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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 | 18.416License

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See all metadata8.324 Relativistic Quantum Field Theory II (MIT) 8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material.Subjects

Quantum Field Theory | Quantum Field Theory | nonabelian gauge theories | nonabelian gauge theories | BRST symmetry | BRST symmetry | Perturbation theory anomalies | Perturbation theory anomalies | Renormalization | Renormalization | symmetry breaking | symmetry breaking | Critical exponents | Critical exponents | scalar field theory | scalar field theory | Conformal field theory | Conformal field theoryLicense

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

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See all metadata8.324 Relativistic Quantum Field Theory II (MIT) 8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics include functional path integrals, renormalization and renormalization groups, quantization of nonabelian gauge theories, BRST symmetry, renormalization and symmetry breaking, critical exponents and scalar field theory, and perturbation theory anomalies. This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics include functional path integrals, renormalization and renormalization groups, quantization of nonabelian gauge theories, BRST symmetry, renormalization and symmetry breaking, critical exponents and scalar field theory, and perturbation theory anomalies.Subjects

Quantum Field Theory | Quantum Field Theory | nonabelian gauge theories | nonabelian gauge theories | BRST symmetry | BRST symmetry | Perturbation theory anomalies | Perturbation theory anomalies | Renormalization | Renormalization | symmetry breaking | symmetry breaking | Critical exponents | Critical exponents | scalar field theory | scalar field theory | Conformal field theory | Conformal field theoryLicense

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

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See all metadata8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics include functional path integrals, renormalization and renormalization groups, quantization of nonabelian gauge theories, BRST symmetry, renormalization and symmetry breaking, critical exponents and scalar field theory, and perturbation theory anomalies.Subjects

Quantum Field Theory | nonabelian gauge theories | BRST symmetry | Perturbation theory anomalies | Renormalization | symmetry breaking | Critical exponents | scalar field theory | Conformal field theoryLicense

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

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See all metadata8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material.Subjects

Quantum Field Theory | nonabelian gauge theories | BRST symmetry | Perturbation theory anomalies | Renormalization | symmetry breaking | Critical exponents | scalar field theory | Conformal field theoryLicense

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

https://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

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See all metadata6.856J 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 | 18.416License

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

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