YSP Day 3: The Ordered Integral Domain and C-rings with 1

Alright. Its a holiday tomorrow, so I don't have an excuse to write poorly. Sorry for journalling the past two days. I still think its important for there to be a mechanical account of YSP because should another poor soul that doesn't like math that much like me want to take a course on analysis in a prestigious university, he or she should have a resource. My friends probably wouldn't care about whatever I'm learning. I don't even care about what I'm learning. Needless to say, I will provide everything I can for the world to read.

I took the train and the bus by myself today.  I don't remember if I drooled on the train. I was lucky to stumble upon a friend on the way, or I might have easily missed my stop. It turns out that I'm the only friend among many who is participating in uninteresting math this summer. I take comfort in that when I go into Multivariable Calculus and Linear Algebra next year, I'll know that nothing can be as bad as proving that x^2 is continuous.

That happened to be the first thing I learned. A function f: R->R is continuous at x(e)R if for all epsilon>0 there exists some delta>0 such that |x-y|<delta -> |f(y)-f(x)|<epsilon. This almost made sense, but our counselors got really excited ("You're gonna have to pull deltas out of your butt!") and started talking about monoids, defined by (delta, #, e) where e is a neutral element such tha a#e=e#a=a. Monoids, are of course associative, just like any other respectable operation except the cross product. Do I really know what I'm talking about? Not a clue. The point was that in the process of completing rationals (Q) to reals (R), analysis comes into play big time. Besides, naturals and integers are just equations (as if the other two sets weren't) and not that topographically interesting. Obviously.

Professor Sally blindly hoisted his prothetic-legged body onto the table. He assigned each of us a coordinate in the lecure room and cut off introduction.
"I have no legs, no eyes, no hair." The class tittered. "But I intend to run. you. to. the. ground."
"Jason!" he shouted. "Write. I will speak."
"ORDERED INTEGRAL DOMAIN." The class jumped to attention. I blinked, hoping that he really was blind so that he couldn't see my careless slouch. "(R,+,*) is a computative ring with 1 if and only if (+,-) are Internal Laws of Composition."
"Give me an example of a c-ring with 1," he demanded of 2-2, the coordinate next to me. The boy failed, as expected. The Professor turned to me.
"Do you know any c-rings?"
"Uh, like 3 times 5 plus 2?" The smart kids who knew real math turned to me.
"Integers," the smart girl hissed.
"Do you know any c-rings with 1?" the Professor demanded again. I decided that I was bad at thinking and caring.
"Do you want an expression?" The smart kids thought about how incredibly stupid I was.
"Integers," the smart girl hissed.
"No," I said firmly. "I don't. Integers?"
"SURE YOU DO," the Professor shouted. "Have you heard of the integers?"
"What? Yeah."
"Do you know the integers?"
"..."
"..."
"Yes." And I promptly fell asleep, ashamed, hoping against all hopes that we would solve some easier modular arithmetic and stop talking about multiplicative cancellation.

I had hot apple cider for lunch. I made $2.50. There is only multiplicative cancellation in n mod m if and only if m is prime. Be sophisticated, baby. An OIDR satisfies WOP if and only if for all S <- R+ and S is non-empty, then S has a smallest element.
Yeah, right.
I ran and turned in the rest of my Consumer Ed homework. UC is very beautiful. Perhap its loveliness will cancel out my nightmarish classroom experiences.

YSP Day 2: Intro to Knot Theory and Kauffman's Polynomial

I promised myself that I would write more because I decided that the math and sciences really suck, and that if I ever want to stand a chance mixing with the humanities flowers, I'm going to need to write frequently, so I can write better. Basically I want to be like John Green and other authors whom I have yet to read, but I'll never to go to a small liberal arts college. Instead, I'm going to review YSP, because no one writes reviews about YSP.

Young Scholars Program, University of Chicago
Advanced Geometry, Knot Theory, and Proof-Based Calculus or Something, Grades 11 and 12

I took the train with my father to the Union Station today. When I stepped into the city, I felt the rush of windy freedom, but mostly, I stumbled across a couple streets and fell promptly back alseep on the bus with Narnia grasped between my palms and my backpack. We talked briefly to a CS Major at UC and I pretended not to be interested in anyone so I could be totally ignored, left in peace to draw the classroom.

We were split into groups, and I was tested into the highest levelled one. It turns out calculus is good for something, or at least Mrs. Moore has done her students well again, even if I haven't done well for her. I ate too much, so I was uncomfortable and fell into my routine AP Chem 1:00 PM food coma, but no before catching several things about our Singaporean transfer counselor, Eldin.

"Who cares about knot theory?" he said, referring to the subject on which we will be spending two of the next four weeks. "Its not deep, not wonderful. Its just a testing base. If you want to impress people, tell them you're studying topological quantum field theories." He proceed to explain that we were studying projections, embeddings, but of course for all intensive purposes, we are studying real knots.
So heres the thing. Circle O is equivalent to the knot diagram of figure 8 (8. duh.)
"What the hell?" Eldin rhetorically posed. On the sliding chalkboards, he wrote in proficient and chicken scratch like letters: Kauffman thing. He paused.
Kauffman thing/polynomial, he added. That's what he meant. Of course the only term I was mildly familiar with, he forgot.
He explained the Kauffman polynomial ("What the hell, we mess the variables?"), and I pretended to care about staying conscious. I fell asleep after another high achieving mathlete applied the Bromian rings (it was denoted on the chalkboard: This is a good one. This is a thing. It should be easier.) to Kauffman. The answer, by the way, is a^2c^2+2abc+b^2c^2. I can't even type in LaTex.

Eldin ended with one last note on his opinion of math.
"You know the stuff they do in the other levels, with probability like that, blue ball, red ball, pick two blue balls? That's bullshit. PDE is where the money is at." Meaning we should all be partial differenial equation theorists one day.

I visited the bookstore and the medical campus later. Mostly the bookstore. I bought Slaughterhouse-Five for $7.99 and Extremely Loud and Incredibly Close for $4.95. The day, in all of these senses, wasn't the worst. Spirit wear is still too expensive.

YSP Day 1: A (P)Review

I thought that students who went to the University of Chicago did not go to kill fun. Fun did not die, because learning was fun. People would sacrifice fun to learn, but they never would have to do so. UChicago was beautiful, but only in its bubble. UChicago was a private liberal arts school. UChicago was basically the best, with foreign exchange students flocking everywhere, brilliant minds floating in the city's veins of wisdom and history and culture.

Then I went to the school. Actually, my dad drove me there as I slept with a fat Designer's Convention book caught between my legs. If I knew anything about architecture, I would say that the buildings were beautiful and majestic, draped in climbing ivy with thick irony, because UC is technically not an Ivy League. But I know jack about architecture, so all I can say is that UC is nice. On the outside, it looks a heck of a lot better than UIUC. The great majority of students don't look like smokers. Intellect oozes between the heavy set doors of inquiry based learning. The school colors aren't orange and red. It disappointed me that Eckhart Hall was equally as depressing as Noyes Lab, brown doors and tiny desks alike. I was sad that Huffington Hall was analagous, if not worse, than the Illini Union.

The diagnostic test was okay, since I remembered to use L'Hopitals on part d of a question concerning series. I met a lot of dorky people who love math a lot more than I do, and I met a lot of people who wouldn't stand a chance of making it to UC for real. The boys needed to wear deodorant, and I needed to get away. One professor wore an eyepatch and was wheeled in a chair because he had two prosthetic legs. He demanded respect in a whisper, although after he rolled away, I wished we'd have a real Professor Moody. Mr. Eby was great, and if Mr. Pearson didn't teach English, he would be amazing too. Our other professor was equally sharp and complicated. He knew everything about over and under 3-foils, but he spoke too slowly about Russian history and didn't bother to teach anything that was more than trivial. Then again, how can I determine what is or isn't trivial? It's just that I don't see how the renaming of Leningrad makes anyone a better person.

One thing worth noting though. Robert Lee Moore established three rules of IBL (inquiry based learning). The second step, called Step 1 (preceded by Step 0) is to send students out with scripts into the desert to work. Since we don't have deserts (the theory was developed in Austin, TX) in Chicago, we're going to have lectures in the barn, which is actually the 3rd floor of another math hall or something. The professor said this as if it were funny. The only humorous encounter I've had was gaining a profit from buying a $3.85 sandwich with my $5 coupon.