{"id":69,"date":"2008-06-22T15:45:47","date_gmt":"2008-06-22T14:45:47","guid":{"rendered":"https:\/\/wpethzprd.ethz.ch\/kowalski\/2008\/06\/22\/an-introductory-course-in-integration-and-probability\/"},"modified":"2024-02-20T13:40:58","modified_gmt":"2024-02-20T11:40:58","slug":"an-introductory-course-in-integration-and-probability","status":"publish","type":"post","link":"https:\/\/blogs.ethz.ch\/kowalski\/2008\/06\/22\/an-introductory-course-in-integration-and-probability\/","title":{"rendered":"An introductory course in integration and probability"},"content":{"rendered":"

A while ago (in 2002 to be precise), I taught an introductory course of integration, Fourier analysis, and probability in Bordeaux (for third-year university students). While giving the lectures during the first year, I typed them more or less in parallel (in fact, sufficiently close to the course that I could probably have done it also on a weblog, as T. Tao has done this year with his course on Ergodic Theory<\/a>, and his course on Perelman’s proof of the Poincar\u00e9 Conjecture<\/a>…).<\/p>\n

Except for using those notes two more years in the same course (or a very similar one the third year), I did not work on them anymore. But since I had spent a fair amount of time to bring the text to a reasonable state of polish, and since I’ve found myself using it a few times as a convenient reference for basic facts that I wanted to show to other students, it seems more than reasonable to put this course on the web somewhere. And so, here it is: Un cours d\u2019int\u00e9gration<\/a><\/em>.<\/p>\n

The text is in French, which diminishes its current interest, but as it is likely that I will teach this topic again in English at ETH, I’ll probably use it as a basis for a translation and\/or adaptation.<\/p>\n

As the introduction indicates, the only noticeable feature of this integration course (though I don’t think it is at all unique) is that I have treated probability theory in parallel with measure theory, instead of treating probabilistic language and its basic results after the main development, as is often done. I find this is better for a first course, because even students who never go on to another probability course can get, if they are attentive, a good immersion in the special langage and frame of mind of probabilists. (And this was a practical concern in Bordeaux because, typically, there wasn’t another probability course following this one, at that time at least).<\/p>\n

The course itself is roughly 140 pages long, and is fairly standard. In measure theory, most of the basic results are treated, though not the Radon-Nykodim theorem. In probability, things go as far as the Central Limit Theorem, but there are no martingales.<\/p>\n

The last 40 pages contain the exams given the first two years I gave the course, with corrections. Some of the problems are dedicated to proofs of quite nice results, including the Radon-Nykodim theorem on [0,1] and Lebesgue’s differentiation theorem, and some are more standard. (Those who have never seen a French-style three\/four hours long exam can have a look to get an idea of how this type of things are done in this strange country; with hindsight, it’s clear the exams were quite a bit too difficult for the students I had…)<\/p>\n","protected":false},"excerpt":{"rendered":"

A while ago (in 2002 to be precise), I taught an introductory course of integration, Fourier analysis, and probability in Bordeaux (for third-year university students). While giving the lectures during the first year, I typed them more or less in parallel (in fact, sufficiently close to the course that I could probably have done it … Continue reading An introductory course in integration and probability<\/span><\/a><\/p>\n","protected":false},"author":625,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-blogroll"],"_links":{"self":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/69","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/users\/625"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/comments?post=69"}],"version-history":[{"count":0,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/69\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/media?parent=69"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/categories?post=69"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/tags?post=69"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}