Thursday, October 4, 2007

"I can call anything anything I want - this is math."

The title is a quote from my Set Theory prof.

It is always interesting when classes overlap :-)

Example One:

Conjecture and Proof: Prove that a cube cannot be tiled with smaller cubes of all distinct sizes.
Geometric Graph Theory: We can use graphs with rubber band edges to find ways to tile rectangles with squares. Here are some examples, including one that shows a way of tiling a square with smaller squares of all distinct sizes.
Conjecture and Proof: Passes around a picture of how to tile a square with smaller squares and explains how to create an electrical circuit that represents such a tiling. This electrical circuit is what would result from viewing our rubber band graph in the context of an electric circuit.

Example Two:

Set Theory: Lets play with cardinalities and different kinds of infinities and such!
Conjecture and Proof: Which of the following sets are countable?

Example Three:
Topics in Geometry: We are looking at affine spaces instead of just linear spaces, so we need generalizations of things like "independent vectors" and "basis". Some of these generalizations involve a configuration known as general position, so we are going to explore it.
Conjecture and Proof: Consider a set of half planes in general position that cover the plane...

I guess by classes overlapping, I mostly mean that conjecture and proof keeps being related to my other classes... But at any rate, I am still very much enjoying my classes. They are providing a nice balance of challenging me and yet not sucking all of my time. Set theory is particularly nice in this regard as it is constantly making me think in new ways, but once I figure out how I am supposed to think, the HW does not take that long.

And now Christina and Mandi and I are going to go find a part of the city we have not yet been to to explore, so I will leave it at that for now.

1 comment:

Max said...

Math?!?! THIS ... IS ... BUDAPEST!!!