Archive for the ‘School’ Category

Spring Break, Math Style

Sunday, March 5th, 2006

Over the weekend, I took a trip to North Caronlina to participate in an Undergraduate Mathematics conference put on by this group called SAMSI. I didn’t really know a lot about it when I signed up to go, other than that it was a free trip to North Carolina over spring break, and that math would be involved.

SAMSI is a research group that does mathematical and statistical work on problems like social networking, anomoly detection, and the spread of diseases. Went went to some talks which were frankly quite boring, but while the people were giving their talks, I was doing some work of my own. Back in december or so I started thinking about finite state automata, which are the simplest type of computers. I started thinking about their abilities as compared to other computational frameworks, and my thoughts on these matters left me with a bunch of questions. I wanted to clarify certain things to myself, and so while these guys were giving their talks on things that weren’t interesting to me, i came up with about 20 pages of notes on the topic i was thinking about. I proved some things which I had already sort of known, and came up with some interesting results which are at least new to me.

In addition to computational theory, I did some work on other random problems of mathematical interest. For example, any number that is divisible by three will have the sum of its digits also divisible by three. Why is this? As I figured while scribbling on a napkin at chili’s in the detroit airport, it’s a result of the fact that we use a base 10 number system. Suppose you have some number X, and you add three to it. If the first digit of X is 0-6, you have simply increased the sum of its digits by three. If the first digit is 7, you decrease the sum by 7 (because the first digit goes from 7 to 0) but then you increase the sum by one when you increase the next number, for a net change of -6, which is a multiple of three. Likewise, if the first digit is 8, you decrease the first digit by 7 (from 8 to 1) and increase the second digit by one. In general, if you have a base x number system, the ’sum of the digits’ rule will work for any number y such that x = ky + 1 for some positive integer K. So, in base 16, the divisibility rule works for 3,5, and 15. Cool, huh?

The other cool part of the trip was the socialization. I met some cool peopel from various colleges, and it was neat to hang out and talk with them. I played guitar with a guy named Bob from minnesota, argued politics with a socialist from Dartmouth and a fellow supply sider from Cornell, who told the darthmouth chap to ‘Read some Milton Friedman.’ I even meet some cool UC students, with whom I may hang out some time later.

North Carolina is a pretty place, and I liked it there. I may even go back this may for a week long thing where i’d actually get to solve some problems. The moral of the story is, if you get a chance to go to some thing, even if you don’t know a lot about it, go to it! You just might end up singing a song about the economy of south africa while enjoying a few adult beverages with people you just met.

Huzzah!

Wednesday, February 15th, 2006

I added a math major today. That brings the total up to 3 (Computer Science, Physics, and now Math). I was so happy. One of the profesors (Joshi) shook my hand and said ‘good job, man!’ as he is want to do. I even teared up a little as I went to go hand in the form to the registrar. I figurd i’d be happy but I didn’t realized I’d be that happy about it. It feels great to do the things you want to do with your life.

Behold My Eloquence!

Tuesday, January 24th, 2006

I’m in a ‘Women and Religion’ course at Xavier. I took it because it fulfills two of the core requirements. There are about 30 girls at 4 guys in this class. Today we were talking about sati, which is when a hindu woman will throw herself on her dead husband’s funeral pyre. Apparently this is considered an honor, and the tradition is perpetuated mainly by women of the higher caste systems. Our teacher asked us why this was.

I raised my hand and, in a manner entirely in my personal style, said “Well, It’s kind of a typical woman thing to do. Women are always trying to put themselves above other women; to enforce a sort of ‘pecking order’ so they can say I’m better than you to other women who aren’t as good as them.”

As soon as I said the phrase ‘typical woman thing’, pretty much all of the girls had their hands in the air. Surprisingly, a fair number of them agreed with them. I realized I had phrased it the wrong way, but basically all I was saying is that women are very competitive with each other. Of course their are exceptions and blah blah blah but when you get down to it women compete with each other and the whole sati buisness is just their way of competition.

Cryptolozoology not so much

Saturday, January 21st, 2006

I thought I’d heard that word somewhere before, so I looked it up on wikipedia, but it doesn’t sound nearly as cool as Cryptology. Oh well.

Edit:
Upon further review, I guess it is somewhat interesting.

Cryptology is Awesome

Saturday, January 21st, 2006

I was signed up for a ‘Discrete Math’ course, which fulfilled a requirement for my Computer Science major, as well as the Math minor that I planned on adding. I knew I’d learned pretty much everything that we would go over in this class, so I decided to switch to a Cryptology class that was being offered and sounded interesting.

I am very glad that I did – I was running out of mathematical phenomena to puzzle and ponder and mull while going about my day, but this field is just full of things to think about. Delightful!

Further Note: I enjoy reading about historical developments in science and philosophy. Occasionally, I run into people who remind of myself or whom I greatly admire. Archimedes is my favorite scientist because of the proliferation of his works and his humble attitude, especially in contrast to the philosophers of his day. Charles Babbage, on the other hand, sounds a lot like me. He thought about many different things, and drew up great plans but usually tired of them in the process.

Another characteristic we share is a nagging desire for mathematical accuracy. Tennyson wrote a poem, “The Vision of Sin,” one line of which is “Every moment dies a man, Every moment one is born.” This line bothered Babbage, who had done a little looking into mortality statistics. He suggested an correction:

It must be manifest that if this were true, the population of the world would be at a standstill … I would suggest that in the next edition of your poem, you have it read – “Every moment dies a man, Every moment 1 1/16 is born.” … The actual figure is so long that I cannot get it onto a line, but I beleive the figure 1 1/16 will be sufficiently accurate for poetry.

I am, Sir, yours, etc.,

Charles Babbage.

This all comes from a very informative and entertaining book.

Who Knows

Wednesday, January 18th, 2006

One of the many annoying characteristics of my mind is its tendency to fluctuate quite frequently on what it is that I want. There are days that I want to go to graduate school and study come crazy computer science/math related things. Then there are days when I just want to get a simple job and just start living. I’ve been told repeatedly that I don’t need to decide these things just now, but for some reason my mind refuses to cooperate with them. My mind creates elaborately detailed fantasies of how my life would be if I made either choice, and I decide I’ll go with whatever
fantasy suits me best at the moment.

It’s rather frustrating..

On the trials of being a geek

Tuesday, January 17th, 2006

I’m taking a basic music class, for my fine arts requirement. I was hoping for a little more theory-based class, but this one fit my schedule best. Today our professor said that if our ability to see was as powerful as our ability to hear, then we could see a dime on the moon.

‘Power’ is given in units Energy/time. Obviously he’s not talking about our ability to do work with our ears. I wanted to ask him what exactly he meant by this, but didn’t have time before class ended. The purprose of sensory organs is to gather information about our surroundings. There are different ways you could ostensibly refer to the power of a sensory organ. For example, our ears respond to fluctuations in air pressure. There is a range of frequencies our ears will pick up (and thus a range of frequncies which we are capable of hearing), and so I could kind of see how you might say that our ears were ‘more powerful’ than our eyes because they could respond to a larger information bandwidth.

There is also the question of precision within a given bandwidth – the ability to spot a dime on the moon is a question of resolving power and not bandwidth, so I guess he meant resolving power; but then what exactly is the ‘resolving power’ of our ears, and how would this be measured?

I’m sitting here thinking about these things, and I realize that most people really could care less. I guess that’s the price you pay for curiosity.

O RLY?

Thursday, January 12th, 2006

Me: So, am I correct in my understanding that there is a finite amount of entropy in the entire universe, and therefore a finite number of states in which the universe could exist?

Dr. Fatuzzo: Well, the entire universe is kind of tricky …

Stupid +/- System

Friday, December 16th, 2005

This year, Xavier started using a +/- grading system. Prior to this year, your grade was either A, B, C, D or F. My grades were typically in the low ‘A’ region, so it worked out for me, because I usually got all A’s. I figured the shift would negatively impact my GPA, because I don’t get B’s, so there weren’t going to be any B’s transformed into B+’s, but likely I would have A’s ‘tuned down’ to A-’s. I was right; I got an A- in both Theoretical Mechanics and Electromagnetism. So I guess my GPA will be slighly lower than I would have been if I’d gotten A’s. Oh well.

If I wanted a Math Major I would have Taken one

Monday, November 28th, 2005

Sometimes physics problems drive me nuts. “Here, do a bunch of math. The application to the real world is easily understood but there isn’t much else to do on this problem, so just derive a bunch of equations that we’ve come up with here, and we’ll call it a day.”

I like it when they give you a problem and you have to figure out how to solve the thing. I hate problems of the form “Show that X Behavior takes the form of this complicated equation. We’ve taken the liberty of replacing these very ugly things with constants, but you’ll still have the manipulate the equation in its gargantuan form if you’re to complete the assignment.” Ugh.

Also, happy thanksgiving I guess.