Hooray for summer! Now that finals are finally over, you can expect a lot more from me over the next few months. I’ve got a lot of exciting things planned, including

• a description and explanation of an algorithm for finding square roots by hand (which most people don’t know anymore);
• finally FINALLY for real finishing my series of posts on Recounting the Rationals (yes, Jason, this one is for you!);
• going through a neat little paper by Ivan Niven giving a proof that pi is irrational;
• a little number theory, focusing on the Fundamental Theorem of Arithmetic;
• fun links to interesting mathematics around the web;
• and whatever else tickles my mathematical fancy!

To get things started, here’s a link for you: Norman Wildberger’s MathFoundations, a series of videos explaining the foundations of mathematics. I don’t agree with all his opinions—particularly regarding infinite sets—but this is a subject on which I’m willing to agree to disagree; as a legitimate, published research mathematician who’s been doing mathematics longer than I’ve been alive, he’s certainly entitled to his opinions! And I certainly do agree with many of his opinions, especially regarding mathematics education. In any event, the videos are very well-done, and there’s lots of interesting stuff there!