications and their relation will be featured in the class.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course will explore educational games and simulations and several computer modeling platforms. We will focus on design and research issues pertinent to learning through simulations and games. Throughout the course we will explore concepts in modeling, simulation, and gaming common to many domains, and investigate specific applications from a variety of fields ranging from weather to ecology to traffic management. This course will explore educational games and simulations and several computer modeling platforms. We will focus on design and research issues pertinent to learning through simulations and games. Throughout the course we will explore concepts in modeling, simulation, and gaming common to many domains, and investigate specific applications from a variety of fields ranging from weather to ecology to traffic management.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This subject is designed for upper level undergraduates and graduate students as an introduction to politics and the policy process in modern Japan. The semester is divided into two parts. After a two-week general introduction to Japan and to the dominant approaches to the study of Japanese history, politics and society, we will begin exploring five aspects of Japanese politics: (1) Party Politics, (2) Electoral Politics, (3) Interest Group Politics, and (4) Bureaucratic Politics. The second part of the semester focuses on public policy, divided into seven major policy areas: (1) Social&#160;Policy, (2) Foreign Policy, (3) Defense Policy, (4) Energy Policy, (5) Science and Technology Policy, (6) Industrial Policy, and (7) Trade Policy. We will try to understand the ways in which the ac This subject is designed for upper level undergraduates and graduate students as an introduction to politics and the policy process in modern Japan. The semester is divided into two parts. After a two-week general introduction to Japan and to the dominant approaches to the study of Japanese history, politics and society, we will begin exploring five aspects of Japanese politics: (1) Party Politics, (2) Electoral Politics, (3) Interest Group Politics, and (4) Bureaucratic Politics. The second part of the semester focuses on public policy, divided into seven major policy areas: (1) Social&#160;Policy, (2) Foreign Policy, (3) Defense Policy, (4) Energy Policy, (5) Science and Technology Policy, (6) Industrial Policy, and (7) Trade Policy. We will try to understand the ways in which the ac

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This seminar provides an overview of the field of international relations. Each week, a different approach to explaining international relations will be examined. By surveying major concepts and theories in the field, the seminar will also assist graduate students in preparing for the comprehensive examination and further study in the department's more specialized offerings in international relations, including 17.420, 17.422, 17.424, 17.430, 17.432 and 17.468. Master's students and undergraduates may enroll only with the instructor's permission. This seminar provides an overview of the field of international relations. Each week, a different approach to explaining international relations will be examined. By surveying major concepts and theories in the field, the seminar will also assist graduate students in preparing for the comprehensive examination and further study in the department's more specialized offerings in international relations, including 17.420, 17.422, 17.424, 17.430, 17.432 and 17.468. Master's students and undergraduates may enroll only with the instructor's permission.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Description

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied. This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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In The Souls of Black Folk (1903), the great cultural critic W. E. B. Du Bois wrote that "&#8230;the problem of the Twentieth Century is the problem of the color line."&#160;A century after Du Bois penned those words, most Americans would agree that at the beginning of the twenty-first century, the color line remains one of our most pressing social issues.&#160;In this course, we will explore the terrain of race in America by reading the works of writers of color and others concerned with the issue of race, by viewing films that address racial issues, and by writing to explore how the fictions and facts of race condition all our lives, social and civic, private and public.&#160;We will consider the complex question of racial identity, test the givens of history by In The Souls of Black Folk (1903), the great cultural critic W. E. B. Du Bois wrote that "&#8230;the problem of the Twentieth Century is the problem of the color line."&#160;A century after Du Bois penned those words, most Americans would agree that at the beginning of the twenty-first century, the color line remains one of our most pressing social issues.&#160;In this course, we will explore the terrain of race in America by reading the works of writers of color and others concerned with the issue of race, by viewing films that address racial issues, and by writing to explore how the fictions and facts of race condition all our lives, social and civic, private and public.&#160;We will consider the complex question of racial identity, test the givens of history by

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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The goal of this course is to illustrate how molecular structure is extracted from a spectrum. In order to achieve this goal it will be necessary to: master the language of spectroscopists; develop facility with quantum mechanical models; predict the relative intensities and selection rules; and learn how to assign spectra. The goal of this course is to illustrate how molecular structure is extracted from a spectrum. In order to achieve this goal it will be necessary to: master the language of spectroscopists; develop facility with quantum mechanical models; predict the relative intensities and selection rules; and learn how to assign spectra.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Student project teams design and fabricate a materials engineering prototype using appropriate processing technologies (injection molding, thermoforming, investment casting, powder processing, brazing, etc.). Emphasis on teamwork, project management, communications and computer skills, and hands-on work using student and MIT laboratory shops. Goals include developing an understanding of the practical applications of MSE; trade-offs between design, processing and performance; and fabrication of a deliverable prototype. Teams document their progress and final results by means of web pages and weekly oral presentations. Instruction and practice in oral communication provided. Student project teams design and fabricate a materials engineering prototype using appropriate processing technologies (injection molding, thermoforming, investment casting, powder processing, brazing, etc.). Emphasis on teamwork, project management, communications and computer skills, and hands-on work using student and MIT laboratory shops. Goals include developing an understanding of the practical applications of MSE; trade-offs between design, processing and performance; and fabrication of a deliverable prototype. Teams document their progress and final results by means of web pages and weekly oral presentations. Instruction and practice in oral communication provided.

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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