{"id":1504,"date":"2025-11-12T13:15:51","date_gmt":"2025-11-12T18:15:51","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/pilyugin\/?page_id=1504"},"modified":"2026-03-19T08:16:36","modified_gmt":"2026-03-19T12:16:36","slug":"map6488-s2025","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map6488-s2025\/","title":{"rendered":"MAP 6488 Biomathematics Seminar 2 (Spring 2026)"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">MAP 6488 Biomathematics Seminar 2 (Spring 2026)<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">MAP 6488 Biomathematics Seminar 2 (25654)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Instructor:\u00a0<a href=\"http:\/\/www.math.ufl.edu\/~pilyugin\">Sergei S. Pilyugin<\/a>\u00a0<br><br>\n<a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map6488_s2025\/\">https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map6488_s2025\/<\/a><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Announcements<\/span><\/span>:\u00a0The lectures will be delivered live in LIT 0217.   <br> <\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Time and Room<\/span><\/span>: MWF 6\u00a0(12:50 &#8211; 1:40 p.m.), LIT 0217.<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Textbook:<\/span><\/span> The Theory of the Chemostat: Dynamics of Microbial Competition by H. L. Smith and P. Waltman, Cambridge University Press, 1995 (ISBN 0-521-47027-7).<\/li>\n<li><span style=\"color: green\"><span style=\"text-decoration: underline\">Critical dates:<\/span><\/span>\u00a0Jan. 12\u00a0(classes begin), Apr. 22\u00a0(classes end).<\/li>\n<li><span style=\"color: green\"><span style=\"text-decoration: underline\">Holidays:<\/span><\/span> Jan. 19 (MLK Day), Mar. 14&#8211;21 (Spring Break).<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Office Hours<\/span><\/span>: MWF 4 &#8211; in LIT 458 or in zoom by appointment. Please, use e-mail:\u00a0<a href=\"mailto:pilyugin@ufl.edu\">pilyugin@ufl.edu<\/a>\u00a0for communication. For more details, see my\u00a0<a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/schedule\/\">schedule.<\/a><\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Description and Objectives of the Course<\/span><\/span>: In this course, I plan go through select chapters from the Smith and Waltman book on the chemostats and a few research papers covering the following topics: <br><br>\n1. Basic equations of microbial growth, batch vs. chemostat, analysis of growth equations, exploitative competition, competitive exclusion, mutations, plasmids, competition modulated by the presence of additional factors.<br><br>\n2. Trophic chains, multi-prey and multi-predator ecosystems, long food chains, competition for multiple resources.<br><br>\n3. Structured models of growth: size-structured and age-structured model of microbial growth.<br><br>\n4. Variable-yield models: Droop cell-quota model, phenomenological variable yield models.<br><br>\n5. Periodically forced chemostats: competitive coexistence in time-varying environments, achieving coexistence via control theory.<br><br>\n6. Removing the well-mixedness hypothesis: gradostats, unstirred chemostats.<br><br>\n7. Additional topics (if time permits)\n<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Grading System:<\/span><\/span>\u00a0The grade is determined by the average of the homework scores.\u00a0The resulting score determines the letter grade according to the following table<br>\n<table id=\"tablepress-grading_scale\" class=\"tablepress tablepress-id-grading_scale\">\n<thead>\n<tr class=\"row-1 odd\">\n<th class=\"column-1\">\n<div>Letter Grade<\/div>\n<\/th>\n<th class=\"column-2\">\n<div>A<\/div>\n<\/th>\n<th class=\"column-3\">\n<div>A-<\/div>\n<\/th>\n<th class=\"column-4\">\n<div>B+<\/div>\n<\/th>\n<th class=\"column-5\">\n<div>B<\/div>\n<\/th>\n<th class=\"column-6\">\n<div>B-<\/div>\n<\/th>\n<th class=\"column-7\">\n<div>C+<\/div>\n<\/th>\n<th class=\"column-8\">\n<div>C<\/div>\n<\/th>\n<th class=\"column-9\">\n<div>C\u2212<\/div>\n<\/th>\n<th class=\"column-10\">\n<div>D+<\/div>\n<\/th>\n<th class=\"column-11\">\n<div>D<\/div>\n<\/th>\n<\/tr>\n<\/thead>\n<tfoot>\n<tr class=\"row-2 even\">\n<th class=\"column-1\">Score<\/th>\n<th class=\"column-2\">100 \u2013 93<\/th>\n<th class=\"column-3\">92 \u2013 88<\/th>\n<th class=\"column-4\">87 \u2013 83<\/th>\n<th class=\"column-5\">82 \u2013 77<\/th>\n<th class=\"column-6\">76 \u2013 71<\/th>\n<th class=\"column-7\">70 \u2013 65<\/th>\n<th class=\"column-8\">64 \u2013 59<\/th>\n<th class=\"column-9\">58 \u2013 53<\/th>\n<th class=\"column-10\">52 \u2013 47<\/th>\n<th class=\"column-11\">46 \u2013 40<\/th>\n<\/tr>\n<\/tfoot>\n<\/table>\n<\/li>\n<li><span style=\"text-decoration: underline\">Course policies:<\/span> This course complies with all UF academic policies. For information on those polices and for resources for students, please use <a href=\"https:\/\/syllabus.ufl.edu\/syllabus-policy\/uf-syllabus-policy-links\/\">this link.<\/a><\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":311,"featured_media":0,"parent":8,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1504","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/1504","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/users\/311"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/comments?post=1504"}],"version-history":[{"count":5,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/1504\/revisions"}],"predecessor-version":[{"id":1529,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/1504\/revisions\/1529"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/8"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/media?parent=1504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}