{"id":479,"date":"2020-09-10T00:19:38","date_gmt":"2020-09-10T05:19:38","guid":{"rendered":"https:\/\/pages.stolaf.edu\/matsuura\/?page_id=479"},"modified":"2022-07-17T23:05:28","modified_gmt":"2022-07-18T04:05:28","slug":"list-of-chapters","status":"publish","type":"page","link":"https:\/\/pages.stolaf.edu\/matsuura\/list-of-chapters\/","title":{"rendered":"List of Chapters"},"content":{"rendered":"<h1>List of Chapters<\/h1>\n<p><a href=\"https:\/\/bookstore.ams.org\/text-72\/\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-756 alignright\" src=\"https:\/\/pages.stolaf.edu\/matsuura\/wp-content\/uploads\/sites\/439\/2022\/07\/text-72-matsuura-cov-210x300.jpg\" alt=\"\" width=\"420\" height=\"600\" srcset=\"https:\/\/pages.stolaf.edu\/matsuura\/wp-content\/uploads\/sites\/439\/2022\/07\/text-72-matsuura-cov-210x300.jpg 210w, https:\/\/pages.stolaf.edu\/matsuura\/wp-content\/uploads\/sites\/439\/2022\/07\/text-72-matsuura-cov-105x150.jpg 105w, https:\/\/pages.stolaf.edu\/matsuura\/wp-content\/uploads\/sites\/439\/2022\/07\/text-72-matsuura-cov-1073x1536.jpg 1073w, https:\/\/pages.stolaf.edu\/matsuura\/wp-content\/uploads\/sites\/439\/2022\/07\/text-72-matsuura-cov.jpg 1788w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<ul>\n<li>Chapter 1: Introduction to Proofs<\/li>\n<li>Chapter 2: Sets and Subsets<\/li>\n<li>Chapter 3: Divisors<\/li>\n<li>Chapter 4: Modular Arithmetic<\/li>\n<li>Chapter 5: Symmetries<\/li>\n<li>Chapter 6: Permutations<\/li>\n<li>Chapter 7: Matrices<\/li>\n<li>Chapter 8: Introduction to Groups<\/li>\n<li>Chapter 9: Groups of Small Size<\/li>\n<li>Chapter 10: Matrix Groups<\/li>\n<li>Chapter 11: Subgroups<\/li>\n<li>Chapter 12: Order of an Element<\/li>\n<li>Chapter 13: Cyclic Groups, Part I<\/li>\n<li>Chapter 14: Cyclic Groups, Part II<\/li>\n<li>Chapter 15: Functions<\/li>\n<li>Chapter 16: Isomorphisms<\/li>\n<li>Chapter 17: Homomorphisms, Part I<\/li>\n<li>Chapter 18: Homomorphisms, Part II<\/li>\n<li>Chapter 19: Introduction to Cosets<\/li>\n<li>Chapter 20: Lagrange&#8217;s Theorem<\/li>\n<li>Chapter 21: Multiplying \/ Adding Cosets<\/li>\n<li>Chapter 22: Quotient Group Examples<\/li>\n<li>Chapter 23: Quotient Group Proofs<\/li>\n<li>Chapter 24: Normal Subgroups<\/li>\n<li>Chapter 25: First Isomorphism Theorem<\/li>\n<li>Chapter 26: Introduction to Rings<\/li>\n<li>Chapter 27: Integral Domains and Fields<\/li>\n<li>Chapter 28: Polynomial Rings, Part I<\/li>\n<li>Chapter 29: Polynomial Rings, Part II<\/li>\n<li>Chapter 30: Factoring Polynomials<\/li>\n<li>Chapter 31: Ring Homomorphisms<\/li>\n<li>Chapter 32: Introduction to Quotient Rings<\/li>\n<li>Chapter 33: Quotient Ring \u2124<sub>7<\/sub>[<em>x<\/em>]\/\u27e8<em>x<\/em><sup>2<\/sup> \u2013 1\u27e9<\/li>\n<li>Chapter 34: Quotient Ring \u211d[<em>x<\/em>]\/\u27e8<em>x<\/em><sup>2<\/sup> + 1\u27e9<\/li>\n<li>Chapter 35: <em>F<\/em>[<em>x<\/em>]\/\u27e8<em>g<\/em>(<em>x<\/em>)\u27e9 Is\/Isn&#8217;t a Field, Part I<\/li>\n<li>Chapter 36: Maximal Ideals<\/li>\n<li>Chapter 37: <em>F<\/em>[<em>x<\/em>]\/\u27e8<em>g<\/em>(<em>x<\/em>)\u27e9 Is\/Isn&#8217;t a Field, Part II<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>List of Chapters Chapter 1: Introduction to Proofs Chapter 2: Sets and Subsets Chapter 3: Divisors Chapter 4: Modular Arithmetic Chapter 5: Symmetries Chapter 6: Permutations Chapter 7: Matrices Chapter 8: Introduction to Groups Chapter 9: Groups of Small Size Chapter 10: Matrix Groups Chapter 11: Subgroups Chapter 12: Order \u2026 <a class=\"continue-reading-link\" href=\"https:\/\/pages.stolaf.edu\/matsuura\/list-of-chapters\/\"> Continue reading <span class=\"meta-nav\">&rarr; <\/span><\/a><\/p>\n","protected":false},"author":949,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-479","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/pages\/479","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/users\/949"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/comments?post=479"}],"version-history":[{"count":11,"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/pages\/479\/revisions"}],"predecessor-version":[{"id":785,"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/pages\/479\/revisions\/785"}],"wp:attachment":[{"href":"https:\/\/pages.stolaf.edu\/matsuura\/wp-json\/wp\/v2\/media?parent=479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}