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18.156 Differential Analysis (MIT) 18.156 Differential Analysis (MIT)

Description

The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis. The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.Subjects

Sobolev spaces | Sobolev spaces | Fredholm alternative | Fredholm alternative | Variable coefficient elliptic | parabolic and hyperbolic linear partial differential equations | Variable coefficient elliptic | parabolic and hyperbolic linear partial differential equations | Variational methods | Variational methods | Viscosity solutions of fully nonlinear partial differential equations | Viscosity solutions of fully nonlinear partial differential equations | Schauder theory | Schauder theory | Holder estimates | Holder estimates | linear equations | linear equations | second derivatives | second derivatives | elliptic | elliptic | parabolic | parabolic | nonlinear partial differential equations | nonlinear partial differential equations | linear partial differential equations | linear partial differential equations | harmonic functions | harmonic functions | elliptic equations | elliptic equations | parabolic equations | parabolic equationsLicense

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

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectsting | foodintoleranceLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectsting | foodintoleranceLicense

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A 3 year old male neutered cat with a swollen lower lip most likely due to an allergy. This had happened before, and was being dug into by the upper teeth.Subjects

svmsvet | cat | cats | feline | felines | lip | lips | bottomlip | catlip | allergicreaction | insectbite | insectsting | allergy | a0033 | catlowerlip | catinsectbite | catallergicreaction | catinsectstingLicense

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This course is an introduction to Java™ programming and software engineering. It is designed for those who have little or no programming experience in Java and covers concepts useful to 6.005. The focus is on developing high quality, working software that solves real problems. Students will learn the fundamentals of Java, and how to use 3rd party libraries to get more done with less work. Each session includes one hour of lecture and one hour of assisted lab work. Short labs are assigned with each lecture.This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month. This course is an introduction to Java™ programming and software engineering. It is designed for those who have little or no programming experience in Java and covers concepts useful to 6.005. The focus is on developing high quality, working software that solves real problems. Students will learn the fundamentals of Java, and how to use 3rd party libraries to get more done with less work. Each session includes one hour of lecture and one hour of assisted lab work. Short labs are assigned with each lecture.This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.Subjects

java; software engineering; programming; introductory programming; object oriented programming; software design; methods; conditionals; loops; arrays; objects; classes; inheritance; abstraction; design; exceptions; eclipse; testing; unit testing; debugging; programming style | java; software engineering; programming; introductory programming; object oriented programming; software design; methods; conditionals; loops; arrays; objects; classes; inheritance; abstraction; design; exceptions; eclipse; testing; unit testing; debugging; programming style | java | java | software engineering | software engineering | programming | programming | introductory programming | introductory programming | object oriented programming | object oriented programming | software design | software design | methods | methods | conditionals | conditionals | loops | loops | arrays | arrays | objects | objects | classes | classes | inheritance | inheritance | abstraction | abstraction | design | design | exceptions | exceptions | eclipse | eclipse | testing | testing | unit testing | unit testing | debugging | debugging | programming style | programming styleLicense

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 metadata14.02 Principles of Macroeconomics (MIT) 14.02 Principles of Macroeconomics (MIT)

Description

This course provides an overview of the following macroeconomic issues: the determination of output, employment, unemployment, interest rates, and inflation. Monetary and fiscal policies are discussed, as are public debt and international economic issues. This course also introduces basic models of macroeconomics and illustrates principles with the experience of the United States and other economies. This course provides an overview of the following macroeconomic issues: the determination of output, employment, unemployment, interest rates, and inflation. Monetary and fiscal policies are discussed, as are public debt and international economic issues. This course also introduces basic models of macroeconomics and illustrates principles with the experience of the United States and other economies.Subjects

macroeconomics | macroeconomics | economics | economics | output | output | employment | employment | determination | determination | unemployment | unemployment | interest rates | interest rates | Federal Reserve | Federal Reserve | inflation | inflation | monetary policy | monetary policy | fiscal policy | fiscal policy | public debt | public debt | international economics | international economics | goods market | goods market | market | market | financial markets | financial markets | open economy | open economy | exchange rate | exchange rate | labor market | labor market | phillips curve | phillips curve | growth | growth | Solow's model | Solow's model | MACROECONOMICS | MACROECONOMICS | ECONOMICS | ECONOMICS | OUTPUT | OUTPUT | Macroeconomics | Macroeconomics | EMPLOYMENT | EMPLOYMENT | DETERMINATION | DETERMINATION | UNEMPLOYMENT | UNEMPLOYMENT | INTEREST RATES | INTEREST RATES | FEDERAL RESERVE | FEDERAL RESERVE | INFLATION | INFLATION | MONETARY POLICY | MONETARY POLICY | FISCAL POLICY | FISCAL POLICY | PUBLIC DEBT | PUBLIC DEBT | INTERNATIONAL ECONOMICS | INTERNATIONAL ECONOMICS | GOODS MARKET | GOODS MARKET | MARKET | MARKET | FINANCIAL MARKETS | FINANCIAL MARKETS | OPEN ECONOMY | OPEN ECONOMY | EXCHANGE RATE | EXCHANGE RATE | LABOR MARKET | LABOR MARKET | PHILLIPS CURVE | PHILLIPS CURVE | GROWTH | GROWTH | SOLOW'S MODEL | SOLOW'S MODEL | Economics | Economics | Output | Output | Employment | Employment | Determination | Determination | Unemployment | Unemployment | Interest Rates | Interest Rates | Inflation | Inflation | Monetary Policy | Monetary Policy | Fiscal Policy | Fiscal Policy | Public Debt | Public Debt | International Economics | International Economics | Goods Market | Goods Market | Market | Market | Financial Markets | Financial Markets | Open Economy | Open Economy | Exchange Rate | Exchange Rate | Labor Market | Labor Market | Phillips Curve | Phillips Curve | Growth | Growth | Solow's Model | Solow's ModelLicense

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 main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible. The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.Subjects

near equivalence | near equivalence | algebraic equivalence | algebraic equivalence | numerical equivalence | numerical equivalence | birational | birational | rational | rational | maps | maps | surfaces | surfaces | ruled surfaces | ruled surfaces | rational surfaces | rational surfaces | linear systems | linear systems | castelnuovo's criterion | castelnuovo's criterion | rationality | rationality | picard | picard | albanese | albanese | classification | classification | K3 | K3 | elliptic | elliptic | Kodaira dimension | Kodaira dimension | bielliptic | biellipticLicense

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 metadata18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

Description

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last 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 metadata18.782 Introduction to Arithmetic Geometry (MIT) 18.782 Introduction to Arithmetic Geometry (MIT)

Description

This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry. This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry.Subjects

algebra | algebra | number theory | number theory | diophantine equations | diophantine equations | algebraic geometry | algebraic geometry | plane conics | plane conics | elliptic curves | elliptic curves | hyperelliptic curves | hyperelliptic curves | abelian varieties | abelian varieties | Tate-Shafarevich group | Tate-Shafarevich groupLicense

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 metadataProfessor James Meade with Phillips Machine, 1996

Description

Professor of Commerce at LSE 1947-1957, received the Nobel Prize in Economic Sciences (jointly) in 1977 Extracts from ?The Phillips Machine Project? by Nicholas Bar, LSE Magazine, June 1988, No75, p.3 A.W. H. ?Bill? Phillips is known worldwide as the originator of the Phillips Curve. Less well known is the remarkable man he was personally, and his extraordinary route to academic prominence via what came to be called the Phillips Machine. Trained as an electrical engineer in his native New Zealand in the 1930s, he caught the travel bug and took up an engineering job in the Australian outback, where he also earned money by running a cinema and hunting crocodiles. He reached London in 1938 via the Trans-Siberian railway and joined the RAF at the outbreak of war. He was captured in Java and spent most of the war in a Japanese POW camp, where he learned Chinese and some Russian from fellow prisoners. Back in Britain he took the BSc (Econ) 1946-49, special subject sociology. He developed a great interest in economics?and like many of his generation, became very caught up with Keynesian theory. Though fascinated he found the Keynesian model hard going. With Walter Newlyn (an undergraduate contemporary, later Professor of Economics at Leeds University) to help with the economic theory, he fell back on his engineering training. He saw that money stocks could be represented as tanks of water, and monetary flows by water circulating round plastic tubes. With a grant of £100 (obtained with Newlyn?s help) he spent the summer of 1949 in a garage in Croydon ?living on air? as James Meade was later to put it, working on a hydraulic representation of the Keynesian model. In the machine he constructed, the circular flow of income was represented by water being pumped round a series of clear plastic tubes, with outflows representing savings, taxes and imports, and inflows representing investment, government spending and exports. The model had three tanks representing the stock of money, one for transaction balances and one for foreign-held sterling balances. The whole system determined the level of income, the rate of interest, imports, exports and the exchange to an accuracy (astonishing at the time) of +two per cent. The time path of income and the other variables was traced out by plotter pens making it possible to analyse the quantitative effects of economic policy. The machine, in the jargon, was a hydraulic representation of an open economy IS-LM model with an explicit underlying dynamic structure. It was this very Heath Robinson prototype which, with the enthusiastic support of James Meade (then Professor of Commerce at the School), Phillips demonstrated to Lionel Robbins? seminar in November 1949. Those attending gazed in wonder at this large (7ft high x 5ft wide x 3ft deep) ?thing? in the middle of the room. Phillips, chain smoking, paced back and forth explaining it in a heavy New Zealand drawl, in the process giving one of the best lectures on Keynes that anyone in the audience had ever heard. Then he switched the machine on. And it worked! According to Lord Robbins? recollections, ?there was income dividing itself into consumption and saving?Keynes and Robertson need never have quarrelled if they had had the Phillips Machine before them??Phillips was made an Assistant Lecturer in Economics in 1950, Lecturer 1951, Reader 1954, and Tooke Professor of Economic Science and Statistics in 1958 (the year his Phillips Curve paper was published). He took up a Chair at the Australian National University in 1967 and, having suffered a major stroke, retired to Auckland in 1970, where he died five years later aged 60, mourned by many friends for personal as much for professional reasons.? IMAGELIBRARY/724 Persistent URL: archives.lse.ac.uk/dserve.exe?dsqServer=lib-4.lse.ac.uk&a...Subjects

lse | londonschoolofeconomics | lselibrary | awphillips | phillips | phillipsmachine | phillipshydraulicmachine | moniacmachine | jamesmeadeLicense

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See all metadataUnveiling of the restored Phillips Machine, 29th June 1989

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Left to right: The team that restored the Phillips Machine, Colin Carter (a professional engineer), Professor James Meade, Professor Walter Newlyn (University of Leeds, LSE Alumnus), Dr Nicholas Barr, Reza Moghadam (Research Assistant, LSE Student) Extracts from ?The Phillips Machine Project? by Nicholas Bar, LSE Magazine, June 1988, No75, p.3 A.W. H. ?Bill? Phillips is known worldwide as the originator of the Phillips Curve. Less well known is the remarkable man he was personally, and his extraordinary route to academic prominence via what came to be called the Phillips Machine. Trained as an electrical engineer in his native New Zealand in the 1930s, he caught the travel bug and took up an engineering job in the Australian outback, where he also earned money by running a cinema and hunting crocodiles. He reached London in 1938 via the Trans-Siberian railway and joined the RAF at the outbreak of war. He was captured in Java and spent most of the war in a Japanese POW camp, where he learned Chinese and some Russian from fellow prisoners. Back in Britain he took the BSc (Econ) 1946-49, special subject sociology. He developed a great interest in economics?and like many of his generation, became very caught up with Keynesian theory. Though fascinated he found the Keynesian model hard going. With Walter Newlyn (an undergraduate contemporary, later Professor of Economics at Leeds University) to help with the economic theory, he fell back on his engineering training. He saw that money stocks could be represented as tanks of water, and monetary flows by water circulating round plastic tubes. With a grant of £100 (obtained with Newlyn?s help) he spent the summer of 1949 in a garage in Croydon ?living on air? as James Meade was later to put it, working on a hydraulic representation of the Keynesian model. In the machine he constructed, the circular flow of income was represented by water being pumped round a series of clear plastic tubes, with outflows representing savings, taxes and imports, and inflows representing investment, government spending and exports. The model had three tanks representing the stock of money, one for transaction balances and one for foreign-held sterling balances. The whole system determined the level of income, the rate of interest, imports, exports and the exchange to an accuracy (astonishing at the time) of +two per cent. The time path of income and the other variables was traced out by plotter pens making it possible to analyse the quantitative effects of economic policy. The machine, in the jargon, was a hydraulic representation of an open economy IS-LM model with an explicit underlying dynamic structure. It was this very Heath Robinson prototype which, with the enthusiastic support of James Meade (then Professor of Commerce at the School), Phillips demonstrated to Lionel Robbins? seminar in November 1949. Those attending gazed in wonder at this large (7ft high x 5ft wide x 3ft deep) ?thing? in the middle of the room. Phillips, chain smoking, paced back and forth explaining it in a heavy New Zealand drawl, in the process giving one of the best lectures on Keynes that anyone in the audience had ever heard. Then he switched the machine on. And it worked! According to Lord Robbins? recollections, ?there was income dividing itself into consumption and saving?Keynes and Robertson need never have quarrelled if they had had the Phillips Machine before them??Phillips was made an Assistant Lecturer in Economics in 1950, Lecturer 1951, Reader 1954, and Tooke Professor of Economic Science and Statistics in 1958 (the year his Phillips Curve paper was published). He took up a Chair at the Australian National University in 1967 and, having suffered a major stroke, retired to Auckland in 1970, where he died five years later aged 60, mourned by many friends for personal as much for professional reasons.? IMAGELIBRARY/401 Persistent URL: archives.lse.ac.uk/dserve.exe?dsqServer=lib-4.lse.ac.uk&a...Subjects

lse | londonschoolofeconomics | lselibrary | aroundtheschool1980s | 1980s | awphillips | phillips | moniacmachine | phillipsmachine | phillipshydraulicmachineLicense

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With restored Phillips Machine Extracts from ?The Phillips Machine Project? by Nicholas Bar, LSE Magazine, June 1988, No75, p.3 A.W. H. ?Bill? Phillips is known worldwide as the originator of the Phillips Curve. Less well known is the remarkable man he was personally, and his extraordinary route to academic prominence via what came to be called the Phillips Machine. Trained as an electrical engineer in his native New Zealand in the 1930s, he caught the travel bug and took up an engineering job in the Australian outback, where he also earned money by running a cinema and hunting crocodiles. He reached London in 1938 via the Trans-Siberian railway and joined the RAF at the outbreak of war. He was captured in Java and spent most of the war in a Japanese POW camp, where he learned Chinese and some Russian from fellow prisoners. Back in Britain he took the BSc (Econ) 1946-49, special subject sociology. He developed a great interest in economics?and like many of his generation, became very caught up with Keynesian theory. Though fascinated he found the Keynesian model hard going. With Walter Newlyn (an undergraduate contemporary, later Professor of Economics at Leeds University) to help with the economic theory, he fell back on his engineering training. He saw that money stocks could be represented as tanks of water, and monetary flows by water circulating round plastic tubes. With a grant of £100 (obtained with Newlyn?s help) he spent the summer of 1949 in a garage in Croydon ?living on air? as James Meade was later to put it, working on a hydraulic representation of the Keynesian model. In the machine he constructed, the circular flow of income was represented by water being pumped round a series of clear plastic tubes, with outflows representing savings, taxes and imports, and inflows representing investment, government spending and exports. The model had three tanks representing the stock of money, one for transaction balances and one for foreign-held sterling balances. The whole system determined the level of income, the rate of interest, imports, exports and the exchange to an accuracy (astonishing at the time) of +two per cent. The time path of income and the other variables was traced out by plotter pens making it possible to analyse the quantitative effects of economic policy. The machine, in the jargon, was a hydraulic representation of an open economy IS-LM model with an explicit underlying dynamic structure. It was this very Heath Robinson prototype which, with the enthusiastic support of James Meade (then Professor of Commerce at the School), Phillips demonstrated to Lionel Robbins? seminar in November 1949. Those attending gazed in wonder at this large (7ft high x 5ft wide x 3ft deep) ?thing? in the middle of the room. Phillips, chain smoking, paced back and forth explaining it in a heavy New Zealand drawl, in the process giving one of the best lectures on Keynes that anyone in the audience had ever heard. Then he switched the machine on. And it worked! According to Lord Robbins? recollections, ?there was income dividing itself into consumption and saving?Keynes and Robertson need never have quarrelled if they had had the Phillips Machine before them??Phillips was made an Assistant Lecturer in Economics in 1950, Lecturer 1951, Reader 1954, and Tooke Professor of Economic Science and Statistics in 1958 (the year his Phillips Curve paper was published). He took up a Chair at the Australian National University in 1967 and, having suffered a major stroke, retired to Auckland in 1970, where he died five years later aged 60, mourned by many friends for personal as much for professional reasons.? IMAGELIBRARY/282 Persistent URL: archives.lse.ac.uk/dserve.exe?dsqServer=lib-4.lse.ac.uk&a...Subjects

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See all metadataProfessor A.W.H (Bill) Phillips with Phillips Machine c1958-67

Description

Extracts from ?The Phillips Machine Project? by Nicholas Bar, LSE Magazine, June 1988, No75, p.3 A.W. H. ?Bill? Phillips is known worldwide as the originator of the Phillips Curve. Less well known is the remarkable man he was personally, and his extraordinary route to academic prominence via what came to be called the Phillips Machine. Trained as an electrical engineer in his native New Zealand in the 1930s, he caught the travel bug and took up an engineering job in the Australian outback, where he also earned money by running a cinema and hunting crocodiles. He reached London in 1938 via the Trans-Siberian railway and joined the RAF at the outbreak of war. He was captured in Java and spent most of the war in a Japanese POW camp, where he learned Chinese and some Russian from fellow prisoners. Back in Britain he took the BSc (Econ) 1946-49, special subject sociology. He developed a great interest in economics?and like many of his generation, became very caught up with Keynesian theory. Though fascinated he found the Keynesian model hard going. With Walter Newlyn (an undergraduate contemporary, later Professor of Economics at Leeds University) to help with the economic theory, he fell back on his engineering training. He saw that money stocks could be represented as tanks of water, and monetary flows by water circulating round plastic tubes. With a grant of £100 (obtained with Newlyn?s help) he spent the summer of 1949 in a garage in Croydon ?living on air? as James Meade was later to put it, working on a hydraulic representation of the Keynesian model. In the machine he constructed, the circular flow of income was represented by water being pumped round a series of clear plastic tubes, with outflows representing savings, taxes and imports, and inflows representing investment, government spending and exports. The model had three tanks representing the stock of money, one for transaction balances and one for foreign-held sterling balances. The whole system determined the level of income, the rate of interest, imports, exports and the exchange to an accuracy (astonishing at the time) of +two per cent. The time path of income and the other variables was traced out by plotter pens making it possible to analyse the quantitative effects of economic policy. The machine, in the jargon, was a hydraulic representation of an open economy IS-LM model with an explicit underlying dynamic structure. It was this very Heath Robinson prototype which, with the enthusiastic support of James Meade (then Professor of Commerce at the School), Phillips demonstrated to Lionel Robbins? seminar in November 1949. Those attending gazed in wonder at this large (7ft high x 5ft wide x 3ft deep) ?thing? in the middle of the room. Phillips, chain smoking, paced back and forth explaining it in a heavy New Zealand drawl, in the process giving one of the best lectures on Keynes that anyone in the audience had ever heard. Then he switched the machine on. And it worked! According to Lord Robbins? recollections, ?there was income dividing itself into consumption and saving?Keynes and Robertson need never have quarrelled if they had had the Phillips Machine before them??Phillips was made an Assistant Lecturer in Economics in 1950, Lecturer 1951, Reader 1954, and Tooke Professor of Economic Science and Statistics in 1958 (the year his Phillips Curve paper was published). He took up a Chair at the Australian National University in 1967 and, having suffered a major stroke, retired to Auckland in 1970, where he died five years later aged 60, mourned by many friends for personal as much for professional reasons.? Reference: IMAGELIBRARY/6 Persistent URL: archives.lse.ac.uk/dserve.exe?dsqServer=lib-4.lse.ac.uk&a...Subjects

lselibrary | lse | londonschoolofeconomics | awphillips | phillips | phillipshydraulicmachine | phillipsmachine | moniacmachineLicense

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See all metadata18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

Description

This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last 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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eclipse | eclipse | queensland | queensland | solareclipse | solareclipse | statelibraryofqueensland | statelibraryofqueensland | sydneyobservatory | sydneyobservatory | slq | slq | thequeenslander | thequeenslander | goodiwindi | goodiwindiLicense

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digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | softwarebookdrivecapture | softwarebookdrivecapture | lightroomccphotoshopcc | lightroomccphotoshopcc | hardwarecanon5dmarkii | hardwarecanon5dmarkiiLicense

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digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | softwarebookdrivecapture | softwarebookdrivecapture | lightroomccphotoshopcc | lightroomccphotoshopcc | hardwarecanon5dmarkii | hardwarecanon5dmarkiiLicense

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digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | softwarebookdrivecapture | softwarebookdrivecapture | lightroomccphotoshopcc | lightroomccphotoshopcc | hardwarecanon5dmarkii | hardwarecanon5dmarkiiLicense

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digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterf | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | digitizedbythegrusslipperdigitallaboratoryatthecenterforjewishhistorywwwcjhorg | softwarebookdrivecapture | softwarebookdrivecapture | lightroomccphotoshopcc | lightroomccphotoshopcc | hardwarecanon5dmarkii | hardwarecanon5dmarkiiLicense

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See all metadata18.783 Elliptic Curves (MIT) 18.783 Elliptic Curves (MIT)

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This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.Subjects

elliptic curves | elliptic curves | number theory | number theory | cryptography | cryptography | point-counting | point-counting | isogenies | isogenies | pairings | pairings | theory of complex multiplication | theory of complex multiplication | integer factorization | integer factorization | primality proving | primality proving | elliptic curve cryptography | elliptic curve cryptography | modular curves | modular curves | Fermat's Last Theorem | Fermat's Last 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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