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6.830 Database Systems (MIT) 6.830 Database Systems (MIT)

Description

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken MIT course 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. Topics related to the engineering and design of database systems, including: data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel, and he This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken MIT course 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. Topics related to the engineering and design of database systems, including: data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel, and he

Subjects

engineering and design of database systems | data models | engineering and design of database systems | data models | database and schema design | database and schema design | schema normalization and integrity constraints | schema normalization and integrity constraints | query processing | query processing | query optimization and cost estimation | query optimization and cost estimation | transactions | transactions | recovery | recovery | concurrency control | concurrency control | isolation and consistency | isolation and consistency | distributed | distributed | parallel | parallel | heterogeneous databases | heterogeneous databases | adaptive databases | adaptive databases | trigger systems | trigger systems | pub-sub systems | pub-sub systems | semi structured data and XML querying | semi structured data and XML querying

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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6.893 Database Systems (MIT) 6.893 Database Systems (MIT)

Description

This course is designed to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, query optimization, query processing, and transactions. This is not a course on database design or SQL programming (though we will discuss these issues briefly). It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. This course is designed to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, query optimization, query processing, and transactions. This is not a course on database design or SQL programming (though we will discuss these issues briefly). It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend.

Subjects

database systems | database systems | data models | data models | database design | database design | schema design | schema design | schema normalization | schema normalization | integrity constraints | integrity constraints | query processing | query processing | query optimization | query optimization | cost estimation | cost estimation | transactions | transactions | recovery | recovery | concurrency control | concurrency control | isolation | isolation | consistency | consistency | distributed | parallel | and heterogeneous databases | distributed | parallel | and heterogeneous databases | adaptive databases | adaptive databases | trigger systems | trigger systems | pub-sub systems | pub-sub systems | semi-structured data | semi-structured data | XML querying | XML querying

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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6.435 System Identification (MIT) 6.435 System Identification (MIT)

Description

This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues. This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues.

Subjects

mathematical models | mathematical models | time series | time series | state-space | state-space | input-output models | input-output models | model structures | model structures | parametrization | parametrization | identifiability | identifiability | non-parametric methods | non-parametric methods | prediction error | prediction error | parameter estimation | parameter estimation | convergence | convergence | consistency | consistency | andasymptotic distribution | andasymptotic distribution | maximum likelihood estimation | maximum likelihood estimation | recursive estimation | recursive estimation | Kalman filters | Kalman filters | structure determination | structure determination | order estimation | order estimation | Akaike criterion | Akaike criterion | bounded noise models | bounded noise models | robustness | robustness

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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6.895 Theory of Parallel Systems (SMA 5509) (MIT) 6.895 Theory of Parallel Systems (SMA 5509) (MIT)

Description

6.895 covers theoretical foundations of general-purpose parallel computing systems, from languages to architecture. The focus is on the algorithmic underpinnings of parallel systems. The topics for the class will vary depending on student interest, but will likely include multithreading, synchronization, race detection, load balancing, memory consistency, routing networks, message-routing algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including high-probability arguments. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5509 (Theory of Parallel Systems). 6.895 covers theoretical foundations of general-purpose parallel computing systems, from languages to architecture. The focus is on the algorithmic underpinnings of parallel systems. The topics for the class will vary depending on student interest, but will likely include multithreading, synchronization, race detection, load balancing, memory consistency, routing networks, message-routing algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including high-probability arguments. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5509 (Theory of Parallel Systems).

Subjects

parallel systems | parallel systems | parallel computing | parallel computing | algorithms | algorithms | multithreading | multithreading | synchronization | synchronization | race detection | race detection | load balancing | load balancing | memory consistency | memory consistency | routing networks | routing networks | message-routing algorithms | message-routing algorithms | VLSI layout theory | VLSI layout theory | randomized algorithms | randomized algorithms | probabilistic analysis | probabilistic analysis | high-probability arguments | high-probability arguments

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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14.471 Public Economics I (MIT) 14.471 Public Economics I (MIT)

Description

This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy. This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | corporate finance | corporate finance | tax reform | tax reform | optimal commodity taxes | optimal commodity taxes | optimal corrective taxation | optimal corrective taxation | optimal stochastic taxes | optimal stochastic taxes | dynamic consistency issues | dynamic consistency issues | debt | debt | equity | equity

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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14.381 Statistical Method in Economics (MIT) 14.381 Statistical Method in Economics (MIT)

Description

´╗┐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

Subjects

statistical theory | statistical theory | econometrics | econometrics | regression analysis | regression analysis | probability | probability | random samples | random samples | asymptotic methods | asymptotic methods | point estimation | point estimation | evaluation of estimators | evaluation of estimators | Cramer-Rao theorem | Cramer-Rao theorem | hypothesis tests | hypothesis tests | Neyman Pearson lemma | Neyman Pearson lemma | Likelihood Ratio test | Likelihood Ratio test | interval estimation | interval estimation | best linear predictor | best linear predictor | best linear approximation | best linear approximation | conditional expectation function | conditional expectation function | building functional forms | building functional forms | regression algebra | regression algebra | Gauss-Markov optimality | Gauss-Markov optimality | finite-sample inference | finite-sample inference | consistency | consistency | asymptotic normality | asymptotic normality | heteroscedasticity | heteroscedasticity | autocorrelation | autocorrelation

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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14.462 Advanced Macroeconomics II (MIT) 14.462 Advanced Macroeconomics II (MIT)

Description

14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information 14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information

Subjects

macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research | macroeconomics research | analytical tools | analytical tools | analysis | analysis | endogenous growth | endogenous growth | coordintation | coordintation | incomplete markets | incomplete markets | technolgy | technolgy | distribution | distribution | employment | employment | intellectual property rights | intellectual property rights | bounded rationality | bounded rationality | demographics | demographics | complementarities | complementarities | amplification | amplification | recursive equilibria | recursive equilibria | uncertainty | uncertainty | morris | morris | shin | shin | global games | global games | policy | policy | price | price | aggregation | aggregation | social learning | social learning | dynamic adjustment | dynamic adjustment | business cycle | business cycle | heterogeneous agents | heterogeneous agents | savings | savings | utility | utility | aiyagari | aiyagari | steady state | steady state | krusell | krusell | smith | smith | idiosyncratic investment risk | idiosyncratic investment risk | growth | growth | fluctuations | fluctuations | heterogeneity | heterogeneity | optimal fiscal policy | optimal fiscal policy | time inconsistency | time inconsistency | reputation | reputation | information | information | coordination games | coordination games

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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18.336 Numerical Methods for Partial Differential Equations (MIT) 18.336 Numerical Methods for Partial Differential Equations (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

advection equation | advection equation | heat equation | heat equation | wave equation | wave equation | Airy equation | Airy equation | convection-diffusion problems | convection-diffusion problems | KdV equation | KdV equation | hyperbolic conservation laws | hyperbolic conservation laws | Poisson equation | Poisson equation | Stokes problem | Stokes problem | Navier-Stokes equations | Navier-Stokes equations | interface problems | interface problems | consistency | consistency | stability | stability | convergence | convergence | Lax equivalence theorem | Lax equivalence theorem | error analysis | error analysis | Fourier approaches | Fourier approaches | staggered grids | staggered grids | shocks | shocks | front propagation | front propagation | preconditioning | preconditioning | multigrid | multigrid | Krylov spaces | Krylov spaces | saddle point problems | saddle point problems | finite differences | finite differences | finite volumes | finite volumes | finite elements | finite elements | ENO/WENO | ENO/WENO | spectral methods | spectral methods | projection approaches for incompressible ows | projection approaches for incompressible ows | level set methods | level set methods | particle methods | particle methods | direct and iterative methods | direct and iterative methods

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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14.471 Public Economics I (MIT) 14.471 Public Economics I (MIT)

Description

Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy. Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | corporate finance | corporate finance | tax reform | tax reform | optimal commodity taxes | optimal commodity taxes | optimal corrective taxation | optimal corrective taxation | optimal stochastic taxes | optimal stochastic taxes | dynamic consistency issues | dynamic consistency issues | debt | debt | equity | equity

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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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity. 18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

Subjects

partial differential equation | partial differential equation | hyperbolic equations | hyperbolic equations | dimensional analysis | dimensional analysis | perturbation methods | perturbation methods | hyperbolic systems | hyperbolic systems | diffusion and reaction processes | diffusion and reaction processes | continuum models | continuum models | equilibrium models | equilibrium models | continuous applied mathematics | continuous applied mathematics | traffic flow | traffic flow | fluids | fluids | elasticity | elasticity | granular flows | granular flows | continuum limit | continuum limit | conservation laws | conservation laws | quasi-equilibrium | quasi-equilibrium | kinematic waves | kinematic waves | characteristics | characteristics | simple waves | simple waves | shocks | shocks | diffusion (linear and nonlinear) | diffusion (linear and nonlinear) | numerical solution of wave equations | numerical solution of wave equations | finite differences | finite differences | consistency | consistency | stability | stability | discrete and fast Fourier transforms | discrete and fast Fourier transforms | spectral methods | spectral methods | transforms and series (Fourier | Laplace) | transforms and series (Fourier | Laplace) | sonic booms | sonic booms | Mach cone | Mach cone | caustics | caustics | lattices | lattices | dispersion | dispersion | group velocity | group velocity

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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14.471 Public Economics I (MIT)

Description

Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | taxation | wealth | financial policy | income | investment | asset | political economy | labor | capital | public policy | corporate finance | tax reform | optimal commodity taxes | optimal corrective taxation | optimal stochastic taxes | dynamic consistency issues | debt | equity

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

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6.830 Database Systems (MIT)

Description

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken MIT course 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. Topics related to the engineering and design of database systems, including: data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel, and he

Subjects

engineering and design of database systems | data models | database and schema design | schema normalization and integrity constraints | query processing | query optimization and cost estimation | transactions | recovery | concurrency control | isolation and consistency | distributed | parallel | heterogeneous databases | adaptive databases | trigger systems | pub-sub systems | semi structured data and XML querying

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

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6.893 Database Systems (MIT)

Description

This course is designed to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, query optimization, query processing, and transactions. This is not a course on database design or SQL programming (though we will discuss these issues briefly). It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend.

Subjects

database systems | data models | database design | schema design | schema normalization | integrity constraints | query processing | query optimization | cost estimation | transactions | recovery | concurrency control | isolation | consistency | distributed | parallel | and heterogeneous databases | adaptive databases | trigger systems | pub-sub systems | semi-structured data | XML querying

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

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14.471 Public Economics I (MIT)

Description

This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | taxation | wealth | financial policy | income | investment | asset | political economy | labor | capital | public policy | corporate finance | tax reform | optimal commodity taxes | optimal corrective taxation | optimal stochastic taxes | dynamic consistency issues | debt | equity

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

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14.381 Statistical Method in Economics (MIT)

Description

?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

Subjects

statistical theory | econometrics | regression analysis | 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 | building functional forms | regression algebra | Gauss-Markov optimality | finite-sample inference | consistency | asymptotic normality | heteroscedasticity | autocorrelation

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

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14.462 Advanced Macroeconomics II (MIT)

Description

14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information

Subjects

macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research | analytical tools | analysis | endogenous growth | coordintation | incomplete markets | technolgy | distribution | employment | intellectual property rights | bounded rationality | demographics | complementarities | amplification | recursive equilibria | uncertainty | morris | shin | global games | policy | price | aggregation | social learning | dynamic adjustment | business cycle | heterogeneous agents | savings | utility | aiyagari | steady state | krusell | smith | idiosyncratic investment risk | growth | fluctuations | heterogeneity | optimal fiscal policy | time inconsistency | reputation | information | coordination games

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

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18.311 Principles of Applied Mathematics (MIT)

Description

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

Subjects

partial differential equation | hyperbolic equations | dimensional analysis | perturbation methods | hyperbolic systems | diffusion and reaction processes | continuum models | equilibrium models | continuous applied mathematics | traffic flow | fluids | elasticity | granular flows | continuum limit | conservation laws | quasi-equilibrium | kinematic waves | characteristics | simple waves | shocks | diffusion (linear and nonlinear) | numerical solution of wave equations | finite differences | consistency | stability | discrete and fast Fourier transforms | spectral methods | transforms and series (Fourier | Laplace) | sonic booms | Mach cone | caustics | lattices | dispersion | group velocity

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

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18.336 Numerical Methods for Partial Differential Equations (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

advection equation | heat equation | wave equation | Airy equation | convection-diffusion problems | KdV equation | hyperbolic conservation laws | Poisson equation | Stokes problem | Navier-Stokes equations | interface problems | consistency | stability | convergence | Lax equivalence theorem | error analysis | Fourier approaches | staggered grids | shocks | front propagation | preconditioning | multigrid | Krylov spaces | saddle point problems | finite differences | finite volumes | finite elements | ENO/WENO | spectral methods | projection approaches for incompressible ows | level set methods | particle methods | direct and iterative methods

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

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6.435 System Identification (MIT)

Description

This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues.

Subjects

mathematical models | time series | state-space | input-output models | model structures | parametrization | identifiability | non-parametric methods | prediction error | parameter estimation | convergence | consistency | andasymptotic distribution | maximum likelihood estimation | recursive estimation | Kalman filters | structure determination | order estimation | Akaike criterion | bounded noise models | robustness

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

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6.895 Theory of Parallel Systems (SMA 5509) (MIT)

Description

6.895 covers theoretical foundations of general-purpose parallel computing systems, from languages to architecture. The focus is on the algorithmic underpinnings of parallel systems. The topics for the class will vary depending on student interest, but will likely include multithreading, synchronization, race detection, load balancing, memory consistency, routing networks, message-routing algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including high-probability arguments. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5509 (Theory of Parallel Systems).

Subjects

parallel systems | parallel computing | algorithms | multithreading | synchronization | race detection | load balancing | memory consistency | routing networks | message-routing algorithms | VLSI layout theory | randomized algorithms | probabilistic analysis | high-probability arguments

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

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