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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT) 8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | correlation functions | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems | correlation functions | correlation functions | and scaling theory | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

License

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18.441 Statistical Inference (MIT) 18.441 Statistical Inference (MIT)

Description

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics). Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

Subjects

probability | probability | statistical inference | statistical inference | Point and interval estimation | Point and interval estimation | The maximum likelihood method | The maximum likelihood method | Hypothesis testing | Hypothesis testing | Likelihood-ratio tests | Likelihood-ratio tests | Bayesian methods | Bayesian methods | Nonparametric methods | Nonparametric methods | Analysis of variance | Analysis of variance | regression analysis | regression analysis | correlation | correlation | Chi-square goodness of fit tests | Chi-square goodness of fit tests | Likelihood-ratio tests and Bayesian methods | Likelihood-ratio tests and Bayesian methods | regression analysis and correlation | regression analysis and correlation | probability | statistical inference | probability | statistical inference | Analysis of variance | regression analysis and correlation | Analysis of variance | regression analysis and correlation

License

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations. Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | Microcanonical | canonical | canonical | grand canonical partition-functions | grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | correlation functions and susceptibilities | Kubo formulae | Kubo formulae | Evolution of distribution functions | Evolution of distribution functions | Boltzmann and Smoluchowski equations | Boltzmann and Smoluchowski equations | correlation functions | correlation functions | susceptibilities | susceptibilities

License

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18.443 Statistics for Applications (MIT) 18.443 Statistics for Applications (MIT)

Description

This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. The course topics include hypothesis testing and estimation. It also includes confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. The course topics include hypothesis testing and estimation. It also includes confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation.

Subjects

hypothesis testing and estimation; confidence intervals; chi-square tests; nonparametric statistics; analysis of variance; regression; correlation | hypothesis testing and estimation; confidence intervals; chi-square tests; nonparametric statistics; analysis of variance; regression; correlation | hypothesis testing and estimation | hypothesis testing and estimation | confidence intervals | confidence intervals | chi-square tests | chi-square tests | nonparametric statistics | nonparametric statistics | analysis of variance | analysis of variance | regression | regression | correlation | correlation

License

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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

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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18.441 Statistical Inference (MIT)

Description

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

Subjects

probability | statistical inference | Point and interval estimation | The maximum likelihood method | Hypothesis testing | Likelihood-ratio tests | Bayesian methods | Nonparametric methods | Analysis of variance | regression analysis | correlation | Chi-square goodness of fit tests | Likelihood-ratio tests and Bayesian methods | regression analysis and correlation | probability | statistical inference | Analysis of variance | regression analysis and correlation

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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2.017J Design of Systems Operating in Random Environments (MIT) 2.017J Design of Systems Operating in Random Environments (MIT)

Description

This class covers the principles for optimal performance and survival of extreme events in a random environment; linear time invariant systems and Fourier transform; random processes, autocorrelation function, and power spectra. We will study statistics of the response of systems and perform optimization using a statistics-based index. The class will also involve sea wave modeling, sea spectra, elements of seakeeping, wind modeling, and wind spectra. Finally, it also covers extreme events and probability of failure; examples include extreme waves and 100-year events. Students undertake a term project, focusing on electronics and instrumentation, and design for the ocean environment. This class covers the principles for optimal performance and survival of extreme events in a random environment; linear time invariant systems and Fourier transform; random processes, autocorrelation function, and power spectra. We will study statistics of the response of systems and perform optimization using a statistics-based index. The class will also involve sea wave modeling, sea spectra, elements of seakeeping, wind modeling, and wind spectra. Finally, it also covers extreme events and probability of failure; examples include extreme waves and 100-year events. Students undertake a term project, focusing on electronics and instrumentation, and design for the ocean environment.

Subjects

optimal performance | optimal performance | extreme events | extreme events | random environment | random environment | linear time invariant systems | linear time invariant systems | random processes | random processes | autocorrelation function | autocorrelation function | power spectra | power spectra | sea wave modeling | sea wave modeling | sea spectra | sea spectra | seakeeping | seakeeping | wind modeling | wind modeling | wind spectra | wind spectra | probability of failure | probability of failure | extreme waves | extreme waves | 100-year events | 100-year events

License

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14.123 Microeconomic Theory III (MIT) 14.123 Microeconomic Theory III (MIT)

Description

This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation. This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation.

Subjects

microeconomics | microeconomics | microeconomic theory | microeconomic theory | preference | preference | utility representation | utility representation | expected utility | expected utility | positive interpretation | positive interpretation | normative interpretation | normative interpretation | risk | risk | stochastic dominance | stochastic dominance | insurance | insurance | finance | finance | supermodularity | supermodularity | comparative statics | comparative statics | decision theory | decision theory | game theory | game theory | rationalizability | rationalizability | iterated strict dominance | iterated strict dominance | iterated conditional dominance | iterated conditional dominance | bargaining | bargaining | equilibrium | equilibrium | sequential equilibrium | sequential equilibrium | trembling-hand perfection | trembling-hand perfection | signaling games | signaling games | auctions | auctions | global games | global games | repeated games | repeated games | correlation | correlation

License

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9.63 Laboratory in Cognitive Science (MIT) 9.63 Laboratory in Cognitive Science (MIT)

Description

9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports. 9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports.

Subjects

cognitive science | cognitive science | human perception | human perception | cognition | cognition | statistical analysis | statistical analysis | signal detection theory | signal detection theory | single factor design | single factor design | factorial design | factorial design | matlab | matlab | correlational studies | correlational studies | ethics in research | ethics in research

License

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11.220 Quantitative Reasoning and Statistical Method for Planning I (MIT) 11.220 Quantitative Reasoning and Statistical Method for Planning I (MIT)

Description

This course develops logical, empirically based arguments using statistical techniques and analytic methods. It covers elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation. Emphasis is placed on the use and limitations of analytical techniques in planning practice. This course is required for and restricted to first-year Master in City Planning students. This course develops logical, empirically based arguments using statistical techniques and analytic methods. It covers elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation. Emphasis is placed on the use and limitations of analytical techniques in planning practice. This course is required for and restricted to first-year Master in City Planning students.

Subjects

statistics | statistics | statistical methods | statistical methods | quantitative research | quantitative research | argument | argument | measurement | measurement | research design | research design | frequency distribution | frequency distribution | histogram | histogram | stemplot | stemplot | boxplot | boxplot | dispersion | dispersion | probability | probability | normal distribution | normal distribution | binomial distribution | binomial distribution | sampling | sampling | confidence interval | confidence interval | significance | significance | correlation | correlation | regression | regression

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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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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14.32 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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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II (MIT) 8.334 Statistical Mechanics II (MIT)

Description

Topics from modern statistical mechanics are explored in 8.334, Statistical Mechanics II, including:The hydrodynamic limit and classical field theories.Phase transitions and broken symmetries: universality, correlation functions, and scaling theory.The renormalization approach to collective phenomena.Integrable models. Quantum phase transitions. Topics from modern statistical mechanics are explored in 8.334, Statistical Mechanics II, including:The hydrodynamic limit and classical field theories.Phase transitions and broken symmetries: universality, correlation functions, and scaling theory.The renormalization approach to collective phenomena.Integrable models. Quantum phase transitions.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems

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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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | Discrete and continuum modeling of diffusion processes in physics | chemistry | chemistry | and economics | and economics | central limit theorems | central limit theorems | ontinuous-time random walks | ontinuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes. 5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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9.29J Introduction to Computational Neuroscience (MIT) 9.29J Introduction to Computational Neuroscience (MIT)

Description

Mathematical introduction to neural coding and dynamics. Convolution, correlation, linear systems, Fourier analysis, signal detection theory, probability theory, and information theory. Applications to neural coding, focusing on the visual system. Hodgkin-Huxley and related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Mathematical introduction to neural coding and dynamics. Convolution, correlation, linear systems, Fourier analysis, signal detection theory, probability theory, and information theory. Applications to neural coding, focusing on the visual system. Hodgkin-Huxley and related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission.

Subjects

neural coding | neural coding | dynamics | dynamics | convolution | convolution | correlation | correlation | linear systems | linear systems | Fourier analysis | Fourier analysis | signal detection theory | signal detection theory | probability theory | probability theory | information theory | information theory | neural excitability | neural excitability | stochastic models | stochastic models | ion channels | ion channels | cable theory | cable theory | 9.29 | 9.29 | 8.261 | 8.261

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

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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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

This course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. This course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

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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2.161 Signal Processing: Continuous and Discrete (MIT) 2.161 Signal Processing: Continuous and Discrete (MIT)

Description

This course provides a solid theoretical foundation for the analysis and processing of experimental data, and real-time experimental control methods. Topics covered include spectral analysis, filter design, system identification, and simulation in continuous and discrete-time domains. The emphasis is on practical problems with laboratory exercises. This course provides a solid theoretical foundation for the analysis and processing of experimental data, and real-time experimental control methods. Topics covered include spectral analysis, filter design, system identification, and simulation in continuous and discrete-time domains. The emphasis is on practical problems with laboratory exercises.

Subjects

analysis and processing of experimental data; real-time experimental control methods; spectral analysis; filter design; system identification; simulation in continuous and discrete-time domains; MATLAB | analysis and processing of experimental data; real-time experimental control methods; spectral analysis; filter design; system identification; simulation in continuous and discrete-time domains; MATLAB | fast Fourier transform | fast Fourier transform | correlation function | correlation function | sampling | sampling | op-amps | op-amps | Chebyshev | Chebyshev | Laplace transform | Laplace transform | Butterworth | Butterworth | convolution | convolution | frequency response | frequency response | windowing | windowing | low-pass | low-pass | poles | poles | zeros | zeros

License

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6.011 Introduction to Communication, Control, and Signal Processing (MIT) 6.011 Introduction to Communication, Control, and Signal Processing (MIT)

Description

This course is taken mainly by undergraduates, and explores ideas involving signals, systems and probabilistic models in the context of communication, control and signal processing applications. The material expands out from the basics in 6.003 and 6.041. The treatment involves aspects of analysis, synthesis, and optimization. Topics covered differ somewhat from semester to semester, but typically include: random processes, correlations, spectral densities, state-space modeling, multirate processing, signal estimation and detection. This course is taken mainly by undergraduates, and explores ideas involving signals, systems and probabilistic models in the context of communication, control and signal processing applications. The material expands out from the basics in 6.003 and 6.041. The treatment involves aspects of analysis, synthesis, and optimization. Topics covered differ somewhat from semester to semester, but typically include: random processes, correlations, spectral densities, state-space modeling, multirate processing, signal estimation and detection.

Subjects

Input-output | Input-output | state-space models | state-space models | linear systems | linear systems | deterministic and random signals | deterministic and random signals | time- and transform-domain representations | time- and transform-domain representations | sampling | sampling | discrete-time processing | discrete-time processing | continuous-time signals | continuous-time signals | state feedback | state feedback | observers | observers | probabilistic models | probabilistic models | stochastic processes | stochastic processes | correlation functions | correlation functions | power spectra | power spectra | whitening filters | whitening filters | Detection | Detection | matched filters | matched filters | Least-mean square error estimation | Least-mean square error estimation | Wiener filtering | Wiener filtering

License

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6.661 Receivers, Antennas, and Signals (MIT) 6.661 Receivers, Antennas, and Signals (MIT)

Description

This course explores the detection and measurement of radio and optical signals encountered in communications, astronomy, remote sensing, instrumentation, and radar. Topics covered include: statistical analysis of signal processing systems, including radiometers, spectrometers, interferometers, and digital correlation systems; matched filters and ambiguity functions; communications channel performance; measurement of random electromagnetic fields, angular filtering properties of antennas, interferometers, and aperture synthesis systems; and radiative transfer and parameter estimation. This course explores the detection and measurement of radio and optical signals encountered in communications, astronomy, remote sensing, instrumentation, and radar. Topics covered include: statistical analysis of signal processing systems, including radiometers, spectrometers, interferometers, and digital correlation systems; matched filters and ambiguity functions; communications channel performance; measurement of random electromagnetic fields, angular filtering properties of antennas, interferometers, and aperture synthesis systems; and radiative transfer and parameter estimation.

Subjects

receiver | receiver | antenna | antenna | signal | signal | radio | radio | optical | optical | detection | detection | communications | communications | astronomy | astronomy | remote sensing | instrumentation | remote sensing | instrumentation | radar | radar | statistics | statistics | signal processing | signal processing | radiometer | radiometer | spectrometer | spectrometer | interferometer | interferometer | digital correlation | digital correlation | matched filter | matched filter | ambiguity function | ambiguity function | channel performance | channel performance | electromagnetic | electromagnetic | angular filtering | angular filtering | aperture synthesis | aperture synthesis | radiative transfer | radiative transfer | parameter estimation | parameter estimation | remote sensing | remote sensing | instrumentation | instrumentation | radio signals | radio signals | optical signals | optical signals | statistical analysis | statistical analysis

License

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses. This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | canonical | and grand canonical partition-functions | Microcanonical | canonical | and grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | and Kubo formulae | correlation functions and susceptibilities | and Kubo formulae | Evolution of distribution functions: Boltzmann and Smoluchowski equations | Evolution of distribution functions: Boltzmann and Smoluchowski equations

License

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9.63 Laboratory in Visual Cognition (MIT) 9.63 Laboratory in Visual Cognition (MIT)

Description

9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports. 9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports.

Subjects

cognitive science | cognitive science | human perception | human perception | cognition | cognition | statistical analysis | statistical analysis | signal detection theory | signal detection theory | single factor design | single factor design | factorial design | factorial design | matlab | matlab | correlational studies | correlational studies | ethics in research | ethics in research | visual cognition | visual cognition | thought | thought | psychology and cognitive science | psychology and cognitive science | information processing | information processing | organization of visual cognitive abilities. | organization of visual cognitive abilities.

License

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9.29J Introduction to Computational Neuroscience (MIT) 9.29J Introduction to Computational Neuroscience (MIT)

Description

This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Visit the Seung Lab Web site. This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Visit the Seung Lab Web site.

Subjects

neural coding | neural coding | dynamics | dynamics | convolution | convolution | correlation | correlation | linear systems | linear systems | Fourier analysis | Fourier analysis | signal detection theory | signal detection theory | probability theory | probability theory | information theory | information theory | neural excitability | neural excitability | stochastic models | stochastic models | ion channels | ion channels | cable theory | cable theory

License

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