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18.725 Algebraic Geometry (MIT) 18.725 Algebraic Geometry (MIT)

Description

This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic varieties and complex analytic varieties. This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic varieties and complex analytic varieties.

Subjects

algebraic varieties over algebraically closed field | algebraic varieties over algebraically closed field | complex algebraic varieties | complex algebraic varieties | complex analytic varieties | complex analytic varieties | curves and surfaces | curves and surfaces | irreducible components | irreducible components | projective space | projective space | topological diversion | topological diversion | sheaves | sheaves | presheaves | presheaves | algebraic geometry | algebraic geometry | fibers | fibers | morphisms | morphisms | varieties | varieties | projective varieties | projective varieties | applications | applications | dimension | dimension | krull dimension | krull dimension | completeness | completeness | complex topology | complex topology | Chow's lemma | Chow's lemma | analytic spaces | analytic spaces | curves | curves

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8.044 Statistical Physics I (MIT) 8.044 Statistical Physics I (MIT)

Description

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third laws of thermodynamics. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. Concurrent enrollment in 8.04, Quantum Physics I, is recommended. Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third laws of thermodynamics. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. Concurrent enrollment in 8.04, Quantum Physics I, is recommended.

Subjects

probability | probability | statistical mechanics | statistical mechanics | thermodynamics | thermodynamics | random variables | random variables | joint and conditional probability densities | joint and conditional probability densities | functions of a random variable | functions of a random variable | macroscopic variables | macroscopic variables | thermodynamic equilibrium | thermodynamic equilibrium | fundamental assumption of statistical mechanics | fundamental assumption of statistical mechanics | microcanonical and canonical ensembles | microcanonical and canonical ensembles | First | First | second | second | and third laws of thermodynamics | and third laws of thermodynamics | magnetism | magnetism | polyatomic gases | polyatomic gases | hermal radiation | hermal radiation | thermal radiation | thermal radiation | electrons in solids | electrons in solids | and noise in electronic devices | and noise in electronic devices | First | second | and third laws of thermodynamics | First | second | and third laws of thermodynamics

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18.024 Calculus with Theory II (MIT) 18.024 Calculus with Theory II (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor

Subjects

linear algebra | linear algebra | vector integral calculus | vector integral calculus | Calculus of several variables | Calculus of several variables | Vector algebra in 3-space | Vector algebra in 3-space | determinants | determinants | matrices | matrices | Vector-valued functions of one variable | Vector-valued functions of one variable | space motion | space motion | Scalar functions of several variables: partial differentiation | Scalar functions of several variables: partial differentiation | gradient | gradient | optimization techniques | optimization techniques | Double integrals and line integrals in the plane | Double integrals and line integrals in the plane | exact differentials and conservative fields | exact differentials and conservative fields | Green's theorem and applications | Green's theorem and applications | triple integrals | triple integrals | line and surface integrals in space | line and surface integrals in space | Divergence theorem | Divergence theorem | Stokes' theorem | Stokes' theorem | applications | applications

License

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12.620J Classical Mechanics: A Computational Approach (MIT) 12.620J Classical Mechanics: A Computational Approach (MIT)

Description

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov 12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov

Subjects

classical mechanics | classical mechanics | phase space | phase space | computation | computation | Lagrangian formulation | Lagrangian formulation | action | action | variational principles | variational principles | equations of motion | equations of motion | Hamilton's principle | Hamilton's principle | conserved quantities | conserved quantities | rigid bodies and tops | rigid bodies and tops | Hamiltonian formulation | Hamiltonian formulation | canonical equations | canonical equations | surfaces of section | surfaces of section | chaos | chaos | canonical transformations | canonical transformations | generating functions | generating functions | Liouville's theorem | Liouville's theorem | Poincar? integral invariants | Poincar? integral invariants | Poincar?-Birkhoff | Poincar?-Birkhoff | KAM theorem | KAM theorem | invariant curves | invariant curves | cantori | cantori | nonlinear resonances | nonlinear resonances | resonance overlap | resonance overlap | transition to chaos | transition to chaos | chaotic motion | chaotic motion | 12.620 | 12.620 | 6.946 | 6.946 | 8.351 | 8.351

License

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ía y Topología (2010) ía y Topología (2010)

Description

Esta asignatura está dedicada a iniciarse en el estudio de las variedades diferenciables, como generalización natural del concepto de superficie, que ya debe conocer el estudiante tras el estudio en tercer curso de la asignatura Geometría Diferencial. Cuando trabajamos con superficies de R3, o en general con subvariedades del espacio euclídeo Rn, estamos disfrutando de la ventaja de la simplicidad conceptual; en general, estamos más cómodos tratando con subespacios de Rn que con espacios métricos o topológicos arbitrarios. Sin embargo, esta aproximación a las variedades diferenciables tiene la desventaja de que importantes ideas están algunas veces ocultas por el familiar ambiente de Rn. Por esta razón, y tras haber motivado las variedades diferenciables con las superficies k-d Esta asignatura está dedicada a iniciarse en el estudio de las variedades diferenciables, como generalización natural del concepto de superficie, que ya debe conocer el estudiante tras el estudio en tercer curso de la asignatura Geometría Diferencial. Cuando trabajamos con superficies de R3, o en general con subvariedades del espacio euclídeo Rn, estamos disfrutando de la ventaja de la simplicidad conceptual; en general, estamos más cómodos tratando con subespacios de Rn que con espacios métricos o topológicos arbitrarios. Sin embargo, esta aproximación a las variedades diferenciables tiene la desventaja de que importantes ideas están algunas veces ocultas por el familiar ambiente de Rn. Por esta razón, y tras haber motivado las variedades diferenciables con las superficies k-d

Subjects

ía y Topología | ía y Topología | formas diferenciales | formas diferenciales | campo de tensores | campo de tensores | variedad diferenciable | variedad diferenciable | ía diferencial | ía diferencial | ón tensorial | ón tensorial | ón en variedades | ón en variedades | campo de vectores | campo de vectores

License

http://creativecommons.org/licenses/by-nc-sa/3.0/

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1.017 Computing and Data Analysis for Environmental Applications (MIT) 1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | probability | statistics | statistics | events | events | random variables | random variables | univariate distributions | univariate distributions | multivariate distributions | multivariate distributions | uncertainty propagation | uncertainty propagation | Bernoulli trials | Bernoulli trials | Poisson processed | Poisson processed | conditional probability | conditional probability | Bayes rule | Bayes rule | random sampling | random sampling | point estimation | point estimation | interval estimation | interval estimation | hypothesis testing | hypothesis testing | analysis of variance | analysis of variance | linear regression | linear regression | computational analysis | computational analysis | data analysis | data analysis | environmental engineering | environmental engineering | applications | applications | MATLAB | MATLAB | numerical modeling | numerical modeling | probabilistic concepts | probabilistic concepts | statistical methods | statistical methods | field data | field data | laboratory data | laboratory data | numerical techniques | numerical techniques | Monte Carlo simulation | Monte Carlo simulation | variability | variability | sampling | sampling | data sets | data sets | computer | computer | uncertainty | uncertainty | interpretation | interpretation | quantitative data | quantitative data

License

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14.382 Econometrics I (MIT) 14.382 Econometrics I (MIT)

Description

This course focuses on the specification and estimation of the linear regression model. The course departs from the standard Gauss-Markov assumptions to include heteroskedasticity, serial correlation, and errors in variables. Advanced topics include generalized least squares, instrumental variables, nonlinear regression, and limited dependent variable models. Economic applications are discussed throughout the course. This course focuses on the specification and estimation of the linear regression model. The course departs from the standard Gauss-Markov assumptions to include heteroskedasticity, serial correlation, and errors in variables. Advanced topics include generalized least squares, instrumental variables, nonlinear regression, and limited dependent variable models. Economic applications are discussed throughout the course.

Subjects

Economics | Economics | econometrics | econometrics | linear regression model | linear regression model | Gauss-Markov | Gauss-Markov | heteroskedasticity | heteroskedasticity | serial correlation | serial correlation | errors | errors | variables | variables | generalized least squares | generalized least squares | instrumental variables | instrumental variables | nonlinear regression | nonlinear regression | limited dependent variable models | limited dependent variable models

License

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12.301 Climate Physics and Chemistry (MIT) 12.301 Climate Physics and Chemistry (MIT)

Description

This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history; methods for detecting climate change, including proxies, ice cores, instrumental records, and time series analysis; physical and chemical processes in climate, including primordial atmosphere, ozone chemistry, carbon and oxygen cycles, and heat and water budgets; internal feedback mechanisms, including ice, aerosols, water vapor, clouds, and ocean circulation; climate forcing, including orbital variations, volcanism, plate tectonics, and solar variability; climate models and mechanisms of variability, including energy balance, coupled models, and global ocean and atmosphere models; and outstanding problems. This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history; methods for detecting climate change, including proxies, ice cores, instrumental records, and time series analysis; physical and chemical processes in climate, including primordial atmosphere, ozone chemistry, carbon and oxygen cycles, and heat and water budgets; internal feedback mechanisms, including ice, aerosols, water vapor, clouds, and ocean circulation; climate forcing, including orbital variations, volcanism, plate tectonics, and solar variability; climate models and mechanisms of variability, including energy balance, coupled models, and global ocean and atmosphere models; and outstanding problems.

Subjects

climate | climate | climate change | climate change | proxies | proxies | ice cores | ice cores | primordial atmosphere | primordial atmosphere | ozone chemistry | ozone chemistry | carbon and oxygen cycles | carbon and oxygen cycles | heat and water budgets | heat and water budgets | aerosols | aerosols | water vapor | water vapor | clouds | clouds | ocean circulation | ocean circulation | orbital variations | orbital variations | volcanism | volcanism | plate tectonics | plate tectonics | solar system | solar system | solar variability | solar variability | climate model | climate model | energy balance | energy balance

License

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1.010 Uncertainty in Engineering (MIT) 1.010 Uncertainty in Engineering (MIT)

Description

This undergraduate class serves as an introduction to probability and statistics, with emphasis on engineering applications. The first segment discusses events and their probability, Bayes' Theorem, discrete and continuous random variables and vectors, univariate and multivariate distributions, Bernoulli trials and Poisson point processes, and full-distribution uncertainty propagation and conditional analysis. The second segment deals with second-moment representation of uncertainty and second-moment uncertainty propagation and conditional analysis. The final segment covers random sampling, point and interval estimation, hypothesis testing, and linear regression. Many of the concepts covered in class are illustrated with real-world examples from various areas of engineering. This undergraduate class serves as an introduction to probability and statistics, with emphasis on engineering applications. The first segment discusses events and their probability, Bayes' Theorem, discrete and continuous random variables and vectors, univariate and multivariate distributions, Bernoulli trials and Poisson point processes, and full-distribution uncertainty propagation and conditional analysis. The second segment deals with second-moment representation of uncertainty and second-moment uncertainty propagation and conditional analysis. The final segment covers random sampling, point and interval estimation, hypothesis testing, and linear regression. Many of the concepts covered in class are illustrated with real-world examples from various areas of engineering.

Subjects

statistics | statistics | decision analysis | decision analysis | random variables and vectors | random variables and vectors | uncertainty propagation | uncertainty propagation | conditional distributions | conditional distributions | second-moment analysis | second-moment analysis | system reliability | system reliability | Bayesian analysis and risk-based decision | Bayesian analysis and risk-based decision | estimation of distribution parameters | estimation of distribution parameters | hypothesis testing | hypothesis testing | simple and multiple linear regressions | simple and multiple linear regressions | Poisson and Markov processes | Poisson and Markov processes

License

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17.874 Quantitative Research Methods: Multivariate (MIT) 17.874 Quantitative Research Methods: Multivariate (MIT)

Description

This course is the second semester in the statistics sequence for political science and public policy offered in the Political Science Department at MIT. The intellectual thrust of the course is a presentation of statistical models for estimating causal effects of variables. The model of an effect is a conditional mean (though we might imagine other effect). The notion of causality is the effect of one variable on another holding all else constant. This course is the second semester in the statistics sequence for political science and public policy offered in the Political Science Department at MIT. The intellectual thrust of the course is a presentation of statistical models for estimating causal effects of variables. The model of an effect is a conditional mean (though we might imagine other effect). The notion of causality is the effect of one variable on another holding all else constant.

Subjects

Quantitative research design | Quantitative research design | Econometrics | Econometrics | Multivariate statistics | Multivariate statistics | Politics | Politics | Matrix algebra | Matrix algebra | Regression | Regression | Voting behavior | Voting behavior | Prediction | Prediction | Qualitative variable | Qualitative variable | Bootstrapping | Bootstrapping | Political model | Political model | Causality | Causality | Conditional mean | Conditional mean | Public policy | Public policy | Analysis | Analysis

License

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12.620J Classical Mechanics: A Computational Approach (MIT) 12.620J Classical Mechanics: A Computational Approach (MIT)

Description

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl

Subjects

classical mechanics | classical mechanics | computational classical mechanics | computational classical mechanics | structure and interpretation of classical mechanics | structure and interpretation of classical mechanics | phase space | phase space | lagrangian | lagrangian | action | action | variational principles | variational principles | equation of motion | equation of motion | hamilton principle | hamilton principle | rigid bodies | rigid bodies | Hamiltonian | Hamiltonian | canonical equations | canonical equations | surfaces of section | surfaces of section | canonical transformations | canonical transformations | liouville | liouville | Poincare | Poincare | birkhoff | birkhoff | kam theorem | kam theorem | invariant curves | invariant curves | resonance | resonance | chaos | chaos

License

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14.32 Econometrics (MIT) 14.32 Econometrics (MIT)

Description

Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement. Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

Subjects

econometrics | econometrics | statistical methods | statistical methods | differences-in-differences | differences-in-differences | 2SLS | 2SLS | FGLS | FGLS | serial correlation | serial correlation | IV | IV | two-stage least squares | two-stage least squares | multivariate regression | multivariate regression | simultaneous equations | simultaneous equations | econometric models | econometric models | program evaluation | program evaluation | linear regression | linear regression | instrumental variables | instrumental variables | panel data methods | panel data methods | measurement error | measurement error | limited dependent variable models | limited dependent variable models

License

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18.024 Multivariable Calculus with Theory (MIT) 18.024 Multivariable Calculus with Theory (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus. This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Subjects

linear algebra | linear algebra | vector integral calculus | vector integral calculus | Calculus of several variables | Calculus of several variables | Vector algebra in 3-space | Vector algebra in 3-space | determinants | determinants | matrices | matrices | Vector-valued functions of one variable | Vector-valued functions of one variable | space motion | space motion | Scalar functions of several variables | Scalar functions of several variables | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | Double integrals and line integrals in the plane | Double integrals and line integrals in the plane | exact differentials and conservative fields | exact differentials and conservative fields | Green's theorem and applications | Green's theorem and applications | triple integrals | triple integrals | line and surface integrals in space | line and surface integrals in space | Divergence theorem | Divergence theorem | Stokes' theorem | Stokes' theorem | applications | applications

License

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18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces (MIT) 18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces (MIT)

Description

The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory. The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory.

Subjects

intersection theory | intersection theory | moduli spaces | moduli spaces | geometry of homogeneous varieties | geometry of homogeneous varieties | Deligne-Mumford moduli spaces | Deligne-Mumford moduli spaces | stable curves | stable curves | Kontsevich moduli spaces | Kontsevich moduli spaces | stable maps | stable maps | Littlewood-Richardson rules | Littlewood-Richardson rules | Grassmannians | Grassmannians | divisor theory | divisor theory | cohomology | cohomology | Brill-Noether theory | Brill-Noether theory | limit linear series | limit linear series | ample cones | ample cones | effective cones | effective cones | Gromov-Witten invariants | Gromov-Witten invariants | simple homogeneous varieties | simple homogeneous varieties

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6.436J Fundamentals of Probability (MIT) 6.436J Fundamentals of Probability (MIT)

Description

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.

Subjects

Introduction to probability theory | Introduction to probability theory | Probability spaces and measures | Probability spaces and measures | Discrete and continuous random variables | Discrete and continuous random variables | Conditioning and independence | Conditioning and independence | Multivariate normal distribution | Multivariate normal distribution | Abstract integration | Abstract integration | expectation | expectation | and related convergence results | and related convergence results | Moment generating and characteristic functions | Moment generating and characteristic functions | Bernoulli and Poisson process | Bernoulli and Poisson process | Finite-state Markov chains | Finite-state Markov chains | Convergence notions and their relations | Convergence notions and their relations | Limit theorems | Limit theorems | Familiarity with elementary notions in probability and real analysis is desirable | Familiarity with elementary notions in probability and real analysis is desirable

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14.384 Time Series Analysis (MIT) 14.384 Time Series Analysis (MIT)

Description

The course is an introduction to univariate and multivariate time series models. It starts by introducing basic concepts and progresses to more complicated models. The course intends to meet two goals. It provides tools for empirical work with time series data and is an introduction into the theoretical foundation of time series models. The course is an introduction to univariate and multivariate time series models. It starts by introducing basic concepts and progresses to more complicated models. The course intends to meet two goals. It provides tools for empirical work with time series data and is an introduction into the theoretical foundation of time series models.

Subjects

time series analysis | time series analysis | univariate time series model | univariate time series model | multivariate time series model | multivariate time series model | time series model | time series model

License

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17.504 Ethnic Politics I (MIT) 17.504 Ethnic Politics I (MIT)

Description

This course is designed to provide students with a broad overview of the major theories on the relationship between ethnicity and politics. The course is divided into three sections. The first covers general theory and discusses the social construction of ethnicity as well as the limits of construction. The second section discusses ethnicity as a dependent variable. This section studies the forces that shape the development of ethnic identities and their motivating power. The third section addresses ethnicity as an independent variable. In other words, it focuses on how ethnicity operates to affect important political and economic outcomes. This course is the first semester of a year-long sequence on ethnic politics. However, each semester is self-contained and students may take the course This course is designed to provide students with a broad overview of the major theories on the relationship between ethnicity and politics. The course is divided into three sections. The first covers general theory and discusses the social construction of ethnicity as well as the limits of construction. The second section discusses ethnicity as a dependent variable. This section studies the forces that shape the development of ethnic identities and their motivating power. The third section addresses ethnicity as an independent variable. In other words, it focuses on how ethnicity operates to affect important political and economic outcomes. This course is the first semester of a year-long sequence on ethnic politics. However, each semester is self-contained and students may take the course

Subjects

Political Science | Political Science | ethinic | ethinic | politics | politics | theories | theories | ethnicity | ethnicity | dependent variable | dependent variable | ethnic identities | ethnic identities | motivating power | motivating power | independent variable | independent variable | political | political | economic | economic | outcomes | outcomes | Graduate students | Graduate students

License

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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18.02 Multivariable Calculus (MIT) 18.02 Multivariable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates. Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.

Subjects

calculus | calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applications

License

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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6.245 Multivariable Control Systems (MIT) 6.245 Multivariable Control Systems (MIT)

Description

This course uses computer-aided design methodologies for synthesis of multivariable feedback control systems. Topics covered include: performance and robustness trade-offs; model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; and nonlinear effects. The assignments for the course comprise of computer-aided (MATLAB®) design problems. This course uses computer-aided design methodologies for synthesis of multivariable feedback control systems. Topics covered include: performance and robustness trade-offs; model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; and nonlinear effects. The assignments for the course comprise of computer-aided (MATLAB®) design problems.

Subjects

multivariable control systems | multivariable control systems | computer-aided design | computer-aided design | MATLAB | MATLAB | multivariable feedback control systems | multivariable feedback control systems | model-based compensators | model-based compensators | Q-parameterization | Q-parameterization | optimization | optimization | dynamic augmentation | dynamic augmentation | linear-quadratic optimization | linear-quadratic optimization | H-infinity controller design | H-infinity controller design | Mu-synthesis | Mu-synthesis | nonlinear systems | nonlinear systems | engineering design | engineering design

License

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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9.07 Statistical Methods in Brain and Cognitive Science (MIT) 9.07 Statistical Methods in Brain and Cognitive Science (MIT)

Description

This course emphasizes statistics as a powerful tool for studying complex issues in behavioral and biological sciences, and explores the limitations of statistics as a method of inquiry. The course covers descriptive statistics, probability and random variables, inferential statistics, and basic issues in experimental design. Techniques introduced include confidence intervals, t-tests, F-tests, regression, and analysis of variance. Assignments include a project in data analysis. This course emphasizes statistics as a powerful tool for studying complex issues in behavioral and biological sciences, and explores the limitations of statistics as a method of inquiry. The course covers descriptive statistics, probability and random variables, inferential statistics, and basic issues in experimental design. Techniques introduced include confidence intervals, t-tests, F-tests, regression, and analysis of variance. Assignments include a project in data analysis.

Subjects

statistics | statistics | standard deviation | standard deviation | ANOVA | ANOVA | variance | variance | chi squared | chi squared | mean | mean | median | median | spread | spread | graphs | graphs | histograms | histograms | binomial distribution | binomial distribution | random variables | random variables | sampling | sampling | experimental design | experimental design | probability | probability | confidence intervals | confidence intervals | error bars | error bars | best fit | best fit | hypothesis testing | hypothesis testing | linear regression | linear regression | regression | regression | correlation | correlation | categorical data | categorical data

License

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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8.044 Statistical Physics I (MIT) 8.044 Statistical Physics I (MIT)

Description

This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.This course is an elective subject in MIT’s undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges. This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.This course is an elective subject in MIT’s undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

Subjects

probability | probability | statistical mechanics | statistical mechanics | thermodynamics | thermodynamics | random variables | random variables | joint and conditional probability densities | joint and conditional probability densities | functions of a random variable | functions of a random variable | macroscopic variables | macroscopic variables | thermodynamic equilibrium | thermodynamic equilibrium | fundamental assumption of statistical mechanics | fundamental assumption of statistical mechanics | microcanonical and canonical ensembles | microcanonical and canonical ensembles | First | second | and third laws of thermodynamics | First | second | and third laws of thermodynamics | magnetism | magnetism | polyatomic gases | polyatomic gases | thermal radiation | thermal radiation | electrons in solids | electrons in solids | noise in electronic devices | noise in electronic devices

License

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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Portrait of Boris Souvarine and Anatoli Lunatscharski [s.d.]

Description

Boris Souvarine Papers - Soviet Russia Photos graduateinstitute.ch/home/research/library/archives/boris... Notes: This document is a photographic reproduction of a portrait. The inscription reads: "Souvarine and Lunatscharski". Anatoli Lunatscharski (1875-1933) was among the "Old Bolsheviks", charged since October Revolution of education and culture questions in the Bolshevik Party. Boris Souvarine was a member of the Secretariat of the Communist International between 1921 and 1924, representing the French Communist Party, of which he was one of the founders. He attempted to defend himself at the XIIIth Congress of the CPSU, and Anatoli Lunatscharski translated his speech. Photographer: V. Shabel'skii. Description: 1 photograph. Black and white ; 17.5 x 12.5 cm. Sources and further reading: Panné, Jean-Louis. 1993. Boris Souvarine: le premier désenchanté du communisme. Paris: R. Laffont. Roche, Anne. 1990. Boris Souvarine et la ?Critique sociale? . Paris : Éd. de la Découverte.

Subjects

portrait | russia | borissouvarine | sovietunion | 20thcentury | vshabelskii | lunacharski? | ??????????? | lunatscharski | lunatscharsky

License

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Sever Hall, Harvard College (Detail of Entrance)

Description

Collection: A. D. White Architectural Photographs, Cornell University Library Accession Number: 15/5/3090.00217 Title: Sever Hall, Harvard College (Detail of Entrance) Architect: Henry Hobson Richardson (American, 1838-1886) Building Date: 1878-1880 Photograph date: ca. 1880-ca. 1895 Location: North and Central America: United States; Massachusetts, Cambridge Materials: albumen print Image: 6 x 7 7/8 in.; 15.24 x 20.0025 cm Style: Romanesque Revival Provenance: Transfer from the College of Architecture, Art and Planning Persistent URI: hdl.handle.net/1813.001/5sd0 There are no known U.S. copyright restrictions on this image. The digital file is owned by the Cornell University Library which is making it freely available with the request that, when possible, the Library be credited as its source. We had some help with the geocoding from Web Services by Yahoo!

Subjects

cornelluniversitylibrary | archedportals | entrances | universitycampuses | plantderivedmotifs | severhallharvarduniversitycambridgemassachusetts | universities | culidentifier:value=155309000217 | culidentifier:lunafield=accessionnumber | severhall | harvarduniversity | harvardyard | cambridge | massachusetts | romanesquerevival | henryhobsonrichardson | adwhitearchitecturalphotographs | harvardcollege | usnationalregisterofhistoricplaces | usnationalhistoriclandmark | historicdistrict | richardsonianromanesque | annesever | jameswarrensever | academicbuilding | redbrick | grossmanlibrary | harvardvisualandenvironmentalstudies | vericon | harvardradcliffesciencefictionassociation

License

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8.044 Statistical Physics I (MIT) 8.044 Statistical Physics I (MIT)

Description

This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.

Subjects

probability | probability | statistical mechanics | statistical mechanics | thermodynamics | thermodynamics | random variables | random variables | joint and conditional probability densities | joint and conditional probability densities | functions of a random variable | functions of a random variable | macroscopic variables | macroscopic variables | thermodynamic equilibrium | thermodynamic equilibrium | fundamental assumption of statistical mechanics | fundamental assumption of statistical mechanics | microcanonical and canonical ensembles | microcanonical and canonical ensembles | First | First | second | second | and third laws of thermodynamics | and third laws of thermodynamics | magnetism | magnetism | polyatomic gases | polyatomic gases | hermal radiation | hermal radiation | thermal radiation | thermal radiation | electrons in solids | electrons in solids | and noise in electronic devices | and noise in electronic devices | First | second | and third laws of thermodynamics | First | second | and third laws of thermodynamics

License

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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Ovarian cancer information centre resource stub

Description

A resource stub for the Ovarian cancer information centre Web page. It covers the causes, diagnosis and treatment of ovarian cancer.

Subjects

ovarian neoplasms | prevention and control | diagnosis | aetiology | epidemiology | surgery | drug therapy | radiotherapy | ovarian cancer | ovary neoplasms | ovary cancer | ovarian carcinoma | Technology | Diseases | SAFETY | Subjects allied to Medicine | UK EL04 = SCQF 4 | Foundational Level | NICAT 1 | CQFW 1 | Foundation | GCSE D-G | NVQ 1 | Intermediate 1 | | UK EL05 = SCQF 5 | Intermediate level | Intermediate | NICAT 2 | CQFW 2 | Intermediate | GSCE A-C | NVQ 2 | | UK EL06 = SCQF 6 | Advanced courses | | NICAT 3 | CQFW 3 | Advanced | A/AS Level | NVQ 3 | Higher | SVQ 3 | UK EL07 = SCQF 7 | Higher Certificate | NICAT 4 | CQFW 4 | NVQ 4 | Advanced Higher | SVQ 4 | HN Certificate | Students | Learning | Teaching | Subjects allied to medicine | B000 | EDUCATION / TRAINING / TEACHING | HEALTH CARE / MEDICINE / HEALTH and SAFETY | INFORMATION TECHNOLOGY and INFORMATION | G | P | C

License

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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