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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesisSubjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402License

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See all metadata8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models. Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402 | plusars | plusars | galaxies | galaxies | normal and active galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe | dynamical expansion and thermal history of the UniverseLicense

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 metadata18.786 Topics in Algebraic Number Theory (MIT) 18.786 Topics in Algebraic Number Theory (MIT)

Description

This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets. This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.Subjects

algebraic number theory | algebraic number theory | number fields | number fields | class numbers | class numbers | Dirichlet's units theorem | Dirichlet's units theorem | cyclotomic fields | cyclotomic fields | local fields | local fields | valuations | valuations | decomposition and inertia groups | decomposition and inertia groups | ramification | ramification | basic analytic methods | basic analytic methods | basic class field theory | basic class field theoryLicense

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See all metadata18.022 Calculus (MIT) 18.022 Calculus (MIT)

Description

This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra. This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra.Subjects

vector algebra | vector algebra | determinant | determinant | matrix | matrix | matrices | matrices | vector-valued | vector-valued | functions | functions | space motion | space motion | scalar functions | scalar functions | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differentials | exact differentials | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem | divergence theorem | Stokes' theorem | Stokes' theorem | geometry | geometry | vector fields | vector fields | linear algebra | linear algebraLicense

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See all metadata8.323 Relativistic Quantum Field Theory I (MIT) 8.323 Relativistic Quantum Field Theory I (MIT)

Description

In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams. In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams.Subjects

Quantum physics | Quantum physics | Classical field theory | Classical field theory | symmetries | symmetries | and Noether's theorem | and Noether's theorem | Quantization of scalar fields | Quantization of scalar fields | spin fields | spin fields | and Gauge bosons | and Gauge bosons | Feynman graphs | Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix | analytic properties of amplitudes and unitarity of the S-matrix | Calculations in quantum electrodynamics (QED) | Calculations in quantum electrodynamics (QED) | Introduction to renormalization | Introduction to renormalizationLicense

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See all metadata22.105 Electromagnetic Interactions (MIT) 22.105 Electromagnetic Interactions (MIT)

Description

Principles and applications of electromagnetism, starting from Maxwell's equations, with emphasis on phenomena important to nuclear engineering and radiation sciences. Solution methods for electrostatic and magnetostatic fields. Charged particle motion in those fields. Particle acceleration and focussing. Collisions with charged particles and with atoms. Electromagnetic waves, wave emission by accelerated particles, Bremsstrahlung. Compton scattering. Photoionization. Elementary applications to ranging, shielding, imaging, and radiation effects. Principles and applications of electromagnetism, starting from Maxwell's equations, with emphasis on phenomena important to nuclear engineering and radiation sciences. Solution methods for electrostatic and magnetostatic fields. Charged particle motion in those fields. Particle acceleration and focussing. Collisions with charged particles and with atoms. Electromagnetic waves, wave emission by accelerated particles, Bremsstrahlung. Compton scattering. Photoionization. Elementary applications to ranging, shielding, imaging, and radiation effects.Subjects

electromagnetism | | electromagnetism | | Maxwell's equations | | Maxwell's equations | | electrostatic fields | | electrostatic fields | | magnetostatic fields | | magnetostatic fields | | Charged particle motion | | Charged particle motion | | Particle acceleration | | Particle acceleration | | Electromagnetic waves | | Electromagnetic waves | | Bremsstrahlung | | Bremsstrahlung | | Compton scattering | | Compton scattering | | Photoionization | PhotoionizationLicense

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 class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site. The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.Subjects

energetics | energetics | materials structure and symmetry: applied fields | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | mechanics and physics of solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalues | eigenvalues | eigenvectors | eigenvectors | quadratic forms | quadratic forms | tensor operations | tensor operations | symmetry operations | symmetry operations | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walks | random walks | mathematical technicques | mathematical technicques | materials science | materials science | materials engineering | materials engineering | materials structure | materials structure | symmetry | symmetry | applied fields | applied fields | materials response | materials response | solids mechanics | solids mechanics | solids physics | solids physics | soft materials | soft materials | multi-variable calculus | multi-variable calculus | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | applied mathematics | applied mathematics | mathematical techniques | mathematical techniquesLicense

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See all metadata6.013 Electromagnetics and Applications (MIT) 6.013 Electromagnetics and Applications (MIT)

Description

Includes audio/video content: AV special element video. This course explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided waves; resonance; acoustic analogs; and forces, power, and energy. Includes audio/video content: AV special element video. This course explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided waves; resonance; acoustic analogs; and forces, power, and energy.Subjects

electromagnetics | electromagnetics | electromagnetic fields | electromagnetic fields | electrodynamics | electrodynamics | devices and circuits | devices and circuits | static and quasistatic fields | static and quasistatic fields | electromagnetic forces | electromagnetic forces | actuators | actuators | sensors | sensors | TEM lines | TEM lines | electromagnetic waves | electromagnetic waves | antennas | antennas | radiation | radiation | optical communications | optical communications | acoustics | acousticsLicense

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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Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets, deformation fields) and useful methods that allow us to extract and manipulate image information, including manifold fitting, markov random fields, expectation maximization, clustering and others. For each concept -- a new representation or an estimation algorithm -- a lecture on the mathematical f Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets, deformation fields) and useful methods that allow us to extract and manipulate image information, including manifold fitting, markov random fields, expectation maximization, clustering and others. For each concept -- a new representation or an estimation algorithm -- a lecture on the mathematical fSubjects

computer vision | computer vision | image analysis | image analysis | representation algorithm | representation algorithm | modeling | modeling | estimation algorithm | estimation algorithm | information | information | objects | objects | modeling techniques | modeling techniques | images | images | representations | representations | contours | contours | level sets | level sets | deformation fields | deformation fields | image information | image information | manifold fitting | manifold fitting | markov random fields | markov random fields | expectation maximization | expectation maximization | clustering | clustering | mathematical foundations | mathematical foundations | medical and biological imaging | medical and biological imagingLicense

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 metadata8.323 Relativistic Quantum Field Theory I (MIT) 8.323 Relativistic Quantum Field Theory I (MIT)

Description

8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics. 8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Subjects

Classical field theory | Classical field theory | symmetries | symmetries | and Noether's theorem. Quantization of scalar fields | and Noether's theorem. Quantization of scalar fields | spin fields | spin fields | and Gauge bosons. Feynman graphs | and Gauge bosons. Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization. | analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.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.htmSite sourced from

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See all metadata8.02 Physics II: Electricity and Magnetism (MIT) 8.02 Physics II: Electricity and Magnetism (MIT)

Description

This freshman-level course is the second semester of introductory physics. The focus is on electricity and magnetism. The subject is taught using the TEAL (Technology Enabled Active Learning) format which utilizes small group interaction and current technology. The TEAL/Studio Project at MIT is a new approach to physics education designed to help students develop much better intuition about, and conceptual models of, physical phenomena. Staff List Visualizations: Prof. John Belcher Instructors: Dr. Peter Dourmashkin Prof. Bruce Knuteson Prof. Gunther Roland Prof. Bolek Wyslouch Dr. Brian Wecht Prof. Eric Katsavounidis Prof. Robert Simcoe Prof. Joseph Formaggio Course Co-Administrators: Dr. Peter Dourmashkin Prof. Robert Redwine Technical Instructors: Andy Neely Matthew Strafuss Course This freshman-level course is the second semester of introductory physics. The focus is on electricity and magnetism. The subject is taught using the TEAL (Technology Enabled Active Learning) format which utilizes small group interaction and current technology. The TEAL/Studio Project at MIT is a new approach to physics education designed to help students develop much better intuition about, and conceptual models of, physical phenomena. Staff List Visualizations: Prof. John Belcher Instructors: Dr. Peter Dourmashkin Prof. Bruce Knuteson Prof. Gunther Roland Prof. Bolek Wyslouch Dr. Brian Wecht Prof. Eric Katsavounidis Prof. Robert Simcoe Prof. Joseph Formaggio Course Co-Administrators: Dr. Peter Dourmashkin Prof. Robert Redwine Technical Instructors: Andy Neely Matthew Strafuss CourseSubjects

electromagnetism | electromagnetism | electrostatics | electrostatics | electric charge | electric charge | Coulomb's law | Coulomb's law | electric structure of matter | electric structure of matter | conductors | conductors | dielectrics | dielectrics | electrostatic field | electrostatic field | potential | potential | electrostatic energy | electrostatic energy | Electric currents | Electric currents | magnetic fields | magnetic fields | Ampere's law | Ampere's law | Magnetic materials | Magnetic materials | Time-varying fields | Time-varying fields | Faraday's law of induction | Faraday's law of induction | electric circuits | electric circuits | Electromagnetic waves | Electromagnetic waves | Maxwell's equations | Maxwell's equationsLicense

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See all metadata8.02T Electricity and Magnetism (MIT) 8.02T Electricity and Magnetism (MIT)

Description

This freshman-level course is the second semester of introductory physics. The focus is on electricity and magnetism. The subject is taught using the TEAL (Technology Enabled Active Learning) format which utilizes small group interaction and current technology. The TEAL/Studio Project at MIT is a new approach to physics education designed to help students develop much better intuition about, and conceptual models of, physical phenomena. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, a This freshman-level course is the second semester of introductory physics. The focus is on electricity and magnetism. The subject is taught using the TEAL (Technology Enabled Active Learning) format which utilizes small group interaction and current technology. The TEAL/Studio Project at MIT is a new approach to physics education designed to help students develop much better intuition about, and conceptual models of, physical phenomena. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, aSubjects

electromagnetism | electromagnetism | electrostatics | electrostatics | electric charge | electric charge | Coulomb's law | Coulomb's law | electric structure of matter | electric structure of matter | conductors | conductors | dielectrics | dielectrics | electrostatic field | electrostatic field | potential | potential | electrostatic energy | electrostatic energy | Electric currents | Electric currents | magnetic fields | magnetic fields | Ampere's law | Ampere's law | Magnetic materials | Magnetic materials | Time-varying fields | Time-varying fields | Faraday's law of induction | Faraday's law of induction | electric circuits | electric circuits | Electromagnetic waves | Electromagnetic waves | Maxwell's equations | Maxwell's equationsLicense

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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

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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

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See all metadata18.022 Calculus of Several Variables (MIT) 18.022 Calculus of Several Variables (MIT)

Description

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.Subjects

vector algebra | vector algebra | determinant | determinant | matrix | matrix | matrices | matrices | vector-valued functions | vector-valued functions | space motion | space motion | scalar functions | scalar functions | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differentials | exact differentials | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem | divergence theorem | Stokes' theorem | Stokes' theorem | geometry | geometry | vector fields | vector fields | linear algebra | linear algebraLicense

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 metadata8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the UniverseLicense

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.htmSite sourced from

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See all metadata8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesisSubjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402License

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.htmSite sourced from

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Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the UniverseLicense

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.htmSite sourced from

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See all metadata18.786 Topics in Algebraic Number Theory (MIT)

Description

This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.Subjects

algebraic number theory | number fields | class numbers | Dirichlet's units theorem | cyclotomic fields | local fields | valuations | decomposition and inertia groups | ramification | basic analytic methods | basic class field theoryLicense

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.htmSite sourced from

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See all metadata18.024 Calculus with Theory II (MIT) 18.024 Calculus with Theory II (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-TaylorSubjects

linear algebra | linear algebra | vector integral calculus | vector integral calculus | Calculus of several variables | Calculus of several variables | Vector algebra in 3-space | Vector algebra in 3-space | determinants | determinants | matrices | matrices | Vector-valued functions of one variable | Vector-valued functions of one variable | space motion | space motion | Scalar functions of several variables: partial differentiation | Scalar functions of several variables: partial differentiation | gradient | gradient | optimization techniques | optimization techniques | Double integrals and line integrals in the plane | Double integrals and line integrals in the plane | exact differentials and conservative fields | exact differentials and conservative fields | Green's theorem and applications | Green's theorem and applications | triple integrals | triple integrals | line and surface integrals in space | line and surface integrals in space | Divergence theorem | Divergence theorem | Stokes' theorem | Stokes' theorem | applications | applicationsLicense

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 metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

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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A proper understanding of modern military operations requires a prior understanding of both the material side of war, including especially weapon, sensor, communication, and information processing technologies, and the human or organizational side of war, including especially military doctrine, which is an institutionalized vision within military organizations that predicts how the material tools of war will be wielded on future battlefields. Military doctrine makes assumptions about the nature of future battlefields, and determines what the division of labor on those battlefields will be between different military tools. Doctrine also therefore determines the organizational hierarchy among the various branches of the military which wield those tools. Thus, one way to think of the relation A proper understanding of modern military operations requires a prior understanding of both the material side of war, including especially weapon, sensor, communication, and information processing technologies, and the human or organizational side of war, including especially military doctrine, which is an institutionalized vision within military organizations that predicts how the material tools of war will be wielded on future battlefields. Military doctrine makes assumptions about the nature of future battlefields, and determines what the division of labor on those battlefields will be between different military tools. Doctrine also therefore determines the organizational hierarchy among the various branches of the military which wield those tools. Thus, one way to think of the relationSubjects

Political science | Political science | military | military | modern | modern | operations | operations | material | material | war | war | weapon | weapon | sensor | sensor | communication | communication | information processing | information processing | technologies | technologies | human | human | organizational | organizational | doctrine | doctrine | future | future | battlefields | battlefields | organizational hierarchy | organizational hierarchy | branches. | branches. | branches | branchesLicense

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 metadata6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following. Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following. Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&aSubjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportationLicense

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 metadata9.01 Introduction to Neuroscience (MIT) 9.01 Introduction to Neuroscience (MIT)

Description

This course begins with the study of nerve cells which includes their structure, the propagation of nerve impulses and transfer of information between nerve cells, the effect of drugs on this process, and the development of nerve cells into the brain and spinal cord. Next, sensory systems such as hearing, vision and touch are covered as well as a discussion on how physical energy such as light is converted into neural signals, where these signals travel in the brain and how they are processed. Other topics include the control of voluntary movement, the neurochemical bases of brain diseases, and those systems which control sleep and consciousness, learning and memory. This course begins with the study of nerve cells which includes their structure, the propagation of nerve impulses and transfer of information between nerve cells, the effect of drugs on this process, and the development of nerve cells into the brain and spinal cord. Next, sensory systems such as hearing, vision and touch are covered as well as a discussion on how physical energy such as light is converted into neural signals, where these signals travel in the brain and how they are processed. Other topics include the control of voluntary movement, the neurochemical bases of brain diseases, and those systems which control sleep and consciousness, learning and memory.Subjects

neuroscience | neuroscience | vision | vision | hearing | hearing | neuroanatomy | neuroanatomy | color vision | color vision | blind spot | blind spot | retinal phototransduction | retinal phototransduction | center-surround receptive fields | center-surround receptive fields | corticalmaps | corticalmaps | primary visual cortex | primary visual cortex | simple cells | simple cells | complex cells | complex cells | extrastriate cortex | extrastriate cortex | ear | ear | cochlea | cochlea | basilar membrane | basilar membrane | auditory transduction | auditory transduction | hair cells | hair cells | phase-locking | phase-locking | tonotopy | tonotopy | sound localization | sound localization | auditory cortex | auditory cortex | somatosensory system | somatosensory system | motor system | motor system | synaptic transmission | synaptic transmission | action potential | action potential | sympathetic neurons | sympathetic neurons | parasympathetic neurons | parasympathetic neurons | cellual neurophysiology | cellual neurophysiology | learning | learning | memory | memoryLicense

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 metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail. The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

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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