### Applied Mathematics

I've been looking at new cars. I thought I should apply algebraic mathematical reasoning to the task, so here is a short glossary for mathematicians:

Automorphism: The process of exchanging your old car and bank account for a new one.

Inner Automorphism: The process of turning oneself inside out in order to get into the new car.

Group: The collection of people you wish to transport.

Subgroup: The subset of the group that will actually fit into the car.

Cyclic subgroup: Those who didn't fit in the car and so must peddle.

Ideal: The car you could have bought for a lot more money.

Abelian Group: Those who need a car because they commute.

Left Coset: Where the commanding officer/driver sets in the US.

Right Coset: Analogous location in UK & a few other benighted realms.

Isomorphism: The car that's just as good as the old car except for costing a lot more.

Homomorphism: This term is deprecated as possibly offensive to some.

Lagrange's Theorem: A notorious mountain in France often featured in the Tour de France. Cannot be climbed by the numerically weak.

Representation Theory: The lies used by the car salesman in order to suck you in.

Finite Dimensional Representation: The sticker price.

Infinite Dimensional Representation: How much you will actually pay.

Galois Theory: Explains why the mechanic cannot get to the root of your car's mechanical problems even by resorting to radical measures.