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8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

This course offers an introduction to the basic concepts of the quantum theory of solids. This course offers an introduction to the basic concepts of the quantum theory of solids.

Subjects

periodic structure | periodic structure | symmetry of crystals | symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | lattice dynamics | lattice dynamics | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem | Bloch theorem | band structure | band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism. | magnetism.

License

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8.511 Theory of Solids I (MIT) 8.511 Theory of Solids I (MIT)

Description

This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity. This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity.

Subjects

physics of solids | physics of solids | elementary excitations | elementary excitations | symmetry | symmetry | theory of representations | theory of representations | energy bands | energy bands | excitons | excitons | critical points | critical points | response functions | response functions | interactions in the electron gas | interactions in the electron gas | electronic structure of metals | semimetals | electronic structure of metals | semimetals | semiconductors | semiconductors | insulators | insulators | Free electron model | Free electron model | Crystalline lattice | Crystalline lattice | Debye Waller factor | Debye Waller factor | Bravais lattice | Bravais lattice | Pseudopotential | Pseudopotential | van Hove singularity | van Hove singularity | Bloch oscillation | Bloch oscillation | quantization of orbits | quantization of orbits | de Haas-van Alphen effect | de Haas-van Alphen effect | Quantum Hall effect | Quantum Hall effect | Electron-electron interaction | Electron-electron interaction | Hartree-Fock approximation | Hartree-Fock approximation | Exchange energy for Jellium | Exchange energy for Jellium | Density functional theory | Density functional theory | Hubbard model | Hubbard model | Electron-phonon coupling | Electron-phonon coupling | phonons | phonons

License

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6.730 Physics for Solid-State Applications (MIT) 6.730 Physics for Solid-State Applications (MIT)

Description

This course examines classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Topics covered include: crystal lattices, electronic energy band structures, phonon dispersion relatons, effective mass theorem, semiclassical equations of motion, and impurity states in semiconductors, band structure and transport properties of selected semiconductors, and connection of quantum theory of solids with quasifermi levels and Boltzmann transport used in device modeling. This course examines classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Topics covered include: crystal lattices, electronic energy band structures, phonon dispersion relatons, effective mass theorem, semiclassical equations of motion, and impurity states in semiconductors, band structure and transport properties of selected semiconductors, and connection of quantum theory of solids with quasifermi levels and Boltzmann transport used in device modeling.

Subjects

physics | physics | solid state application | solid state application | quantum model | quantum model | electron | electron | lattice vibration | lattice vibration | electronic transport | electronic transport | heat capacity | heat capacity | elastic properties | elastic properties | cystal lattice | cystal lattice | electronic energy band | electronic energy band | phonon dispersion relatons | phonon dispersion relatons | effective mass theorem | effective mass theorem | motion equation | motion equation | impurity state | impurity state | semiconductor | semiconductor | band structure | band structure | transport properties | transport properties | quantum theory of solids | quantum theory of solids | quasifermi | quasifermi | Boltzmann transport | Boltzmann transport | device modeling | device modeling

License

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1A1182101_283348X019

Description

En Amérique. Navire construit en bois dans Union Square à New York, pour servir d'école aux engagés dans la marine américaine.

Subjects

bleu | manhattan | unionsquare | unitedstatesnavy | usnavy | usn | ussrecruit1917 | ussrecruit | landshiprecruit | cagemasts | cagemast | latticemast | latticemasts | landship | ussreruit | 1917 | navy | training | ship

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12.108 Structure of Earth Materials (MIT) 12.108 Structure of Earth Materials (MIT)

Description

This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets. This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets.

Subjects

Crystal Symmetry | Crystal Symmetry | Point Groups | Point Groups | Space Groups | Space Groups | Crystal Chemistry | Crystal Chemistry | Bonding | Bonding | Electron Diffraction | Electron Diffraction | Crystal lattices | Crystal lattices | Tensor Analysis | Tensor Analysis | Optical Properties | Optical Properties | Elastic Properties | Elastic Properties | Magnetic Properties | Magnetic Properties | Stress | Stress | Strain | Strain

License

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8.333 Statistical Mechanics (MIT) 8.333 Statistical Mechanics (MIT)

Description

8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory. 8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

Subjects

hermodynamics | hermodynamics | entropy | entropy | mehanics | mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions | grand canonical distributions | lattice vibrations | lattice vibrations | ideal gas | ideal gas | photon gas | photon gas | quantum statistical mechanics | quantum statistical mechanics | Fermi systems | Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory | mean-field theory

License

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1A1182101_283348X046

Description

11 novembre 2013. Les cuirassés américains dans les eaux de Marseille. Le cuirassé Vermont.

Subjects

bleu | ship | warship | unitedstatesnavy | usnavy | usn | ussvermontbb20 | bb20 | ussvermont | connecticutclass | predreadnought | predreadnoughtbattleship | battleship | latticemast | latticemasts | cagemast | cagemasts

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8.511 Theory of Solids I (MIT)

Description

This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity.

Subjects

physics of solids | elementary excitations | symmetry | theory of representations | energy bands | excitons | critical points | response functions | interactions in the electron gas | electronic structure of metals | semimetals | semiconductors | insulators | Free electron model | Crystalline lattice | Debye Waller factor | Bravais lattice | Pseudopotential | van Hove singularity | Bloch oscillation | quantization of orbits | de Haas-van Alphen effect | Quantum Hall effect | Electron-electron interaction | Hartree-Fock approximation | Exchange energy for Jellium | Density functional theory | Hubbard model | Electron-phonon coupling | phonons

License

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18.786 Topics in Algebraic Number Theory (MIT) 18.786 Topics in Algebraic Number Theory (MIT)

Description

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants. This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

Subjects

number fields | number fields | dedekind domain | dedekind domain | prime ideal | prime ideal | class group | class group | lattice method | lattice method

License

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3.014 Materials Laboratory (MIT) 3.014 Materials Laboratory (MIT)

Description

This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre

Subjects

electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosion

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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1A1182101_283348XVIII001

Description

A propos des incidents mexico-américains. La flotte américaine quittant le port de New York pour se rendre au Mexique.

Subjects

bleu | semaphore | unitedstatesnavy | usnavy | usn | hudsonriver | sailor | semaphoresignals | newyorkcity | battleship | cagemast | cagemasts | latticemast | latticemasts | sailors

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1A1182101_283348XVIII002

Description

La flotte américaine se rend à Vera Cruz.

Subjects

bleu | unitedstatesnavy | usnavy | usn | warship | warships | battleship | latticemast | cagemast | cagemasts | latticemasts

License

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8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism

Subjects

periodic structure and symmetry of crystals | periodic structure and symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem and band structure | Bloch theorem and band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism | magnetism

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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8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry. This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry.

Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zero modes | zero modes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) and SO(10) | unification in SU(5) and SO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton and baryon number violation | lepton and baryon number violation | nonperturbative (lattice) formulation | nonperturbative (lattice) formulation

License

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3.054 Cellular Solids: Structure, Properties and Applications (MIT) 3.054 Cellular Solids: Structure, Properties and Applications (MIT)

Description

This course reviews the processing and structure of cellular materials as they are created from polymers, metals, ceramics, glasses, and composites, develops models for the mechanical behavior of cellular solids, and shows how the unique properties of honeycombs and foams are exploited in applications such as lightweight structural panels, energy absorption devices and thermal insulation. The applications of cellular solids in medicine include increased fracture risk due to trabecular bone loss in patients with osteoporosis, the development of metal foam coatings for orthopaedic implants, and designing porous scaffolds for tissue engineering that mimic the extracellular matrix. Modelling of cellular materials applied to natural materials and biomimicking is explored. Students taking the gr This course reviews the processing and structure of cellular materials as they are created from polymers, metals, ceramics, glasses, and composites, develops models for the mechanical behavior of cellular solids, and shows how the unique properties of honeycombs and foams are exploited in applications such as lightweight structural panels, energy absorption devices and thermal insulation. The applications of cellular solids in medicine include increased fracture risk due to trabecular bone loss in patients with osteoporosis, the development of metal foam coatings for orthopaedic implants, and designing porous scaffolds for tissue engineering that mimic the extracellular matrix. Modelling of cellular materials applied to natural materials and biomimicking is explored. Students taking the gr

Subjects

honeycombs | honeycombs | foams | foams | lattices | lattices | stress strain | stress strain | elasticity | elasticity | bending compressive collapse stress | bending compressive collapse stress | fracture | fracture | trabecular bone | trabecular bone | osteoporosis | osteoporosis | tissue engineering | tissue engineering | scaffolds | scaffolds | energy absorption devices | energy absorption devices | structural sandwich panels | structural sandwich panels | cellular structures in plants | cellular structures in plants

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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5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

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

Subjects

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

License

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3.014 Materials Laboratory (MIT) 3.014 Materials Laboratory (MIT)

Description

This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre

Subjects

electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosion

License

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3.60 Symmetry, Structure, and Tensor Properties of Materials (MIT) 3.60 Symmetry, Structure, and Tensor Properties of Materials (MIT)

Description

This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity. This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.

Subjects

crystallography | crystallography | rotation | rotation | translation | translation | lattice | lattice | plane | plane | point group | point group | space group | space group | motif | motif | glide plane | glide plane | mirror plane | mirror plane | reflection | reflection | spherical trigonometry | spherical trigonometry | binary compound | binary compound | coordination number | coordination number | ion | ion | crystal structure | crystal structure | tetrahedral | tetrahedral | octahedral | octahedral | packing | packing | monoclinic | monoclinic | triclinic | triclinic | orthorhombic | orthorhombic | cell | cell | screw axis | screw axis | eigenvector | eigenvector | stress | stress | strain | strain | anisotropy | anisotropy | anisotropic | anisotropic | piezoelectric | piezoelectric

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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8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it. This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it.

Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zeromodes | zeromodes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) andSO(10) | unification in SU(5) andSO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton andbaryon number violation | lepton andbaryon number violation | nonperturbative (lattice)formulation | nonperturbative (lattice)formulation

License

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18.318 Topics in Algebraic Combinatorics (MIT) 18.318 Topics in Algebraic Combinatorics (MIT)

Description

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings. The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

Subjects

algebraic combinatorics | algebraic combinatorics | matrix-tree theorem | matrix-tree theorem | linear algebra | linear algebra | commutative algebra | commutative algebra | exterior algebra | exterior algebra | counting faces of simplicial complexes | counting faces of simplicial complexes | tilings | tilings | Young's lattice | Young's lattice | Shannon capacity | Shannon capacity | Fisher inequality | Fisher inequality | Hadamard matrices | Hadamard matrices | f-vectors | f-vectors | Sperner Property | Sperner Property | -Binomial Coeffcients | -Binomial Coeffcients

License

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HUNTINGTON (LOC) HUNTINGTON (LOC)

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libraryofcongress | libraryofcongress | unitedstatesnavy | unitedstatesnavy | usnavy | usnavy | usn | usn | navalaviation | navalaviation | ship | ship | warship | warship | usswestvirginiaacr5 | usswestvirginiaacr5 | usswestvirginia | usswestvirginia | acr5 | acr5 | usswestvirginiaarmoredcruiserno5 | usswestvirginiaarmoredcruiserno5 | armoredcruiserno5 | armoredcruiserno5 | pennsylvaniaclass | pennsylvaniaclass | usshuntingtonca5 | usshuntingtonca5 | usshuntington | usshuntington | ca5 | ca5 | armoredcruiser | armoredcruiser | cruiser | cruiser | cagemast | cagemast | latticemast | latticemast | starsstripes | starsstripes | redcross | redcross

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18.315 Combinatorial Theory: Hyperplane Arrangements (MIT) 18.315 Combinatorial Theory: Hyperplane Arrangements (MIT)

Description

This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.

Subjects

Combinatorial Theory | Combinatorial Theory | Hyperplane Arrangements | Hyperplane Arrangements | Intersection Poset | Intersection Poset | Matroids | Matroids | Geometric Lattices | Geometric Lattices | Broken Circuits | Broken Circuits | Modular Elements | Modular Elements | Supersolvability | Supersolvability | Finite Fields | Finite Fields | Hyperplane | Hyperplane | Arrangements | Arrangements | intersection poset | intersection poset | geometric lattices | geometric lattices | Broken circuits | Broken circuits | modular elements | modular elements | supersolvability | supersolvability | Finite fields | Finite fields

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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5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

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

Subjects

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

License

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

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity. 18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

Subjects

partial differential equation | partial differential equation | hyperbolic equations | hyperbolic equations | dimensional analysis | dimensional analysis | perturbation methods | perturbation methods | hyperbolic systems | hyperbolic systems | diffusion and reaction processes | diffusion and reaction processes | continuum models | continuum models | equilibrium models | equilibrium models | continuous applied mathematics | continuous applied mathematics | traffic flow | traffic flow | fluids | fluids | elasticity | elasticity | granular flows | granular flows | continuum limit | continuum limit | conservation laws | conservation laws | quasi-equilibrium | quasi-equilibrium | kinematic waves | kinematic waves | characteristics | characteristics | simple waves | simple waves | shocks | shocks | diffusion (linear and nonlinear) | diffusion (linear and nonlinear) | numerical solution of wave equations | numerical solution of wave equations | finite differences | finite differences | consistency | consistency | stability | stability | discrete and fast Fourier transforms | discrete and fast Fourier transforms | spectral methods | spectral methods | transforms and series (Fourier | Laplace) | transforms and series (Fourier | Laplace) | sonic booms | sonic booms | Mach cone | Mach cone | caustics | caustics | lattices | lattices | dispersion | dispersion | group velocity | group velocity

License

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

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18.S66 The Art of Counting (MIT) 18.S66 The Art of Counting (MIT)

Description

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment. The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

Subjects

enumerative combinatorics | enumerative combinatorics | finite set | finite set | sum of positive integers | sum of positive integers | bijective proofs | bijective proofs | bijection (one-to-one correspondence) | bijection (one-to-one correspondence) | permutations | permutations | partitions | partitions | Catalan numbers | Catalan numbers | Young tableaux | Young tableaux | lattice paths and tilings | lattice paths and tilings

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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