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This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in MIT course 6.431 but at a faster pace and in more depth. Topics covered include: probability spaces and measures; discrete and continuous random variables; conditioning and independence; multivariate normal distribution; abstract integration, expectation, and related convergence results; moment generating and characteristic functions; Bernoulli and Poisson processes; finite-state Markov chains; convergence notions and their relations; and limit theorems. Familiarity with elementary notions in probability and real analysis is desirable. This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in MIT course 6.431 but at a faster pace and in more depth. Topics covered include: probability spaces and measures; discrete and continuous random variables; conditioning and independence; multivariate normal distribution; abstract integration, expectation, and related convergence results; moment generating and characteristic functions; Bernoulli and Poisson processes; finite-state Markov chains; convergence notions and their relations; and limit theorems. Familiarity with elementary notions in probability and real analysis is desirable.

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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8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments.&nbsp; Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, 8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments.&nbsp; Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories,

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 course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations. This is a course on the fundamentals of probability geared towards first- or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.

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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Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets, deformation fields) and useful methods that allow us to extract and manipulate image information, including manifold fitting, markov random fields, expectation maximization, clustering and others. For each concept -- a new representation or an estimation algorithm -- a lecture on the mathematical f Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets, deformation fields) and useful methods that allow us to extract and manipulate image information, including manifold fitting, markov random fields, expectation maximization, clustering and others. For each concept -- a new representation or an estimation algorithm -- a lecture on the mathematical f

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 examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, 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. This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, 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.

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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8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments. Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, physics, m 8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments. Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, physics, m

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 divided into two sections, Part I and Part II.  Part I provides an introduction to statistical theory and can be found by visiting 14.381 Fall 2013. Part II, found here, prepares students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, buil ﻿This course is divided into two sections, Part I and Part II.  Part I provides an introduction to statistical theory and can be found by visiting 14.381 Fall 2013. Part II, found here, prepares students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, buil

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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Numerous recent studies have shown that the U.S. has relatively low percentages of students who enter science and engineering and a high drop-out rate. Some other countries are producing many more scientists and engineers per capita than the U.S. What does this mean for the future of the U.S. and the global economy? In this readings and discussion-based seminar you will meet weekly with the Dean of Undergraduate Education to explore the kind of education MIT and other institutions are and should be giving. Based on data from National Academy and other reports, along with what pundits have been saying, we'll see if we can decide how much the U.S. may or may not be at risk. Numerous recent studies have shown that the U.S. has relatively low percentages of students who enter science and engineering and a high drop-out rate. Some other countries are producing many more scientists and engineers per capita than the U.S. What does this mean for the future of the U.S. and the global economy? In this readings and discussion-based seminar you will meet weekly with the Dean of Undergraduate Education to explore the kind of education MIT and other institutions are and should be giving. Based on data from National Academy and other reports, along with what pundits have been saying, we'll see if we can decide how much the U.S. may or may not be at risk.

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 module framework. It can be viewed online or downloaded as a zip file. As taught Autumn Semester 2010/2011. This is a self-contained study of the institutions and processes of the government and politics of the United States. It explores the concepts of limited government, constitutionalism and checks and balances, and the way in which they operate in the American political system. It examines how American governments seek to make policy, the extent to which they can make an impact on society and the different types of constraints on their actions. It also looks at democracy in the American context, how citizens attempt to influence the activities of government and their expectations and beliefs about what is the appropriate role of government. Module Code: M12019 Suit This is a module framework. It can be viewed online or downloaded as a zip file. As taught Autumn Semester 2010/2011. This is a self-contained study of the institutions and processes of the government and politics of the United States. It explores the concepts of limited government, constitutionalism and checks and balances, and the way in which they operate in the American political system. It examines how American governments seek to make policy, the extent to which they can make an impact on society and the different types of constraints on their actions. It also looks at democracy in the American context, how citizens attempt to influence the activities of government and their expectations and beliefs about what is the appropriate role of government. Module Code: M12019 Suit

Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA) Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA)

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Includes audio/video content: AV selected lectures. This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams. Includes audio/video content: AV selected lectures. This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.

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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No known copyright restrictions

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8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments. Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, physics, m

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 https://ocw.mit.edu/terms/index.htm

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Part of a series of worksheets covering Mathematical Case Studies for Economists from Nottingham Trent University. They are downloadable in Word format with embedded links. They can be adapted, printed and/or put in a Virtual Learning Environment. A booklet giving guideline answers for the task questions is available on request from the Economics Network.

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Factors to consider in implementing coaching

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This module aims to enable the learner to plan the implementation of coaching in an organisation. The module summary provides an overview and links to the resources.

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DeSTRESS films combine live-action explanation and interviews, filmed in a variety of locations, with narrated animations that take the viewer through a worked example. This film talks about variation in the context of different ways of saving for the future, and in the context of the varying output of a firm. It explains step-by-step the formula for standard deviation and related formulae. Duration 19'43"

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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This course is designed to provide a thorough understanding of the importance of money, banking, and financial markets of a developed economy. Money, financial institutions, and financial markets have emerged as instruments of payments for the services of factors of production, such as labor and capital. The use of money facilitates business in a market by acting as a common medium of exchange. Of course, as that market expands and develops on a national and international level, the importance of money, banking, and other financial markets expands to accommodate innumerable exchanges. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Economics 302)

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This unit is designed to enable the student to gain an understanding of the reasons why young children behave the way they do and the factors that influence this behaviour. This unit will also enable you to explore strategies to use in the support of a range of behaviours, with consideration of the additional support needs for more challenging behaviour. Outcomes: 1.Identify and explain factors that influence children's behaviour. 2.Analyse and evaluate a range of strategies in the support of positive behaviour. 3.Investigate causes for concern and additional support needs. 4.Demonstrate an awareness of the roles of other professionals and the strategies they use in the support of positive behaviour in children with additional support needs.

Copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG). None of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG). None of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Licensed to colleges in Scotland only Licensed to colleges in Scotland only http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 COLEG COLEG

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This unit is designed to enable the student to gain an understanding of the reasons why young children behave the way they do and the factors that influence this behaviour. This unit will also enable you to explore strategies to use in the support of a range of behaviours, with consideration of the additional support needs for more challenging behaviour. Outcomes: 1.Identify and explain factors that influence children's behaviour. 2.Analyse and evaluate a range of strategies in the support of positive behaviour. 3.Investigate causes for concern and additional support needs. 4.Demonstrate an awareness of the roles of other professionals and the strategies they use in the support of positive behaviour in children with additional support needs.

Copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG). None of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository for the purposes of which these materials are COLEG Materials. Copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG). None of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository for the purposes of which these materials are COLEG Materials. Licensed to colleges in Scotland only Licensed to colleges in Scotland only http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 COLEG COLEG

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Interview (6 min) about the experience of studying on a distance learning course at Brookes, the Masters of Children, Young People and Family Wellbeing, which (from 2016 onwards) will be called 'Child Welfare and Wellbeing'. The interview is conducted over the phone. Tutor and student are located 200 miles apart. The student was on her landline while the tutor used her laptop, skype and an audio recording software package.

copyright Oxford Brookes University, except where indicated in the item description.

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This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in MIT course 6.431 but at a faster pace and in more depth. Topics covered include: probability spaces and measures; discrete and continuous random variables; conditioning and independence; multivariate normal distribution; abstract integration, expectation, and related convergence results; moment generating and characteristic functions; Bernoulli and Poisson processes; finite-state Markov chains; convergence notions and their relations; and limit theorems. Familiarity with elementary notions in probability and real analysis is desirable.

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 https://ocw.mit.edu/terms/index.htm

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8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments.&nbsp; Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories,

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 https://ocw.mit.edu/terms/index.htm

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Description

8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments. Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, physics, m

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 https://ocw.mit.edu/terms/index.htm

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?This course is divided into two sections, Part I and Part II.  Part I provides an introduction to statistical theory and can be found by visiting 14.381 Fall 2013. Part II, found here, prepares students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, buil

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 https://ocw.mit.edu/terms/index.htm

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Numerous recent studies have shown that the U.S. has relatively low percentages of students who enter science and engineering and a high drop-out rate. Some other countries are producing many more scientists and engineers per capita than the U.S. What does this mean for the future of the U.S. and the global economy? In this readings and discussion-based seminar you will meet weekly with the Dean of Undergraduate Education to explore the kind of education MIT and other institutions are and should be giving. Based on data from National Academy and other reports, along with what pundits have been saying, we'll see if we can decide how much the U.S. may or may not be at risk.

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 https://ocw.mit.edu/terms/index.htm

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