{"id":269,"date":"2024-07-29T10:29:43","date_gmt":"2024-07-29T10:29:43","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/komer\/?page_id=269"},"modified":"2024-09-24T13:32:33","modified_gmt":"2024-09-24T13:32:33","slug":"m503fa24","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/komer\/m503fa24\/","title":{"rendered":"Math 503 – Algebra I – Fall 2024"},"content":{"rendered":"

This page contains some information that can be helpful before you register for the course. After registration, we will use ODTUclass<\/a>. You should follow ODTUclass<\/a> and check your emails regularly for important announcements during the semester.<\/p>\n

\n

Course Objectives<\/h2>\n

This is the first part of a classical graduate algebra course that covers some basic concepts in the theory of groups<\/strong> and rings<\/strong>.<\/p>\n

\n

Lecture Hours<\/h2>\n

The lectures will be in M203 – Tosun Terzio\u011flu Seminar Room.<\/p>\n

    \n
  • Tuesday 9:40-10:30<\/li>\n
  • Thursday 8:40-10:30<\/li>\n<\/ul>\n
    \n

    Homework, Exams, and Grading<\/h2>\n

    Homework will be assigned on a regular basis, and there will be 4-6<\/strong> homework sets by the end of the semester. There will be one midterm and a final. The time and the method of each exam will be announced later.<\/b><\/p>\n

      \n
    • Midterm, 30 points – around the 8th week.<\/li>\n
    • Final, 30 points – during the final exam period.<\/li>\n
    • Homework, 40 points.<\/li>\n<\/ul>\n

      Homework Policy:<\/b> You should write your solutions on your own. You are allowed to consult other people’s solutions for homework problems, but you must express everything in your own words. If you copy a solution, which is referred to as cheating, you will probably gain nothing and may encounter penalties.<\/p>\n

      \n

      Textbooks<\/h2>\n
        \n
      • Hungerford<\/b>, Algebra.<\/li>\n
      • Dummit and Foote<\/b>, Abstract Algebra, 3rd edition.<\/li>\n<\/ul>\n
        \n

        Tentative Course Outline<\/h2>\n

        The course content, together with a tentative course outline, can be found below. We will attempt to cover the related parts of the above textbooks each week.<\/p>\n

        Groups<\/h4>\n
          \n
        • Week 1:<\/b> (Sep 30 – Oct 4) Introduction to groups. Some examples.<\/li>\n
        • Week 2:<\/strong>\u00a0(Oct 7 – Oct 11) Subgroups. Centralizer, normalizer, stabilizer. Cyclic groups.<\/li>\n
        • Week 3:<\/strong>\u00a0(Oct 14 – Oct 18) Quotient groups and isomorphism theorems.<\/li>\n
        • Week 4:<\/strong>\u00a0(Oct 21 – Oct 25) Group Actions.<\/li>\n
        • Week 5:<\/strong>\u00a0(Oct 28 – Nov 1) Sylow Theorems.<\/li>\n
        • Week 6:<\/strong>\u00a0(Nov 4 – Nov 8) Direct products and sums. Finitely generated abelian groups.<\/li>\n
        • Week 7:<\/strong>\u00a0(Nov 11 – Nov 15) Nilpotent and solvable groups.<\/li>\n
        • Week 8:<\/strong> (Nov 18 – Nov 22) Free groups, generators, and relations.<\/li>\n<\/ul>\n

          Rings<\/h4>\n
            \n
          • Week 9:<\/strong>\u00a0(Nov 25 – Nov 29) Polynomial rings, matrix rings and group rings.<\/li>\n
          • Week 10:<\/strong>\u00a0(Dec 2 – Dec 6) Ideals and quotient rings.<\/li>\n
          • Week 11:<\/strong>\u00a0(Dec 9 – Dec 13) Euclidean domains, principal ideal domains, unique factorization domains.<\/li>\n
          • Week 12:<\/strong>\u00a0(Dec 16 – Dec 20) Continued.<\/li>\n
          • Week 13:<\/strong>\u00a0(Dec 23 – Dec 27) Polynomial rings and formal power series.<\/li>\n
          • Week 14:<\/strong>\u00a0(Dec 30 – Jan 3) Continued.<\/li>\n<\/ul>\n
            \n\n\n

            <\/p>\n","protected":false},"excerpt":{"rendered":"

            This page contains some information that can be helpful before you register for the course. After registration, we will use […]<\/p>\n","protected":false},"author":584,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-269","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages\/269","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/users\/584"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/comments?post=269"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages\/269\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/media?parent=269"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}