Timeline for What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2011 at 23:48 | comment | added | Suvrit | In my undergrad, after 2 classes on calculus, we had complex analysis (in the 2nd year of undergrad)---I still like that subject a lot, but unfortunately, did not get to meet it again, and have largely forgotten the best bits. | |
| Jun 16, 2010 at 8:35 | comment | added | Lennart Meier | In Germany, linear algebra is emphasized very much. Every university I know has a compulsory one-year linear algebra course along with the one-year analysis course (whose second semester is devoted to multivariate calculus) in the first year. Complex numbers are usually one of the first things which are introduced. Sometimes, they are even introduced in the first week of both courses since the professors talk less to each other than they should ;). But then, in most courses in analysis one is not really told what to do to solve an integral. | |
| May 20, 2010 at 1:33 | comment | added | Harry Gindi | @Michael: We have done the exact opposite. Our sequence covers linear algebra in the second semester, with a bit of the overflow into the third semester. However, I have never been assigned a system of ODEs problem in my entire career (of being a student). | |
| May 7, 2010 at 5:12 | comment | added | The Mathemagician | @ Micheal It sounds like you weren't trained in the states,Micheal.A lot of universities in the US DO offer both kinds of linear algebra courses.Sadly,what's missing and would be great is a FULL YEAR COURSE in linear algebra.There's so much students don't see because a semester just isn't enough to cover much of this vast topic. | |
| Nov 6, 2009 at 22:59 | comment | added | Greg Kuperberg | My son took a really good AP calculus course at the local high school, using the most standard textbook and in some sense the most standard syllabus. So I've seen it from the other side. I don't think it's fair to call it "mindless symbol manipulation". But it is true that American universities sell calculus short in various ways. One reflection of that is that a good AP calculus course can be harder than the university product. | |
| Nov 6, 2009 at 22:32 | comment | added | Ryan Budney | Adding emphasis to your comment (3), I find especially in the States there's a rather artificial distinction between "analysis" and "calculus". To the point that calculus is seen as mindless symbol manipulation, but in analysis thought is allowed. John Hubbard's textbook does a great job of blurring those boundaries, especially when it comes to things like the inverse function theorem and Newton's method. | |
| Nov 4, 2009 at 13:31 | comment | added | Michael Lugo | Linear algebra. At least, it's not taught to math majors. They tend to see little bits of it in the calculus sequence (in order to solve systems of ODEs, for example) and then again in an abstract algebra class (matrices being a nice source of examples of groups) but never see a coherent treatment of it. At least this is true at the universities I'm familiar with. In both cases there is a linear algebra course mostly taken by nonmajors, but it's not possible for majors to get credit for both linear algebra and first-semester abstract algebra (basically the group theory course). | |
| Nov 4, 2009 at 4:20 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |