{"id":84,"date":"2012-06-12T00:00:29","date_gmt":"2012-06-11T18:30:29","guid":{"rendered":"http:\/\/ckraju.net\/blog\/?p=84"},"modified":"2012-06-12T00:00:29","modified_gmt":"2012-06-11T18:30:29","slug":"calculus-without-limits-in-tehran","status":"publish","type":"post","link":"https:\/\/ckraju.net\/wordpress_F\/?p=84","title":{"rendered":"Calculus without Limits in Tehran"},"content":{"rendered":"<p>Here is the poster<br \/>\n<img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/ckraju.net\/gif\/Iran-poster-English.gif\" alt=\"English poster\" \/><br \/>\n\u00a0<br \/>\nand the group photo<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/ckraju.net\/gif\/Iran-group-photo.gif\" alt=\"Iran group photo\" \/><br \/>\n\u00a0<br \/>\nInterestingly, this group included students from humanities, engineering, and also a mathematician and a physicist.<\/p>\n<p><!--more--><\/p>\n<p>The mathematician had to be told that there was a separate course on calculus without limits\u00a0for post-graduates in mathematics. In this course,\u00a0 tried out at USM, I thought I would go into details of the philosophy of mathematics. But the students did not understand even the formal mathematics I sought to criticise.\u00a0\u00a0Hence, half the people dropped out because they found the pre-test too tough (since it tested them on basic concepts (complete metric space, Lebesgue integral, Schwartz derivative)\u00a0related to\u00a0limits, and the failure of the formal definition of the derivative, whichever way one looks at it (as in\u00a0elementary analysis or in the Schwartz theory). \u00a0\u00a0<\/p>\n<p>In that USM test, the one and only one question which everyone could manage was a question taken from a school exam, related to differentiability and continuity. They had all memorised that a differentiable function must be continuous, without a thought to the Schwartz theory (which enables discontinuous functions to be differentiated)\u00a0or to\u00a0the meaning of the differential equations of physics, when one encounters discontinuous phenomena such as shock waves (especially those cases which cannot be handled by the simple-minded technique of going over to integral formulations). Also, if one is doing physics, it has to be refutable,\u00a0one cannot jump about between different definitions of the derivative.\u00a0The physicist, at least,\u00a0was convinced.<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is the poster \u00a0 and the group photo \u00a0 Interestingly, this group included students from humanities, engineering, and also a mathematician and a physicist.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,3],"tags":[],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-education","category-history-and-philosophy-of-mathematics"],"_links":{"self":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=84"}],"version-history":[{"count":0,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/84\/revisions"}],"wp:attachment":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}