{"id":554,"date":"2013-09-29T18:03:44","date_gmt":"2013-09-29T22:03:44","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/groisser\/?page_id=554"},"modified":"2026-03-19T08:13:06","modified_gmt":"2026-03-19T12:13:06","slug":"syllabus","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/groisser\/classes\/6257_s13\/syllabus\/","title":{"rendered":"Syllabus and Course Information"},"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\">Syllabus and Course Information<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">MTG 6257, Spring 2013<br>\nDifferential Geometry II<\/h3>\n\n\n\n<p><a name=\"contact\"><\/a> Professor David Groisser<br>\nOffice: Little 308<br>\nPhone: 392-0281 ext. 261<br>\nEmail: <a href=\"mailto:groisser@ufl.edu\">groisser@ufl.edu<\/a><\/p>\n\n\n\n\n\n<p><a name=\"officehrs\"><\/a> <strong> Office Hours: <\/strong> Tentatively Monday and Friday 7th period (1:55-2:45), and Wednesday 4th period<br>\n(10:40-11:30). Please come early in the period or let me know to expect you later; otherwise<br>\nI may not stay in my office for the whole period. See <a href=\"..\/..\/my_schedule\"> my schedule <\/a> for updates. Students who can&#8217;t<br>\nmake scheduled office hours may see me by appointment on most weekdays.<\/p>\n\n\n\n\n\n<p><a name=\"text\"><\/a><br>\n<strong> Textbook:<\/strong> None required. However, please see<br>\nthe <a href=\"..\/6256_f12\/syllabus\"> MTG 6256 syllabus<br>\n<\/a> for information about a recommended book (Boothby, <i> An<br>\nIntroduction to Differentiable Manifolds and Riemannian Geometry<\/i>),<br>\nand for a link to some other references.<\/p>\n\n\n\n\n\n<p><a name=\"course_summary\"><\/a> <strong>Course description:<\/strong> MTG 6257 is<br>\nthe second semester of a year-long graduate sequence that introduces<br>\nthe tools of differential geometry and differential topology. The<br>\nfirst part of the semester will be devoted to some basics that we<br>\ndidn&#8217;t cover, or covered incompletely, including some basic Riemannian<br>\ngeometry. The topics for the rest of the semester will be selected<br>\nbased on input from students, with higher priority given to<br>\nthe <i>registered<\/i> students. Some of the possible topics, several<br>\nof which are interdependent, are listed below.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Riemannian geometry (a more in-depth study of Riemannian<br>\nmanifolds): covariant derivatives, curvature, geodesics, and other<br>\nfeatures<\/li>\n<li>Geometry of surfaces in <strong>R<\/strong><sup>3<\/sup>. Subtopics include<br>\nprincipal curvatures, Gaussian curvature, and the Gauss-Bonnet<br>\nTheorem.<\/li>\n<li>Further topics in Riemannian geometry. Among these are:<br>\ngeodesics, Jacobi fields, Hopf-Rinow Theorem, and curvature-comparison<br>\ntheorems.<\/li>\n<li>Connections on vector bundles. Subtopics include<br>\ncurvature, parallel transport, and holonomy.<\/li>\n<li>Lie groups (and, possibly, homogeneous spaces)<\/li>\n<li>Principal fiber bundles. Subtopics include:\n<ul>\n<li>reduction and enlargement of structure group<\/li>\n<li>associated vector bundles<\/li>\n<li>connections on principal bundles, with sub-subtopics\n<ul>\n<li>curvature, parallel transport, and holonomy, and the induced<br>\nstructures on associated vector bundles<\/li>\n<li>holonomy groups<\/li>\n<\/ul>\n<\/li><\/ul>\n<\/li><li>Chern-Weil theory and characteristic classes<\/li>\n<li>Symplectic geometry and its relation to classical mechanics<\/li>\n<li>Introduction to complex manifolds and Kaehler manifolds<\/li>\n<li>Selected topics in differential topology, such as the Poincare-Hopf<br>\nTheorem, degree theory, Sard&#8217;s theorem and some applications (such<br>\nas embedding theorems), and the Lefschetz Fixed-Point Theorem.<\/li>\n<li>Morse Theory<\/li><\/ul>\n\n\n\n<p><a name=\"prereqs\"><\/a> <strong> Prerequisite<\/strong>: Grade of C or better<br>\nin MTG 6256, <!--(taken Fall 2010),--> or permission of the instructor. Students who did not attend the first<br>\nsemester of this course should obtain and read notes from someone who<br>\ndid attend. Students who were not registered in the first semester<br>\n(whether or not they attended) should read the fall homework<br>\nassignments; in the spring I may make use of facts asserted in these<br>\nassignments. All the materials for the fall semester can be<br>\nfound <a href=\"https:\/\/people.clas.ufl.edu\/groisser\/classes\/past_classes-original\/6256_f99\/course_announcement\/\">here<\/a>.<\/p>\n\n\n\n\n\n<p><a name=\"exgrd\"><\/a><br>\n<strong> Exams, Homework, and Grading: <\/strong> There will be no exams.<br>\nYour final grade will be determined by homework and attendance. I<br>\nexpect to assign and collect approximately four to eight problem-sets<br>\nover the course of the semester. I will grade some subset of the<br>\nproblems. How large that subset is will depend on how many students<br>\nhanded in the assignment, how successful they were solving the<br>\nproblems, and how well-written their solutions are.<\/p>\n\n\n\n\n\n<p><strong>Attendance:<\/strong> I work hard to prepare my lectures, and I<br>\nexpect students to attend all of them (and to arrive <strong>on time<\/strong>),<br>\nwith the usual allowances for illness, emergency, conference-travel,<br>\netc. When you must miss a class, please obtain notes from a<br>\nclassmate.<\/p>\n\n\n\n\n\n<p><strong> Homework rules:<\/strong> The rules from last semester apply<br>\n(see <a href=\"..\/6256_f12\/syllabus#homework\">here<\/a>, from the start<br>\nof the section &#8220;More about homework&#8221; to the end of the section<br>\n&#8220;Student Honor Code&#8221;). To emphasize some of these rules more<br>\nexplicitly:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>&#8220;<strong>Leave enough space for me to write comments<\/strong>&#8221; means,<br>\namong other things, that you should leave ample margins. <strong>Please<br>\nleave margins of at least 1.25 inches at the top, bottom, and both<br>\nsides of each page.<\/strong>\u00a0<\/li>\n<li>All parts of the instruction &#8220;<strong>Staple<\/strong> the sheets<br>\ntogether in the upper left-hand corner&#8221; should be taken literally. In<br>\naddition, the request, &#8220;Please do not make this process [grading] more<br>\nburdensome than it intrinsically needs to be,&#8221; means, among other<br>\nthings, that when you staple your pages together, you should make sure<br>\nthat the staple is positioned so that when I open your booklet to any<br>\npage, the booklet lies flat and I can easily see everything you&#8217;ve<br>\nwritten on that page. (If you&#8217;ve followed the instructions to <strong>leave<br>\nadequate margins<\/strong> and to put the staple in the <strong>upper left-hand<br>\ncorner<\/strong>, this should happen automatically. Contrapositively, if<br>\nthis is not happening, then you have not followed one of these<br>\ninstructions.)<\/li>\n<\/ul>\n\n\n\n<p><strong> Accommodations for students with disabilities: <\/strong> Students<br>\nrequesting classroom accommodation must first register with the Dean<br>\nof Students Office. The Dean of Students Office will provide<br>\ndocumentation to the student who must then provide this documentation<br>\nto the instructor when requesting accommodation. See <a href=\"http:\/\/www.dso.ufl.edu\/drc\"> http:\/\/www.dso.ufl.edu\/drc<\/a>.<\/p>\n\n\n\n\n\n<p><strong> Letter grades and their grade-point equivalents at UF:<\/strong> see <a href=\"https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/grades.aspx\">this page<\/a>.<\/p>\n\n\n\n<p><i>Last update made by D. Groisser Fri Jan 4 18:44:34 EST 2013<br>\n<\/i><\/p>\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":245,"featured_media":0,"parent":552,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-554","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/pages\/554","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/users\/245"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/comments?post=554"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/pages\/554\/revisions"}],"predecessor-version":[{"id":5245,"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/pages\/554\/revisions\/5245"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/pages\/552"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/groisser\/wp-json\/wp\/v2\/media?parent=554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}