Because this is the type of thing that a blog (particularly a WordPress blog) allows you to do, I have decided to begin an absurdly ambitious project: to put a complete course of mathematics (okay, well, as much of it as I can manage) online at this site. The guiding philosophy will be that every mathematical topic worth studying ought to be presented as an intellectually exciting and important idea. (This philosophy will be particularly operative in the Bourbaki for Beginners course, the most “cultural” and least ad-hoc of them all.) Among the goals of this enterprise are:
- to present mathematical topics in the way(s) that I would like to see them presented
- to help me in my own mathematical work
- to help fill the enormous gap in mathematical exposition on the web that stands between “math help” websites on the one hand, and technical blogs authored by active researchers on the other. (I haven’t, for example, found many blogs by first-year graduate students about what they learned in class today.)
The format, I imagine, will be much like Scott Aaronson’s Democritus, except that the “lectures” won’t, in general, be based on real lectures that have already been given: you can think of them as hypothetical lectures that I (or someone) might give at an imaginary university. I am currently planning five “supercourses”:
- Elementary: calculus and below
- Undergraduate: the curriculum I would design for math majors
- Graduate: divided into “Basics” (first-year) and “Topics” (second-year and beyond)
- Advanced: ideally, a course in each research area; the kind of courses advisors might give to their Ph.D. students, reaching all the way to the research frontier
- Bourbaki for Beginners: for those with culture and patience, who like to savor ideas; based on Bourbaki’s Éléments de Mathématique; encompasses all of the above (or at least through “Graduate”), yet starts at the very beginning, requiring no math background
Obviously, this is a long-term project! Feedback will be welcomed at all stages, of course.
August 9, 2007 at 4:44 pm |
Having just discovered this blog, I think this is a fantastic idea. I’m looking forward to reading more.
August 10, 2007 at 2:44 am |
Eric,
Thanks! It shouldn’t be too long before the material starts making its way here.
For the most part, I will be creating and uploading the “lectures” in whatever random order I happen to feel like, but if there’s a particular topic you’re interested in, feel free to let me know.
October 5, 2007 at 1:34 pm |
Just found this site through Pianophilia and I’m very interested in seeing what transpires with this ambitious and important project.
October 6, 2007 at 9:34 pm |
Everyone:
Apologies for the delay that this project is experiencing! There are several reasons for this: (1) it’s inherently time-consuming; (2) I have been working on a number of different lectures at once, rather than finishing one and proceeding to another; (3) the appearance of a number of new blogs and resources has forced me to carefully (re)consider exactly what niche I want to fill; (4) writing about a topic forces me to relearn (or just plain learn) it, which often leads to second thoughts about how it should be presented; (5) other reasons I can’t think of at the moment.
Rest assured, there will eventually be material here!