{"id":202,"date":"2017-08-01T21:03:14","date_gmt":"2017-08-01T21:03:14","guid":{"rendered":"https:\/\/sites.wcsu.edu\/roccac\/?page_id=202"},"modified":"2017-08-15T17:26:25","modified_gmt":"2017-08-15T17:26:25","slug":"app_number_theory","status":"publish","type":"page","link":"https:\/\/sites.wcsu.edu\/roccac\/homepage\/app_number_theory\/","title":{"rendered":"Applications in Number Theory"},"content":{"rendered":"<h3 style=\"text-align: center\">MAT 599-61:<\/h3>\n<h3 style=\"text-align: center\">Applications in Number Theory<\/h3>\n<h3 style=\"text-align: center\">Summer 2017<\/h3>\n<ul>\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2017\/08\/2017-Summer-Number-Theory-II.pdf\" target=\"_blank\" rel=\"noopener\">Syllabus<\/a><\/li>\n<li>Presentations:\n<ol style=\"font-size: small\">\n<li><span style=\"color: #339966\">Chinese Remainder Theorem &#8211; Rocca \u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Euler&#8217;s \\(\\phi\\)-Function and Euler&#8217;s Theorem \u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Pseudoprimes, Miller&#8217;s Test, Theorem 6.8, Rabin&#8217;s Probabilistic Test (Theorem 6.11) &#8211; D. Ciskowski \u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Mersenne Primes, Lucas-Lehmer Test &#8211; K. Ciskowski\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Lucas&#8217;s Converse to Fermat&#8217;s Little (Theorem 9.18) and Corollary 9.18.1 &#8211; D. Cook\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Theorem 9.19 and Big O-Notation &#8211; Rocca\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Pocklington&#8217;s and Proth&#8217;s Primality Tests &#8211; D. Ciskowski\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Sections 11.1-11.3 &#8211; Rocca\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Euler Pseudoprimes, Solovay-Strassen Probabilistic Test &#8211; K. Ciskowski\u00a0\u2713<\/span><\/li>\n<li><del>Fermat Factorization &#8211; D. Cook<\/del><\/li>\n<li><del>Pollard&#8217;s Rho Factorization Method &#8211; D. Ciskowski<\/del><\/li>\n<li><span style=\"color: #339966\">Continued Fractions and theorem 12.8 &#8211; Rocca\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">Theorem 12.7 &#8211; K. Ciskowski\u00a0\u2713<\/span><\/li>\n<li><span style=\"color: #339966\">\\(k^{th}\\)-Convergent, Theorem 12.9 &#8211; D. Cook\u00a0\u2713<\/span><\/li>\n<li>Theorem 12.15 &#8211; Rocca<\/li>\n<li>Theorem 12.24 (including Lemma 12.6), Continued Fraction Factorization &#8211; D. Ciskowski<\/li>\n<li>Rabin Cryptosystem (p. 329 and exercise 49 in section 11.1) &#8211; K. Ciskowski<\/li>\n<li>Knapsack Problem and Super Increasing Sequences (pp. 331-333) &#8211; Rocca<\/li>\n<li>Knapsack Ciphers (pp. 334-336) &#8211; D. Cook<\/li>\n<li>Electronic Poker &#8211; Rocca<\/li>\n<li>El Gamal Cryptosystem &#8211; Rocca<\/li>\n<\/ol>\n<\/li>\n<li>Programing Assignments: These are listed on <a href=\"https:\/\/cocalc.com\/\" target=\"_blank\" rel=\"noopener\">CoCalc.com<\/a><\/li>\n<li>Text Exercises: Do 8 of the following\n<ul style=\"font-size: small\">\n<li>p.170 15 and 19<\/li>\n<li>p. 170 27-29 (use the result from #19, change periods to 23, 27, and 31 (why?))<\/li>\n<li>???<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>MAT 599-61: Applications in Number Theory Summer 2017 Syllabus Presentations: Chinese Remainder Theorem &#8211; Rocca \u2713 Euler&#8217;s \\(\\phi\\)-Function and Euler&#8217;s Theorem \u2713 Pseudoprimes, Miller&#8217;s Test, Theorem 6.8, Rabin&#8217;s Probabilistic Test (Theorem 6.11) &#8211; D. Ciskowski \u2713 Mersenne Primes, Lucas-Lehmer Test &hellip; <a href=\"https:\/\/sites.wcsu.edu\/roccac\/homepage\/app_number_theory\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":35,"featured_media":0,"parent":2,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"wpo365_audiences":[],"wpo365_private":false,"footnotes":""},"class_list":["post-202","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/202","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/users\/35"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/comments?post=202"}],"version-history":[{"count":0,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/202\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/media?parent=202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}