{"id":660,"date":"2023-09-29T20:26:58","date_gmt":"2023-09-30T03:26:58","guid":{"rendered":"https:\/\/dornsife.usc.edu\/samihassaf\/?page_id=660"},"modified":"2024-05-22T15:45:45","modified_gmt":"2024-05-22T22:45:45","slug":"math-432","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/","title":{"rendered":"Combinatorics Lectures"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

The videos below are the lectures for Math 432 – Applied Combinatorics<\/strong> which I taught as a flipped class in Spring 2021. Each lecture has 3 associated videos, about 5 minutes each, following the content of Miklos Bona’s textbook, A Walk Through Combinatorics<\/em>.<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n

\n\n \n
\n\n \n
\n\n \n

\n Basic Counting\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapters 1 and 2<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Pigeonhole Principle\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Mathematical Induction\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Counting in Two Ways\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Order and Choice\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 3<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Linear Orders\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Binomial Coefficients\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n The Binomial Theorem\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 4<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n The Binomial Theorem\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Pascal’s Triangle\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Generalized Binomial Theorem\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Integer Sequences\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapters\u00a0<\/span>5 and 6<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Compositions\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Partitions\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n The Twelvefold Way\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Permutations\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter\u00a0<\/span>7<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Permutation Notation\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Stirling Numbers\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Derangements\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Generating Functions\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 8<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Recurrence Relations\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Partition Generating Function\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Exponential Generating Function\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Graph Theory\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 9<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Eulerian Walks\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Directed Graphs\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Hamiltonian Cycles\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Trees\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 10<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Trees\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Spanning Trees\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n The Matrix-Tree Theorem\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Colorings and Matchings\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 12<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Chromatic Numbers\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Planar Graphs\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Map Coloring\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Triangulations\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 11<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Art Gallery\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Matchings\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Ramsey Theory\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook<\/strong><\/em>:\u00a0Chapter 13<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Ramsey Numbers\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Computing Ramsey Numbers\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n Probabilistic Methods\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n\n\n\n \n \n \n \n \n\n\n\n\n\n\n\n
\n\n \n
\n\n \n
\n\n \n

\n Discrete Probability\n <\/h2>\n\n\n<\/div>\n \n
\n\n \n

Textbook:\u00a0<\/strong><\/em>Chapter 15<\/p>\n\n\n\n<\/div>\n <\/div>\n \n

\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n The Birthday Problem\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n \n
\n\n \n \n \n
\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n <\/a>\n \n\n<\/div>\n \n
\n \n

\n \n \n The Coupon Collector\n\n <\/a>\n <\/h3>\n \n <\/div>\n\n\n <\/div>\n <\/div>\n \n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":413,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-660","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nCombinatorics Lectures - Sami H. Assaf<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Combinatorics Lectures - Sami H. Assaf\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/\" \/>\n<meta property=\"og:site_name\" content=\"Sami H. Assaf\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-22T22:45:45+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/\",\"url\":\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/\",\"name\":\"Combinatorics Lectures - Sami H. Assaf\",\"isPartOf\":{\"@id\":\"https:\/\/dornsife.usc.edu\/samihassaf\/#website\"},\"datePublished\":\"2023-09-30T03:26:58+00:00\",\"dateModified\":\"2024-05-22T22:45:45+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/dornsife.usc.edu\/samihassaf\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Combinatorics Lectures\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/dornsife.usc.edu\/samihassaf\/#website\",\"url\":\"https:\/\/dornsife.usc.edu\/samihassaf\/\",\"name\":\"Sami H. Assaf\",\"description\":\"Sami Assaf\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/dornsife.usc.edu\/samihassaf\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Combinatorics Lectures - Sami H. Assaf","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/","og_locale":"en_US","og_type":"article","og_title":"Combinatorics Lectures - Sami H. Assaf","og_url":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/","og_site_name":"Sami H. Assaf","article_modified_time":"2024-05-22T22:45:45+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/","url":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/","name":"Combinatorics Lectures - Sami H. Assaf","isPartOf":{"@id":"https:\/\/dornsife.usc.edu\/samihassaf\/#website"},"datePublished":"2023-09-30T03:26:58+00:00","dateModified":"2024-05-22T22:45:45+00:00","breadcrumb":{"@id":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/dornsife.usc.edu\/samihassaf\/math-432\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/dornsife.usc.edu\/samihassaf\/"},{"@type":"ListItem","position":2,"name":"Combinatorics Lectures"}]},{"@type":"WebSite","@id":"https:\/\/dornsife.usc.edu\/samihassaf\/#website","url":"https:\/\/dornsife.usc.edu\/samihassaf\/","name":"Sami H. Assaf","description":"Sami Assaf","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/dornsife.usc.edu\/samihassaf\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/pages\/660","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/users\/413"}],"replies":[{"embeddable":true,"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/comments?post=660"}],"version-history":[{"count":136,"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/pages\/660\/revisions"}],"predecessor-version":[{"id":975,"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/pages\/660\/revisions\/975"}],"wp:attachment":[{"href":"https:\/\/dornsife.usc.edu\/samihassaf\/wp-json\/wp\/v2\/media?parent=660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}