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8.321 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 dynamics

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8.322 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 dynamics

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14.121 Microeconomic Theory I (MIT) 14.121 Microeconomic Theory I (MIT)

Description

This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered. This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered.

Subjects

microeconomic theory | microeconomic theory | demand theory | demand theory | producer theory; partial equilibrium | producer theory; partial equilibrium | competitive markets | competitive markets | general equilibrium | general equilibrium | externalities | externalities | Afriat's theorem | Afriat's theorem | pricing | pricing | robust comparative statics | robust comparative statics | utility theory | utility theory | properties of preferences | properties of preferences | choice as primitive | choice as primitive | revealed preference | revealed preference | classical demand theory | classical demand theory | Kuhn-Tucker necessary conditions | Kuhn-Tucker necessary conditions | implications of Walras?s law | implications of Walras?s law | indirect utility functions | indirect utility functions | theorem of the maximum (Berge?s theorem) | theorem of the maximum (Berge?s theorem) | expenditure minimization problem | expenditure minimization problem | Hicksian demands | Hicksian demands | compensated law of demand | compensated law of demand | Slutsky substitution | Slutsky substitution | price changes and welfare | price changes and welfare | compensating variation | compensating variation | and welfare from new goods | and welfare from new goods | price indexes | price indexes | bias in the U.S. consumer price index | bias in the U.S. consumer price index | integrability | integrability | demand aggregation | demand aggregation | aggregate demand and welfare | aggregate demand and welfare | Frisch demands | Frisch demands | and demand estimation | and demand estimation | increasing differences | increasing differences | producer theory applications | producer theory applications | the LeCh?telier principle | the LeCh?telier principle | Topkis? theorem | Topkis? theorem | Milgrom-Shannon monotonicity theorem | Milgrom-Shannon monotonicity theorem | monopoly pricing | monopoly pricing | monopoly and product quality | monopoly and product quality | nonlinear pricing | nonlinear pricing | and price discrimination | and price discrimination | simple models of externalities | simple models of externalities | government intervention | government intervention | Coase theorem | Coase theorem | Myerson-Sattherthwaite proposition | Myerson-Sattherthwaite proposition | missing markets | missing markets | price vs. quantity regulations | price vs. quantity regulations | Weitzman?s analysis | Weitzman?s analysis | uncertainty | uncertainty | common property externalities | common property externalities | optimization | optimization | equilibrium number of boats | equilibrium number of boats | welfare theorems | welfare theorems | uniqueness and determinacy | uniqueness and determinacy | price-taking assumption | price-taking assumption | Edgeworth box | Edgeworth box | welfare properties | welfare properties | Pareto efficiency | Pareto efficiency | Walrasian equilibrium with transfers | Walrasian equilibrium with transfers | Arrow-Debreu economy | Arrow-Debreu economy | separating hyperplanes | separating hyperplanes | Minkowski?s theorem | Minkowski?s theorem | Existence of Walrasian equilibrium | Existence of Walrasian equilibrium | Kakutani?s fixed point theorem | Kakutani?s fixed point theorem | Debreu-Gale-Kuhn-Nikaido lemma | Debreu-Gale-Kuhn-Nikaido lemma | additional properties of general equilibrium | additional properties of general equilibrium | Microfoundations | Microfoundations | core | core | core convergence | core convergence | general equilibrium with time and uncertainty | general equilibrium with time and uncertainty | Jensen?s inequality | Jensen?s inequality | and security market economy | and security market economy | arbitrage pricing theory | arbitrage pricing theory | and risk-neutral probabilities | and risk-neutral probabilities | Housing markets | Housing markets | competitive equilibrium | competitive equilibrium | one-sided matching house allocation problem | one-sided matching house allocation problem | serial dictatorship | serial dictatorship | two-sided matching | two-sided matching | marriage markets | marriage markets | existence of stable matchings | existence of stable matchings | incentives | incentives | housing markets core mechanism | housing markets core mechanism

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18.238 Geometry and Quantum Field Theory (MIT) 18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory. Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | perturbative quantum field theory | classical field theory | classical field theory | free quantum theories | free quantum theories | Feynman diagrams | Feynman diagrams | Renormalization theory | Renormalization theory | Local operators | Local operators | Operator product expansion | Operator product expansion | Renormalization group equation | Renormalization group equation | classical | classical | field | field | theory | theory | Feynman | Feynman | diagrams | diagrams | free | free | quantum | quantum | theories | theories | local | local | operators | operators | product | product | expansion | expansion | perturbative | perturbative | renormalization | renormalization | group | group | equations | equations | functional | functional | function | function | intergrals | intergrals | operator | operator | QFT | QFT | string | string | physics | physics | mathematics | mathematics | geometry | geometry | geometric | geometric | algebraic | algebraic | topology | topology | number | number | 0-dimensional | 0-dimensional | 1-dimensional | 1-dimensional | d-dimensional | d-dimensional | supergeometry | supergeometry | supersymmetry | supersymmetry | conformal | conformal | stationary | stationary | phase | phase | formula | formula | calculus | calculus | combinatorics | combinatorics | matrix | matrix | mechanics | mechanics | lagrangians | lagrangians | hamiltons | hamiltons | least | least | action | action | principle | principle | limits | limits | formalism | formalism | Feynman-Kac | Feynman-Kac | current | current | charges | charges | Noether?s | Noether?s | theorem | theorem | path | path | integral | integral | approach | approach | divergences | divergences | functional integrals | functional integrals | fee quantum theories | fee quantum theories | renormalization theory | renormalization theory | local operators | local operators | operator product expansion | operator product expansion | renormalization group equation | renormalization group equation | mathematical language | mathematical language | string theory | string theory | 0-dimensional QFT | 0-dimensional QFT | Stationary Phase Formula | Stationary Phase Formula | Matrix Models | Matrix Models | Large N Limits | Large N Limits | 1-dimensional QFT | 1-dimensional QFT | Classical Mechanics | Classical Mechanics | Least Action Principle | Least Action Principle | Path Integral Approach | Path Integral Approach | Quantum Mechanics | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Operator Formalism | Feynman-Kac Formula | Feynman-Kac Formula | d-dimensional QFT | d-dimensional QFT | Formalism of Classical Field Theory | Formalism of Classical Field Theory | Currents | Currents | Noether?s Theorem | Noether?s Theorem | Path Integral Approach to QFT | Path Integral Approach to QFT | Perturbative Expansion | Perturbative Expansion | Renormalization Theory | Renormalization Theory | Conformal Field Theory | Conformal Field Theory | algebraic topology | algebraic topology | algebraic geometry | algebraic geometry | number theory | number theory

License

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8.851 Strong Interactions (MIT) 8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects. Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems | strong force | strong force | quarks | quarks | relativistic quantum field theory | relativistic quantum field theory | quantum chromodynamics | quantum chromodynamics | QCD | QCD | QCD Langrangian | QCD Langrangian | asymptotic freedom | asymptotic freedom | deep inelastic scattering | deep inelastic scattering | jets | jets | QCD vacuum | QCD vacuum | instantons | instantons | U(1) proglem | U(1) proglem | lattice gauge theory | lattice gauge theory | strong interactions | strong interactions | standard model | standard model | operator product expansion | operator product expansion | factorization | factorization | hard processes | hard processes | exclusive processes | exclusive processes | non-relativistic bound states | non-relativistic bound states | QED | QED | massive particles | massive particles | effective field theory | effective field theory | soft-collinear effective theory | soft-collinear effective 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 http://ocw.mit.edu/terms/index.htm

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

Description

This course is a one-semester introduction to the economic analysis of taxation. It covers both theoretical contributions, such as the theory of optimal income and commodity taxation, as well as empirical work, such as the study of how taxes affect labor supply. The course is designed to acquaint students with key questions in the economics of taxation, and to equip them to carry out their own research in this field. This course is a one-semester introduction to the economic analysis of taxation. It covers both theoretical contributions, such as the theory of optimal income and commodity taxation, as well as empirical work, such as the study of how taxes affect labor supply. The course is designed to acquaint students with key questions in the economics of taxation, and to equip them to carry out their own research in this field.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | theory | theory | evidence | evidence | government taxation policy | government taxation policy | tax incidence | tax incidence | optimal tax theory | optimal tax theory | labor supply | labor supply | savings | savings | corrective taxes for externalities | corrective taxes for externalities | corporate behavior | corporate behavior | tax expenditure policy | tax expenditure policy | theory of optimal income | theory of optimal income | commodity taxation | commodity taxation | calculus-based microeconomic analysis | calculus-based microeconomic analysis | duality methods | duality methods | household theory | household theory | firm theory | firm theory | growth theory | growth 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 http://ocw.mit.edu/terms/index.htm

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5.62 Physical Chemistry II (MIT) 5.62 Physical Chemistry II (MIT)

Description

This subject deals primarily with elementary statistical mechanics, transport properties, kinetic theory, solid state, reaction rate theory, and chemical reaction dynamics.AcknowledgementsThe lecture note materials for this course include contributions from Professor Sylvia T. Ceyer. The Staff for this course would like to acknowledge that these course materials include contributions from past instructors, textbooks, and other members of the MIT Chemistry Department affiliated with course #5.62. Since the following works have evolved over a period of many years, no single source can be attributed. This subject deals primarily with elementary statistical mechanics, transport properties, kinetic theory, solid state, reaction rate theory, and chemical reaction dynamics.AcknowledgementsThe lecture note materials for this course include contributions from Professor Sylvia T. Ceyer. The Staff for this course would like to acknowledge that these course materials include contributions from past instructors, textbooks, and other members of the MIT Chemistry Department affiliated with course #5.62. Since the following works have evolved over a period of many years, no single source can be attributed.

Subjects

physical chemistry | physical chemistry | partition functions | partition functions | atomic degrees of freedom | atomic degrees of freedom | molecular degrees of freedom | molecular degrees of freedom | chemical equilibrium | chemical equilibrium | thermodynamics | thermodynamics | intermolecular potentials | intermolecular potentials | equations of state | equations of state | solid state chemistry | solid state chemistry | einstein and debye solids | einstein and debye solids | kinetic theory | kinetic theory | rate theory | rate theory | chemical kinetics | chemical kinetics | transition state theory | transition state theory | RRKM theory | RRKM theory | collision theory | collision theory | equipartition | equipartition | fermi-dirac statistics | fermi-dirac statistics | boltzmann statistics | boltzmann statistics | bose-einstein statistics | bose-einstein statistics | statistical mechanics | statistical mechanics

License

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8.512 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 function

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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5.62 Physical Chemistry II (MIT) 5.62 Physical Chemistry II (MIT)

Description

This course covers elementary statistical mechanics, transport properties, kinetic theory, solid state, reaction rate theory, and chemical reaction dynamics. Acknowledgements The staff for this course would like to acknowledge that these course materials include contributions from past instructors, textbooks, and other members of the MIT Chemistry Department affiliated with course #5.62. Since the following works have evolved over a period of many years, no single source can be attributed. This course covers elementary statistical mechanics, transport properties, kinetic theory, solid state, reaction rate theory, and chemical reaction dynamics. Acknowledgements The staff for this course would like to acknowledge that these course materials include contributions from past instructors, textbooks, and other members of the MIT Chemistry Department affiliated with course #5.62. Since the following works have evolved over a period of many years, no single source can be attributed.

Subjects

physical chemistry | physical chemistry | partition functions | partition functions | atomic degrees of freedom | atomic degrees of freedom | molecular degrees of freedom | molecular degrees of freedom | chemical equilibrium | chemical equilibrium | thermodynamics | thermodynamics | intermolecular potentials | intermolecular potentials | equations of state | equations of state | solid state chemistry | solid state chemistry | einstein and debye solids | einstein and debye solids | kinetic theory | kinetic theory | rate theory | rate theory | chemical kinetics | chemical kinetics | transition state theory | transition state theory | RRKM theory | RRKM theory | collision theory | collision theory | equipartition | equipartition | fermi-dirac statistics | fermi-dirac statistics | boltzmann statistics | boltzmann statistics | bose-einstein statistics | bose-einstein statistics | statistical mechanics | statistical mechanics

License

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8.512 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 function

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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8.321 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.

Subjects

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

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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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.

Subjects

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

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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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.

Subjects

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

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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.

Subjects

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

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

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5.04 Principles of Inorganic Chemistry II (MIT) 5.04 Principles of Inorganic Chemistry II (MIT)

Description

This course provides a systematic presentation of the chemical applications of group theory with emphasis on the formal development of the subject and its applications to the physical methods of inorganic chemical compounds. Against the backdrop of electronic structure, the electronic, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy described. This course provides a systematic presentation of the chemical applications of group theory with emphasis on the formal development of the subject and its applications to the physical methods of inorganic chemical compounds. Against the backdrop of electronic structure, the electronic, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy described.

Subjects

inorganic chemistry | inorganic chemistry | group theory | group theory | electronic structure of molecules | electronic structure of molecules | transition metal complexes | transition metal complexes | spectroscopy | spectroscopy | symmetry elements | symmetry elements | mathematical groups | mathematical groups | character tables | character tables | molecular point groups | molecular point groups | Huckel Theory | Huckel Theory | N-Dimensional cyclic systems | N-Dimensional cyclic systems | solid state theory | solid state theory | band theory | band theory | frontier molecular orbitals | frontier molecular orbitals | similarity transformations | similarity transformations | complexes | complexes | organometallic complexes | organometallic complexes | two electron bond | two electron bond | vibrational spectroscopy | vibrational spectroscopy | symmetry | symmetry | overtones | overtones | normal coordinat analysis | normal coordinat analysis | AOM | AOM | single electron CFT | single electron CFT | tanabe-sugano diagram | tanabe-sugano diagram | ligand | ligand | crystal field theory | crystal field theory | LCAO | LCAO

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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18.466 Mathematical Statistics (MIT) 18.466 Mathematical Statistics (MIT)

Description

This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis. This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.

Subjects

decision theory | decision theory | testing simple hypothesis | testing simple hypothesis | Neyman-Pearson Lemma | Neyman-Pearson Lemma | Bayes decision theory | Bayes decision theory | sufficiency | sufficiency | estimation | estimation | convexity | convexity | Lehmann-Scheff'e property | Lehmann-Scheff'e property | Exponential families | Exponential families | Stein?s phenomenon | Stein?s phenomenon | James-Stein estimators | James-Stein estimators | M-estimation | M-estimation | Solari?s example | Solari?s example | Wilks?s theorem | Wilks?s theorem | stochastic processes | stochastic processes | probability theory | probability theory | confidence intervals | confidence intervals | large sample theory | large sample theory | sequential analysis | sequential analysis | asymptotic efficiency | asymptotic efficiency

License

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14.01SC Principles of Microeconomics (MIT) 14.01SC Principles of Microeconomics (MIT)

Description

Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmen Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmen

Subjects

Microeconomics | Microeconomics | prices | prices | normative economics | normative economics | positive economics | positive economics | microeconomic applications | microeconomic applications | supply | supply | demand | demand | equilibrium | equilibrium | demand shift | demand shift | supply shift | supply shift | government interference | government interference | elasticity | elasticity | revenue | revenue | empirical economics | empirical economics | consumer theory | consumer theory | preference assumptions | preference assumptions | indifference curves | indifference curves | utility functions | utility functions | marginal utility | marginal utility | budget constraints | budget constraints | marginal rate of transformation | marginal rate of transformation | opportunity cost | opportunity cost | constrained utility maximization | constrained utility maximization | corner solutions | corner solutions | Engel curves | Engel curves | income effect | income effect | substitution effect | substitution effect | Giffin good | Giffin good | labor economics | labor economics | child labor | child labor | producer theory | producer theory | variable inputs | variable inputs | fixed inputs | fixed inputs | firm production functions | firm production functions | marginal rate of technical substitution | marginal rate of technical substitution | returns to scale | returns to scale | productivity | productivity | perfect competition | perfect competition | search theory | search theory | residual demand | residual demand | shutdown decisions | shutdown decisions | market equilibrium | market equilibrium | agency problem | agency problem | welfare economics | welfare economics | consumer surplus | consumer surplus | producer surplus | producer surplus | dead weight loss | dead weight loss | monopoly | monopoly | oligopoly | oligopoly | market power | market power | price discrimination | price discrimination | price regulation | price regulation | antitrust policy | antitrust policy | mergers | mergers | cartel | cartel | game theory | game theory | Nash equilibrium | Nash equilibrium | Cournot model | Cournot model | duopoly | duopoly | non-cooperative competition | non-cooperative competition | Bertrand competition | Bertrand competition | factor markets | factor markets | international trade | international trade | uncertainty | uncertainty | capital markets | capital markets | intertemporal choice | intertemporal choice | real interest rate | real interest rate | compounding | compounding | inflation | inflation | investment | investment | discount rate | discount rate | net present value | net present value | income distribution | income distribution | social welfare function | social welfare function | Utilitarianism | Utilitarianism | Raulsian criteria | Raulsian criteria | Nozickian | Nozickian | commodity egalitarianism | commodity egalitarianism | isowelfare curves | isowelfare curves | social insurance | social insurance | social security | social security | moral hazard | moral hazard | taxation | taxation | EITC | EITC | healthcare | healthcare | PPACA | PPACA

License

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

Description

Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world. Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world.

Subjects

sorting algorithms | sorting algorithms | information theory | information theory | coding theory | coding theory | secret codes | secret codes | generating functions | generating functions | linear programming | linear programming | game theory | game theory | discrete applied mathematics | discrete applied mathematics | mathematical analysis | mathematical analysis | sorting data | sorting data | efficient data storage | efficient data storage | efficient data transmission | efficient data transmission | error correction | error correction | secrecy | secrecy | Fast Fourier Transform | Fast Fourier Transform | network-flow problems | network-flow problems | mathematical economics | mathematical economics | statistics | statistics | probability theory | probability theory | combinatorics | combinatorics | linear algebra | linear algebra

License

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14.121 Microeconomic Theory I (MIT)

Description

This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered.

Subjects

microeconomic theory | demand theory | producer theory; partial equilibrium | competitive markets | general equilibrium | externalities | Afriat's theorem | pricing | robust comparative statics | utility theory | properties of preferences | choice as primitive | revealed preference | classical demand theory | Kuhn-Tucker necessary conditions | implications of Walras?s law | indirect utility functions | theorem of the maximum (Berge?s theorem) | expenditure minimization problem | Hicksian demands | compensated law of demand | Slutsky substitution | price changes and welfare | compensating variation | and welfare from new goods | price indexes | bias in the U.S. consumer price index | integrability | demand aggregation | aggregate demand and welfare | Frisch demands | and demand estimation | increasing differences | producer theory applications | the LeCh?telier principle | Topkis? theorem | Milgrom-Shannon monotonicity theorem | monopoly pricing | monopoly and product quality | nonlinear pricing | and price discrimination | simple models of externalities | government intervention | Coase theorem | Myerson-Sattherthwaite proposition | missing markets | price vs. quantity regulations | Weitzman?s analysis | uncertainty | common property externalities | optimization | equilibrium number of boats | welfare theorems | uniqueness and determinacy | price-taking assumption | Edgeworth box | welfare properties | Pareto efficiency | Walrasian equilibrium with transfers | Arrow-Debreu economy | separating hyperplanes | Minkowski?s theorem | Existence of Walrasian equilibrium | Kakutani?s fixed point theorem | Debreu-Gale-Kuhn-Nikaido lemma | additional properties of general equilibrium | Microfoundations | core | core convergence | general equilibrium with time and uncertainty | Jensen?s inequality | and security market economy | arbitrage pricing theory | and risk-neutral probabilities | Housing markets | competitive equilibrium | one-sided matching house allocation problem | serial dictatorship | two-sided matching | marriage markets | existence of stable matchings | incentives | housing markets core mechanism

License

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18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | classical field theory | free quantum theories | Feynman diagrams | Renormalization theory | Local operators | Operator product expansion | Renormalization group equation | classical | field | theory | Feynman | diagrams | free | quantum | theories | local | operators | product | expansion | perturbative | renormalization | group | equations | functional | function | intergrals | operator | QFT | string | physics | mathematics | geometry | geometric | algebraic | topology | number | 0-dimensional | 1-dimensional | d-dimensional | supergeometry | supersymmetry | conformal | stationary | phase | formula | calculus | combinatorics | matrix | mechanics | lagrangians | hamiltons | least | action | principle | limits | formalism | Feynman-Kac | current | charges | Noether?s | theorem | path | integral | approach | divergences | functional integrals | fee quantum theories | renormalization theory | local operators | operator product expansion | renormalization group equation | mathematical language | string theory | 0-dimensional QFT | Stationary Phase Formula | Matrix Models | Large N Limits | 1-dimensional QFT | Classical Mechanics | Least Action Principle | Path Integral Approach | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Feynman-Kac Formula | d-dimensional QFT | Formalism of Classical Field Theory | Currents | Noether?s Theorem | Path Integral Approach to QFT | Perturbative Expansion | Renormalization Theory | Conformal Field Theory | algebraic topology | algebraic geometry | number theory

License

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18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT) 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT)

Description

This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.

Subjects

linear algebra | linear algebra | eigensystems for Maxwell's equations | eigensystems for Maxwell's equations | symmetry groups | symmetry groups | representation theory | representation theory | Bloch's theorem | Bloch's theorem | numerical eigensolver methods | numerical eigensolver methods | time and frequency-domain computation | time and frequency-domain computation | perturbation theory | perturbation theory | coupled-mode theories | coupled-mode theories | waveguide theory | waveguide theory | adiabatic transitions | adiabatic transitions | Optical phenomena | Optical phenomena | photonic crystals | photonic crystals | band gaps | band gaps | anomalous diffraction | anomalous diffraction | mechanisms for optical confinement | mechanisms for optical confinement | optical fibers | optical fibers | integrated optical devices | integrated optical devices

License

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SP.268 The Mathematics in Toys and Games (MIT) SP.268 The Mathematics in Toys and Games (MIT)

Description

We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class. We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class.

Subjects

toys | toys | games | games | mathematics | mathematics | game theory | game theory | probability | probability | group theory | group theory | programming | programming | combinatorial game theory | combinatorial game theory

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2.717J Optical Engineering (MIT) 2.717J Optical Engineering (MIT)

Description

This course concerns the theory and practice of optical methods in engineering and system design, with an emphasis on diffraction, statistical optics, holography, and imaging. It provides the engineering methodology skills necessary to incorporate optical components in systems serving diverse areas such as precision engineering and metrology, bio-imaging, and computing (sensors, data storage, communication in multi-processor systems). Experimental demonstrations and a design project are included. This course concerns the theory and practice of optical methods in engineering and system design, with an emphasis on diffraction, statistical optics, holography, and imaging. It provides the engineering methodology skills necessary to incorporate optical components in systems serving diverse areas such as precision engineering and metrology, bio-imaging, and computing (sensors, data storage, communication in multi-processor systems). Experimental demonstrations and a design project are included.

Subjects

optical methods in engineering and system design | optical methods in engineering and system design | diffraction | statistical optics | holography | and imaging | diffraction | statistical optics | holography | and imaging | Statistical Optics | Inverse Problems (i.e. theory of imaging) | Statistical Optics | Inverse Problems (i.e. theory of imaging) | applications in precision engineering and metrology | bio-imaging | and computing (sensors | data storage | communication in multi-processor systems) | applications in precision engineering and metrology | bio-imaging | and computing (sensors | data storage | communication in multi-processor systems) | Fourier optics | Fourier optics | probability | probability | stochastic processes | stochastic processes | light statistics | light statistics | theory of light coherence | theory of light coherence | van Cittert-Zernicke Theorem | van Cittert-Zernicke Theorem | statistical optics applications | statistical optics applications | inverse problems | inverse problems | information-theoretic views | information-theoretic views | information theory | information theory | 2.717 | 2.717 | MAS.857 | MAS.857

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