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21M.380 Music and Technology: Algorithmic and Generative Music (MIT) 21M.380 Music and Technology: Algorithmic and Generative Music (MIT)

Description

Includes audio/video content: AV special element audio. This course examines the history, techniques, and aesthetics of mechanical and computer-aided approaches to algorithmic music composition and generative music systems. Through creative hands-on projects, readings, listening assignments, and lectures, students will explore a variety of historical and contemporary approaches. Diverse tools and systems will be employed, including applications in Python, MIDI, Csound, SuperCollider, and Pure Data. Includes audio/video content: AV special element audio. This course examines the history, techniques, and aesthetics of mechanical and computer-aided approaches to algorithmic music composition and generative music systems. Through creative hands-on projects, readings, listening assignments, and lectures, students will explore a variety of historical and contemporary approaches. Diverse tools and systems will be employed, including applications in Python, MIDI, Csound, SuperCollider, and Pure Data.

Subjects

Music composition | Music composition | music history | music history | music aesthetics | music aesthetics | algorithmic composition | algorithmic composition | generative music | generative music | computer music | computer music | electronic music | electronic music | contemporary music | contemporary music | music synthesis | music synthesis

License

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21W.780 Communicating in Technical Organizations (MIT) 21W.780 Communicating in Technical Organizations (MIT)

Description

This class offers students an opportunity to experiment with various forms and practices of cellphone communication and, most importantly, to propose and develop a semester-long project using advanced A780 cellphones donated by Motorola along with access to J2ME™ source code for programming cellphone applications. Class size is limited. Students in small collaborative groups will propose, implement and report on a semester-long project. This class offers students an opportunity to experiment with various forms and practices of cellphone communication and, most importantly, to propose and develop a semester-long project using advanced A780 cellphones donated by Motorola along with access to J2ME™ source code for programming cellphone applications. Class size is limited. Students in small collaborative groups will propose, implement and report on a semester-long project.

Subjects

communication | communication | contemporary engineering and science professional | contemporary engineering and science professional | analyzing how composition and publication contribute to work management and knowledge production | analyzing how composition and publication contribute to work management and knowledge production | writing specific kinds of documents in a clear style | writing specific kinds of documents in a clear style | communication as organizational process | communication as organizational process | electronic modes such as e-mail and the Internet | electronic modes such as e-mail and the Internet | the informational and social roles of specific document forms | the informational and social roles of specific document forms | writing as collaboration | writing as collaboration | the writing process | the writing process | the elements of style | the elements of style | methods of oral presentation | and communication ethics | methods of oral presentation | and communication ethics | case studies | case studies | writing assignments | writing assignments | oral presentation | oral presentation | methods of oral presentation | and communication ethics | methods of oral presentation | and communication ethics

License

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21M.304 Writing in Tonal Forms II (MIT) 21M.304 Writing in Tonal Forms II (MIT)

Description

Includes audio/video content: AV selected lectures, AV special element audio. This course builds on the composition techniques practiced in 21M.303 Writing in Tonal Forms I. Students undertake further written and analytic exercises in tonal music, including a sonata-form movement for string quartet. Students will also have the opportunity to write short works that experiment with the expanded tonal techniques of the late 19th and early 20th centuries. Musicianship laboratory is required. Includes audio/video content: AV selected lectures, AV special element audio. This course builds on the composition techniques practiced in 21M.303 Writing in Tonal Forms I. Students undertake further written and analytic exercises in tonal music, including a sonata-form movement for string quartet. Students will also have the opportunity to write short works that experiment with the expanded tonal techniques of the late 19th and early 20th centuries. Musicianship laboratory is required.

Subjects

composition | composition | composing | composing | listening | listening | form | form | structure | structure | harmony | harmony | melody | melody | rhythm | rhythm | motif | motif | theme | theme | voicing | voicing | chord | chord | scale | scale | cadence | cadence | tonality | tonality | tonal music | tonal music | atonal music | atonal music | phrasing | phrasing | canon | canon | classical music | classical music | chamber music | chamber music | aesthetics | aesthetics | musical analysis | musical analysis | string quartet | string quartet | prokofiev | prokofiev | sonata form | sonata form | Haydn | Haydn | Mozart | Mozart | Beethoven | Beethoven

License

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21M.303 Writing in Tonal Forms I (MIT) 21M.303 Writing in Tonal Forms I (MIT)

Description

Includes audio/video content: AV special element audio, AV special element video, AV special element audio. Written and analytic exercises based on 18th- and 19th-century small forms and harmonic practice found in music such as the chorale preludes of Bach; minuets and trios of Haydn, Mozart, and Beethoven; and the songs and character pieces of Schubert and Schumann. Musicianship laboratory is required. Includes audio/video content: AV special element audio, AV special element video, AV special element audio. Written and analytic exercises based on 18th- and 19th-century small forms and harmonic practice found in music such as the chorale preludes of Bach; minuets and trios of Haydn, Mozart, and Beethoven; and the songs and character pieces of Schubert and Schumann. Musicianship laboratory is required.

Subjects

composition | composition | composing | composing | listening | listening | form | form | structure | structure | harmony | harmony | melody | melody | rhythm | rhythm | motif | motif | theme | theme | voicing | voicing | chord | chord | scale | scale | cadence | cadence | tonality | tonality | tonal music | tonal music | phrasing | phrasing | canon | canon | classical music | classical music | chamber music | chamber music | aesthetics | aesthetics | musical analysis | musical analysis | romantic music | romantic music | romantic poetry | romantic poetry | lieder | lieder | string quartet | string quartet

License

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3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

The central point of this course is to provide a physical basis that links the structure of materials with their properties, focusing primarily on metals. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals. The central point of this course is to provide a physical basis that links the structure of materials with their properties, focusing primarily on metals. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals.

Subjects

point | point | line and interfacial defects | line and interfacial defects | stereographic projection | stereographic projection | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | growth | growth | particle coarsening | particle coarsening | structure-function relationships | structure-function relationships | interstitial and substitutional solid solutions | interstitial and substitutional solid solutions | processing and structure of metals | processing and structure of metals | strength | strength | stiffness | stiffness | and ductility | and ductility | crystallography | crystallography | phase transformations | phase transformations | microstructural evolution | microstructural evolution | steel | steel | aluminum | aluminum

License

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3.22 Mechanical Behavior of Materials (MIT) 3.22 Mechanical Behavior of Materials (MIT)

Description

Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, fracture and fatigue of materials including crystalline and amorphous metals, semiconductors, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. We will cover special topics in mechanical behavior for material systems of your choice, with reference to current research and publications. Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, fracture and fatigue of materials including crystalline and amorphous metals, semiconductors, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. We will cover special topics in mechanical behavior for material systems of your choice, with reference to current research and publications.

Subjects

Phenomenology | Phenomenology | mechanical behavior | mechanical behavior | material structure | material structure | deformation | deformation | failure | failure | elasticity | elasticity | viscoelasticity | viscoelasticity | plasticity | plasticity | creep | creep | fracture | fracture | fatigue | fatigue | metals | metals | semiconductors | semiconductors | ceramics | ceramics | polymers | polymers | microstructure | microstructure | composition | composition | semiconductor diodes | semiconductor diodes | thin films | thin films | carbon nanotubes | carbon nanotubes | battery materials | battery materials | superelastic alloys | superelastic alloys | defect nucleation | defect nucleation | student projects | student projects | viral capsides | viral capsides

License

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3.225 Electronic and Mechanical Properties of Materials (MIT) 3.225 Electronic and Mechanical Properties of Materials (MIT)

Description

This course covers the fundamental concepts that determine the electrical, optical, magnetic and mechanical properties of metals, semiconductors, ceramics and polymers. The roles of bonding, structure (crystalline, defect, energy band and microstructure) and composition in influencing and controlling physical properties are discussed. Also included are case studies drawn from a variety of applications: semiconductor diodes and optical detectors, sensors, thin films, biomaterials, composites and cellular materials, and others. This course covers the fundamental concepts that determine the electrical, optical, magnetic and mechanical properties of metals, semiconductors, ceramics and polymers. The roles of bonding, structure (crystalline, defect, energy band and microstructure) and composition in influencing and controlling physical properties are discussed. Also included are case studies drawn from a variety of applications: semiconductor diodes and optical detectors, sensors, thin films, biomaterials, composites and cellular materials, and others.

Subjects

metals | metals | semiconductors | semiconductors | ceramics | ceramics | polymers | polymers | bonding | bonding | structure | structure | energy band | energy band | microstructure | microstructure | composition | composition | semiconductor diodes | semiconductor diodes | optical detectors | optical detectors | sensors | sensors | thin films | thin films | biomaterials | biomaterials | cellular materials | cellular materials | magnetism | magnetism | polarity | polarity | viscoelasticity | viscoelasticity | plasticity | plasticity | fracture | fracture | materials selection | materials selection

License

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21M.342 Composing for Jazz Orchestra (MIT) 21M.342 Composing for Jazz Orchestra (MIT)

Description

Includes audio/video content: AV selected lectures, AV special element audio. This class explores composition and arrangement for the large jazz ensemble from 1920s foundations to current postmodern practice. Consideration given to a variety of styles and to the interaction of improvisation and composition. Study of works by Basie, Ellington, Evans, Gillespie, Golson, Mingus, Morris, Nelson, Williams, and others. Open rehearsals, workshops, and performances of student compositions by the MIT Festival Jazz Ensemble and the Aardvark Jazz Orchestra.   Includes audio/video content: AV selected lectures, AV special element audio. This class explores composition and arrangement for the large jazz ensemble from 1920s foundations to current postmodern practice. Consideration given to a variety of styles and to the interaction of improvisation and composition. Study of works by Basie, Ellington, Evans, Gillespie, Golson, Mingus, Morris, Nelson, Williams, and others. Open rehearsals, workshops, and performances of student compositions by the MIT Festival Jazz Ensemble and the Aardvark Jazz Orchestra.  

Subjects

jazz band | jazz band | large ensemble jazz | large ensemble jazz | modern jazz | modern jazz | contemporary jazz | contemporary jazz | big band | big band | swing | swing | Duke Ellington | Duke Ellington | George Russell | George Russell | Bill Lowe | Bill Lowe | Mulatu Astatke | Mulatu Astatke | Ethiojazz | Ethiojazz | Ethio-jazz | Ethio-jazz | ethiopian jazz | ethiopian jazz | Ethiopiques | Ethiopiques | Either-Orchestra | Either-Orchestra | Russ Gershon | Russ Gershon | Aardvark Jazz Orchestra | Aardvark Jazz Orchestra | Gil Evans | Gil Evans | Miles Davis | Miles Davis | Birth of the Cool | Birth of the Cool | Steve Lajoie | Steve Lajoie | jazz arranging | jazz arranging | jazz composition | jazz composition | improvisation | improvisation | Walter Thompson | Walter Thompson | Soundpainting | Soundpainting

License

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18.335J Introduction to Numerical Methods (MIT) 18.335J Introduction to Numerical Methods (MIT)

Description

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®. This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

Subjects

numerical linear algebra | numerical linear algebra | linear systems | linear systems | eigenvalue decomposition | eigenvalue decomposition | QR/SVD factorization | QR/SVD factorization | numerical algorithms | numerical algorithms | IEEE floating point standard | IEEE floating point standard | sparse matrices | sparse matrices | structured matrices | structured matrices | preconditioning | preconditioning | linear algebra software | linear algebra software | Matlab | Matlab

License

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21M.361 Composing with Computers I (Electronic Music Composition) (MIT) 21M.361 Composing with Computers I (Electronic Music Composition) (MIT)

Description

Includes audio/video content: AV special element audio. This class explores sound and what can be done with it. Sources are recorded from students' surroundings - sampled and electronically generated (both analog and digital). Assignments include composing with the sampled sounds, feedback, and noise, using digital signal processing (DSP), convolution, algorithms, and simple mixing. The class focuses on sonic and compositional aspects rather than technology, math, or acoustics, though these are examined in varying detail. Students complete weekly composition and listening assignments; material for the latter is drawn from sound art, experimental electronica, conventional and non-conventional classical electronic works, popular music, and previous students' compositions. Includes audio/video content: AV special element audio. This class explores sound and what can be done with it. Sources are recorded from students' surroundings - sampled and electronically generated (both analog and digital). Assignments include composing with the sampled sounds, feedback, and noise, using digital signal processing (DSP), convolution, algorithms, and simple mixing. The class focuses on sonic and compositional aspects rather than technology, math, or acoustics, though these are examined in varying detail. Students complete weekly composition and listening assignments; material for the latter is drawn from sound art, experimental electronica, conventional and non-conventional classical electronic works, popular music, and previous students' compositions.

Subjects

computer music | computer music | sound | sound | music | music | audio | audio | listening | listening | electronic music | electronic music | new music | new music | electronica | electronica | sound art | sound art | noise | noise | noise music | noise music | avant-garde | avant-garde | contemporary music | contemporary music | modern music | modern music | composition | composition | recording | recording | music production | music production | recording studio | recording studio | audio software | audio software | recording software | recording software | sampling | sampling | synthesis | synthesis | audio engineering | audio engineering | mixing | mixing | Radiohead | Radiohead

License

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3.024 Electronic, Optical and Magnetic Properties of Materials (MIT) 3.024 Electronic, Optical and Magnetic Properties of Materials (MIT)

Description

This course describes how electronic, optical and magnetic properties of materials originate from their electronic and molecular structure and how these properties can be designed for particular applications. It offers experimental exploration of the electronic, optical and magnetic properties of materials through hands-on experimentation and practical materials examples. This course describes how electronic, optical and magnetic properties of materials originate from their electronic and molecular structure and how these properties can be designed for particular applications. It offers experimental exploration of the electronic, optical and magnetic properties of materials through hands-on experimentation and practical materials examples.

Subjects

electronic properites | electronic properites | optical properties | optical properties | magnetic properties | magnetic properties | materials | materials | Hamilton approach | Hamilton approach | Schrödinger’s Equation | Schrödinger’s Equation | mechanics | mechanics | quantum mechanics | quantum mechanics | spectral decomposition | spectral decomposition | symmetries | symmetries | angular momentum | angular momentum | periodic potentials | periodic potentials | band diagrams | band diagrams | Fermi | Fermi | Fermi-Dirac | Fermi-Dirac | p-n junction | p-n junction | light emitting diodes | light emitting diodes | wave optics | wave optics | electromagnetic waves | electromagnetic waves | magnetization | magnetization | semiconductor devices | semiconductor devices | Maxwell's equations | Maxwell's equations | photonic bands | photonic bands

License

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3.21 Kinetic Processes in Materials (MIT) 3.21 Kinetic Processes in Materials (MIT)

Description

This course presents a unified treatment of phenomenological and atomistic kinetic processes in materials. It provides the foundation for the advanced understanding of processing, microstructural evolution, and behavior for a broad spectrum of materials. The course emphasizes analysis and development of rigorous comprehension of fundamentals. Topics include: irreversible thermodynamics; diffusion; nucleation; phase transformations; fluid and heat transport; morphological instabilities; gas-solid, liquid-solid, and solid-solid reactions. This course presents a unified treatment of phenomenological and atomistic kinetic processes in materials. It provides the foundation for the advanced understanding of processing, microstructural evolution, and behavior for a broad spectrum of materials. The course emphasizes analysis and development of rigorous comprehension of fundamentals. Topics include: irreversible thermodynamics; diffusion; nucleation; phase transformations; fluid and heat transport; morphological instabilities; gas-solid, liquid-solid, and solid-solid reactions.

Subjects

Thermodynamics | Thermodynamics | field | field | gradient | gradient | continuity equation | continuity equation | irreversible thermodynamics | irreversible thermodynamics | entropy | entropy | Onsager's symmetry principle | Onsager's symmetry principle | diffusion | diffusion | capillarity | capillarity | stress | stress | diffusion equation | diffusion equation | crystal | crystal | jump process | jump process | jump rate | jump rate | diffusivity | diffusivity | interstitial | interstitial | Kroger-Vink | Kroger-Vink | grain boundary | grain boundary | isotropic | isotropic | Rayleigh instability | Rayleigh instability | Gibbs-Thomson | Gibbs-Thomson | particle coarsening | particle coarsening | growth kinetics | growth kinetics | phase transformation | phase transformation | nucleation | nucleation | spinoldal decomposition | spinoldal decomposition

License

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12.742 Marine Chemistry (MIT) 12.742 Marine Chemistry (MIT)

Description

Includes audio/video content: AV selected lectures. This course is an introduction to chemical oceanography. It describes reservoir models and residence time, major ion composition of seawater, inputs to and outputs from the ocean via rivers, the atmosphere, and the sea floor. Biogeochemical cycling within the oceanic water column and sediments, emphasizing the roles played by the formation, transport, and alteration of oceanic particles and the effects that these processes have on seawater composition. Cycles of carbon, nitrogen, phosphorus, oxygen, and sulfur. Uptake of anthropogenic carbon dioxide by the ocean. Material presented through lectures and student-led presentation and discussion of recent papers. Includes audio/video content: AV selected lectures. This course is an introduction to chemical oceanography. It describes reservoir models and residence time, major ion composition of seawater, inputs to and outputs from the ocean via rivers, the atmosphere, and the sea floor. Biogeochemical cycling within the oceanic water column and sediments, emphasizing the roles played by the formation, transport, and alteration of oceanic particles and the effects that these processes have on seawater composition. Cycles of carbon, nitrogen, phosphorus, oxygen, and sulfur. Uptake of anthropogenic carbon dioxide by the ocean. Material presented through lectures and student-led presentation and discussion of recent papers.

Subjects

chemical oceanography | chemical oceanography | biogeochemical cycling | biogeochemical cycling | water column processes | water column processes | ocean particles | ocean particles | seawater composition | seawater composition | ocean particle transport | ocean particle transport | carbon | carbon | oxygen | oxygen | nitrogen | nitrogen | phosphorus | phosphorus | sulfur | sulfur | carbon dioxide | carbon dioxide | sediment chemistry | sediment chemistry

License

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3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications. This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications.

Subjects

1- | 2- and 3D defects | 1- | 2- and 3D defects | second phases | second phases | mechanical | electromagnetic and chemical behavior of metals and alloys | mechanical | electromagnetic and chemical behavior of metals and alloys | point | line and interfacial defects | point | line and interfacial defects | structural transformations | structural transformations | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | growth | growth | particle coarsening | particle coarsening | structure-function relationships | structure-function relationships | grain size | grain size | interstitial and substitutional solid solutions | interstitial and substitutional solid solutions | second-phase particles | second-phase particles | microelectronic circuitry | microelectronic circuitry | magnetic memory | magnetic memory | drug delivery applications | drug delivery applications | 3.40 | 3.40 | 22.71 | 22.71

License

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18.409 Algorithmic Aspects of Machine Learning (MIT) 18.409 Algorithmic Aspects of Machine Learning (MIT)

Description

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems. This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

Subjects

Machine learning | Machine learning | nonnegative matrix factorization | nonnegative matrix factorization | tensor decomposition | tensor decomposition | tensor rank | tensor rank | border rank | border rank | sparse coding | sparse coding | sparse recovery | sparse recovery | learning mixture model | learning mixture model | matrix completion | matrix completion

License

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3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

Discusses structure-property relationships in metallic alloys selected to illustrate some basic concepts of physical metallurgy and alloy design. Fundamentals of annealing, spinodal decomposition, nucleation, growth, and particle coarsening. Concentrates on structure, structure formation, and structure-properties relationships. Also considers structural features: grain size, interstitial and substitutional solutes, precipitates, second-phase particles, and eutectoids. Examples from advanced structural alloys and low-dimensional alloys for magnetic recording media and integrated circuits. Discusses structure-property relationships in metallic alloys selected to illustrate some basic concepts of physical metallurgy and alloy design. Fundamentals of annealing, spinodal decomposition, nucleation, growth, and particle coarsening. Concentrates on structure, structure formation, and structure-properties relationships. Also considers structural features: grain size, interstitial and substitutional solutes, precipitates, second-phase particles, and eutectoids. Examples from advanced structural alloys and low-dimensional alloys for magnetic recording media and integrated circuits.

Subjects

metallic alloys | metallic alloys | physical metallurgy | physical metallurgy | alloy design | alloy design | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | particle coarsening | particle coarsening | structure | structure | structure formation | structure formation | structure-properties relationships | structure-properties relationships | structural features | structural features | 3.40 | 3.40 | 22.71 | 22.71

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18.705 Commutative Algebra (MIT) 18.705 Commutative Algebra (MIT)

Description

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory. In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

Subjects

rings | rings | ideals | ideals | modules | modules | chain conditions | chain conditions | integral | integral | localization | localization | decomposition | decomposition | dedekind domain | dedekind domain | tensor | tensor | dimension theory | dimension theory | Zorn's lemma | Zorn's lemma | hilbert theorem | hilbert theorem | DVR | DVR | normalization | normalization | artin ring | artin ring | nakayama's lemma | nakayama's lemma | zerodivisors | zerodivisors | noether | noether | nullsetellensatz | nullsetellensatz

License

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18.785 Number Theory I (MIT) 18.785 Number Theory I (MIT)

Description

This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry. This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

Subjects

number theory | number theory | Dedekind domains | Dedekind domains | decomposition of prime ideals | decomposition of prime ideals | local field | local field | ideal class groups | ideal class groups | Dirichlet's unit theorm | Dirichlet's unit theorm | ring of adeles | ring of adeles | group of ideles | group of ideles | zeta functions | zeta functions | L-functions | L-functions | Chebotarev density theorem | Chebotarev density theorem | Sato-Tate theorem | Sato-Tate theorem

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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21G.301 French I (MIT) 21G.301 French I (MIT)

Description

21G.301/351 offers an introduction to the French language and culture with an emphasis on the acquisition of vocabulary and grammatical concepts through active communication. The course is conducted entirely in French, and students interact in French with their classmates from the very beginning. They also receive exposure to the language via a variety of authentic sources such as the Internet, audio, video and printed materials which help them develop cultural awareness as well as linguistic proficiency. There is a coordinated language lab program.This course is taught in rotation by the following instructors: Laura Ceia-Minjares, Cathy Culot, Gilberte Furstenberg, and Johann Sadock. 21G.301/351 offers an introduction to the French language and culture with an emphasis on the acquisition of vocabulary and grammatical concepts through active communication. The course is conducted entirely in French, and students interact in French with their classmates from the very beginning. They also receive exposure to the language via a variety of authentic sources such as the Internet, audio, video and printed materials which help them develop cultural awareness as well as linguistic proficiency. There is a coordinated language lab program.This course is taught in rotation by the following instructors: Laura Ceia-Minjares, Cathy Culot, Gilberte Furstenberg, and Johann Sadock.

Subjects

French | French | introduction | introduction | understand | understand | speak | speak | write | write | present | present | future | future | past | past | tense | tense | family | family | food | food | travel | travel | hobbies | hobbies | activities | activities | environment | environment | context | context | compositions | compositions | Francophone | Francophone | customs | customs | history | history | civilization | civilization | 21F.301 | 21F.301 | 21F.351 | 21F.351

License

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

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Mathematical Methods II Mathematical Methods II

Description

This course consists of a introduction to linear algebra. This course consists of a introduction to linear algebra.

Subjects

Bachelor in Statistics and Business | Bachelor in Statistics and Business | Algebra | Algebra | Prerequisites | Prerequisites | Systems of linear equations | Systems of linear equations | Eigenvalues and eigenvectors | Eigenvalues and eigenvectors | General information | General information | Orthogonality and least-square problems | Orthogonality and least-square problems | Singular value decomposition | Singular value decomposition | stica y Empresa | stica y Empresa | Real vector spaces | Real vector spaces | Matrices and determinants | Matrices and determinants | Diagonalization | Diagonalization | 2012 | 2012

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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18.786 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 theory

License

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

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18.117 Topics in Several Complex Variables (MIT) 18.117 Topics in Several Complex Variables (MIT)

Description

This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed. This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed.

Subjects

Harmonic theory | Harmonic theory | complex manifolds | complex manifolds | Hodge decomposition theorem | Hodge decomposition theorem | Hard Lefschetz theorem | Hard Lefschetz theorem | Vanishing theorems | Vanishing theorems | deformation of complex manifolds | deformation of complex manifolds | uniformization of complex manifolds | uniformization of complex manifolds

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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11.479J Water and Sanitation Infrastructure in Developing Countries (MIT) 11.479J Water and Sanitation Infrastructure in Developing Countries (MIT)

Description

This course deals with the principles of infrastructure planning in developing countries, with a focus on appropriate and sustainable technologies for water and sanitation. It also incorporates technical, socio-cultural, public health, and economic factors into the planning and design of water and sanitation systems. Upon completion, students will be able to plan simple, yet reliable, water supply and sanitation systems for developing countries that are compatible with local customs and available human and material resources. Graduate and upper division students from any department who are interested in international development at the grassroots level are encouraged to participate in this interdisciplinary subject. Acknowledgment This course was jointly developed by Earthea Nance and Sus This course deals with the principles of infrastructure planning in developing countries, with a focus on appropriate and sustainable technologies for water and sanitation. It also incorporates technical, socio-cultural, public health, and economic factors into the planning and design of water and sanitation systems. Upon completion, students will be able to plan simple, yet reliable, water supply and sanitation systems for developing countries that are compatible with local customs and available human and material resources. Graduate and upper division students from any department who are interested in international development at the grassroots level are encouraged to participate in this interdisciplinary subject. Acknowledgment This course was jointly developed by Earthea Nance and Sus

Subjects

chemical oceanography | chemical oceanography | biogeochemical cycling | biogeochemical cycling | water column processes | water column processes | ocean particles | ocean particles | seawater composition | seawater composition | ocean particle transport | ocean particle transport | carbon | carbon | oxygen | oxygen | nitrogen | nitrogen | phosphorus | phosphorus | sulfur | sulfur | carbon dioxide | carbon dioxide | sediment chemistry | sediment chemistry

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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21G.106 Chinese VI (Regular): Discovering Chinese Cultures and Societies (MIT) 21G.106 Chinese VI (Regular): Discovering Chinese Cultures and Societies (MIT)

Description

This course is the continuation of 21G.105. It is designed to further help students develop sophisticated conversational, reading and writing skills by combining traditional textbook material with their own explorations of Chinese speaking societies, using the human, literary, and electronic resources available at MIT and in the Boston area. Some special features of Chinese society, its culture, its customs and habits, its history, and the psychology of its people are introduced. The class consists of reading, discussion, composition, network exploration, and conversational practice. The course is conducted in Mandarin. This course is the continuation of 21G.105. It is designed to further help students develop sophisticated conversational, reading and writing skills by combining traditional textbook material with their own explorations of Chinese speaking societies, using the human, literary, and electronic resources available at MIT and in the Boston area. Some special features of Chinese society, its culture, its customs and habits, its history, and the psychology of its people are introduced. The class consists of reading, discussion, composition, network exploration, and conversational practice. The course is conducted in Mandarin.

Subjects

language | language | china | china | mandarin | mandarin | reading | reading | writing | writing | speaking | speaking | comprehension | comprehension | culture | culture | society | society | conversational skills | conversational skills | reading skills | reading skills | Chinese speaking societies | Chinese speaking societies | writing skills | writing skills | Chinese society | Chinese society | Chinese culture | Chinese culture | Chinese customs | Chinese customs | Chinese history | Chinese history | discussion | discussion | composition | composition | network exploration | network exploration

License

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

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Society (MIT) Society (MIT)

Description

This course is the continuation of 21G.104/108. It is designed to further help students develop sophisticated conversational, reading and writing skills by combining traditional textbook material with their own explorations of Chinese speaking societies, using the human, literary, and electronic resources available at in the Boston area. Some of special features of Chinese society, its culture, its customs and habits, its history, and the psychology of its people are be introduced. The class consists of reading, discussion, composition, network exploration, and conversational practice. The course is conducted in Mandarin. This course is the continuation of 21G.104/108. It is designed to further help students develop sophisticated conversational, reading and writing skills by combining traditional textbook material with their own explorations of Chinese speaking societies, using the human, literary, and electronic resources available at in the Boston area. Some of special features of Chinese society, its culture, its customs and habits, its history, and the psychology of its people are be introduced. The class consists of reading, discussion, composition, network exploration, and conversational practice. The course is conducted in Mandarin.

Subjects

chinese | chinese | language | language | mandarin | mandarin | reading | reading | conversation | conversation | writing | writing | culture | culture | china | china | society | society | custom | custom | conversational skills | conversational skills | reading skills | reading skills | Chinese speaking societies | Chinese speaking societies | writing skills | writing skills | Chinese society | Chinese society | Chinese culture | Chinese culture | Chinese customs | Chinese customs | Chinese history | Chinese history | discussion | discussion | composition | composition | network exploration | network exploration

License

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

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