Ars Mathematica

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.

The Economist has an article on the question of the hardest language to learn. They suggest that a language called Tuyuca is the answer. What makes Tuyuca unusual is that verbs carry an ending that indicates whether the statement is thought to be true or known to be true with certainty. Imagine a language with one tense for conjectures, and another for theorems.