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15.082J Network Optimization (MIT) 15.082J Network Optimization (MIT)

Description

15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. 15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem.Subjects

network flows | network flows | extensions | extensions | network flow problems | network flow problems | transportation | transportation | logistics | logistics | manufacturing | manufacturing | computer science | computer science | project management | project management | finance | finance | the shortest path problem | the shortest path problem | the maximum flow problem | the maximum flow problem | the minimum cost flow problem | the minimum cost flow problem | the multi-commodity flow problem | the multi-commodity flow problem | communication | communication | systems | systems | applications | applications | efficiency | efficiency | algorithms | algorithms | traffic | traffic | equilibrium | equilibrium | design | design | mplementation | mplementation | linear programming | linear programming | implementation | implementation | computer | computer | science | science | linear | linear | programming | programming | network | network | flow | flow | problems | problems | project | project | management | management | maximum | maximum | minimum | minimum | cost | cost | multi-commodity | multi-commodity | shortest | shortest | path | path | 15.082 | 15.082 | 6.855 | 6.855License

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

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This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Subjects

advection equation | advection equation | heat equation | heat equation | wave equation | wave equation | Airy equation | Airy equation | convection-diffusion problems | convection-diffusion problems | KdV equation | KdV equation | hyperbolic conservation laws | hyperbolic conservation laws | Poisson equation | Poisson equation | Stokes problem | Stokes problem | Navier-Stokes equations | Navier-Stokes equations | interface problems | interface problems | consistency | consistency | stability | stability | convergence | convergence | Lax equivalence theorem | Lax equivalence theorem | error analysis | error analysis | Fourier approaches | Fourier approaches | staggered grids | staggered grids | shocks | shocks | front propagation | front propagation | preconditioning | preconditioning | multigrid | multigrid | Krylov spaces | Krylov spaces | saddle point problems | saddle point problems | finite differences | finite differences | finite volumes | finite volumes | finite elements | finite elements | ENO/WENO | ENO/WENO | spectral methods | spectral methods | projection approaches for incompressible ows | projection approaches for incompressible ows | level set methods | level set methods | particle methods | particle methods | direct and iterative methods | direct and iterative methodsLicense

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 metadataón a la Filosofía ón a la Filosofía

Description

La asignatura plantea de manera sistemática algunas de las cuestiones que recorren la historia de la filosofía, como problemas tradicionales, que, no obstante, alcanzan nuestro presente. Por tanto, se puede considerar una asignatura básica para comenzar a comprender los fundamentos de la epistemología, le metafísica, la ética, la política o la antropología filosófica. Sin embargo, el abordaje de estas cuestiones abstractas se hará partiendo de la que puede considerarse la figura fundacional de la filosofía: Sócrates. constituye un foco de interés en el contexto de un life-long training, tal como se manifiesta en la permanente demanda de este tipo de estudios en los cursos de educación permanente, en todos los niveles. En tercer lugar, enseñar a leer filosofía, a buscar las La asignatura plantea de manera sistemática algunas de las cuestiones que recorren la historia de la filosofía, como problemas tradicionales, que, no obstante, alcanzan nuestro presente. Por tanto, se puede considerar una asignatura básica para comenzar a comprender los fundamentos de la epistemología, le metafísica, la ética, la política o la antropología filosófica. Sin embargo, el abordaje de estas cuestiones abstractas se hará partiendo de la que puede considerarse la figura fundacional de la filosofía: Sócrates. constituye un foco de interés en el contexto de un life-long training, tal como se manifiesta en la permanente demanda de este tipo de estudios en los cursos de educación permanente, en todos los niveles. En tercer lugar, enseñar a leer filosofía, a buscar lasSubjects

El problema del escepticismo | El problema del escepticismo | El conocimiento y el amor | El conocimiento y el amor | Humanidades | Humanidades | El problema del bien | El problema del bien | El problema mente/cuerpo | El problema mente/cuerpo | ócrates | ócrates | ía | ía | El problema del conocimiento | El problema del conocimiento | La vida examinada | La vida examinada | ófico | ófico | 2012 | 2012 | Filosofia | FilosofiaLicense

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See all metadata16.346 Astrodynamics (MIT) 16.346 Astrodynamics (MIT)

Description

Includes audio/video content: AV selected lectures. This course covers the fundamentals of astrodynamics, focusing on the two-body orbital initial-value and boundary-value problems with applications to space vehicle navigation and guidance for lunar and planetary missions, including both powered flight and midcourse maneuvers. Other topics include celestial mechanics, Kepler's problem, Lambert's problem, orbit determination, multi-body methods, mission planning, and recursive algorithms for space navigation. Selected applications from the Apollo, Space Shuttle, and Mars exploration programs are also discussed. Includes audio/video content: AV selected lectures. This course covers the fundamentals of astrodynamics, focusing on the two-body orbital initial-value and boundary-value problems with applications to space vehicle navigation and guidance for lunar and planetary missions, including both powered flight and midcourse maneuvers. Other topics include celestial mechanics, Kepler's problem, Lambert's problem, orbit determination, multi-body methods, mission planning, and recursive algorithms for space navigation. Selected applications from the Apollo, Space Shuttle, and Mars exploration programs are also discussed.Subjects

space navigation | space navigation | two body problem | two body problem | boundary value problem | boundary value problem | Kepler | Kepler | astrodynamics | astrodynamics | orbital transfer | orbital transfer | satellite | satellite | hyperbolic orbits | hyperbolic orbits | planetary flybys | planetary flybys | hypergeometric functions | hypergeometric functions | flight guidance | flight guidance | three body problem | three body problem | Clohessy-Wiltshire equation | Clohessy-Wiltshire equation | Hodograph plane | Hodograph plane | Battin-vaughan formulation | Battin-vaughan formulation | atmospheric drag | atmospheric drag | disturbing function | disturbing functionLicense

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

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This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications. This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.Subjects

diffusion | diffusion | elliptic | elliptic | hyperbolic | hyperbolic | partial differential equation | partial differential equation | Initial and boundary value problems for ordinary differential equations | Initial and boundary value problems for ordinary differential equations | Sturm-Liouville theory and eigenfunction expansions | Sturm-Liouville theory and eigenfunction expansions | initial value problems | initial value problems | wave equation;heat equation | wave equation;heat equation | Dirichlet problem | Dirichlet problem | Laplace operator and potential theory | Laplace operator and potential theory | Black-Scholes equation | Black-Scholes equation | water waves | water waves | scalar conservation laws | scalar conservation laws | first order equations | first order 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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See all metadata15.082J Network Optimization (MIT)

Description

15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem.Subjects

network flows | extensions | network flow problems | transportation | logistics | manufacturing | computer science | project management | finance | the shortest path problem | the maximum flow problem | the minimum cost flow problem | the multi-commodity flow problem | communication | systems | applications | efficiency | algorithms | traffic | equilibrium | design | mplementation | linear programming | implementation | computer | science | linear | programming | network | flow | problems | project | management | maximum | minimum | cost | multi-commodity | shortest | path | 15.082 | 6.855License

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 metadata18.335J Introduction to Numerical Methods (MIT) 18.335J Introduction to Numerical Methods (MIT)

Description

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems. The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.Subjects

linear algebra | linear algebra | ordinary differential equations | ordinary differential equations | linear systems of equations | linear systems of equations | least square problems | least square problems | eigenvalue problems | eigenvalue problems | singular value problems | singular value problemsLicense

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

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This course analyzes initial and boundary value problems for ordinary differential equations and the wave and heat equation in one space dimension. It also covers the Sturm-Liouville theory and eigenfunction expansions, as well as the Dirichlet problem for Laplace's operator and potential theory. This course analyzes initial and boundary value problems for ordinary differential equations and the wave and heat equation in one space dimension. It also covers the Sturm-Liouville theory and eigenfunction expansions, as well as the Dirichlet problem for Laplace's operator and potential theory.Subjects

Initial and boundary value problems for ordinary differential equations | Initial and boundary value problems for ordinary differential equations | Sturm-Liouville theory and eigenfunction expansions | Sturm-Liouville theory and eigenfunction expansions | Initial value problems for the wave equation and heat equation | Initial value problems for the wave equation and heat equation | The Dirichlet problem for Laplace's operator and potential theory | The Dirichlet problem for Laplace's operator and potential 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 http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.856J Randomized Algorithms (MIT) 6.856J Randomized Algorithms (MIT)

Description

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms. This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.Subjects

Randomized Algorithms | Randomized Algorithms | algorithms | algorithms | efficient in time and space | efficient in time and space | randomization | randomization | computational problems | computational problems | data structures | data structures | graph algorithms | graph algorithms | optimization | optimization | geometry | geometry | Markov chains | Markov chains | sampling | sampling | estimation | estimation | geometric algorithms | geometric algorithms | parallel and distributed algorithms | parallel and distributed algorithms | parallel and ditributed algorithm | parallel and ditributed algorithm | parallel and distributed algorithm | parallel and distributed algorithm | random sampling | random sampling | random selection of witnesses | random selection of witnesses | symmetry breaking | symmetry breaking | randomized computational models | randomized computational models | hash tables | hash tables | skip lists | skip lists | minimum spanning trees | minimum spanning trees | shortest paths | shortest paths | minimum cuts | minimum cuts | convex hulls | convex hulls | linear programming | linear programming | fixed dimension | fixed dimension | arbitrary dimension | arbitrary dimension | approximate counting | approximate counting | parallel algorithms | parallel algorithms | online algorithms | online algorithms | derandomization techniques | derandomization techniques | probabilistic analysis | probabilistic analysis | computational number theory | computational number theory | simplicity | simplicity | speed | speed | design | design | basic probability theory | basic probability theory | application | application | randomized complexity classes | randomized complexity classes | game-theoretic techniques | game-theoretic techniques | Chebyshev | Chebyshev | moment inequalities | moment inequalities | limited independence | limited independence | coupon collection | coupon collection | occupancy problems | occupancy problems | tail inequalities | tail inequalities | Chernoff bound | Chernoff bound | conditional expectation | conditional expectation | probabilistic method | probabilistic method | random walks | random walks | algebraic techniques | algebraic techniques | probability amplification | probability amplification | sorting | sorting | searching | searching | combinatorial optimization | combinatorial optimization | approximation | approximation | counting problems | counting problems | distributed algorithms | distributed algorithms | 6.856 | 6.856 | 18.416 | 18.416License

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 metadataReadme file for Introduction to Artificial Intelligence

Description

This readme file contains details of links to all the Introduction to Artificial Intelligence module's material held on Jorum and information about the module as well.Subjects

ukoer | evolutionary algorithm lecture | algorithm tutorial | genetic algorithm lecture | genetic algorithm example | evolutionary computation tutorial | artificial intelligence lecture | artificial intelligence tutorial | random processes reading material | semantic web reading material | neural networks video | evolutionary computation test | artificial intelligence test | knowledge representation test | neural networks test | evolutionary algorithm | genetic computation | genetic programming | evolutionary computation | artificial intelligence | introduction to artificial intelligence | search | problem solving | revision | knowledge representation | semantic web | neural network | neural networks | artificial neural networks | swarm intelligence | collective intelligence | robot societies | genetic computation lecture | genetic programming lecture | evolutionary computation lecture | introduction to artificial intelligence lecture | evolutionary algorithm tutorial | genetic computation tutorial | genetic programming tutorial | introduction to artificial intelligence tutorial | evolutionary algorithm example | genetic computation example | genetic programming example | evolutionary computation example | artificial intelligence example | introduction to artificial intelligence example | search lecture | problem solving lecture | search tutorial | problem solving tutorial | search example | problem solving example | revision reading material | search reading material | artificial intelligence reading material | introduction to artificial intelligence reading material | revision lecture | knowledge representation lecture | semantic web lecture | knowledge representation practical | semantic web practical | artificial intelligence practical | introduction to artificial intelligence practical | knowledge representation reading material | knowledge representation notes | semantic web notes | artificial intelligence notes | introduction to artificial intelligence notes | neural network lecture | neural networks lecture | artificial neural networks lecture | neural network reading material | neural networks reading material | artificial neural networks reading material | neural network practical | neural networks practical | artificial neural networks practical | neural network viewing material | neural networks viewing material | artificial neural networks viewing material | artificial intelligence viewing material | introduction to artificial intelligence viewing material | swarm intelligence lecture | collective intelligence lecture | robot societies lecture | swarm intelligence tutorial | collective intelligence tutorial | robot societies tutorial | evolutionary algorithm test | genetic computation test | genetic programming test | introduction to artificial intelligence test | search test | problem solving test | semantic web test | neural network test | artificial neural networks test | g700 | ai | g700 lecture | ai lecture | g700 tutorial | ai tutorial | g700 example | ai example | g700 reading material | ai reading material | g700 practical | ai practical | g700 notes | ai notes | g700 viewing material | ai viewing material | g700 test | ai test | Computer science | I100License

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See all metadataReadme file for Introduction to OO Programming in Java

Description

This readme file contains details of links to all the Introduction to OO Programming in Java module's material held on Jorum and information about the module as well.Subjects

ukoer | programming task guide | programming lecture | programming reading material | software design reading material | classes guide | libraries lecture | classes reading material | classes visual aid | software objects guide | graphics reading material | attributes reading material | attributes visual guide | naming conventions reading material | code reading material | java keywords reading material | variables visual guide | arithmetic reading material | java assignment | making decisions task guide | making decisions lecture | making decisions reading material | boolean expressions visual guide | repetition reading material | while loops visual guide | methods reading material | methods practical | access modifiers reading material | objects reading material | classes assignment | classes practical | child classes task guide | inheritance task guide | extending classes lecture | inheritance reading material | inheritance visual guide | inheritance practical | graphics task guide | awt reading material | graphics visual aid | awt class library reading material | event-driven programming reading material | scrollbars reading material | reflective practice visual guide | mobile phone task guide | mobile phone lecture | fixed repitition reading material | fixed repitition visual guide | mobile phone library reading material | mobile phone reading material | arrays task guide | arrays lecture | arrays reading material | arrays visual guide | creating software objects reading material | software objects visual guide | java practical | generic array list task guide | overriding methods reading material | menu and switch task guide | multi-way decisions reading material | multi-way decisions visual guide | searching task guide | searching lecture | searching reading material | software quality task guide | software quality lecture | software quality reading material | programming assignment | applet reading material | classes visual guide | object-oriented programming | object-oriented | programming | java | problem solving | java program | software design | programming languages | computers | class task guide | class reading material | class assignment | class practical | java classes | variables | attributes | arithmetic | java class | classes and arithmetic | classes | class | decisions | boolean expression | boolean expressions | repetition | methods | aggregate classes | access modifier | access modifiers | child classes | inheritance | child class | graphics | awt class library | fixed repetition | for loop | for loops | array | arrays | iteration | software object | definite iteration | generic lists | generic array list | cast | casting | overriding method | overriding methods | generic list | menu-driven program | menu-driven programs | multi-way decisions | menu and switch | search | searching | software quality | testing | software quality and testing | assessment | computers task guide | programming languages task guide | software design task guide | java program task guide | problem-solving task guide | problem solving task guide | object-oriented programming task guide | java task guide | object-oriented task guide | object oriented task guide | computers lecture | programming languages lecture | software design lecture | java program lecture | problem solving lecture | object-oriented programming lecture | java lecture | object oriented programming lecture | object-oriented lecture | computers reading material | programming languages reading material | java program reading material | problem solving reading material | object-oriented programming reading material | java reading material | object-oriented reading material | object oriented reading material | java classes task guide | variables task guide | attributes task guide | arithmetic task guide | java class task guide | classes and arithmetic task guide | classes task guide | java classes lecture | variables lecture | attributes lecture | arithmetic lecture | java class lecture | classes and arithmetic lecture | classes lecture | class lecture | java classes reading material | variables reading material | java class reading material | classes and arithmetic reading material | java classes visual aid | variables visual aid | attributes visual aid | arithmetic visual aid | java class visual aid | classes and arithmetic visual aid | class visual aid | java visual aid | object-oriented programming visual aid | programming visual aid | object-oriented visual aid | decisions task guide | boolean expression task guide | boolean expressions task guide | repetition task guide | methods task guide | decisions lecture | boolean expression lecture | boolean expressions lecture | repetition lecture | methods lecture | decisions reading material | boolean expression reading material | boolean expressions reading material | decisions visual aid | boolean expression visual aid | boolean expressions visual aid | repetition visual aid | methods visual aid | decisions practical | boolean expression practical | boolean expressions practical | repetition practical | programming practical | object oriented programming practical | object-oriented programming practical | object-oriented practical | object oriented practical | aggregate classes task guide | access modifier task guide | access modifiers task guide | aggregate classes lecture | access modifier lecture | access modifiers lecture | aggregate classes reading material | access modifier reading material | aggregate classes assignment | java classes assignment | access modifier assignment | access modifiers assignment | object oriented programming assignment | object-oriented programming assignment | object-oriented assignment | object oriented assignment | child class task guide | child classes lecture | inheritance lecture | child class lecture | child classes reading material | child class reading material | child classes visual aid | inheritance visual aid | child class visual aid | awt class library task guide | graphics lecture | awt class library lecture | awt class library visual aid | graphics assignment | awt class library assignment | fixed repetition task guide | fixed repetition lecture | fixed repetition visual aid | fixed repetition reading material | for loop task guide | for loops task guide | array task guide | iteration task guide | software object task guide | definite iteration task guide | for loop lecture | for loops lecture | array lecture | iteration lecture | software object lecture | definite iteration lecture | for loop reading material | for loops reading material | array reading material | iteration reading material | software object reading material | definite iteration reading material | for loop visual aid | for loops visual aid | array visual aid | arrays visual aid | iteration visual aid | software object visual aid | definite iteration visual aid | generic lists task guide | cast task guide | casting task guide | overriding method task guide | overriding methods task guide | generic list task guide | generic lists lecture | generic array list lecture | cast lecture | casting lecture | overriding method lecture | overriding methods lecture | generic list lecture | generic lists reading material | generic array list reading material | cast reading material | casting reading material | overriding method reading material | generic list reading material | menu-driven program task guide | menu-driven programs task guide | multi-way decisions task guide | menu-driven program lecture | menu-driven programs lecture | multi-way decisions lecture | menu and switch lecture | menu-driven program reading material | menu-driven programs reading material | menu and switch reading material | menu-driven program visual aid | menu-driven programs visual aid | multi-way decisions visual aid | menu and switch visual aid | search task guide | search lecture | search reading material | testing task guide | software quality and testing task guide | testing lecture | software quality and testing lecture | testing reading material | software quality and testing reading material | assessment reading material | assessment assignment | fixed repetition practical | jcreator guide | g622 | oo | oop | oo programming | awt | oo programming task guide | oop task guide | oo task guide | g622 task guide | oo programming lecture | oop lecture | oo lecture | g622 lecture | oo programming reading material | oop reading material | oo reading material | g622 reading material | g622 visual aid | oop visual aid | oo visual aid | oo programming visual aid | g622 practical | oo practical | oo programming practical | oop practical | g622 assignment | oo assignment | oop assignment | oo programming assignment | awt task guide | awt lecture | awt visual aid | awt assignment | Computer science | I100License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

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This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problemsSubjects

optimization | optimization | algorithms | algorithms | linear programming | linear programming | network flow problems | network flow problems | integer programming | integer programming | combinatorial problems | combinatorial problems | mathematics | mathematics | mathematical programming | mathematical programming | 6.251 | 6.251 | 15.081 | 15.081License

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 metadataDescription

Includes audio/video content: AV lectures. This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language. Includes audio/video content: AV lectures. This subject is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class will use the Python™ programming language.Subjects

computer science | computer science | computation | computation | problem solving | problem solving | Python programming | Python programming | recursion | recursion | binary search | binary search | classes | classes | inheritance | inheritance | libraries | libraries | algorithms | algorithms | optimization problems | optimization problems | modules | modules | simulation | simulation | big O notation | big O notation | control flow | control flow | exceptions | exceptions | building computational models | building computational models | software engineering | software engineeringLicense

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 metadata14.121 Microeconomic Theory I (MIT) 14.121 Microeconomic Theory I (MIT)

Description

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

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

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 metadata14.461 Advanced Macroeconomics I (MIT) 14.461 Advanced Macroeconomics I (MIT)

Description

This course covers three sets of topics. The first part will cover business cycle models with imperfect information. We will ask questions such as: What shocks drive business cycles? What is the relative role of shocks to fundamentals and shocks affecting expectations about (current and future) economic developments? How do informational frictions affect the shape of the responses to various shocks? The second part will cover models of investment with credit constraints. We will ask questions such as: What is the transmission mechanism from shocks to the financial sector to the real economy? What determines optimal decisions about capitalization at the individual and at the social level? The third part will cover search models of decentralized trade applied both to labor markets and to This course covers three sets of topics. The first part will cover business cycle models with imperfect information. We will ask questions such as: What shocks drive business cycles? What is the relative role of shocks to fundamentals and shocks affecting expectations about (current and future) economic developments? How do informational frictions affect the shape of the responses to various shocks? The second part will cover models of investment with credit constraints. We will ask questions such as: What is the transmission mechanism from shocks to the financial sector to the real economy? What determines optimal decisions about capitalization at the individual and at the social level? The third part will cover search models of decentralized trade applied both to labor markets and toSubjects

news about the future and fluctuations | news about the future and fluctuations | dispersed information | dispersed information | estimating models with imperfect information | estimating models with imperfect information | models with limited pledgeability | models with limited pledgeability | models with corporate control problems | models with corporate control problems | models with intermediation and securitization | models with intermediation and securitization | financial frictions | financial frictions | investment | investment | labor market search and inefficiency | labor market search and inefficiency | wage dispersion | wage dispersion | moral hazard | moral hazard | optimal unemployment insurance | optimal unemployment insurance | money search | money search | liquidity | liquidity | adverse selection and lemons problem | adverse selection and lemons problem | decentralized trading in financial markets | decentralized trading in financial marketsLicense

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

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This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functionsORDS | Bessel functionsORDSLicense

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

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This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples. This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functionsORDS | Bessel functionsORDSLicense

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 focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc. The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.Subjects

partial differential equations (pde) | partial differential equations (pde) | nonlinear pde. Diffusion | nonlinear pde. Diffusion | dispersion | dispersion | Initial and boundary value problems | Initial and boundary value problems | Characteristics and shocks | Characteristics and shocks | Separation of variables | Separation of variables | transform methods | transform methods | Green's functions | Green's functions | Asymptotics | Asymptotics | geometrical theory | geometrical theory | Dimensional analysis | Dimensional analysis | self-similarity | self-similarity | traveling waves | traveling waves | Singular perturbation and boundary layers | Singular perturbation and boundary layers | Solitons | Solitons | Variational methods | Variational methods | Free-boundary problems | Free-boundary problemsLicense

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

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Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines. Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Subjects

Unified | Unified | Unified Engineering | Unified Engineering | aerospace | aerospace | CDIO | CDIO | C-D-I-O | C-D-I-O | conceive | conceive | design | design | implement | implement | operate | operate | team | team | team-based | team-based | discipline | discipline | materials | materials | structures | structures | materials and structures | materials and structures | computers | computers | programming | programming | computers and programming | computers and programming | fluids | fluids | fluid mechanics | fluid mechanics | thermodynamics | thermodynamics | propulsion | propulsion | signals | signals | systems | systems | signals and systems | signals and systems | systems problems | systems problems | fundamentals | fundamentals | technical communication | technical communication | graphical communication | graphical communication | communication | communication | reading | reading | research | research | experimentation | experimentation | personal response system | personal response system | prs | prs | active learning | active learning | First law | First law | first law of thermodynamics | first law of thermodynamics | thermo-mechanical | thermo-mechanical | energy | energy | energy conversion | energy conversion | aerospace power systems | aerospace power systems | propulsion systems | propulsion systems | aerospace propulsion systems | aerospace propulsion systems | heat | heat | work | work | thermal efficiency | thermal efficiency | forms of energy | forms of energy | energy exchange | energy exchange | processes | processes | heat engines | heat engines | engines | engines | steady-flow energy equation | steady-flow energy equation | energy flow | energy flow | flows | flows | path-dependence | path-dependence | path-independence | path-independence | reversibility | reversibility | irreversibility | irreversibility | state | state | thermodynamic state | thermodynamic state | performance | performance | ideal cycle | ideal cycle | simple heat engine | simple heat engine | cycles | cycles | thermal pressures | thermal pressures | temperatures | temperatures | linear static networks | linear static networks | loop method | loop method | node method | node method | linear dynamic networks | linear dynamic networks | classical methods | classical methods | state methods | state methods | state concepts | state concepts | dynamic systems | dynamic systems | resistive circuits | resistive circuits | sources | sources | voltages | voltages | currents | currents | Thevinin | Thevinin | Norton | Norton | initial value problems | initial value problems | RLC networks | RLC networks | characteristic values | characteristic values | characteristic vectors | characteristic vectors | transfer function | transfer function | ada | ada | ada programming | ada programming | programming language | programming language | software systems | software systems | programming style | programming style | computer architecture | computer architecture | program language evolution | program language evolution | classification | classification | numerical computation | numerical computation | number representation systems | number representation systems | assembly | assembly | SimpleSIM | SimpleSIM | RISC | RISC | CISC | CISC | operating systems | operating systems | single user | single user | multitasking | multitasking | multiprocessing | multiprocessing | domain-specific classification | domain-specific classification | recursive | recursive | execution time | execution time | fluid dynamics | fluid dynamics | physical properties of a fluid | physical properties of a fluid | fluid flow | fluid flow | mach | mach | reynolds | reynolds | conservation | conservation | conservation principles | conservation principles | conservation of mass | conservation of mass | conservation of momentum | conservation of momentum | conservation of energy | conservation of energy | continuity | continuity | inviscid | inviscid | steady flow | steady flow | simple bodies | simple bodies | airfoils | airfoils | wings | wings | channels | channels | aerodynamics | aerodynamics | forces | forces | moments | moments | equilibrium | equilibrium | freebody diagram | freebody diagram | free-body | free-body | free body | free body | planar force systems | planar force systems | equipollent systems | equipollent systems | equipollence | equipollence | support reactions | support reactions | reactions | reactions | static determinance | static determinance | determinate systems | determinate systems | truss analysis | truss analysis | trusses | trusses | method of joints | method of joints | method of sections | method of sections | statically indeterminate | statically indeterminate | three great principles | three great principles | 3 great principles | 3 great principles | indicial notation | indicial notation | rotation of coordinates | rotation of coordinates | coordinate rotation | coordinate rotation | stress | stress | extensional stress | extensional stress | shear stress | shear stress | notation | notation | plane stress | plane stress | stress equilbrium | stress equilbrium | stress transformation | stress transformation | mohr | mohr | mohr's circle | mohr's circle | principal stress | principal stress | principal stresses | principal stresses | extreme shear stress | extreme shear stress | strain | strain | extensional strain | extensional strain | shear strain | shear strain | strain-displacement | strain-displacement | compatibility | compatibility | strain transformation | strain transformation | transformation of strain | transformation of strain | mohr's circle for strain | mohr's circle for strain | principal strain | principal strain | extreme shear strain | extreme shear strain | uniaxial stress-strain | uniaxial stress-strain | material properties | material properties | classes of materials | classes of materials | bulk material properties | bulk material properties | origin of elastic properties | origin of elastic properties | structures of materials | structures of materials | atomic bonding | atomic bonding | packing of atoms | packing of atoms | atomic packing | atomic packing | crystals | crystals | crystal structures | crystal structures | polymers | polymers | estimate of moduli | estimate of moduli | moduli | moduli | composites | composites | composite materials | composite materials | modulus limited design | modulus limited design | material selection | material selection | materials selection | materials selection | measurement of elastic properties | measurement of elastic properties | stress-strain | stress-strain | stress-strain relations | stress-strain relations | anisotropy | anisotropy | orthotropy | orthotropy | measurements | measurements | engineering notation | engineering notation | Hooke | Hooke | Hooke's law | Hooke's law | general hooke's law | general hooke's law | equations of elasticity | equations of elasticity | boundary conditions | boundary conditions | multi-disciplinary | multi-disciplinary | models | models | engineering systems | engineering systems | experiments | experiments | investigations | investigations | experimental error | experimental error | design evaluation | design evaluation | evaluation | evaluation | trade studies | trade studies | effects of engineering | effects of engineering | social context | social context | engineering drawings | engineering drawingsLicense

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

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This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research. This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research.Subjects

Principal Component Analysis (PCA) | Principal Component Analysis (PCA) | random matrix theory | random matrix theory | spike model | spike model | manifold learning | manifold learning | Diffusion Maps | Diffusion Maps | Sobolev Embedding Theorem | Sobolev Embedding Theorem | Spectral Clustering | Spectral Clustering | Cheegerâ€™s inequality | Cheegerâ€™s inequality | Mesh Theorem | Mesh Theorem | Number Theory | Number Theory | Approximation algorithms | Approximation algorithms | Max-Cut problem | Max-Cut problem | Stochastic Block Model | Stochastic Block Model | Synchronization | Synchronization | inverse problems | inverse problemsLicense

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

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Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programmingLicense

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

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This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computingLicense

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 metadata18.404J Theory of Computation (MIT) 18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory. This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.Subjects

Computability | computational complexity theory | Computability | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systemsLicense

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 metadata18.336 Numerical Methods for Partial Differential Equations (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Subjects

advection equation | heat equation | wave equation | Airy equation | convection-diffusion problems | KdV equation | hyperbolic conservation laws | Poisson equation | Stokes problem | Navier-Stokes equations | interface problems | consistency | stability | convergence | Lax equivalence theorem | error analysis | Fourier approaches | staggered grids | shocks | front propagation | preconditioning | multigrid | Krylov spaces | saddle point problems | finite differences | finite volumes | finite elements | ENO/WENO | spectral methods | projection approaches for incompressible ows | level set methods | particle methods | direct and iterative methodsLicense

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 metadata2.23 Hydrofoils and Propellers (13.04) (MIT) 2.23 Hydrofoils and Propellers (13.04) (MIT)

Description

This course deals with theory and design of hydrofoil sections; lifting and thickness problems for sub-cavitating sections, unsteady flow problems. It focuses on computer-aided design of low drag, cavitation free sections. The course also covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, and control surface design. Topics include propeller lifting line and lifting surface theory; computer-aided design of wake adapted propellers, unsteady propeller thrust and torque. The course is also an introduction to subjects like flow about axially symmetric bodies and low-aspect ratio lifting surfaces, and hydrodynamic performance and design of waterjets. We will also do an analysis of performance and design of wind turbine rotors in steady and stochastic win This course deals with theory and design of hydrofoil sections; lifting and thickness problems for sub-cavitating sections, unsteady flow problems. It focuses on computer-aided design of low drag, cavitation free sections. The course also covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, and control surface design. Topics include propeller lifting line and lifting surface theory; computer-aided design of wake adapted propellers, unsteady propeller thrust and torque. The course is also an introduction to subjects like flow about axially symmetric bodies and low-aspect ratio lifting surfaces, and hydrodynamic performance and design of waterjets. We will also do an analysis of performance and design of wind turbine rotors in steady and stochastic winSubjects

Theory and design of hydrofoil sections | Theory and design of hydrofoil sections | lifting and thickness problems | lifting and thickness problems | sub-cavitating sections | sub-cavitating sections | unsteady flow problems | unsteady flow problems | computer-aided design | computer-aided design | low drag | low drag | cavitation free sections | cavitation free sections | Lifting line and lifting surface theory | Lifting line and lifting surface theory | hydrofoil craft | hydrofoil craft | rudder | rudder | and control surface design | and control surface design | propeller lifting line | propeller lifting line | lifting surface theory | lifting surface theory | wake adapted propellers | wake adapted propellers | unsteady propeller thrust and torque | unsteady propeller thrust and torque | axially symmetric bodies | axially symmetric bodies | low-aspect ratio lifting surfaces | low-aspect ratio lifting surfaces | Hydrodynamic performance | Hydrodynamic performance | design of waterjets | design of waterjets | wind turbine rotors in steady and stochastic wind | wind turbine rotors in steady and stochastic wind | hydrofoil craft | rudder | and control surface design | hydrofoil craft | rudder | and control surface design | 9. low drag | cavitation free sections | 9. low drag | cavitation free sections | 5. hydrofoil craft | rudder | and control surface design | 5. hydrofoil craft | rudder | and control surface design | low drag | cavitation free sections | low drag | cavitation free sectionsLicense

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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