Lock and Key
I don't understand my door's locking mechanism. I have discovered that I can lock myself in my room in such a way that I can't get out without somebody letting me out.

This reminds me of a fun riddle. Imagine two people (Beth and Stephanie) in a country with an extremely corrupt government (Molly). The corruption has spread as far as, and beyond, the postal service. In order to send anything through the mail safely is to send a locked box. Without being able to communicate with each other, how can Beth safely send an arbitrary item to Stephanie without Molly intercepting it?
So for example, say Beth sends a package to Stephanie. Then Molly can just swipe it. If Beth sends the package in a locked box, she must also send the key, without it being intercepted, bringing us back to the same problem.

Indecision
I was playing games the other night with some friends, and we reached a point where we didn't know what to do next. There were votes for all sorts of games from Puerto Rico to Wii Mario Kart. There were 4 of us, and after enough bickering about what to do next, I suggested, as a joke, that we flip 2 coins. For each coin, there are 2 possible outcomes (made distinct by the fact that one was an Ohio state quarter, and the other was an Idaho state quarter), so they multiply to give a total of 4 possibilities.

It took us about 10 minutes to vote for games (Wii, Puerto Rico, Ticket to Ride, and Citadels for John, Heather, Becky, and me, respectively), and coin combinations (heads-idaho, ohio-idaho, heads-heads, and ohio-heads, again, respectively). In the end, Puerto Rico won.

Thus, in the end, we spent at least 15 minutes unsuccessfully trying to figure out what to do, another 10 minutes to explain and settle on a method of choosing a board game, and about a minute to decide who flipped the coins. After that, we played Wii Mario Kart, which is a pretty cool game.

Normal Hair

Recently I've been studying for the qualifying exam in algebra, which I will be taking on Wednesday. However, as a result of the excessive studying, my dreams have been affected. Several dreams last night reflected some math stuff.

In the first, and less exciting of the two I will share, I was going to a pizza place with a few friends. I was on the other side of the street and it was taking forever. I took a very roundabout way of getting there. Once I finally met up with my friends again, we concluded that I had merely proved something more than I needed to, but it still worked.

In the other dream, I was the target of a serial killer. This killer went around killing people with normal hair. I was at my apartment when a detective came in and asked if I had normal hair, to determine if I was in danger or not. Well, how did he determine if my hair was normal? He conjugated it! As he was conugating it, another detective came in, saw what was going on, and then there was some ordeal about the first really being the killer... don't know, don't care. Anyways, what you're really interested in:

The Mathematics Involved...
Given a group G with a subgroup H in G, we say that H is normal in G if for every g in G, we have gHg^-1=H. That is to say, for any g in G and for any h in H, we have ghg^-1 is an element of H. Multiplying on either side by g and g^-1 is called conjugating, which is a primary method of seeing if a subgroup is normal or not.

In England, instead of the gcd (greatest common divisor), they have the hcf (high common factor).

Stupid vs. 100

I am home working on some calculus homework for the class I'm TAing, and Robert's watching the TV game show 1 vs. 100. Just so you're aware of how it works, they ask a general knowledge question to a 'mob' of 100 people, and then a single competitor. The 1 person then faces off against everybody that got it correct in the next question. This continues until the entire mob is eliminated, the 1 person gets a question wrong, or the 1 person stops.

In this episode, a (stupid) girl faced off against 100 guys. After reducing the mob down to 44, after correctly guessing that Sy Sperling founded the Hair Club for Men, she was faced with a different type of question.

A prime number is in the title of which of the following movie?
A.) Scary Movie 4
B.) Ocean's 11
C.) Police Academy 6: City Under Siege


She had no idea. She said that she thought it was a number that was multiplied twice. She used a help, listening to a guy that guessed correctly, and listening to a guy that guessed incorrectly. This narrowed it down to A and B. She picked A.

A Prime Number!!! Come on!!! A prime number is a number that is only divisible by 1 and itself. Now please, nobody else make this egregious error.

Two Sweet Quotes

"Does p^2 divide p^3?" (yes)

"How about we write down all the primes and then list all their factors." (really? all of them)

5th Grade Math Humor

I started this quarter in the 700 level algebra class, which was awful. I had no idea what was going on. As it turns out, this is how most people felt about the class. Anyways, I switched into the 600 level algebra class to give me a better background, since they would've assumed I'd seen this stuff before. Before I switched out, however, there was an awesome lecture. First, let me warn you that the mathematics I discuss here is far from accurate.

So we were sitting in class, and he draws a sweet pictures of 6 points on an equilateral triangle: one at each vertex of the triangle, and one at each midpoint of the edges of the triangle. He drew the medians in and inscribed a circle. You can picture it, but if you swore to forget your high school geometry class, you can view it here: http://math.ucr.edu/home/baez/octonions/fano.gif

His lecture got to the point where he mentioned something like a Tietze Groups, or maybe a Teets Group. Well he mentioned it several more times, and then he went to write it up. Tits. Named after Jacques Tits, it is a derived subgroup of the twisted Chevalley Group ^2F_4(2) (if anybody knows how to write subscripts and superscripts, I'd appreciate you telling me how). What's so special about this Tits Groups? well it's a finite simple group (of Lie-type) of order 17971200, as opposed to a finite simple group of order 2 (http://youtube.com/watch?v=UTby_e4-Rhg).

Fact

OSU defines a riot as five or more people engaged in disorderly conduct.