Applied mathematics is concerned with calculation. Getting the right answers. Building things. Making sure the probe lands safely on Mars, that the bridge can withstand high winds, that revenue will exceed expenses. Utilitarian math.
I've always been interested in pure mathematics: the study of numbers, purely, for no other reason. Useless math, in other words. Math for the sake of math, only. Utterly non-utilitarian math.
The purest of pure math is logic, the foundation of mathematics. Mathematical logic is "meta-mathematics," the software running the machine, the engine under the hood.
One my favorite undergrad courses was an upper-division class in mathematical logic. Not long ago, I decided to take out some old textbooks, and summarize what I'd learned decades ago. The result was a set of simple notes for doing "Truth-Tree" proofs, one my favorite class activities.
You'll find those notes here.
-----
Copyright © 2006-present: Christopher R. Borland. All rights reserved.
No comments:
Post a Comment