{"id":164,"date":"2007-08-04T11:15:16","date_gmt":"2007-08-04T11:15:16","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=164"},"modified":"2020-03-14T19:29:30","modified_gmt":"2020-03-14T19:29:30","slug":"164","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=164","title":{"rendered":"Mathematics Summer School in Sirince in Turkey"},"content":{"rendered":"<p>Those of us involved in mathematics education often whinge about current\u00c2\u00a0standards, the lack of enthusiasm\u00c2\u00a0in students etc so it is refreshing to read Alexander Borovik&#8217;s\u00c2\u00a0reports <a target=\"_blank\" href=\"http:\/\/www.maths.manchester.ac.uk\/~avb\/micromathematics\/2007\/07\/gold-sand-in-stream.html\" title=\"Gold Sand in a Stream\" rel=\"noopener noreferrer\">Gold Sand in a Stream<\/a> and <a target=\"_blank\" href=\"http:\/\/www.maths.manchester.ac.uk\/~avb\/micromathematics\/2007\/07\/photos-from-mathematical-village_26.html\" title=\"Photos from Mathematical Village \" rel=\"noopener noreferrer\">Photos from Mathematical Village<\/a> about a mathematics summer school for undergraduate students in Sirince in Turkey. The summer school was\u00c2\u00a0run by Professor Ali Nesin, who is\u00c2\u00a0 Chair of the Department of Mathematics of the Istanbul Bilgi University. Professor Borovik was enchanted not just by the beautiful setting but also by the &#8216;bright motivated students&#8217;.<\/p>\n<p>The level of education was high\u00c2\u00a0including a crash course in reflection groups. One of the blackboards photographed includes the following mathematics:<\/p>\n<blockquote><p>If <img src='\/maths\/latexrender\/pictures\/dfcf28d0734569a6a693bc8194de62bf.gif' title='G' alt='G' align=absmiddle> is a group then the set <img src='\/maths\/latexrender\/pictures\/3123cf4d77c2f49ed3abf9f9f3609beb.gif' title='\\text{Aut}(G)' alt='\\text{Aut}(G)' align=absmiddle> of automorphisms of <img src='\/maths\/latexrender\/pictures\/dfcf28d0734569a6a693bc8194de62bf.gif' title='G' alt='G' align=absmiddle> forms a group under composition. If <img src='\/maths\/latexrender\/pictures\/7fc56270e7a70fa81a5935b72eacbe29.gif' title='A' alt='A' align=absmiddle> is abelian then <img src='\/maths\/latexrender\/pictures\/bddbcf3626e7235ebd432e33ecffa120.gif' title='\\text{Aut}(G)\\subset \\text{End}(A) ' alt='\\text{Aut}(G)\\subset \\text{End}(A) ' align=absmiddle>.<br \/>\n<img src='\/maths\/latexrender\/pictures\/0a9f5bd59d2640e35648d2cf7a35b88e.gif' title='\\text{Aut}(\\mathbb{Z})=\\text{End}(\\mathbb{Z}^*)\\simeq \\mathbb{Z}^*' alt='\\text{Aut}(\\mathbb{Z})=\\text{End}(\\mathbb{Z}^*)\\simeq \\mathbb{Z}^*' align=absmiddle><\/p>\n<p>Homework:<br \/>\nFind<br \/>\n<img src='\/maths\/latexrender\/pictures\/c814fd88bdbdc5b61f9aa44deaa15027.gif' title='\\text{End}(\\mathbb{Z}\\times \\mathbb{Z}), \\ \\text{Aut}(\\mathbb{Z}\\times \\mathbb{Z})' alt='\\text{End}(\\mathbb{Z}\\times \\mathbb{Z}), \\ \\text{Aut}(\\mathbb{Z}\\times \\mathbb{Z})' align=absmiddle><br \/>\n<img src='\/maths\/latexrender\/pictures\/d1fc7bc5b2372bc90c41ecd3e2534fe6.gif' title='\\text{Aut}(Sym(3))' alt='\\text{Aut}(Sym(3))' align=absmiddle><br \/>\n<img src='\/maths\/latexrender\/pictures\/e917d343b40689bab75de12daaec86a6.gif' title='\\text{Aut}(\\mathbb{Q}),\\ \\text{End}(\\mathbb{Q})' alt='\\text{Aut}(\\mathbb{Q}),\\ \\text{End}(\\mathbb{Q})' align=absmiddle><br \/>\n<img src='\/maths\/latexrender\/pictures\/49cabdd9650f32b6f6e23807f2e01f31.gif' title='\\text{Aut}(\\mathbb{Q}^{&amp;gt;0}),\\ \\text{\\text{End}}(\\mathbb{Q}^{&amp;gt;0})' alt='\\text{Aut}(\\mathbb{Q}^{&amp;gt;0}),\\ \\text{\\text{End}}(\\mathbb{Q}^{&amp;gt;0})' align=absmiddle><br \/>\nShow that if <img src='\/maths\/latexrender\/pictures\/d0c471d2ac1345f54eb4b594c7ea8224.gif' title='G\\simeq H' alt='G\\simeq H' align=absmiddle> then <img src='\/maths\/latexrender\/pictures\/6587c39186b33411c540b621d5850ec9.gif' title='\\text{Aut}(G) \\simeq \\text{Aut}(H)' alt='\\text{Aut}(G) \\simeq \\text{Aut}(H)' align=absmiddle>\u00c2\u00a0\u00c2\u00a0<\/p><\/blockquote>\n<p>But then the story goes sour. The authorities have closed the summer school &#8211; see <a target=\"_blank\" href=\"http:\/\/www.maths.manchester.ac.uk\/~avb\/micromathematics\/2007\/08\/blackboard-under-arrest.html\" title=\"A Blackboard under Arrest \" rel=\"noopener noreferrer\">A Blackboard under Arrest<\/a>, <a target=\"_blank\" href=\"http:\/\/www.maths.manchester.ac.uk\/~avb\/micromathematics\/2007\/08\/blackboard-under-arrest-ii.html\" title=\"A Blackboard under Arrest, II\" rel=\"noopener noreferrer\">A Blackboard under Arrest, II <\/a>\u00c2\u00a0&#8211; which is such a shame. There is a petition to save the school at <a target=\"_blank\" href=\"http:\/\/savesummerschool.blogspot.com\/\" title=\"Save Mathematical Summer School\" rel=\"noopener noreferrer\">Save Mathematical Summer School<\/a>\u00c2\u00a0you may wish to support, but also, can I ask other bloggers, mathematical or otherwise, to spread the news in the hope that it will help find some way round the problem?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Those of us involved in mathematics education often whinge about current\u00c2\u00a0standards, the lack of enthusiasm\u00c2\u00a0in students etc so it is refreshing to read Alexander Borovik&#8217;s\u00c2\u00a0reports Gold Sand in a Stream and Photos from Mathematical Village about a mathematics summer school for undergraduate students in Sirince in Turkey. The summer school was\u00c2\u00a0run by Professor Ali Nesin, [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-164","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=164"}],"version-history":[{"count":1,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions"}],"predecessor-version":[{"id":282,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions\/282"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}