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6.856J Randomized Algorithms (MIT) 6.856J Randomized Algorithms (MIT)

Description

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

Subjects

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

License

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

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

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18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT) 18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT)

Description

This course covers a collection of geometric techniques that apply broadly in modern algorithm design. This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

Subjects

Spectral graph theory | Spectral graph theory | Iterative methods for linear algebra | Iterative methods for linear algebra | Convex geometry | Convex geometry | Lattices and basis reduction | Lattices and basis reduction | LPs and SDPs for approximating NP-hard problems | LPs and SDPs for approximating NP-hard problems | Graph Laplacians | Graph Laplacians | Cheeger inequalities | Cheeger inequalities | Fritz John?s theorem | Fritz John?s theorem

License

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

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

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

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18.465 Topics in Statistics: Statistical Learning Theory (MIT) 18.465 Topics in Statistics: Statistical Learning Theory (MIT)

Description

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory. The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

Subjects

machine learning algorithms | machine learning algorithms | boosting | boosting | support | support | support vector machines | support vector machines | neural networks | neural networks | Vapnik- Chervonenkis theory | Vapnik- Chervonenkis theory | concentration inequalities in product spaces | concentration inequalities in product spaces | empirical process theory | empirical process theory

License

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

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18.465 Topics in Statistics: Statistical Learning Theory (MIT) 18.465 Topics in Statistics: Statistical Learning Theory (MIT)

Description

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory. The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

Subjects

machine learning algorithms | machine learning algorithms | boosting | boosting | support | support | support vector machines | support vector machines | neural networks | neural networks | Vapnik- Chervonenkis theory | Vapnik- Chervonenkis theory | concentration inequalities in product spaces | concentration inequalities in product spaces | empirical process theory | empirical process theory

License

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

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18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT) 18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT)

Description

This course covers a collection of geometric techniques that apply broadly in modern algorithm design. This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

Subjects

Spectral graph theory | Spectral graph theory | Iterative methods for linear algebra | Iterative methods for linear algebra | Convex geometry | Convex geometry | Lattices and basis reduction | Lattices and basis reduction | LPs and SDPs for approximating NP-hard problems | LPs and SDPs for approximating NP-hard problems | Graph Laplacians | Graph Laplacians | Cheeger inequalities | Cheeger inequalities | Fritz John?s theorem | Fritz John?s theorem

License

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

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18.996A Simplicity Theory (MIT) 18.996A Simplicity Theory (MIT)

Description

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases. This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

Subjects

universal domains | universal domains | compact abstract theories | compact abstract theories | indiscernibility | indiscernibility | indiscernible sequences | indiscernible sequences | dividing | dividing | simplicity | simplicity | independence | independence | Lascar strong types | Lascar strong types | independence theorem | independence theorem | hyperimaginaries | hyperimaginaries | canonical bases | canonical bases | supersimplicity | supersimplicity | Lascar inequalities | Lascar inequalities | stability | stability | stable theories | stable theories | generic automorphism | generic automorphism | type-definable groups | type-definable groups | lovely pairs | lovely pairs

License

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

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6.856J Randomized Algorithms (MIT)

Description

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

Subjects

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

License

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

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6.972 Algebraic Techniques and Semidefinite Optimization (MIT) 6.972 Algebraic Techniques and Semidefinite Optimization (MIT)

Description

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications. This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subjects

algebraic and computational techniques | algebraic and computational techniques | optimization problems | optimization problems | polynomial equations | polynomial equations | inequalities | inequalities | semidefinite optimization | semidefinite optimization | convexity-based ideas | convexity-based ideas | complexity results | complexity results | efficient implementations | efficient implementations

License

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

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18.657 Mathematics of Machine Learning (MIT) 18.657 Mathematics of Machine Learning (MIT)

Description

Broadly speaking, Machine Learning refers to the automated identification of patterns in data. As such it has been a fertile ground for new statistical and algorithmic developments. The purpose of this course is to provide a mathematically rigorous introduction to these developments with emphasis on methods and their analysis.You can read more about Prof. Rigollet's work and courses on his website. Broadly speaking, Machine Learning refers to the automated identification of patterns in data. As such it has been a fertile ground for new statistical and algorithmic developments. The purpose of this course is to provide a mathematically rigorous introduction to these developments with emphasis on methods and their analysis.You can read more about Prof. Rigollet's work and courses on his website.

Subjects

Binary Classification | Binary Classification | Concentration inequalities | Concentration inequalities | VC theory | VC theory | VC inequality | VC inequality | Gradient Descent | Gradient Descent | Mirror Descent | Mirror Descent | Stochastic Bandits | Stochastic Bandits | Adversarial bandits | Adversarial bandits | Linear bandits | Linear bandits | Blackwell's approachability | Blackwell's approachability

License

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

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

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

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18.657 Mathematics of Machine Learning (MIT)

Description

Broadly speaking, Machine Learning refers to the automated identification of patterns in data. As such it has been a fertile ground for new statistical and algorithmic developments. The purpose of this course is to provide a mathematically rigorous introduction to these developments with emphasis on methods and their analysis.You can read more about Prof. Rigollet's work and courses on his website.

Subjects

Binary Classification | Concentration inequalities | VC theory | VC inequality | Gradient Descent | Mirror Descent | Stochastic Bandits | Adversarial bandits | Linear bandits | Blackwell's approachability

License

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

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Improving the health of the population and evidence based medicine

Description

This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009 This module has two essential components: Evidence-Based Medicine and Public Health. Evidence-Based Medicine was introduced as a new discipline because traditionally the teaching of medicine was heavily reliant on an apprenticeship-type system with emphasis on learning from observing one’s teachers. One of the guiding principles in the NHS today is that all health care should be based on research evidence. One of the aims of this module is to cover core concepts in epidemiology and basic statistics so that you are able to understand the evidence presented in research papers and apply it to your clinical practice. The Public Health component of this module will provide you wi

Subjects

evidence based medicine | ukoer | public health | health of the population | determinants of health | inequalities in health | obesity | diet and physical activity | screening | positive predictive value of screening tests | multidisciplinary approach to population health | Subjects allied to medicine | B000

License

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

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6.972 Algebraic Techniques and Semidefinite Optimization (MIT)

Description

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subjects

algebraic and computational techniques | optimization problems | polynomial equations | inequalities | semidefinite optimization | convexity-based ideas | complexity results | efficient implementations

License

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

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18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT)

Description

This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

Subjects

Spectral graph theory | Iterative methods for linear algebra | Convex geometry | Lattices and basis reduction | LPs and SDPs for approximating NP-hard problems | Graph Laplacians | Cheeger inequalities | Fritz John?s 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 https://ocw.mit.edu/terms/index.htm

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Social Problems: who makes them?

Description

Anti-social behaviour, homelessness, drugs, metal illness: all problems in today’s society. But what makes a problem social? This unit will help you to discover how these issues are identified, defined, given meaning and acted upon. You will also look at the conflicts within social science in this area.

Subjects

society | antisocial_behaviour | ideology | inequalities | poverty | social_problems | social science | Education | X000

License

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

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18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

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

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18.465 Topics in Statistics: Statistical Learning Theory (MIT)

Description

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

Subjects

machine learning algorithms | boosting | support | support vector machines | neural networks | Vapnik- Chervonenkis theory | concentration inequalities in product spaces | empirical process theory

License

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

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18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

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

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18.996A Simplicity Theory (MIT)

Description

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

Subjects

universal domains | compact abstract theories | indiscernibility | indiscernible sequences | dividing | simplicity | independence | Lascar strong types | independence theorem | hyperimaginaries | canonical bases | supersimplicity | Lascar inequalities | stability | stable theories | generic automorphism | type-definable groups | lovely pairs

License

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

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18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

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

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18.465 Topics in Statistics: Statistical Learning Theory (MIT)

Description

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

Subjects

machine learning algorithms | boosting | support | support vector machines | neural networks | Vapnik- Chervonenkis theory | concentration inequalities in product spaces | empirical process theory

License

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

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18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit (MIT)

Description

This course covers a collection of geometric techniques that apply broadly in modern algorithm design.

Subjects

Spectral graph theory | Iterative methods for linear algebra | Convex geometry | Lattices and basis reduction | LPs and SDPs for approximating NP-hard problems | Graph Laplacians | Cheeger inequalities | Fritz John?s 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 https://ocw.mit.edu/terms/index.htm

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The lottery of birth

Description

This free course, The lottery of birth, will look at both the big picture of the ?lottery of birth? and the smaller, human stories. You will examine the inequalities of birth, particularly being born rich or poor and being born female or male. First published on Wed, 12 Oct 2016 as The lottery of birth. To find out more visit The Open University's Openlearn website. Creative-Commons 2016

Subjects

Health | Sports & Psychology | OUFL_21 | birth | gender inequalities | health | society | children | childbirth

License

Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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http://www.open.edu/openlearn/rss/try-content

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