{"id":259,"date":"2005-01-30T10:52:09","date_gmt":"2005-01-30T15:52:09","guid":{"rendered":"https:\/\/www.goer.org\/wordpress\/mathematical_background"},"modified":"2005-01-30T10:52:09","modified_gmt":"2005-01-30T15:52:09","slug":"mathematical_background","status":"publish","type":"post","link":"https:\/\/www.goer.org\/Journal\/2005\/01\/mathematical_background.html","title":{"rendered":"Mathematical Background"},"content":{"rendered":"<p>As I was reading Jacques&#8217;s post about <a href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000501.html\" title=\"'Linear Deficit'\">UT&#8217;s undergraduate math requirements for upper-division physics<\/a>, I knew he would get at least one comment or trackback about the general watering down of standards, or some such. I was not disappointed. <\/p>\n<p>The issue Jacques describes has <em>nothing<\/em> to do with watering down of standards. Four semesters of math is (or should be) sufficient to get through upper-division Quantum Mechanics. Linear Algebra issues aside, the difficulty of upper-division Quantum Mechanics stems from the conceptual issues, not the math. The problem, <a href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000501.html#c001928\">as Jacques points out<\/a>, is a mismatch between the math curriculum and the physics curriculum.<\/p>\n<p>The UT physics department could do one of three things to fix this problem.<\/p>\n<ul>\n<li>\n<p>Require all physics students to take, or test out of, both the Advanced Calculus class <em>and<\/em> the Linear Algebra class. Physics majors really ought to have both under their belts.<\/p>\n<\/li>\n<li>\n<p>Forget about those two a la carte classes. Instead, require all upper-division majors to take a &#8220;Mathematical Methods for Physicists&#8221; class, designed to ensure that everyone has the right machinery to forge through their upper-division work.<\/p>\n<\/li>\n<li>\n<p>Coordinate with the math department; adjust the mathematical core accordingly.<\/p>\n<\/li>\n<\/ul>\n<p>My alma mater used the third approach. The math, engineering, computer science, and natural science departments all coordinated closely on the base four-semester mathematics core. Individual departments could then layer additional requirements, but at least everyone had a common foundation, even the biologists and computer scientists. This solution worked great for a school with 700 undergrads, where all the professors knew each other personally, shared babysitters, and so on. It would probably work less well for UT.<sup>[<a href=\"#30-1\">1<\/a>]<\/sup><\/p>\n<p><small><a name=\"30-1\"><\/a>1. The main disadvantage of this &#8220;Grand Unified Core&#8221; approach is that it generates a great deal of whining from certain students over &#8220;taking math that I&#8217;ll never use!&#8221; Long ago, I used to sympathize with my oppressed computer science and biology brethren. But now&#8230; not so much. Over the last few years, I have run into senior developers who did not understand that <code>ln (A + B)<\/code> is not equal to <code>ln A + ln B<\/code>. And who when queried about this responded, &#8220;Look, <em>I<\/em> have a <em>mathematical<\/em> background, I really can&#8217;t explain it to you.&#8221; Professors of All and Sundry Technical Disciplines: please don&#8217;t let this happen to your graduating seniors. Thank you.<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>As I was reading Jacques&#8217;s post about UT&#8217;s undergraduate math requirements for upper-division physics, I knew he would get at least one comment or trackback about the general watering down of standards, or some such. I was not disappointed.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-259","post","type-post","status-publish","format-standard","hentry","category-science"],"_links":{"self":[{"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/posts\/259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/comments?post=259"}],"version-history":[{"count":0,"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/posts\/259\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/media?parent=259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/categories?post=259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.goer.org\/Journal\/wp-json\/wp\/v2\/tags?post=259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}