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

Description

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

microeconomic theory | microeconomic theory | demand theory | demand theory | producer theory; partial equilibrium | producer theory; partial equilibrium | competitive markets | competitive markets | general equilibrium | general equilibrium | externalities | externalities | Afriat's theorem | Afriat's theorem | pricing | pricing | robust comparative statics | robust comparative statics | utility theory | utility theory | properties of preferences | properties of preferences | choice as primitive | choice as primitive | revealed preference | revealed preference | classical demand theory | classical demand theory | Kuhn-Tucker necessary conditions | Kuhn-Tucker necessary conditions | implications of Walras?s law | implications of Walras?s law | indirect utility functions | indirect utility functions | theorem of the maximum (Berge?s theorem) | theorem of the maximum (Berge?s theorem) | expenditure minimization problem | expenditure minimization problem | Hicksian demands | Hicksian demands | compensated law of demand | compensated law of demand | Slutsky substitution | Slutsky substitution | price changes and welfare | price changes and welfare | compensating variation | compensating variation | and welfare from new goods | and welfare from new goods | price indexes | price indexes | bias in the U.S. consumer price index | bias in the U.S. consumer price index | integrability | integrability | demand aggregation | demand aggregation | aggregate demand and welfare | aggregate demand and welfare | Frisch demands | Frisch demands | and demand estimation | and demand estimation | increasing differences | increasing differences | producer theory applications | producer theory applications | the LeCh?telier principle | the LeCh?telier principle | Topkis? theorem | Topkis? theorem | Milgrom-Shannon monotonicity theorem | Milgrom-Shannon monotonicity theorem | monopoly pricing | monopoly pricing | monopoly and product quality | monopoly and product quality | nonlinear pricing | nonlinear pricing | and price discrimination | and price discrimination | simple models of externalities | simple models of externalities | government intervention | government intervention | Coase theorem | Coase theorem | Myerson-Sattherthwaite proposition | Myerson-Sattherthwaite proposition | missing markets | missing markets | price vs. quantity regulations | price vs. quantity regulations | Weitzman?s analysis | Weitzman?s analysis | uncertainty | uncertainty | common property externalities | common property externalities | optimization | optimization | equilibrium number of boats | equilibrium number of boats | welfare theorems | welfare theorems | uniqueness and determinacy | uniqueness and determinacy | price-taking assumption | price-taking assumption | Edgeworth box | Edgeworth box | welfare properties | welfare properties | Pareto efficiency | Pareto efficiency | Walrasian equilibrium with transfers | Walrasian equilibrium with transfers | Arrow-Debreu economy | Arrow-Debreu economy | separating hyperplanes | separating hyperplanes | Minkowski?s theorem | Minkowski?s theorem | Existence of Walrasian equilibrium | Existence of Walrasian equilibrium | Kakutani?s fixed point theorem | Kakutani?s fixed point theorem | Debreu-Gale-Kuhn-Nikaido lemma | Debreu-Gale-Kuhn-Nikaido lemma | additional properties of general equilibrium | additional properties of general equilibrium | Microfoundations | Microfoundations | core | core | core convergence | core convergence | general equilibrium with time and uncertainty | general equilibrium with time and uncertainty | Jensen?s inequality | Jensen?s inequality | and security market economy | and security market economy | arbitrage pricing theory | arbitrage pricing theory | and risk-neutral probabilities | and risk-neutral probabilities | Housing markets | Housing markets | competitive equilibrium | competitive equilibrium | one-sided matching house allocation problem | one-sided matching house allocation problem | serial dictatorship | serial dictatorship | two-sided matching | two-sided matching | marriage markets | marriage markets | existence of stable matchings | existence of stable matchings | incentives | incentives | housing markets core mechanism | housing markets core 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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One summer in the 1960s a young Japanese researcher, with the help of a few high school students, chopped up ten thousand jellyfish. As a by-product of this harvest, they isolated a green fluorescent protein (GFP). Since then, GFP has triggered a revolution in our understanding of gene expression and signaling in live cells. In this seminar, we will examine how this small protein generates fluorescence, i.e. absorbs light of one wavelength and emits light of a longer wavelength. We will discuss how the color palette has been extended from green to blue, red and many other colors, based on protein engineering of GFP and the study of vividly colorful coral reefs. We will then investigate how these fluorescent proteins can be used to track the motion of DNA, RNA and protein in living cells, a One summer in the 1960s a young Japanese researcher, with the help of a few high school students, chopped up ten thousand jellyfish. As a by-product of this harvest, they isolated a green fluorescent protein (GFP). Since then, GFP has triggered a revolution in our understanding of gene expression and signaling in live cells. In this seminar, we will examine how this small protein generates fluorescence, i.e. absorbs light of one wavelength and emits light of a longer wavelength. We will discuss how the color palette has been extended from green to blue, red and many other colors, based on protein engineering of GFP and the study of vividly colorful coral reefs. We will then investigate how these fluorescent proteins can be used to track the motion of DNA, RNA and protein in living cells, aSubjects

Green Fluorescent Protein | Green Fluorescent Protein | Fluorescent protein engineering | Fluorescent protein engineering | Photoconversion | Photoconversion | fluorescent protein variants | fluorescent protein variants | fluorescent microscopy facility | fluorescent microscopy facility | Quantitative fluorescent imaging | Quantitative fluorescent imaging | ultra-sensitive fluorescent imaging | ultra-sensitive fluorescent imaging | high-throughput analysis | high-throughput analysis | Fluorescent imaging in living organisms | Fluorescent imaging in living organisms | phycoerythrin | phycoerythrin | phytochrome | phytochrome | jellyfish | jellyfish | red fluorescent protein | red fluorescent protein | photoactivation | photoactivation | chromophore | chromophore | protonation | protonation | lysosomes | lysosomes | recombinant protein molecules | recombinant protein moleculesLicense

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 metadata18.997 Topics in Combinatorial Optimization (MIT) 18.997 Topics in Combinatorial Optimization (MIT)

Description

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms. In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.Subjects

combinatorial optimization | combinatorial optimization | Ear decompositions | Ear decompositions | Nonbipartite matching | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Minimization of submodular functions | Matroid intersection | Matroid intersection | Polymatroid intersection | Polymatroid intersection | Jump systems | Jump systems | Matroid union | Matroid union | Matroid matching | path matchings | Matroid matching | path matchings | Packing trees and arborescences | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Graph orientation | Connectivity tree and connectivity augmentation | Connectivity tree and connectivity augmentation | Multicommodity flows | Multicommodity flows | Connectivity tree | Connectivity tree | connectivity augmentation | connectivity augmentation | Gallai-Milgram Theorem | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | Bessy-Thomasse Theorem | paritioning graphs | paritioning graphs | covering graphs | covering graphs | directed paths | directed paths | directed cycles | directed cycles | matroid matching | matroid matching | path matching | path matching | packing directed cuts | packing directed cuts | Luchessi-Younger Theorem | Luchessi-Younger Theorem | packing trees | packing trees | arborescences | arborescences | submodular flows | submodular flows | Edmonds-Giles Theorem | Edmonds-Giles TheoremLicense

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)

Description

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

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

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This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s TheoremLicense

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 field seminar in international political economy covers major theoretical, empirical, and policy perspectives. The basic orientation is disciplinary and comparative (over time and across countries, regions, firms), spanning issues relevant to both industrial and developing states. Special attention is given to challenges and dilemmas shaped by the macro-level consequences of micro-level behavior, and by micro-level adjustments to macro-level influences. This field seminar in international political economy covers major theoretical, empirical, and policy perspectives. The basic orientation is disciplinary and comparative (over time and across countries, regions, firms), spanning issues relevant to both industrial and developing states. Special attention is given to challenges and dilemmas shaped by the macro-level consequences of micro-level behavior, and by micro-level adjustments to macro-level influences.Subjects

international relations | international relations | political science | political science | economics | economics | wealth | wealth | neoclassical | neoclassical | development | development | ecology | ecology | power | power | trade | trade | capital | capital | foreign investment | foreign investment | intellectual property | intellectual property | migration | migration | foreignpolicy | foreignpolicy | globalization | globalization | internet | internet | sustainability | sustainability | institutions | institutions | foreign policy | foreign policy | IPE | IPE | dual national objectives | dual national objectives | global context | global context | pursuit of power | pursuit of power | pursuit of wealth | pursuit of wealth | international political economy | international political economy | neoclassical economics | neoclassical economics | development economics | development economics | ecological economics | ecological economics | lateral pressure | lateral pressure | perspectives | perspectives | structural views | structural views | power relations | power relations | politics | politics | international trade | international trade | capital flows | capital flows | intellectual property rights | intellectual property rights | international migration | international migration | foreign economic policy | foreign economic policy | international economic institutions | international economic institutions | theoretical perspectives | theoretical perspectives | empirical perspectives | empirical perspectives | policy perspectives | policy perspectives | disciplinary | disciplinary | comparative | comparative | time | time | countries | countries | regions | regions | firms | firms | industrial states | industrial states | developing states | developing states | macro-level consequences | macro-level consequences | micro-level behavior | micro-level behavior | micro-level adjustments | micro-level adjustments | macro-level influences | macro-level influences | complexity | complexity | localization | localization | technology | technology | knowledge economy | knowledge economy | finance | finance | global markets | global markets | political economy | political economy | e-commerce | e-commerceLicense

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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Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems. Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.Subjects

Forecasting | Forecasting | model validation | model validation | prediction quality | prediction quality | operational atmosphere and ocean forecasting systems | operational atmosphere and ocean forecasting systems | limiting factors | limiting factors | prediction | prediction | operational atmosphere forecasting systems | operational atmosphere forecasting systems | ocean forecasting systems | ocean forecasting systems | chaos | chaos | probabilistic forecasting | probabilistic forecasting | data assimilation | data assimilation | adaptive observations | adaptive observations | model error | model error | attractors | attractors | dimensions | dimensions | sensitive dependence | sensitive dependence | initial conditions | initial conditionsLicense

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 goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s TheoremLicense

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 field seminar in international political economy covers major theoretical, empirical, and policy perspectives. The basic orientation is disciplinary and comparative (over time and across countries, regions, firms), spanning issues relevant to both industrial and developing states. Special attention is given to challenges and dilemmas shaped by the macro-level consequences of micro-level behavior, and by micro-level adjustments to macro-level influences. This field seminar in international political economy covers major theoretical, empirical, and policy perspectives. The basic orientation is disciplinary and comparative (over time and across countries, regions, firms), spanning issues relevant to both industrial and developing states. Special attention is given to challenges and dilemmas shaped by the macro-level consequences of micro-level behavior, and by micro-level adjustments to macro-level influences.Subjects

international relations | international relations | political science | political science | economics | economics | wealth | wealth | neoclassical | neoclassical | development | development | ecology | ecology | power | power | trade | trade | capital | capital | foreign investment | foreign investment | intellectual property | intellectual property | migration | migration | foreignpolicy | foreignpolicy | globalization | globalization | internet | internet | sustainability | sustainability | institutions | institutions | foreign policy | foreign policy | IPE | IPE | dual national objectives | dual national objectives | global context | global context | pursuit of power | pursuit of power | pursuit of wealth | pursuit of wealth | international political economy | international political economy | neoclassical economics | neoclassical economics | development economics | development economics | ecological economics | ecological economics | lateral pressure | lateral pressure | perspectives | perspectives | structural views | structural views | power relations | power relations | politics | politics | international trade | international trade | capital flows | capital flows | intellectual property rights | intellectual property rights | international migration | international migration | foreign economic policy | foreign economic policy | international economic institutions | international economic institutions | theoretical perspectives | theoretical perspectives | empirical perspectives | empirical perspectives | policy perspectives | policy perspectives | disciplinary | disciplinary | comparative | comparative | time | time | countries | countries | regions | regions | firms | firms | industrial states | industrial states | developing states | developing states | macro-level consequences | macro-level consequences | micro-level behavior | micro-level behavior | micro-level adjustments | micro-level adjustments | macro-level influences | macro-level influences | complexity | complexity | localization | localization | technology | technology | knowledge economy | knowledge economy | finance | finance | global markets | global markets | political economy | political economy | e-commerce | e-commerceLicense

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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Subjects

libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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Subjects

libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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Subjects

libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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See all metadataR-34 [blimp] (LOC) R-34 [blimp] (LOC)

Description

Subjects

libraryofcongress | libraryofcongress | r34 | r34 | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | mineola | mineola | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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See all metadataLt. Com. Z. Lansdowne (LOC) Lt. Com. Z. Lansdowne (LOC)

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libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | zacharylansdowne | zacharylansdowne | lansdowne | lansdowne | unitedstatesnavy | unitedstatesnavy | usnavy | usnavy | usn | usn | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | aviator | aviator | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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See all metadataPilot House R-34 -- just after landing (LOC) Pilot House R-34 -- just after landing (LOC)

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libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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See all metadataPilot House of R-34 (LOC) Pilot House of R-34 (LOC)

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libraryofcongress | libraryofcongress | r34 | r34 | july61919 | july61919 | mineola | mineola | hazelhurstfield | hazelhurstfield | aviation | aviation | mineolanewyork | mineolanewyork | mineolalongisland | mineolalongisland | mineolany | mineolany | mineolali | mineolali | gardencitynewyork | gardencitynewyork | gardencityny | gardencityny | gardencitylongisland | gardencitylongisland | gardencityli | gardencityli | longisland | longisland | gardencity | gardencity | rooseveltfield | rooseveltfield | hmar34 | hmar34 | airshipr34 | airshipr34 | royalairforce | royalairforce | raf | raf | royalnavy | royalnavy | rn | rn | royalnavalairservice | royalnavalairservice | rnas | rnas | r33classairship | r33classairship | aircraft | aircraft | lighterthanair | lighterthanair | airship | airship | dirigible | dirigible | williambeardmorecompany | williambeardmorecompany | williambeardmoreandcompany | williambeardmoreandcompany | bearmorecompany | bearmorecompany | beardmoreandcompany | beardmoreandcompany | beardmore | beardmore | sunbeammotorcarcompany | sunbeammotorcarcompany | sunbeammotorcar | sunbeammotorcar | sunbeam | sunbeam | sunbeammaori | sunbeammaori | maoriengine | maoriengine | sunbeammaorimkiv | sunbeammaorimkiv | sunbeammarkiv | sunbeammarkiv | maorimkiv | maorimkiv | maorimarkiv | maorimarkiv | r33class | r33classLicense

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One summer in the 1960s a young Japanese researcher, with the help of a few high school students, chopped up ten thousand jellyfish. As a by-product of this harvest, they isolated a green fluorescent protein (GFP). Since then, GFP has triggered a revolution in our understanding of gene expression and signaling in live cells. In this seminar, we will examine how this small protein generates fluorescence, i.e. absorbs light of one wavelength and emits light of a longer wavelength. We will discuss how the color palette has been extended from green to blue, red and many other colors, based on protein engineering of GFP and the study of vividly colorful coral reefs. We will then investigate how these fluorescent proteins can be used to track the motion of DNA, RNA and protein in living cells, aSubjects

Green Fluorescent Protein | Fluorescent protein engineering | Photoconversion | fluorescent protein variants | fluorescent microscopy facility | Quantitative fluorescent imaging | ultra-sensitive fluorescent imaging | high-throughput analysis | Fluorescent imaging in living organisms | phycoerythrin | phytochrome | jellyfish | red fluorescent protein | photoactivation | chromophore | protonation | lysosomes | recombinant protein moleculesLicense

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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One summer in the 1960s a young Japanese researcher, with the help of a few high school students, chopped up ten thousand jellyfish. As a by-product of this harvest, they isolated a green fluorescent protein (GFP). Since then, GFP has triggered a revolution in our understanding of gene expression and signaling in live cells. In this seminar, we will examine how this small protein generates fluorescence, i.e. absorbs light of one wavelength and emits light of a longer wavelength. We will discuss how the color palette has been extended from green to blue, red and many other colors, based on protein engineering of GFP and the study of vividly colorful coral reefs. We will then investigate how these fluorescent proteins can be used to track the motion of DNA, RNA and protein in living cells, aSubjects

Green Fluorescent Protein | Fluorescent protein engineering | Photoconversion | fluorescent protein variants | fluorescent microscopy facility | Quantitative fluorescent imaging | ultra-sensitive fluorescent imaging | high-throughput analysis | Fluorescent imaging in living organisms | phycoerythrin | phytochrome | jellyfish | red fluorescent protein | photoactivation | chromophore | protonation | lysosomes | recombinant protein moleculesLicense

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 metadata18.997 Topics in Combinatorial Optimization (MIT)

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In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.Subjects

combinatorial optimization | Ear decompositions | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Matroid intersection | Polymatroid intersection | Jump systems | Matroid union | Matroid matching | path matchings | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Connectivity tree and connectivity augmentation | Multicommodity flows | Connectivity tree | connectivity augmentation | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | paritioning graphs | covering graphs | directed paths | directed cycles | matroid matching | path matching | packing directed cuts | Luchessi-Younger Theorem | packing trees | arborescences | submodular flows | Edmonds-Giles TheoremLicense

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 metadataón electrónica I ón electrónica I

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Se trata de conocer los conceptos de un sistema generalizado de instrumentación y medida, centrándonos en el estudio de los sensores y transductores de tipo eléctrico y de los circuitos acondicionadores asociados. Mediante el estudio de las características estáticas de los sensores y analizando los circuitos potenciométrico, puente de Wheatstone y circuitos amplificadores, en especial el amplificador de instrumentación; se dotará al alumno de los esquemas básicos utilizados en instrumentación electrónica. Finalmente, se analizarán los sensores y los circuitos acondicionadores correspondientes que se utilizan en las medidas de mayor uso y aplicación industrial. Se trata de conocer los conceptos de un sistema generalizado de instrumentación y medida, centrándonos en el estudio de los sensores y transductores de tipo eléctrico y de los circuitos acondicionadores asociados. Mediante el estudio de las características estáticas de los sensores y analizando los circuitos potenciométrico, puente de Wheatstone y circuitos amplificadores, en especial el amplificador de instrumentación; se dotará al alumno de los esquemas básicos utilizados en instrumentación electrónica. Finalmente, se analizarán los sensores y los circuitos acondicionadores correspondientes que se utilizan en las medidas de mayor uso y aplicación industrial.Subjects

ón | ón | Transductores para la medida de temperatura | Transductores para la medida de temperatura | 2008 | 2008 | Sensores para la medida de deformaciones | Sensores para la medida de deformaciones | étrico | étrico | ón y nivel | ón y nivel | ópticos | ópticos | Tecnologia Electronica | Tecnologia Electronica | Transductores | Transductores | Circuito puente | Circuito puente | ía Técnica Industrial: Electrónica Industrial | ía Técnica Industrial: Electrónica Industrial | Sensores | SensoresLicense

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The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, the instructors will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will also introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be i The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, the instructors will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will also introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be iSubjects

Core Mantle Boundary (CMB) | Core Mantle Boundary (CMB) | deep Earth | deep Earth | lower mantle | lower mantle | outer core | outer core | integrated seismological | integrated seismological | mineral physics and geodynamical perspectives | mineral physics and geodynamical perspectives | CMB detection and topography | CMB detection and topography | D'' anisotropy | D'' anisotropy | seismic velocity anomalies (e.g. | seismic velocity anomalies (e.g. | ultra-low velocity zones) | ultra-low velocity zones) | temperature | temperature | chemical reactions | chemical reactions | phase relations | phase relations | mineral fabrications | mineral fabrications | cmb detection | cmb detection | topography | topography | mineral physics | mineral physics | geodynamical perspectives | geodynamical perspectives | D" Region | D" Region | ultra-low velocity zones | ultra-low velocity zones | partial melting | partial melting | mineral texture | mineral texture | core rigidity zones | core rigidity zones | sedimentation | sedimentation | mantle flow | mantle flow | core mantle coupling | core mantle coupling | geomagnetic field | geomagnetic fieldLicense

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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18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory. 18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.Subjects

Infinitude of the primes | Infinitude of the primes | Summing powers of integers | Summing powers of integers | Bernoulli polynomials | Bernoulli polynomials | sine product formula | sine product formula | $\zeta(2n)$ | $\zeta(2n)$ | Fermat's Little Theorem | Fermat's Little Theorem | Fermat's Great Theorem | Fermat's Great Theorem | Averages of arithmetic functions | Averages of arithmetic functions | arithmetic-geometric mean | arithmetic-geometric mean | Gauss' theorem | Gauss' theorem | Wallis's formula | Wallis's formula | Stirling's formula | Stirling's formula | prime number theorem | prime number theorem | Riemann's hypothesis | Riemann's hypothesis | Euler's proof of infinitude of primes | Euler's proof of infinitude of primes | Density of prime numbers | Density of prime numbers | Euclidean algorithm | Euclidean algorithm | Golden Ratio | Golden RatioLicense

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 metadata18.338J Infinite Random Matrix Theory (MIT) 18.338J Infinite Random Matrix Theory (MIT)

Description

In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices. In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices.Subjects

Infinite Random Matrices | Infinite Random Matrices | The Hermite Ensemble | The Hermite Ensemble | Wigner's Semi-Circle Law; | Wigner's Semi-Circle Law; | The Laguerre Ensemble | The Laguerre Ensemble | Marcenko-Pastur Theorem | Marcenko-Pastur Theorem | The Jacobi Ensemble | The Jacobi Ensemble | McKay's Random Graph Theorem | McKay's Random Graph Theorem | The ?Semi-Circular? Element | The ?Semi-Circular? Element | Central Limit Theorem | Central Limit Theorem | Free Cumulants in Free Probability | Free Cumulants in Free Probability | Non-Crossing Partitionsm | Non-Crossing Partitionsm | Free Cumulants | Free Cumulants | The Semi-Circular and ?Free Poisson? distributions | The Semi-Circular and ?Free Poisson? distributions | Additive Free Convolution | Additive Free Convolution | The R-Transform and the Marcenko-Pastur Theorem | The R-Transform and the Marcenko-Pastur Theorem | Multiplicative Free Convolution | Multiplicative Free Convolution | The S-Transform | The S-Transform | Non-Crossing Partitions | Non-Crossing Partitions | Orthogonal Polynomials and the Classical Matrix Ensembles | Orthogonal Polynomials and the Classical Matrix Ensembles | Tracy Widom Distribution | Tracy Widom Distribution | Eigenvalue Spectrum Fluctuations | Eigenvalue Spectrum Fluctuations | Free Probability and Fluctuations | Free Probability and Fluctuations | Zonal Polynomials and Random Matrices | Zonal Polynomials and Random Matrices | Symmetric Group Representations and Free Probability | Symmetric Group Representations and Free Probability | 18.338 | 18.338 | 16.394 | 16.394 | Wigner's Semi-Circle Law | Wigner's Semi-Circle LawLicense

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 metadata18.125 Measure and Integration (MIT) 18.125 Measure and Integration (MIT)

Description

This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform. This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.Subjects

Lebesgue integral | Lebesgue integral | convergence theorems | convergence theorems | Lebesgue measure in Rn | Lebesgue measure in Rn | Lpspaces | Lpspaces | Radon-Nikodym Theorem | Radon-Nikodym Theorem | Lebesgue Differentiation Theorem | Lebesgue Differentiation Theorem | Fubini Theorem | Fubini Theorem | Hausdorff measure | Hausdorff measure | Area and Coarea Formulas | Area and Coarea Formulas | measure theory | measure theory | convolution | convolution | Fourier transform | Fourier transform | Lebesque Integration Theory | Lebesque Integration 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 metadata24.242 Logic II (MIT) 24.242 Logic II (MIT)

Description

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt GÃ¶del's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt GÃ¶del's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus;Subjects

Logic | Logic | theory of computability | theory of computability | Kurt G?del | Kurt G?del | theorem | theorem | system | system | true | true | arithmetical | arithmetical | statements | statements | axiomatic basis | axiomatic basis | proving | proving | truths of arithmetic | truths of arithmetic | history applications | history applications | technique | technique | Church?s theorem | Church?s theorem | algorithm | algorithm | formula | formula | valid | valid | predicate calculus | predicate calculus | Tarski?s theorem | Tarski?s theorem | G?del?s second incompleteness theorem. | G?del?s second incompleteness 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.htmSite sourced from

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