{"id":404,"date":"2018-12-27T16:20:32","date_gmt":"2018-12-28T00:20:32","guid":{"rendered":"https:\/\/blogs.ubc.ca\/organizingchaos\/?p=404"},"modified":"2018-12-27T16:26:36","modified_gmt":"2018-12-28T00:26:36","slug":"course-review-math-420","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/organizingchaos\/2018\/12\/27\/course-review-math-420\/","title":{"rendered":"Course Review: MATH 420"},"content":{"rendered":"<p><span style=\"font-style: normal;\"><b>Real Analysis I<\/b><\/span><\/p>\n<p><em>&#8220;F just comes along for the ride&#8230;&#8221;<\/em><\/p>\n<p><strong>Text:\u00a0<\/strong>Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland<\/p>\n<p><strong>Prof:<\/strong>\u00a0Dr\u00a0Stephen Gustafson<\/p>\n<p>Prof Gustafson is an engaging professor. He is able to give a quick, intuitive overview of quite complex topics in class, leaving us to work out the technical details on our own. He also is very helpful during office hours. He also posted his notes online.<\/p>\n<p><strong>Difficulty<\/strong><\/p>\n<p>The classes move very fast\u00a0so one might find it challenging keeping up with the readings.\u00a0Also, though the classes are easy to follow, the homework is increasingly challenging and time-consuming. The final exam was quite hard, practice and recalling theorems and definitions\u00a0are all important. This course covers a lot of material, so watch out!<\/p>\n<hr \/>\n<p><strong> Key Concepts<\/strong><\/p>\n<p>Sigma-Algebras<\/p>\n<p>Measures<\/p>\n<p>Differentiation of Measures<\/p>\n<p>Lebesgue integration<\/p>\n<p>Convergence of Functions<\/p>\n<p>LP spaces<\/p>\n<p><strong>Hard Concepts<\/strong><\/p>\n<p>Lebesgue Radon Nikodyn Theorem: Quite powerful theorem, need to notice where to apply it. Also can be hard to find the decomposition at times.<\/p>\n<p>Fatou&#8217;s Lemma: Tricky working with the limit infimum, also quite powerful and pops up in unexpected places.<\/p>\n<p><strong>Conclusion<\/strong><\/p>\n<p>One of the harder courses I have ever taken. Started learning some really powerful theorems about convergence, for example.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Real Analysis I &#8220;F just comes along for the ride&#8230;&#8221; Text:\u00a0Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland Prof:\u00a0Dr\u00a0Stephen Gustafson Prof Gustafson is an engaging professor. He is able to give a quick, intuitive overview of quite complex topics in class, leaving us to work out the technical details on our own. [&hellip;]<\/p>\n","protected":false},"author":28516,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[281864],"tags":[3957460,3957458,3957459,1171202,3957457,37],"class_list":["post-404","post","type-post","status-publish","format-standard","hentry","category-course-reviews","tag-lebesgue-integration","tag-math420","tag-measure-theory","tag-real-analysis","tag-stephen-gustafson","tag-ubc"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/404","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/users\/28516"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/comments?post=404"}],"version-history":[{"count":1,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/404\/revisions"}],"predecessor-version":[{"id":405,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/404\/revisions\/405"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/media?parent=404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/categories?post=404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/tags?post=404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}