{"id":2950,"date":"2025-10-24T10:58:06","date_gmt":"2025-10-24T14:58:06","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/avince\/?page_id=2950"},"modified":"2026-03-19T08:15:14","modified_gmt":"2026-03-19T12:15:14","slug":"reasoning-and-proof-in-mathematics","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/avince\/reasoning-and-proof-in-mathematics\/","title":{"rendered":"Reasoning and Proof in Mathematics"},"content":{"rendered":"\r\n
\r\n\t
\r\n\t\t
\r\n\t\t\t
\r\n\t\t\t\t\n

Reasoning and Proof in Mathematics<\/h1>\n\n\n\n

MHF 3202<\/span><\/p>\n\n\n\n\n\n

Spring 2026<\/span><\/p>\n\n\n\n\n\n\n\n\n\n

______________________________________________________<\/p>\n\n\n\n\n\n

Time:<\/span><\/b>\u00a0 MWF period\u00a0<\/span><\/p>\n\n\n\n\n\n

Place:<\/span><\/b>\u00a0 \u00a0207 Little Hall<\/span><\/p>\n\n\n\n\n\n

Email<\/b>:\u00a0 avince@ufl.edu\u00a0<\/span><\/p>\n\n\n\n\n\n

Office <\/strong>:\u00a0 438 Little Hall<\/span><\/p>\n\n\n\n\n\n

Office hours<\/strong>: MWF period 4 or by appointment<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n

Textbook:<\/b>\u00a0 Proof and the Art of Mathematics by J. D. Hamkins<\/span><\/p>\n\n\n\n\n\n

<\/p>\n\n\n\n\n\n\n\n\n\n

<\/a>Course Description<\/span><\/h3>\n\n\n\n


\nA main goal is to prepare prospective mathematics majors for courses in which obtaining and proving mathematical statements is essential.\u00a0 To quote George Polya fon solving a problem: <\/span><\/span><\/p>\n\n\n\n\n\n

“If it challengses your curiousity and brings into play your invention, faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.”\u00a0<\/span><\/span><\/p>\n\n\n\n\n\n\n\n\n\n

\n\n\n\n

<\/a>Suggested Weekly Problems<\/span><\/h3>\n\n\n\n
See canvas.<\/span><\/pre>\n\n\n\n
\n\n\n\n
Topics\u00a0<\/span><\/h3>\n\n\n\n
Deductive reasoning <\/span><\/p>\n\n\n\n\n\n
Mathematical Induction<\/span><\/p>\n\n\n\n\n\n
Four basic steps:\u00a0 (1) Understanding the problem, (2) devising a plan, (3) carrying out the plan, (3) looking back<\/span><\/p>\n\n\n\n\n\n
Heuristicss<\/span><\/p>\n\n\n\n\n\n
Examples from the following subjects:<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Number theory <\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Discrete Mathematics<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Geometry<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Graph Theory<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Real Analysis<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
\n\n\n\n
<\/a>Grades<\/span><\/h3>\n\n\n\n
Three exams, each worth a third of the final grade.<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Exam 1.\u00a0 \u00a0February 9<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Exam 2.\u00a0 \u00a0March 13<\/span><\/p>\n\n\n\n\n\n
\u00a0 \u00a0 \u00a0Exam 3.\u00a0 \u00a0April 20<\/span><\/p>\n\n\n\n\n\n
The exams will be graded on a sliding scale, the harder the exam, the more lenient the grading.\u00a0 Out of 100, it will never be stricter than 90A, 80B, 70C, 60D.<\/span><\/p>\n\n\n\n\n\n
Weekly problems will be suggested, but not graded.<\/span><\/p>\n\n\n\n\n\n
At most 5 unexcused absences.\u00a0 More than this will result in a reduction of one letter grade (A->B, B->C, C->D, D->F) in the course.<\/span><\/p>\n\n\n\n
\n\n\n\n
<\/p>\n\n\n\n
<\/a>Campus Resources<\/span><\/h3>\n\n\n\n
\u00a0 \u00a0 \u00a0 \u00a0This course complies with all UF academic policies. For information on those polices and for resources for students, please see <\/span>this link.<\/a><\/span>
\n<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
\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":289,"featured_media":0,"parent":0,"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-2950","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/2950","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/users\/289"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/comments?post=2950"}],"version-history":[{"count":7,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/2950\/revisions"}],"predecessor-version":[{"id":2971,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/2950\/revisions\/2971"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/media?parent=2950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}