I ran across this interesting post by a historian who was an undergraduate mathematics major. She found her old linear algebra notes, and was surprised to find how little of it she still understood:

It’s not just that I can’t answer this question now, it’s that I can barely comprehend even what it means. The terminology bounces through my brain, stirring vague imprecise echoes… It’s disconcerting enough to come across the ghost of your own self. It would be even more disconcerting to know for sure that part of your intellect is now forever closed off to you.

Like many people, while a graduate student Roger L. Goodwin took a wide variety of courses in applied probability, statistics, and operations research. Unlike the others, though, he compiled lecture notes from all of his classes into one big book, available for download.

In addition to individual articles, the Electronic Journal of Differential Equations also publishes monographs in the area of differential equations. The first one was a book that I think I remember seeing on library bookshelves: Showalter’s Hilbert Space Methods for Differential Equations.

I was reading some political blogs this morning, when I came across this quote:

Look, there’s an endless list of topics I don’t understand at all. I went through an entire semester of pre-Calculus in high school and was never able to understand what a function is. I still don’t. It’s a complicated subject and I was a lazy student.

I don’t know what to say to that.

Qiaochu Yuan recommended Stevenhagen’s mathematical writings in general, so I did some additional searching. I found this page of lecture notes for algebraic number theory courses at Leiden University.

Stevenhagen’s notes on class field theory look particularly interesting. They start with particular examples, and explain what the theory means in those particular examples.

These notes by Stevenhagen provide an elementary introduction to rings of algebraic numbers.

The Geometry Center at the University of Minnesota was a pioneer in putting mathematics on the web. The Center specialized in visualization of advanced geometric topics.

The Center itself was closed in 1998, but their website is still available. The site is quite old (the pages that note that Netscape 2.0 is required are particularly poignant reminders), and many parts of it no longer work, but much of the content is still there.

Here is a page with individual GIFs/PNGs for each math symbol. This is useful for the occasional inclusion of math formulas on a web page, for example. It also has directions on how to build more complex formulas using just HTML. The page is part of the Metamath project.