## Finite Simple Group (of Order Two)

Oh god. Commence the groaning. It’s a Valentines-themed song using math lingo. It’s probably one of the nerdiest things I’ve ever seen. I seem like an uneducated barbarian (pre-fire era) before these guys. But it’s amusing. It’s kinda fun trying to identify which words are math keywords. Once you start wiki-ing them, it kinda makes you marvel how much knowledge mankind has acquired, and how it could all be lost so quickly given the right (or wrong) catastrophe.

http://www.youtube.com/watch?v=UTby_e4-Rhg

Most of the terms are beyond the math I learned in college, but one of the commenters (Nightbreeze1) attempted to explain them:

Kernel: All of the domain of a function (map) which is mapped to zero

Rank-one: meaning the range-space has dimension one (such as the real line!)

See zeroes: he’s in the kernel!

Smooth path: A smooth function has derivatives of all orders, a path is a special type of function (in some sense)

Continuous: meaning without ‘holes’ or ‘jumps’, as in a function

Upper bound: Just an upper bound on some quantity, used often

Axiom of Choice: Controversial, but famous, axiom. gogo wiki

Relation, well-defined, function, proposition: All terms you encounter every other paragraph of any math book

Finite simple group of order two: Ironically, ‘simple’ is too complicated to explain here. A group is a mathematical object measuring symmetry (wiki!) and the ‘order’ is just the number of elements in it

Identity: Identity element or ~map in a group is that which leaves everything unchanged

Tensor: Rather complicated mathematical object.. (wiki)

Without loss of generality: WLOG, found in manymanymany mathproofs, which makes it funny

‘Quotient out’: Operation done on groups/spaces/etc, very important!

Map-image : Map is a function, the image is the image

one-to-one : Property of a function, meaning for every element in the image of a function, precisely 1 is mapped into it from the domain

Equivalence: Equivalence relation, found often… wiki

Bundle: very complicated, wiki won’t help much

wedge between two-forms: Too complicated

Complexified: Extending ‘something’ to incorporate the complex numbers (not just reals)

Simply connected: Property of a set, meaning every two points can be connected via a path (think circle!)

Open-dense: Properties of sets…

System: System of sets collection of sets

Finite limit: Well, this combined with the previous line has something to do with a very abstract limiting process, probably in terms of a set of systems. This could be in the context of sigma-algebra’s or just general topology or any other context in which limits ‘in some sense’ may arise..

Operator, class : Both words found often. Operator is a special kind of function, class is just a class (we class our operators!)

Mirror pair: Forget it

Forgetful functors: nah.. can’t explain this either

Associative : Algebraic property! (a+b)+c = a+(b+c) meaning order of operation is irrelevant (all groups have this)

Free: Another groupproperty..definition a bit too complicated

corollary: Something found in every math textbook after many of the theorems and lemma’s

Q.E.D.: Everybody knows this one, Quod Erat Demonstrandum!

Simply connected actually means that any two paths with the same endpoint can be connected by a ‘path of paths’, so ironically the circle you use as an example is actually NOT simply connected.