CLASS:Basic Topology

The basics of Basic Topology
What is topology? You know, not a day goes by that I don't ask myself the same question...

Just kidding. Topology is the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching. Difficult to understand? Then let me give you an example.

Behold, the Möbius strip! This strange creature differs from an ordinary ring in one aspect: it has a twist in it. This twist, however, makes all the difference. Because of this twist, the Möbius strip gains a unique property: it only has one surface!

"Certainly not!" you cry. "Absolutely, positively impossible! You cannot have only one surface in 3 dimensions! If such a thing can have one surface, why haven't we boarded a dragon and informed the Wizard Council?"

Ah, but young Smotchkkiss, it is possible. And as you trace your finger along every part of its surface without lifting your finger, you will see how this can be.

What this course covers, and why it prevents economical disasters
The key word in "Basic Topology" is "topology". However, in the context of this infinitely-small-in-the-eyes-of-the-universe paragraph, the key word is "basic". Unfortunately, our current grade levels and limited mathematical experience prevent us from going too deeply into the concepts of topology. Still, topological problem-solving may prove to be a useful tool in years to come. It will give you an advantage in geometry later on, and it will probably be helpful if you plan on pursuing a career as an economist or (surprisingly) a mathematician. One day, the US governments hopes to supplant the current Witch Doctor Wonkawhipplscrumshusfudgemallow economic analysis methods with math. This course will serve as a springboard off of which you may jump and sucker-punch the voodoo economist in the jaw.

Basic Topology starts out by covering the concept of metrics and distance functions. We will get into some examples of metrics, such as the Euclidean and Taxicab metrics. Then we will move on to open balls, open sets, and finally we will come to the fundamental principle of topology: the topological space.

Here are the links to the necessary lectures (right-click and select "Save target as..."):


 * Lesson 1: Distance

Participants
Hi, Noah. This is Owen. I took the liberty of adding this section to your page, as it will be essential. People who want to take this class should sign up here.

Owen Leddy