The Hallway - gateway to a new world

this is where the fun starts

In the hallway, we're going to explore an area of mathematics called Group Theory. Don't let the fancy name scare you. We're going to do some experiments, and invent group theory for ourselves, a little bit at a time. Groups are the about the simplest mathematical structure that you can build interesting results with.

I put this in the hallway because it leads to the rest of the house. The rest of the house contains lots of different experiments about lots of other things beside group theory. But you should come through the hallway first, because here we will practice the methods of inventing mathematics. We'll go slowly at first. If you're used to just plugging numbers into formulas and hitting some buttons on a calculator and turning out an answer, this will seem very strange and different. Inventing mathematics IS strange and different, and fun.

The hallway is divided into sections. You should go through all the sections in the order they are listed. The later lessons depend on discoveries from the earlier experiments.

You'll need to stop along the way, to build little models, to do exercises, and mainly to let the new material sink in. Abstract mathematics is best absorbed one little nibble at a time.

Click on a link from the list to see more

Section 1	Rotating a square
Section 2	Motions of a rectangle
Section 3	Clock arithmetic
Section 4	Iso what?

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