{"id":3921,"date":"2026-04-23T10:05:08","date_gmt":"2026-04-23T14:05:08","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/turull\/?page_id=3921"},"modified":"2026-08-28T22:05:40","modified_gmt":"2026-08-29T02:05:40","slug":"f26-mas4301-homework","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/turull\/f26-mas4301-homework\/","title":{"rendered":"f26-mas4301-homework"},"content":{"rendered":"\n<section class=\"fullwidth-text-block\"><div class=\"container px-0\"><div class=\"row align-items-start\"><div class=\"col-12\">\n<h2 class=\"wp-block-heading\">MAS 4301 Abstract Algebra 1 &#8212; Homework assignments<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Every day<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Master sections already covered in class.<\/li>\n\n\n\n<li>Do the homework assigned bellow.<\/li>\n\n\n\n<li>Read the section scheduled in the <a href=\"..\/f26-mas4301-calendar\" target=\"_top\" rel=\"noopener\">calendar<\/a> to be discussed in the following class.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Minimum Homework by Due Date<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Due August 26. <\/strong> Do the problems in Homework 1.<\/li>\n\n\n\n<li><strong>Due August 31.<\/strong>  Calculate the Cayley table of the dihedral group D<sub>4<\/sub>.<\/li>\n\n\n\n<li><strong>Due September 2. <\/strong> Section 1, numbers 10, 13 and 15.<\/li>\n\n\n\n<li><strong>Due September 4. <\/strong> Section 2, numbers 2, and 3. (Note: The book may be wrong when it says that some of these are binary operations.)<\/li>\n\n\n\n<li><strong>Due September 9. <\/strong> Section 2, numbers 6, 7 and 10.<\/li>\n\n\n\n<li><strong>Due September 11.<\/strong> Section 2, numbers 14, 16 and 18.<\/li>\n\n\n\n<li><strong>Due September 14. <\/strong> Section 2, numbers 20, 24 and 26.<\/li>\n\n\n\n<li><strong>Due September 14. <\/strong> Section 2, numbers 28, 30, and 31.<\/li>\n\n\n\n<li><strong>Due September 21.<\/strong> 1) Let E be the set of even integers. Prove that E is a subgroup of the additive group of all integers.<br><br>2) Let O be the set of all odd integers. Prove that O is not a subgroup of the additive group of all integers.<br><br>3) Is the set of integers a subgroup of the additive group of all real numbers?<br><br>4) Is the empty set a subgroup of the additive group of all integers?<\/li>\n\n\n\n<li><strong>Due September 23<\/strong>&nbsp;Section 3, numbers 26, 28, 48, and 51.<\/li>\n\n\n\n<li><strong>Due September 25. <\/strong> Section 4, numbers 1 -7 odd and 11.<\/li>\n\n\n\n<li><strong>Due October 2. <\/strong> Section 5, numbers 1 \u2013 5.<\/li>\n\n\n\n<li><strong>Due October 8. <\/strong> Section 5, numbers 6, 7, 36 and 41.<\/li>\n\n\n\n<li><strong>Due October 14. <\/strong> Section 6, numbers 3, 6, 7, 12, 16, and 27.<\/li>\n\n\n\n<li><strong>Due October 16. <\/strong> Section 7, numbers 1, 2, 3, 6, 7, 8, and 9.<\/li>\n\n\n\n<li><strong>Due October 19. <\/strong> Section 7, numbers 19, 21, 26, and 28.<\/li>\n\n\n\n<li><strong>Due October 21. <\/strong> Section 8, numbers 14, 16, and 18.<\/li>\n\n\n\n<li><strong>Due October 23. <\/strong> Section 8, numbers 17, 19, 23, and 26.<\/li>\n\n\n\n<li><strong>Due October 26. <\/strong> Section 10, numbers 2, 6, 26, and 36.<\/li>\n\n\n\n<li><strong>Due October 28. <\/strong> Section 10, numbers 8, 22, and 25.<\/li>\n\n\n\n<li><strong>Due October 30. <\/strong> Section 9, numbers 1, 2, 3, and 4.<\/li>\n\n\n\n<li><strong>Due November 2. <\/strong> Section 9, numbers 6, 7, 10, and 25.<\/li>\n\n\n\n<li><strong>Due November 9. <\/strong> Section 11, numbers 16, 34, and 36.<\/li>\n\n\n\n<li><strong>Due November 16. <\/strong> Section 12, numbers 2, 3, 6, and 7.<\/li>\n\n\n\n<li><strong>Due November 18. <\/strong> Section 12, numbers 18, 44, 52, and 53.<\/li>\n\n\n\n<li><strong>Due November 20. <\/strong> Section 13, numbers 9, 10, 18, and 27.<\/li>\n\n\n\n<li><strong>Due November 30. <\/strong> Section 15, numbers 17, 18, 25, 27, and 35.<\/li>\n\n\n\n<li><strong>Due December 2. <\/strong> Section 14, numbers 4, 5, 15, and 18.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><a href=\"..\/f26-mas4301-calendar\" target=\"top\" rel=\"noopener\">Return to Calendar <\/a><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><a href=\"..\/f26-mas4301-syllabus\" target=\"top\" rel=\"noopener\">Return to Syllabus<\/a><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":141,"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-3921","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/pages\/3921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/users\/141"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/comments?post=3921"}],"version-history":[{"count":9,"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/pages\/3921\/revisions"}],"predecessor-version":[{"id":4016,"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/pages\/3921\/revisions\/4016"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/turull\/wp-json\/wp\/v2\/media?parent=3921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}