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Description

This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s TheoremLicense

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.htmSite sourced from

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See all metadata5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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.htmSite sourced from

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See all metadata8.512 Theory of Solids II (MIT) 8.512 Theory of Solids II (MIT)

Description

This is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory. This is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory.Subjects

Linear response theory | Linear response theory | Fluctuation dissipation theorem | Fluctuation dissipation theorem | Scattering experiment | Scattering experiment | f-sum rule | f-sum rule | Physics of disorder | Physics of disorder | Kubo formula for conductivity | Kubo formula for conductivity | Conductance and sensitivity to boundary conditions | Conductance and sensitivity to boundary conditions | Scaling theory of localization | Scaling theory of localization | Mott variable range hopping | Mott variable range hopping | Superconductor | Superconductor | Transverse response | Transverse response | Landau diamagnetism | Landau diamagnetism | Microscopic derivation of London equation | Microscopic derivation of London equation | Effect of disorder | Effect of disorder | Quasiparticles and coherence factors | Quasiparticles and coherence factors | Tunneling and Josephson effect | Tunneling and Josephson effect | Magnetism | Magnetism | Local moment magnetism | Local moment magnetism | exchange interaction | exchange interaction | Ferro- and anti-ferro magnet and spin wave theory | Ferro- and anti-ferro magnet and spin wave theory | Band magnetism | Band magnetism | Stoner theory | Stoner theory | spin density wave | spin density wave | Local moment in metals | Local moment in metals | Friedel sum rule | Friedel sum rule | Friedel-Anderson model | Friedel-Anderson model | Kondo problem | Kondo problem | Fermi liquid theory | Fermi liquid theory | Electron Green?s function | Electron Green?s functionLicense

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.htmSite sourced from

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See all metadata12.003 Physics of Atmospheres and Oceans (MIT) 12.003 Physics of Atmospheres and Oceans (MIT)

Description

The laws of classical mechanics and thermodynamics are used to explore how the properties of fluids on a rotating Earth manifest themselves in, and help shape, the global patterns of atmospheric winds, ocean currents, and the climate of the Earth. Theoretical discussion focuses on the physical processes involved. Underlying mechanisms are illustrated through laboratory demonstrations, using a rotating table, and through analysis of atmospheric and oceanic data. The laws of classical mechanics and thermodynamics are used to explore how the properties of fluids on a rotating Earth manifest themselves in, and help shape, the global patterns of atmospheric winds, ocean currents, and the climate of the Earth. Theoretical discussion focuses on the physical processes involved. Underlying mechanisms are illustrated through laboratory demonstrations, using a rotating table, and through analysis of atmospheric and oceanic data.Subjects

1. Characteristics of the atmosphere | 1. Characteristics of the atmosphere | Characteristics of the atmosphere | Characteristics of the atmosphere | global energy balance | global energy balance | greenhouse effect | greenhouse effect | greenhouse gases | greenhouse gases | Atmospheric layers | Atmospheric layers | pressure and density | pressure and density | Convection | Convection | adiabatic lapse rate | adiabatic lapse rate | Humidity | Humidity | Convective clouds | Convective clouds | Temperature | Temperature | Pressure and geopotential height | Pressure and geopotential height | Winds | Winds | Fluids in motion | Fluids in motion | Hydrostatic balance | Hydrostatic balance | Incompressible flow | Incompressible flow | compressible flow | compressible flow | radial inflow | radial inflow | Geostrophic motion | Geostrophic motion | Taylor-Proudman Theorem | Taylor-Proudman Theorem | Ekman layer | Ekman layer | Coriolis force | Coriolis force | Rossby number | Rossby number | Hadley circulation | Hadley circulation | ocean | ocean | seawater | seawater | salinity | salinity | geostrophic and hydrostatic balance | geostrophic and hydrostatic balance | inhomogeneity | inhomogeneity | Abyssal circulation | Abyssal circulation | thermohaline circulation | thermohaline circulationLicense

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.htmSite sourced from

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See all metadata6.867 Machine Learning (MIT) 6.867 Machine Learning (MIT)

Description

6.867 is an introductory course on machine learning which provides an overview of many techniques and algorithms in machine learning, beginning with topics such as simple perceptrons and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course gives the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how and why they work. The underlying theme in the course is statistical inference as this provides the foundation for most of the methods covered.  6.867 is an introductory course on machine learning which provides an overview of many techniques and algorithms in machine learning, beginning with topics such as simple perceptrons and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course gives the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how and why they work. The underlying theme in the course is statistical inference as this provides the foundation for most of the methods covered. Subjects

machine learning | machine learning | perceptrons | perceptrons | boosting | boosting | support vector machines | support vector machines | Markov | Markov | hidden Markov models | hidden Markov models | HMM | HMM | Bayesian networks | Bayesian networks | statistical inference | statistical inference | regression | regression | clustering | clustering | bias | bias | variance | variance | regularization | regularization | Generalized Linear Models | Generalized Linear Models | neural networks | neural networks | Support Vector Machine | Support Vector Machine | SVM | SVM | mixture models | mixture models | kernel density estimation | kernel density estimation | gradient descent | gradient descent | quadratic programming | quadratic programming | EM algorithm | EM algorithm | orward-backward algorithm | orward-backward algorithm | junction tree algorithm | junction tree algorithm | Gibbs sampling | Gibbs samplingLicense

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.htmSite sourced from

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This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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.htmSite sourced from

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See all metadata6.685 Electric Machines (MIT) 6.685 Electric Machines (MIT)

Description

6.685 explores concepts in electromechanics, using electric machinery as examples. It teaches an understanding of principles and analysis of electromechanical systems. By the end of the course, students are capable of doing electromechanical design of the major classes of rotating and linear electric machines, and have an understanding of the principles of the energy conversion parts of Mechatronics. In addition to design, students learn how to estimate the dynamic parameters of electric machines and understand what the implications of those parameters are on the performance of systems incorporating those machines. 6.685 explores concepts in electromechanics, using electric machinery as examples. It teaches an understanding of principles and analysis of electromechanical systems. By the end of the course, students are capable of doing electromechanical design of the major classes of rotating and linear electric machines, and have an understanding of the principles of the energy conversion parts of Mechatronics. In addition to design, students learn how to estimate the dynamic parameters of electric machines and understand what the implications of those parameters are on the performance of systems incorporating those machines.Subjects

electric | electric | machine | machine | transformers | transformers | electromechanical | electromechanical | transducers | transducers | rotating | rotating | linear electric machines | linear electric machines | lumped parameter | lumped parameter | dc | dc | induction | induction | synchronous | synchronous | energy conversion | energy conversion | electromechanics | electromechanics | Mechatronics | Mechatronics | Electromechanical transducers | Electromechanical transducers | rotating electric machines | rotating electric machines | lumped-parameter elecromechanics | lumped-parameter elecromechanics | interaction electromechanics | interaction electromechanics | device characteristics | device characteristics | energy conversion density | energy conversion density | efficiency | efficiency | system interaction characteristics | system interaction characteristics | regulation | regulation | stability | stability | controllability | controllability | response | response | electric machines | electric machines | drive systems | drive systems | electric machinery | electric machinery | electromechanical systems | electromechanical systems | design | design | dynamic parameters | dynamic parameters | phenomena | phenomena | interactions | interactions | classical mechanics | classical mechanicsLicense

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See all metadata4.175 Case Studies in City Form (MIT) 4.175 Case Studies in City Form (MIT)

Description

This course serves as an introduction to urban form and design, focusing on the physical, historical, and social form of cities. Selected cities are analyzed, drawn, and compared, to develop a working understanding of urban and architectural form. The development of map making and urban representation is discussed, and use of the computer is required. A special focus is placed on the historical development of the selected cities, especially mid-nineteenth and mid-twentieth century periods of expansion. Readings focus on urban design theory in the twentieth century and will be discussed during a weekly seminar on them. This is a methods class for S.M.Arch.S. students in Architecture and Urbanism. This course serves as an introduction to urban form and design, focusing on the physical, historical, and social form of cities. Selected cities are analyzed, drawn, and compared, to develop a working understanding of urban and architectural form. The development of map making and urban representation is discussed, and use of the computer is required. A special focus is placed on the historical development of the selected cities, especially mid-nineteenth and mid-twentieth century periods of expansion. Readings focus on urban design theory in the twentieth century and will be discussed during a weekly seminar on them. This is a methods class for S.M.Arch.S. students in Architecture and Urbanism.Subjects

Ishfahan | Ishfahan | Alexandria | Alexandria | Washington | DC | Washington | DC | Amsterdam | Amsterdam | street network | street network | city form | city form | urban | urban | design | design | block types | block types | housing | housing | density | density | social form | social form | building types | building types | edges | edges | fields | fields | streets | streets | squares | squares | monuments | monuments | civic structure | civic structure | map-making | map-making | urban history | urban historyLicense

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.htmSite sourced from

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See all metadata4.163J Urban Design Studio: Providence (MIT) 4.163J Urban Design Studio: Providence (MIT)

Description

This studio discusses in great detail the design of urban environments, specifically in Providence, RI. It will propose strategies for change in large areas of cities, to be developed over time, involving different actors. Fitting forms into natural, man-made, historical, and cultural contexts; enabling desirable activity patterns; conceptualizing built form; providing infrastructure and service systems; guiding the sensory character of development: all are topics covered in the studio. The course integrates architecture and planning students in joint work and requires individual designs and planning guidelines as a final product. This studio discusses in great detail the design of urban environments, specifically in Providence, RI. It will propose strategies for change in large areas of cities, to be developed over time, involving different actors. Fitting forms into natural, man-made, historical, and cultural contexts; enabling desirable activity patterns; conceptualizing built form; providing infrastructure and service systems; guiding the sensory character of development: all are topics covered in the studio. The course integrates architecture and planning students in joint work and requires individual designs and planning guidelines as a final product.Subjects

urban planning | urban planning | community | community | stakeholders | stakeholders | development | development | urban growth | urban growth | Providence | Providence | Rhode Island | Rhode Island | institutional mechanisms | institutional mechanisms | housing | housing | waterfront | waterfront | port | port | built form | built form | public space | public space | landscape | landscape | path and access systems | path and access systems | parking | parking | density | density | activity location and intensity | activity location and intensity | planning | planning | finance | finance | public/private partnerships | public/private partnerships | parcelization | parcelization | phasing | phasing | multi-disciplinary teams | multi-disciplinary teams | 4.163 | 4.163 | 11.332 | 11.332License

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.htmSite sourced from

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Includes audio/video content: AV special element video. This undergraduate class is designed to introduce students to the physics that govern the circulation of the ocean and atmosphere. The focus of the course is on the processes that control the climate of the planet.AcknowledgmentsProf. Ferrari wishes to acknowledge that this course was originally designed and taught by Prof. John Marshall. Includes audio/video content: AV special element video. This undergraduate class is designed to introduce students to the physics that govern the circulation of the ocean and atmosphere. The focus of the course is on the processes that control the climate of the planet.AcknowledgmentsProf. Ferrari wishes to acknowledge that this course was originally designed and taught by Prof. John Marshall.Subjects

1. Characteristics of the atmosphere | 1. Characteristics of the atmosphere | Characteristics of the atmosphere | Characteristics of the atmosphere | global energy balance | global energy balance | greenhouse effect | greenhouse effect | greenhouse gases | greenhouse gases | Atmospheric layers | Atmospheric layers | pressure and density | pressure and density | Convection | Convection | adiabatic lapse rate | adiabatic lapse rate | Humidity | Humidity | Convective clouds | Convective clouds | Temperature | Temperature | Pressure and geopotential height | Pressure and geopotential height | Winds | Winds | Fluids in motion | Fluids in motion | Hydrostatic balance | Hydrostatic balance | Incompressible flow | Incompressible flow | compressible flow | compressible flow | radial inflow | radial inflow | Geostrophic motion | Geostrophic motion | Taylor-Proudman Theorem | Taylor-Proudman Theorem | Ekman layer | Ekman layer | Coriolis force | Coriolis force | Rossby number | Rossby number | Hadley circulation | Hadley circulation | ocean | ocean | seawater | seawater | salinity | salinity | geostrophic and hydrostatic balance | geostrophic and hydrostatic balance | inhomogeneity | inhomogeneity | Abyssal circulation | Abyssal circulation | thermohaline circulation | thermohaline circulationLicense

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See all metadata3.37 Welding and Joining Processes (MIT) 3.37 Welding and Joining Processes (MIT)

Description

Discusses a wide variety of processes and materials from the viewpoint of their fundamental physical and chemical properties. Specific topics: cold welding, adhesive bonding, diffusion bonding, soldering, brazing, flames, arcs, high-energy density heat sources, solidification, cracking resistance, shielding methods, and electric contacts. Emphasis on underlying science of a given process rather than a detailed description of the technique or equipment. This course meets with the first half of 3.371J in the Fall Term. Discusses a wide variety of processes and materials from the viewpoint of their fundamental physical and chemical properties. Specific topics: cold welding, adhesive bonding, diffusion bonding, soldering, brazing, flames, arcs, high-energy density heat sources, solidification, cracking resistance, shielding methods, and electric contacts. Emphasis on underlying science of a given process rather than a detailed description of the technique or equipment. This course meets with the first half of 3.371J in the Fall Term.Subjects

cold welding | cold welding | adhesive bonding | adhesive bonding | diffusion bonding | diffusion bonding | soldering | soldering | brazing | brazing | flames | flames | arcs | arcs | high-energy density heat sources | high-energy density heat sources | solidification | solidification | cracking resistance | cracking resistance | shielding methods | shielding methods | electric contacts | electric contactsLicense

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.htmSite sourced from

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See all metadata5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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.htmSite sourced from

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This course examines signals, systems and inference as unifying themes in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; group delay; state feedback and observers; probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization; least-mean square error estimation; Wiener filtering; hypothesis testing; detection; matched filters. This course examines signals, systems and inference as unifying themes in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; group delay; state feedback and observers; probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization; least-mean square error estimation; Wiener filtering; hypothesis testing; detection; matched filters.Subjects

signals and systems | signals and systems | transform representation | transform representation | state-space models | state-space models | state observers | state observers | state feedback | state feedback | probabilistic models | probabilistic models | random processes | random processes | power spectral density | power spectral density | hypothesis testing | hypothesis testing | signal detection | signal detectionLicense

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.htmSite sourced from

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See all metadata8.512 Theory of Solids II (MIT) 8.512 Theory of Solids II (MIT)

Description

This is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory. This is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory.Subjects

Linear response theory | Linear response theory | Fluctuation dissipation theorem | Fluctuation dissipation theorem | Scattering experiment | Scattering experiment | f-sum rule | f-sum rule | Physics of disorder | Physics of disorder | Kubo formula for conductivity | Kubo formula for conductivity | Conductance and sensitivity to boundary conditions | Conductance and sensitivity to boundary conditions | Scaling theory of localization | Scaling theory of localization | Mott variable range hopping | Mott variable range hopping | Superconductor | Superconductor | Transverse response | Transverse response | Landau diamagnetism | Landau diamagnetism | Microscopic derivation of London equation | Microscopic derivation of London equation | Effect of disorder | Effect of disorder | Quasiparticles and coherence factors | Quasiparticles and coherence factors | Tunneling and Josephson effect | Tunneling and Josephson effect | Magnetism | Magnetism | Local moment magnetism | Local moment magnetism | exchange interaction | exchange interaction | Ferro- and anti-ferro magnet and spin wave theory | Ferro- and anti-ferro magnet and spin wave theory | Band magnetism | Band magnetism | Stoner theory | Stoner theory | spin density wave | spin density wave | Local moment in metals | Local moment in metals | Friedel sum rule | Friedel sum rule | Friedel-Anderson model | Friedel-Anderson model | Kondo problem | Kondo problem | Fermi liquid theory | Fermi liquid theory | Electron Green?s function | Electron Green?s functionLicense

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.htmSite sourced from

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See all metadata8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamicsLicense

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.htmSite sourced from

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See all metadata8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamicsLicense

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.htmSite sourced from

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The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering. The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering.Subjects

comonent analysis | comonent analysis | PCA | PCA | ICA | ICA | fourier analysis | fourier analysis | vision | vision | machine vision | machine vision | pattern matching | pattern matching | pattern analysis | pattern analysis | pattern recognition | pattern recognition | scene analysis | scene analysis | tracking | tracking | feature extraction | feature extraction | color | color | color space | color space | clustering | clustering | bayesian decisions | bayesian decisions | gesture recognition | gesture recognition | action recognition | action recognition | image processing | image processing | image formation | image formation | density estimation | density estimation | classification | classification | morphable models | morphable models | component analysis | component analysisLicense

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.htmSite sourced from

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The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems. The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems.Subjects

quantum mechanics | quantum mechanics | computational quantum mechanics | computational quantum mechanics | molecular systems | molecular systems | extended systems | extended systems | Hartree-Fock theory | Hartree-Fock theory | density functional theory | density functional theory | DFT | DFT | many-electron problem | many-electron problem | electron correlation | electron correlation | chemical systems | chemical systems | reactivity | reactivity | spectroscopic properties | spectroscopic properties | thermodynamics | thermodynamics | kinetics | kinetics | chemical processes | chemical processes | complex hypersurfaces | complex hypersurfaces | CPMD | CPMD | Car-Parrinello Molecular Dynamics | Car-Parrinello Molecular Dynamics | 10.675 | 10.675 | 5.675 | 5.675License

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.htmSite sourced from

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See all metadata11.332J Urban Design (MIT) 11.332J Urban Design (MIT)

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For many years, Cambridge, MA, as host to two major research universities, has been the scene of debates as to how best to meet the competing expectations of different stakeholders. Where there has been success, it has frequently been the result, at least in part, of inventive urban design proposals and the design and implementation of new institutional arrangements to accomplish those proposals. Where there has been failure it has often been explained by the inability - or unwillingness - of one stakeholder to accept and accommodate the expectations of another. The two most recent fall Urban Design Studios have examined these issues at a larger scale. In 2001 we looked at the possible patterns for growth and change in Cambridge, UK, as triggered by the plans of Cambridge University. And i For many years, Cambridge, MA, as host to two major research universities, has been the scene of debates as to how best to meet the competing expectations of different stakeholders. Where there has been success, it has frequently been the result, at least in part, of inventive urban design proposals and the design and implementation of new institutional arrangements to accomplish those proposals. Where there has been failure it has often been explained by the inability - or unwillingness - of one stakeholder to accept and accommodate the expectations of another. The two most recent fall Urban Design Studios have examined these issues at a larger scale. In 2001 we looked at the possible patterns for growth and change in Cambridge, UK, as triggered by the plans of Cambridge University. And iSubjects

urban planning | urban planning | community | community | stakeholders | stakeholders | development | development | urban growth | urban growth | MIT | MIT | Cambridge | Cambridge | Cambridgeport | Cambridgeport | institutional mechanisms | institutional mechanisms | housing | housing | universities | universities | built form | built form | public space | public space | landscape | landscape | path and access systems | path and access systems | parking | parking | density | density | activity location and intensity | activity location and intensity | planning | planning | finance | finance | public/private partnerships | public/private partnerships | parcelization | parcelization | phasing | phasing | multi-disciplinary teams | multi-disciplinary teams | town and gown | town and gown | Massachusetts | Massachusetts | research universities | research universities | urban design | urban design | Fort Washington | Fort Washington | urban form | urban form | biotech research industry | biotech research industry | activity location | activity location | activity intensity | activity intensity | access systems | access systems | paths | paths | 11.332 | 11.332 | 4.163 | 4.163License

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This seminar is intended for doctoral students and discusses topics in applied probability. This semester includes a variety of fields, namely statistical physics (local weak convergence and correlation decay), artificial intelligence (belief propagation algorithms), computer science (random K-SAT problem, coloring, average case complexity) and electrical engineering (low density parity check (LDPC) codes). This seminar is intended for doctoral students and discusses topics in applied probability. This semester includes a variety of fields, namely statistical physics (local weak convergence and correlation decay), artificial intelligence (belief propagation algorithms), computer science (random K-SAT problem, coloring, average case complexity) and electrical engineering (low density parity check (LDPC) codes).Subjects

doctoral | doctoral | seminar | seminar | applied probability | applied probability | stochastic processes | stochastic processes | statistical physics | statistical physics | artificial intelligence | artificial intelligence | computer science | computer science | belief propagation algorithms | belief propagation algorithms | K-SAT problem | K-SAT problem | coloring | coloring | average case complexity | average case complexity | low density parity check codes | low density parity check codesLicense

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See all metadata16.120 Compressible Flow (MIT) 16.120 Compressible Flow (MIT)

Description

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear. The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.Subjects

compressible fluid dynamics | compressible fluid dynamics | fluid dynamics | fluid dynamics | external flows | external flows | internal flows | internal flows | quasi-on-dimensional | quasi-on-dimensional | quasi-1D | quasi-1D | channel flow | channel flow | multi-dimensional flows | multi-dimensional flows | nozzles | nozzles | diffusers | diffusers | inlets | inlets | loss generation | loss generation | interactions | interactions | aerodynamic shapes | aerodynamic shapes | subsonic | subsonic | supersonic | supersonic | transonic | transonic | hypersonic | hypersonic | shock waves | shock waves | vortices | vortices | disturbance behavior | disturbance behavior | unsteady | unsteady | speed of sound | speed of sound | isentropic flows | isentropic flows | non-isentropic flows | non-isentropic flows | potential flows | potential flows | rotational flows | rotational flows | shaft work | shaft work | heat addition | heat addition | mass addition | mass addition | flow states | flow states | flow regime | flow regime | velocity non-uniformities | velocity non-uniformities | density non-uniformities | density non-uniformities | fluid system components | fluid system components | lift | lift | drag | drag | continuum flow | continuum flow | shock strength | shock strength | characteristics | characteristics | governing equations | governing equations | thermodynamic context | thermodynamic context | characteristic parameters | characteristic parameters | quasi-one-dimensional flow | quasi-one-dimensional flow | disturbances | disturbances | unsteady flow | unsteady flow | gas dynamic discontinuities | gas dynamic discontinuities | detonations | detonations | linear two-dimensional flows | linear two-dimensional flows | non-linear two-dimensional flows | non-linear two-dimensional flowsLicense

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.htmSite sourced from

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The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s TheoremLicense

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.htmSite sourced from

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This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications. This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.Subjects

Random matrix theory | Random matrix theory | Matrix Jacobians | Matrix Jacobians | Wishart Matrices | Wishart Matrices | Wigner's Semi-Circular laws | Wigner's Semi-Circular laws | Matrix beta ensembles | Matrix beta ensembles | free probability | free probability | spherical coordinates | spherical coordinates | wedging | wedging | Plucker coordinates | Plucker coordinates | matrix factorizations | matrix factorizations | householder transformations | householder transformations | Stiefel manifold | Stiefel manifold | Cauchey-Binet theorem | Cauchey-Binet theorem | Telatar's paper | Telatar's paper | level densities | level densities | orthogonal polynomials | orthogonal polynomials | matrix integrals | matrix integrals | hypergeometric functions | hypergeometric functions | wireless communictions | wireless communictions | eigenvalue density | eigenvalue density | sample covariance matrices | sample covariance matrices | Marcenko-Pastur theorem | Marcenko-Pastur theorem | wireless communications | wireless communicationsLicense

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.htmSite sourced from

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License

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The oceans cover more than 70 per cent of our planet. In this free course you will learn about the depths of the oceans and the properties of the water that fills them, what drives the ocean circulation and how the oceans influence our climate. First published on Mon, 20 Jul 2015 as The oceans. To find out more visit The Open University's Openlearn website. Creative-Commons 2015 The oceans cover more than 70 per cent of our planet. In this free course you will learn about the depths of the oceans and the properties of the water that fills them, what drives the ocean circulation and how the oceans influence our climate. First published on Mon, 20 Jul 2015 as The oceans. To find out more visit The Open University's Openlearn website. Creative-Commons 2015Subjects

Science | Maths & Technology | Science | Maths & Technology | Physics and Astronomy | Physics and Astronomy | S206_1 | S206_1 | oceans | oceans | bathymetry | bathymetry | salinity | salinity | temperature | temperature | density | density | circulation | circulationLicense

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open UniversitySite sourced from

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