Tables are turning

UPDATED! I came across something called Aristotle’s Wheel Paradox long before. As the larger wheel rolls from to , the smaller wheel rolls from to . If the larger wheel rolls without slipping, there is, at any given time, a point on the circumference of the larger wheel touching , and at the same time, there is a point at the circumference of the small wheel touching . So every point in the large wheel can be mapped with every point in the small wheel. Would this show that the two circumferences are equal?

I got two answers to this paradox. (more…)

I received my first credit card billing yesterday. I have no idea how credit cards were billed, and I was surprised that every transaction was itemized — I thought only the total amount would appear, which would have been weird, by the way. My mom was there and so, she knew (and questioned) every restaurant transaction I had last week, though she wasn’t furious. Well, I made excuses, given that last week is still my birthday week, and blah blah. No regrets still, my business transactions need not be private, especially to my mom.

Speaking of credit cards (and bills, interest, etc.) Dr. Jose Maria Escaner accepted my requested to be his thesis advisee. [Background info: I am enjoying Math 162 more than any other subject this term, and I want to have my undergrad research on this field; plus he was recommended by Juvelene Itum (UP Valedictorian 2005), Carmel Felicitas (UP Math Club former Secretary) and Patrick Lubenia (a nobody).] We were set to meet on the morning of March 18 to get started, at least, with some topics. I forgot that we’re supposed meet, however, and that I had classes, too. To cut the story short, I met him in the afternoon, with Phia, and started, even though I wasn’t ready. Don’t get it wrong; had I not forgotten the meeting, my only time available would still have been in the afternoon.

As of now, I don’t have a topic yet. I’m still looking for one.

Well, Dr. Escaner asked me to look for some topics in the internet while we were meeting yesterday. Since I was not in the mood for anything related to my research yet, I did it quite passively and ended up getting a discussion manuscript instead of a publication. He didn’t seem satisfied, too, with the results of my ’searches’, but he still asked whether I liked what I found. I frankly said no, but I promised that I’ll follow it up once I got home, and that I ‘d still have to attend my 123.2 class and I have to leave. I left the room without anything accomplished, compared to Phia and Francis already dealing with publications involving 29 differential equations. I don’t want something like that. I like 30.

I’m narrowing my search on Processes involving Stochastic models. It’s kinda cool to do a research on Stochastic processes when it’s a fact that the current industry uses a different kind of approach — they rely on Deterministic models. A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of initial conditions. Conversely, in a stochastic model, randomness is present, and variable states are not described by unique values, but rather by probability distributions.

There are lots of publications available from the Society of Actuaries, and Dr. Escaner recommended that I search there. I’m doing it now and I can’t understand the depth of the mathematics involved. (Not yet!) Haha. Perhaps, it will continue like this until I get a PhD. Or forever. Haha. Kidding.