Searching for Markov processes : 24 results found | RSS Feed for this search

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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

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

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

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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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations | linear algebra | linear algebra | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks

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

Description

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

Subjects

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

License

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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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

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

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

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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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc. Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations

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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18.06SC Linear Algebra (MIT) 18.06SC Linear Algebra (MIT)

Description

Includes audio/video content: AV lectures. This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra. Includes audio/video content: AV lectures. This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Subjects

matrix theory | matrix theory | linear algebra | linear algebra | systems of equations | systems of equations | vector spaces | vector spaces | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | positive definite matrices | positive definite matrices | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks | Fourier transforms | Fourier transforms | Markov processes | Markov processes

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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6.262 Discrete Stochastic Processes (MIT) 6.262 Discrete Stochastic Processes (MIT)

Description

Includes audio/video content: AV lectures. Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance. Includes audio/video content: AV lectures. Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

Subjects

probability | probability | Poisson processes | Poisson processes | finite-state Markov chains | finite-state Markov chains | renewal processes | renewal processes | countable-state Markov chains | countable-state Markov chains | Markov processes | Markov processes | countable state spaces | countable state spaces | random walks | random walks | large deviations | large deviations | martingales | martingales

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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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

Includes audio/video content: AV special element video, AV lectures. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Includes audio/video content: AV special element video, AV lectures. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | matrix theory | linear algebra | linear algebra | systems of equations | systems of equations | vector spaces | vector spaces | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | positive definite matrices | positive definite matrices | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks | Fourier transforms | Fourier transforms | Markov processes | Markov processes

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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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

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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1.151 Probability and Statistics in Engineering (MIT) 1.151 Probability and Statistics in Engineering (MIT)

Description

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems. This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

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 | 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

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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1.151 Probability and Statistics in Engineering (MIT)

Description

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

Subjects

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

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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16.410 Principles of Autonomy and Decision Making (MIT)

Description

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

Subjects

autonomy | decision | decision-making | reasoning | optimization | autonomous | autonomous systems | decision support | algorithms | artificial intelligence | a.i. | operations | operations research | logic | deduction | heuristic search | constraint-based search | model-based reasoning | planning | execution | uncertainty | machine learning | linear programming | dynamic programming | integer programming | network optimization | decision analysis | decision theoretic planning | Markov decision process | scheme | propositional logic | constraints | Markov processes | computational performance | satisfaction | learning algorithms | system state | state | search treees | plan spaces | model theory | decision trees | function approximators | optimization algorithms | limitations | tradeoffs | search and reasoning | game tree search | local stochastic search | stochastic | genetic algorithms | constraint satisfaction | propositional inference | rule-based systems | rule-based | model-based diagnosis | neural nets | reinforcement learning | web-based | search trees

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Linear algebra | Algebra | Universal | Mathematical analysis | Calculus of operations | Line geometry | Topology | matrix theory | systems of equations | vector spaces | systems determinants | eigen values | positive definite matrices | Markov processes | Fourier transforms | differential equations | linear algebra | determinants | eigenvalues | similarity | least-squares approximations | stability of differential equations | networks

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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1.010 Uncertainty in Engineering (MIT)

Description

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

Subjects

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

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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16.410 Principles of Autonomy and Decision Making (MIT)

Description

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

Subjects

autonomy | decision | decision-making | reasoning | optimization | autonomous | autonomous systems | decision support | algorithms | artificial intelligence | a.i. | operations | operations research | logic | deduction | heuristic search | constraint-based search | model-based reasoning | planning | execution | uncertainty | machine learning | linear programming | dynamic programming | integer programming | network optimization | decision analysis | decision theoretic planning | Markov decision process | scheme | propositional logic | constraints | Markov processes | computational performance | satisfaction | learning algorithms | system state | state | search treees | plan spaces | model theory | decision trees | function approximators | optimization algorithms | limitations | tradeoffs | search and reasoning | game tree search | local stochastic search | stochastic | genetic algorithms | constraint satisfaction | propositional inference | rule-based systems | rule-based | model-based diagnosis | neural nets | reinforcement learning | web-based | search trees

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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18.06 Linear Algebra (MIT)

Description

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Generalized spaces | Linear algebra | Algebra | Universal | Mathematical analysis | Calculus of operations | Line geometry | Topology | matrix theory | systems of equations | vector spaces | systems determinants | eigen values | positive definite matrices | Markov processes | Fourier transforms | differential equations

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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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.

Subjects

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

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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1.151 Probability and Statistics in Engineering (MIT)

Description

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

Subjects

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

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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18.06SC Linear Algebra (MIT)

Description

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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6.262 Discrete Stochastic Processes (MIT)

Description

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

Subjects

probability | Poisson processes | finite-state Markov chains | renewal processes | countable-state Markov chains | Markov processes | countable state spaces | random walks | large deviations | martingales

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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