Lesson 1: Introduction

Congratulations!  By arriving at this page you have started your journey into a whole new world of mathematics.  I must warn you: this might be a journey that you’ll never want to stop.  In my opinion, that’s not such a bad thing.

You might be wondering why the beginning of this journey requires an introduction.  In fact, the whole point of writing an introduction to these lessons is to explain why it needs an introduction (logical circularity is purposeful here).  This journey needs an introduction because it will be unlike any other intellectual journey you’ve ever been on.  It will require you to think in ways that you haven’t thought before—or at least not to this degree.  I have done and will continue to do my best to make this transition as easy and as fun as possible, but I can’t lie and say that every single step of every lesson will be easy.  What I can guarantee, however, is that every step of every lesson will be possible.

What do I mean by that last statement?  I mean that everyone has the ability to do and understand and fully appreciate this new kind of mathematics (and all the beauty that lies within), so long as they are patient (!!) and willing.  I ask for your patience in letting yourself mull over certain ideas and concepts, letting them fully sink in.  And I ask for your willingness to understand that you can do this.  I will never ask you to memorize some fact or string of instructions. I will never ask you to carry out some nasty calculation, and I will never ask you to remember anything from your high school (or middle school, or elementary school) math courses without first reintroducing it and breaking it down to its essential, beautiful parts.  I ask for your willingness to understand that this is not your middle school math class.  There will be no test.  There will be no grade.  To a very large degree, I want you to forget about what math should be, because we’re going to be building from the ground up.

Accordingly, much if not all of what we do will seem completely different from what you’re used to.  GOOD!  That’s exactly my point!  That’s exactly the whole point of this site—to show you that the math you’ve learned in high school is only the tiniest fraction of what is out there to learn, and that a lot of this new stuff is completely new and different and awesome.  The math that you’re about to learn could have been understood in middle school, if not earlier.  Why we don’t introduce it earlier is beyond me.  All I can do is try to fill this gap as much as possible, and that’s what the coming lessons are for.

So if you’re ready to dive into this brand new world of math, and if you’ve opened up to the possibility that math can be so much more than what you previously thought, then congratulations, you’ve just completed lesson 1!

On to Lesson 2…