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22.101 Applied Nuclear Physics (MIT) 22.101 Applied Nuclear Physics (MIT)

Description

The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions. The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions.

Subjects

Nuclear physics | Nuclear physics | Nuclear reaction | Nuclear reaction | Nucleus | Nucleus | Nuclear radiation | Nuclear radiation | Quantum mechanics | Quantum mechanics | Deuteron bound-state wave function and energy | Deuteron bound-state wave function and energy | n-p scattering cross-section | n-p scattering cross-section | Transition probability per unit time | Transition probability per unit time | Barrier transmission probability | Barrier transmission probability | Binding energy | Binding energy | Nuclear stability | Nuclear stability | Interactions of charged particles neutrons and gamma rays with matter | Interactions of charged particles neutrons and gamma rays with matter | Radioactive decay | Radioactive decay | Energetics | Energetics | nuclear physics | nuclear physics | nuclear reaction | nuclear reaction | nucleus | nucleus | nuclear radiation | nuclear radiation | quantum mechanics | quantum mechanics | deuteron bound-state wave function and energy | deuteron bound-state wave function and energy | transition probability per unit time | transition probability per unit time | barrier transmission probability | barrier transmission probability | nuclear stability | nuclear stability | Interactions of charged particles | Interactions of charged particles | neutrons | neutrons | and gamma rays with matter | and gamma rays with matter | energetics | energetics

License

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15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.

Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimization

License

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15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year Sloan MBA students to the fundamental techniques of using data. In particular, the course focuses on various ways of modeling, or thinking structurally about decision problems in order to make informed management decisions. This course is designed to introduce first-year Sloan MBA students to the fundamental techniques of using data. In particular, the course focuses on various ways of modeling, or thinking structurally about decision problems in order to make informed management decisions.

Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimization

License

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15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.

Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimization

License

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15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.

Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimization

License

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15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.

Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimization

License

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18.05 Introduction to Probability and Statistics (MIT) 18.05 Introduction to Probability and Statistics (MIT)

Description

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

Subjects

probability | probability | statistics | statistics | models | models | combinatorics | combinatorics | expectation | expectation | variance | variance | random variable | random variable | discrete probability distribution | discrete probability distribution | continuous probability distribution | continuous probability distribution | Bayes | Bayes | distribution | distribution | statistical estimation | statistical estimation | statistical testing | statistical testing | confidence interval | confidence interval | linear regression | linear regression | normal | normal | significance testing | significance testing | bootstrapping | bootstrapping

License

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18.05 Introduction to Probability and Statistics (MIT) 18.05 Introduction to Probability and Statistics (MIT)

Description

This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression. This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.

Subjects

probability models | probability models | combinatorics | combinatorics | random variables | random variables | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | statistical estimation | statistical estimation | statistical testing | statistical testing | confidence intervals | confidence intervals | linear regression | linear regression

License

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22.38 Probability And Its Applications To Reliability, Quality Control, And Risk Assessment (MIT) 22.38 Probability And Its Applications To Reliability, Quality Control, And Risk Assessment (MIT)

Description

This course covers interpretations of the concept of probability. Topics include basic probability rules; random variables and distribution functions; functions of random variables; and applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. The course also considers elements of statistics; Bayesian methods in engineering; methods for reliability and risk assessment of complex systems (event-tree and fault-tree analysis, common-cause failures, human reliability models); uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling); and an introduction to Markov models. Examples and applications are drawn from nuclear and other industries, waste repositories, and mech This course covers interpretations of the concept of probability. Topics include basic probability rules; random variables and distribution functions; functions of random variables; and applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. The course also considers elements of statistics; Bayesian methods in engineering; methods for reliability and risk assessment of complex systems (event-tree and fault-tree analysis, common-cause failures, human reliability models); uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling); and an introduction to Markov models. Examples and applications are drawn from nuclear and other industries, waste repositories, and mech

Subjects

risk | risk | uncertainty | uncertainty | nuclear accident | nuclear accident | disaster | disaster | meltdown | meltdown | probability | probability | risk assessment | risk assessment | PRA | PRA | probabalistic risk assessment | probabalistic risk assessment | NUREG-1150 | NUREG-1150 | WASH-1400 | WASH-1400 | failure | failure | applied probability | applied probability | applied statistics | applied statistics | system performance | system performance | MTBF | MTBF | decision | decision | hazard | hazard | fault tree analysis | fault tree analysis | event tree analysis | event tree analysis

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

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

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

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14.30 Introduction to Statistical Methods in Economics (MIT) 14.30 Introduction to Statistical Methods in Economics (MIT)

Description

This course will provide a solid foundation in probability and statistics for economists and other social scientists. We will emphasize topics needed for further study of econometrics and provide basic preparation for 14.32. Topics include elements of probability theory, sampling theory, statistical estimation, and hypothesis testing. This course will provide a solid foundation in probability and statistics for economists and other social scientists. We will emphasize topics needed for further study of econometrics and provide basic preparation for 14.32. Topics include elements of probability theory, sampling theory, statistical estimation, and hypothesis testing.

Subjects

statistics | statistics | economic applications | economic applications | probability theory | probability theory | sampling theory | sampling theory | statistical estimation | statistical estimation | regression analysis | regression analysis | hypothesis testing | hypothesis testing | Elementary econometrics | Elementary econometrics | statistical tools | statistical tools | economic data | economic data | economics | economics | statistical | statistical | probability distribution function | probability distribution function | cumulative distribution function | cumulative distribution function | normal | normal | Student's t | Student's t | chi-squared | chi-squared | central limit theorem | central limit theorem | law of large numbers | law of large numbers | Bayes theorem | Bayes theorem

License

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18.310 Principles of Discrete Applied Mathematics (MIT) 18.310 Principles of Discrete Applied Mathematics (MIT)

Description

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component. This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Subjects

probability | probability | probability theory counting | probability theory counting | pigeonhole principle | pigeonhole principle | Van der Waerden's theorem | Van der Waerden's theorem | Chernoff bounds | Chernoff bounds | counting | counting | coding | coding | sampling | sampling | random sampling | random sampling | Catalan families | Catalan families | generating functions | generating functions | chord diagrams | chord diagrams | linear programming | linear programming | simplex method | simplex method | Zero-Sum matrix | Zero-Sum matrix | network flows | network flows | maximum flow problem | maximum flow problem | sorting algorithms | sorting algorithms | QUICKSORT | QUICKSORT | median finding | median finding | sorting networks | sorting networks | Batcher's algorithm | Batcher's algorithm | Euclid's algorithm | Euclid's algorithm | Chinese Remainder Theorem | Chinese Remainder Theorem | cryptography | cryptography | RSA code | RSA code | primaility testing | primaility testing | FFT | FFT | Fast Fourier Transform | Fast Fourier Transform | Shannon's coding theorems | Shannon's coding theorems | Lempel-Ziv codes | Lempel-Ziv codes | linear codes | linear codes | hamming code | hamming code

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

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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

License

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14.32 Econometrics (MIT) 14.32 Econometrics (MIT)

Description

This course covers the statistical tools needed to understand empirical economic research and to plan and execute independent research projects. Topics include statistical inference, regression, generalized least squares, instrumental variables, simultaneous equations models, and the evaluation of government policies and programs.Technical RequirementsAny text editor can be used to view the .asc files found on this course site. Please refer to the course materials for any specific instructions or recommendations. Any number of software tools can be used to import the data files found on this course site. Please refer to the course materials for any specific instructions or recommendations. This course covers the statistical tools needed to understand empirical economic research and to plan and execute independent research projects. Topics include statistical inference, regression, generalized least squares, instrumental variables, simultaneous equations models, and the evaluation of government policies and programs.Technical RequirementsAny text editor can be used to view the .asc files found on this course site. Please refer to the course materials for any specific instructions or recommendations. Any number of software tools can be used to import the data files found on this course site. Please refer to the course materials for any specific instructions or recommendations.

Subjects

probability | probability | distribution | distribution | sampling | sampling | confidence intervals | confidence intervals | bivariate regression | bivariate regression | residuals | residuals | fitted values | fitted values | goodness of fit | | goodness of fit | | multivariate regression | multivariate regression | heteroscedasticity | heteroscedasticity | linear probability models | linear probability models | serial correlation | serial correlation | measurement error | measurement error | goodness of fit | goodness of fit

License

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6.041SC Probabilistic Systems Analysis and Applied Probability (MIT) 6.041SC Probabilistic Systems Analysis and Applied Probability (MIT)

Description

Includes audio/video content: AV lectures. This course introduces students to the modeling, quantification, and analysis of uncertainty.  The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management. Includes audio/video content: AV lectures. This course introduces students to the modeling, quantification, and analysis of uncertainty.  The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management.

Subjects

probability | probability | probability models | probability models | bayes rule | bayes rule | discrete random variables | discrete random variables | continuous random variables | continuous random variables | bernoulli process | bernoulli process | poisson process | poisson process | markov chains | markov chains | central limit theorem | central limit theorem | statistical inference | statistical inference

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

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

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

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

Description

This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life. This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.

Subjects

fundamentals of probability | fundamentals of probability | random processes | random processes | 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 | Bayes theorem | Bayes theorem | total probability theorem | total probability theorem | 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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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

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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

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10.34 Numerical Methods Applied to Chemical Engineering (MIT) 10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site. Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equations | Navier-Stokes equations | Navier-Stokes equations

License

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10.34 Numerical Methods Applied to Chemical Engineering (MIT) 10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment. This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.

Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equations

License

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6.01 Introduction to Electrical Engineering and Computer Science I (MIT) 6.01 Introduction to Electrical Engineering and Computer Science I (MIT)

Description

6.01 explores fundamental ideas in electrical engineering and computer science, in the context of working with mobile robots. Key engineering principles, such as abstraction and modularity, are applied in the design of computer programs, electronic circuits, discrete-time controllers, and noisy and/or uncertain systems. 6.01 explores fundamental ideas in electrical engineering and computer science, in the context of working with mobile robots. Key engineering principles, such as abstraction and modularity, are applied in the design of computer programs, electronic circuits, discrete-time controllers, and noisy and/or uncertain systems.

Subjects

robots | robots | python | python | computer programs | computer programs | circuits | circuits | systems | systems | inheritance | inheritance | recursion | recursion | functional programming | functional programming | signals | signals | control | control | circuit abstractions | circuit abstractions | probability | probability | discrete probability | discrete probability | search algorithms | search algorithms | state machines | state machines | probabilistic state estimation | probabilistic state estimation | decision-making | decision-making | search | search | python robots | python robots

License

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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

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MAS.622J Pattern Recognition and Analysis (MIT) MAS.622J Pattern Recognition and Analysis (MIT)

Description

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class. This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.

Subjects

MAS.622 | MAS.622 | 1.126 | 1.126 | pattern recognition | pattern recognition | feature detection | feature detection | classification | classification | probability theory | probability theory | pattern analysis | pattern analysis | conditional probability | conditional probability | bayes rule | bayes rule | random vectors | decision theory | random vectors | decision theory | ROC curves | ROC curves | likelihood ratio test | likelihood ratio test | fisher discriminant | fisher discriminant | template-based recognition | template-based recognition | feature extraction | feature extraction | eigenvector and multilinear analysis | eigenvector and multilinear analysis | linear discriminant | linear discriminant | perceptron learning | perceptron learning | optimization by gradient descent | optimization by gradient descent | support vecotr machines | support vecotr machines | K-nearest-neighbor classification | K-nearest-neighbor classification | parzen estimation | parzen estimation | unsupervised learning | unsupervised learning | clustering | clustering | vector quantization | vector quantization | K-means | K-means | Expectation-Maximization | Expectation-Maximization | Hidden markov models | Hidden markov models | viterbi algorithm | viterbi algorithm | Baum-Welch algorithm | Baum-Welch algorithm | linear dynamical systems | linear dynamical systems | Kalman filtering | Kalman filtering | Bayesian networks | Bayesian networks | decision trees | decision trees | reinforcement learning | reinforcement learning | genetic algorithms | genetic algorithms

License

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