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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power. This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Subjects

finite automata | finite automata | Turing machine | Turing machine | halting problem | halting problem | computability | computability | computational complexity | computational complexity | polynomial time | polynomial time | P | P | NP | NP | NP complete | NP complete | probabilistic algorithms | probabilistic algorithms | private-key cryptography | private-key cryptography | public-key cryptography | public-key cryptography | randomness | randomness

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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15.099 Readings in Optimization (MIT) 15.099 Readings in Optimization (MIT)

Description

In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention. In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention.

Subjects

deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization | deterministic optimization | algorithms | algorithms | stochastic processes | stochastic processes | random number generation | random number generation | simplex method | simplex method | nonlinear | nonlinear | convex | convex | complexity analysis | complexity analysis | semidefinite programming | semidefinite programming | heuristic | heuristic | global optimization | global optimization | Las Vegas algorithm | Las Vegas algorithm | randomized algorithm | randomized algorithm | linear programming | linear programming | search techniques | search techniques | hit and run | hit and run | NP-hard | NP-hard | approximation | approximation

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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18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomization

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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18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomization

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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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

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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15.012 Applied Macro- and International Economics (MIT) 15.012 Applied Macro- and International Economics (MIT)

Description

This course will focus on the environment of firms with particular emphasis on economic variables such as GNP, inflation, interest rates, exchange rates and international trade. The course is divided into five parts: The first presents the basic tools of macroeconomic management by focusing on historical episodes, particularly in the United States. The second looks at national economic strategies for development. The third section concentrates on the recent financial and currency crises in emerging markets. The fourth part looks at the problems faced by transition economies. Finally, the last module looks at challenges of developed countries. This course will focus on the environment of firms with particular emphasis on economic variables such as GNP, inflation, interest rates, exchange rates and international trade. The course is divided into five parts: The first presents the basic tools of macroeconomic management by focusing on historical episodes, particularly in the United States. The second looks at national economic strategies for development. The third section concentrates on the recent financial and currency crises in emerging markets. The fourth part looks at the problems faced by transition economies. Finally, the last module looks at challenges of developed countries.

Subjects

economic variables | economic variables | GNP | GNP | inflation | inflation | interest rates | interest rates | exchange rates | exchange rates | international trade | international trade | macroeconomic management | macroeconomic management | history | history | historical episodes | historical episodes

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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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

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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22.106 Neutron Interactions and Applications (MIT) 22.106 Neutron Interactions and Applications (MIT)

Description

This course is  a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas. This course is  a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas.

Subjects

neutron distributions | neutron distributions | fission | fission | fusion | fusion | RST | RST | Particle simulation methods | Particle simulation methods | complex processes | complex processes | numerical solutions of equations | numerical solutions of equations | basic concepts | basic concepts | underlying scientific connections | underlying scientific connections | current research areas | current research areas | angular distributions | angular distributions | energy distributions | energy distributions | single collision | single collision | multiple collisions | multiple collisions | neutron interactions | neutron interactions | elastic scattering | elastic scattering | inelastic scattering | inelastic scattering | MCNP | MCNP | Monte Carlo | Monte Carlo | molecular dynamics | molecular dynamics

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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The Constitutional Issues surrounding devolution in the UK

Description

Iain MacLean, Professor of Politics and fellow of Nuffield College, the British Academy and the Royal Society Edinburgh, has published widely on constitutional issues. MacLean is joined by Professor Will Hutton. His What's wrong with the British Constitution? co-won the WJM Mackenzie Prize for the best politics book of the year and was a member of the Independent Expert Group advising the Calman Commission on Scottish Devolution. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

parliament | alumni | devolution | SNP | oxford | plitics | parliament | alumni | devolution | SNP | oxford | plitics | 2012-09-15

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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The Constitutional Issues surrounding devolution in the UK

Description

Iain MacLean, Professor of Politics and fellow of Nuffield College, the British Academy and the Royal Society Edinburgh, has published widely on constitutional issues. MacLean is joined by Professor Will Hutton. His What's wrong with the British Constitution? co-won the WJM Mackenzie Prize for the best politics book of the year and was a member of the Independent Expert Group advising the Calman Commission on Scottish Devolution. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

parliament | alumni | devolution | SNP | oxford | plitics | parliament | alumni | devolution | SNP | oxford | plitics | 2012-09-15

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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15.031J Energy Decisions, Markets, and Policies (MIT) 15.031J Energy Decisions, Markets, and Policies (MIT)

Description

Includes audio/video content: AV lectures. This course examines the choices and constraints regarding sources and uses of energy by households, firms, and governments through a number of frameworks to describe and explain behavior at various levels of aggregation. Examples include a wide range of countries, scope, settings, and analytical approaches. This course is one of many OCW Energy Courses, and it is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges. Includes audio/video content: AV lectures. This course examines the choices and constraints regarding sources and uses of energy by households, firms, and governments through a number of frameworks to describe and explain behavior at various levels of aggregation. Examples include a wide range of countries, scope, settings, and analytical approaches. This course is one of many OCW Energy Courses, and it is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

Subjects

15.031 | 15.031 | 14.43 | 14.43 | 21A.341 | 21A.341 | 11.161 | 11.161 | energy | energy | energy systems | energy systems | oil reserves | oil reserves | public policy | public policy | environmental policy | environmental policy | path dependence | path dependence | climate science | climate science | business decisions | business decisions | NPV analysis | NPV analysis | negotiations | negotiations | globalization | globalization | regulation | regulation | power systems | power systems

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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HST.508 Quantitative Genomics (MIT) HST.508 Quantitative Genomics (MIT)

Description

This course provides a foundation in the following four areas: evolutionary and population genetics; comparative genomics; structural genomics and proteomics; and functional genomics and regulation. This course provides a foundation in the following four areas: evolutionary and population genetics; comparative genomics; structural genomics and proteomics; and functional genomics and regulation.

Subjects

genomics | genomics | quantitative genomics | quantitative genomics | comparative genomics | comparative genomics | genes | genes | genome | genome | SNPs | SNPs | haplotypes | haplotypes | sequence alignment | sequence alignment | protein structure | protein structure | protein folding | protein folding | proteomics | proteomics | structural genomics | structural genomics | functional genomics | functional genomics | networks | networks | systems biology | systems biology | biological networks | biological networks | RNA | RNA | DNA | DNA | gene expression | gene expression | evolutionary genetics | evolutionary genetics | population genetics | population genetics

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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Complejidad y Optimización Complejidad y Optimización

Description

Subjects

Optimización | Optimización | NP-completitud | NP-completitud | Programación entera | Programación entera | Programación lineal | Programación lineal | Reducción polinomial | Reducción polinomial | Simplex | Simplex | Bound | Bound | Ingeniería de Sistemas y Automática | Ingeniería de Sistemas y Automática

License

http://creativecommons.org/licenses/by-nc-sa/3.0/

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7.342 Personal Genomics and Medicine: What's in Your Genome? (MIT) 7.342 Personal Genomics and Medicine: What's in Your Genome? (MIT)

Description

Human genome sequencing has revolutionized our understanding of disease susceptibility, drug metabolism and human ancestry. This course will explore how these advances have been made possible by revolutionary new sequencing methodologies that have decreased costs and increased throughput of genome analysis, making it possible to examine genetic correlates for a variety of biological processes and disorders. The course will combine discussions of primary scientific research papers with hands-on data analysis and small group presentations. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a Human genome sequencing has revolutionized our understanding of disease susceptibility, drug metabolism and human ancestry. This course will explore how these advances have been made possible by revolutionary new sequencing methodologies that have decreased costs and increased throughput of genome analysis, making it possible to examine genetic correlates for a variety of biological processes and disorders. The course will combine discussions of primary scientific research papers with hands-on data analysis and small group presentations. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a

Subjects

genome sequencing | genome sequencing | genome analysis | genome analysis | disease susceptibility | disease susceptibility | drug metabolism | drug metabolism | human ancestry | human ancestry | mitochondrial DNA | mitochondrial DNA | tyrosine kinase inhibitors | tyrosine kinase inhibitors | BCR-ABL gene fusion | BCR-ABL gene fusion | PCSK9 inhibitors | PCSK9 inhibitors | hypercholesterolemia | hypercholesterolemia | genetic testing | genetic testing | next generation sequencing | next generation sequencing | Single-nucleotide polymorphisms (SNPs) | Single-nucleotide polymorphisms (SNPs) | copy number variations (CNVs) | copy number variations (CNVs) | genome-wide association studies (GWAS) | genome-wide association studies (GWAS) | Chronic myelogenous leukemia (CML) | Chronic myelogenous leukemia (CML) | mosaics | mosaics | chimeras | chimeras | bioinformatics | bioinformatics

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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Scottish Referendum

Description

Panel discussion on the Scottish Referendum. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

politics | history | Scotland | referendum | SNP | politics | history | Scotland | referendum | SNP

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT) 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT)

Description

Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions). Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Subjects

NP-completeness | NP-completeness | 3SAT | 3SAT | 3-partition | 3-partition | Hamiltonicity | Hamiltonicity | PSPACE | PSPACE | EXPTIME | EXPTIME | EXPSPACE | EXPSPACE | games | games | puzzles | puzzles | computation | computation | Tetris | Tetris | Nintendo | Nintendo | Super Mario Bros. | Super Mario Bros. | The Legend of Zelda | The Legend of Zelda | Metroid | Metroid | Pokémon | Pokémon | constraint logic | constraint logic | Sudoku | Sudoku | Nikoli | Nikoli | Chess | Chess | Go | Go | Othello | Othello | board games | board games | inapproximability | inapproximability | PCP theorem | PCP theorem | OPT-preserving reduction | OPT-preserving reduction | APX-hardness | APX-hardness | vertex cover | vertex cover | Set-cover hardness | Set-cover hardness | Group Steiner tree | Group Steiner tree | k-dense subgraph | k-dense subgraph | label cover | label cover | Unique Games Conjecture | Unique Games Conjecture | independent set | independent set | fixed-parameter intractability | fixed-parameter intractability | parameter-preserving reduction | parameter-preserving reduction | W hierarchy | W hierarchy | clique-hardness | clique-hardness | 3SUM-hardness | 3SUM-hardness | exponential time hypothesis | exponential time hypothesis | counting problems | counting problems | solution uniqueness | solution uniqueness | game theory | game theory | Existential theory of the reals | Existential theory of the reals | undecidability | undecidability

License

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7.15 Experimental Molecular Genetics (MIT) 7.15 Experimental Molecular Genetics (MIT)

Description

This project-based laboratory course provides students with in-depth experience in experimental molecular genetics, using modern methods of molecular biology and genetics to conduct original research. The course is geared towards students (including sophomores) who have a strong interest in a future career in biomedical research. This semester will focus on chemical genetics using Caenorhabditis elegans as a model system. Students will gain experience in research rationale and methods, as well as training in the planning, execution, and communication of experimental biology. WARNING NOTICE The experiments described in these materials are potentially hazardous and require a high level of safety training, special facilities and equipment, and supervision by appropriate individuals. You bear This project-based laboratory course provides students with in-depth experience in experimental molecular genetics, using modern methods of molecular biology and genetics to conduct original research. The course is geared towards students (including sophomores) who have a strong interest in a future career in biomedical research. This semester will focus on chemical genetics using Caenorhabditis elegans as a model system. Students will gain experience in research rationale and methods, as well as training in the planning, execution, and communication of experimental biology. WARNING NOTICE The experiments described in these materials are potentially hazardous and require a high level of safety training, special facilities and equipment, and supervision by appropriate individuals. You bear

Subjects

molecular genetics | molecular genetics | molecular biology | molecular biology | chemical genetics | chemical genetics | Caenorhabditis elegans | Caenorhabditis elegans | experimental biology | experimental biology | bioinformatics | bioinformatics | genetic linkage | genetic linkage | SNP mapping | SNP mapping | RNAi | RNAi | Gibson assembly | Gibson assembly | cDNA | cDNA | PCR | PCR | Primer design | Primer design | RNA extraction | RNA extraction | chemotaxis assay | chemotaxis assay | Next Generation Sequencing | Next Generation Sequencing

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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15.099 Readings in Optimization (MIT)

Description

In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention.

Subjects

deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization | algorithms | stochastic processes | random number generation | simplex method | nonlinear | convex | complexity analysis | semidefinite programming | heuristic | global optimization | Las Vegas algorithm | randomized algorithm | linear programming | search techniques | hit and run | NP-hard | approximation

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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18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | combinatorial optimization | network flow | matching theory | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms | NP-hard problems | discrete mathematics | fundamental algorithmic techniques | convex programming | flow theory | randomization

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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6.045J Automata, Computability, and Complexity (MIT)

Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Subjects

finite automata | Turing machine | halting problem | computability | computational complexity | polynomial time | P | NP | NP complete | probabilistic algorithms | private-key cryptography | public-key cryptography | randomness

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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What would change if the voting age was lowered to 16?

Description

This autumn, in his speech to the Labour party conference, Ed Miliband called for the voting age to be lowered to 16. This follows legislation by the SNP government in Scotland to allow 16 and 17 year olds to vote in the forthcoming referendum on Scottish independence. Explanations of the merits of extending the franchise to younger people normally begin with statements such as ‘if someone’s old enough to X…’ with X replaced by ‘marry’, ‘go to war’, ‘pay taxes’ and so on. We might note that these are, at best, weak arguments since 16 year olds can only marry and join the army with their parents’ permission and even 5 year olds pay tax in the form of VAT when their pocket money is translated into sweets.[1] Either way, it seems likely t

Subjects

Politics In Spires Schools | Labour Party | Scottish Referendum | SNP | voting age

License

http://creativecommons.org/licenses/by-sa/3.0/

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Learn Direct and Build eLearning Resources

Description

A range of interactive eLearning materials for training and up-skilling within the built environment industry.

Subjects

built environment | carpentry and joinery | construction planning | NPA Conservation | painting and decorating | plastering | stonemasonry | virtual environment | brickwork | T : Construction and Property (Built Environment) | SCQF Level 5

License

Licensee is permitted to distribute Learn Direct and Build materials to multiple clients in a closed network environment. Licensee is permitted to distribute Learn Direct and Build materials to multiple clients by including the associated files on CD's DVD's or other physical media. Licensee must use the files as is without modification. Distribution and usage is for educational purposes only and may not be used for any commerical purpose. The Intellectual Property Rights IPR will be owned by Learn Direct and Build. Licensee is permitted to distribute Learn Direct and Build materials to multiple clients in a closed network environment. Licensee is permitted to distribute Learn Direct and Build materials to multiple clients by including the associated files on CD's DVD's or other physical media. Licensee must use the files as is without modification. Distribution and usage is for educational purposes only and may not be used for any commerical purpose. The Intellectual Property Rights IPR will be owned by Learn Direct and Build. http://www.beeldb.com/UserLogin.aspx?ReturnUrl=%2fdefault.aspx http://www.beeldb.com/UserLogin.aspx?ReturnUrl=%2fdefault.aspx Learn Direct and Build

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National Progression Award in Bakery

Description

National Progression Award in Bakery at SCQF level 4, Group Award Code: G9T5 44. This NPA in Bakery has been designed to equip candidates with the skills required for success in current and future employment within the bakery industry or for progression to further academic qualifications. This award is aimed at candidates who are interested in pursuing a career in the bakery and catering industries but do not necessarily have any prior experience.

Subjects

G9T5 44 | National Progression Award | NPA | bread making | bakery | NE : Baking/Dairy/Food and Drink Processing | SCQF Level 4

License

Attribution-NonCommercial-ShareAlike 3.0 Unported Attribution-NonCommercial-ShareAlike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0/ http://creativecommons.org/licenses/by-nc-sa/3.0/ SFEU (College Development Network) SFEU (College Development Network)

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