In a previous post I mentioned that I was going to get a copy of the book What is Mathematics by Richard Courant and Herbert Robbins. Well, I've now got a copy of it and I'm reading through it. And I'm thoroughly enjoying it! The book is a mathematics book---it talks about the techniques and results in mathematics, often with proofs (at least when the proofs don't involve advanced techniques). But it's written in a very conversational style---as if Courant was sitting across the dining table from you and sharing with you his love of mathematics. (That imagery makes sense only if you can imagine discussing mathematics at the dinner table...:-)
As I read this book, I thought I'd put together a series of posts highlighting some of the most interesting and important methods and theorems that I encounter. Part of my purpose is to share this with you (and encourage you to get the book); but the other part is to summarize it for my own benefit. I'll keep this post updated with the list of all posts in this series. Here are the posts.