18.218 Probabilistic Method in Combinatorics, Spring 2019
This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with posit...
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| Language: | en-US |
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2023
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| Online Access: | https://hdl.handle.net/1721.1/151192 |
| _version_ | 1811082593338130432 |
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| author | Zhao, Yufei |
| author_facet | Zhao, Yufei |
| author_sort | Zhao, Yufei |
| collection | MIT |
| description | This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. The course focuses on methodology as well as combinatorial applications. |
| first_indexed | 2024-09-23T12:05:52Z |
| id | mit-1721.1/151192 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2024-09-23T12:05:52Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | mit-1721.1/1511922023-08-01T03:47:54Z 18.218 Probabilistic Method in Combinatorics, Spring 2019 Probabilistic Method in Combinatorics Zhao, Yufei probabilistic method Ramsey numbers Lovász Local Lemma hypergraph colorings balancing vectors sum-free sets second Moment Method Chernoff bound Moser-Tardos algorithm Janson’s inequalities Harris-FKG inequality Martingale convergence Azuma’s inequality entropy methods occupancy method This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. The course focuses on methodology as well as combinatorial applications. 2023-07-31T17:33:43Z 2023-07-31T17:33:43Z 2019-06 2023-07-31T17:33:50Z 18.218-Spring2019 18.218 IMSCP-MD5-0282d72460e569d6f4bd54e8bbdcfeab https://hdl.handle.net/1721.1/151192 en-US This site (c) Massachusetts Institute of Technology 2023. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license") unless otherwise noted. The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. Attribution-NonCommercial-ShareAlike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0/ text/plain text/html image/jpeg image/jpeg text/html application/pdf text/html application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf text/html application/pdf application/pdf text/html image/jpeg image/png text/html text/html application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream application/octet-stream text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/css text/html image/png image/png image/png image/png image/gif image/png image/png image/png image/jpeg image/gif image/png image/png image/png image/gif image/png image/png image/png image/png image/png image/png image/gif image/png image/png image/gif image/gif image/png image/png image/png image/png image/png image/png image/png image/png image/png image/gif image/jpeg image/gif image/png image/jpeg image/png image/png image/png image/png image/png image/png image/png image/png image/png image/gif image/png image/png image/jpeg image/gif image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/gif image/png image/gif application/octet-stream image/gif image/gif image/png image/gif image/gif image/gif image/png image/png application/octet-stream image/gif image/gif image/gif image/gif image/png image/gif image/gif application/octet-stream image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png image/png application/rdf+xml; charset=utf-8 text/html image/png image/png image/jpeg image/png image/png image/png image/png image/png text/html text/html Spring 2019 |
| spellingShingle | probabilistic method Ramsey numbers Lovász Local Lemma hypergraph colorings balancing vectors sum-free sets second Moment Method Chernoff bound Moser-Tardos algorithm Janson’s inequalities Harris-FKG inequality Martingale convergence Azuma’s inequality entropy methods occupancy method Zhao, Yufei 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title | 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title_full | 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title_fullStr | 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title_full_unstemmed | 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title_short | 18.218 Probabilistic Method in Combinatorics, Spring 2019 |
| title_sort | 18 218 probabilistic method in combinatorics spring 2019 |
| topic | probabilistic method Ramsey numbers Lovász Local Lemma hypergraph colorings balancing vectors sum-free sets second Moment Method Chernoff bound Moser-Tardos algorithm Janson’s inequalities Harris-FKG inequality Martingale convergence Azuma’s inequality entropy methods occupancy method |
| url | https://hdl.handle.net/1721.1/151192 |
| work_keys_str_mv | AT zhaoyufei 18218probabilisticmethodincombinatoricsspring2019 AT zhaoyufei probabilisticmethodincombinatorics |