Category: Math

Stuff about math

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Perfect Synergy

The past summer, I was at the REU in UMBC. The head of the math department guy preached about the future of mathematics is the intersection of mathematics, statistics and computing; I agree to a large extent. 

What I ended up working on seemed to be computing, with more computing, with very little mathematical analysis. The system of differential equations that described pancreatic cells was far too advanced for me to do some significant analysis. Heck, that’s how I feel about most of pure mathematics: the interesting problems are always out of reach from what I know.

Before this past winter break, I found a cool book called “Risk and Reward” in the math library. It’s all about the, surprisingly deep, game of casino blackjack, from the strategies to the mathematics behind the analysis. In the analysis portion of the book, 90% of all the results seems to be dependent on the a computer, but with relatively simple probability concepts.

If I ever do become a professor of some sorts, I want to be able to teach a class based on games like blackjack and poker. For projects of sorts, the task will be to calculate the probability of various conditions and to figure out the strategies from the math I provide in class. Maybe for a (optional) final, it’s to actually play the games that we studied in class…

As an exercise over the break, I took an existing program and added the functionality to “practice” the card counting went over the book. It’s based on this project which I butchered (honestly, I spent 2 days doing this… trying to understand someone else’s code is tough). To run the program, make sure Python is installed, and run Blackjack.py. Download

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Equation to a Modern Family

vlcsnap-2014-01-16-12h30m49s7

 

On the recent Modern Family episode, Claire was seen giving a lecture to the AP Calculus teacher on how many hours each student are expected to spend each night on school work (totally off for the record…).

Strangely enough there was the word “Schrodinger’s” on the board. Never in AP calculus did I

  1. Do partial differentiation
  2. Learn about Schrodinger’s

To be honest, I’m not entirely sure of the derivation to that equation…

Still, they did get something right! The theorem to the far left seems to be Rolle’s Theorem!

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/r/math Problem of the Week 2

Two real numbers x and y are chosen at random in the interval (0, 1) with respect to the uniform distribution. What is the probability that the closest integer to x/y is even? Express your answer in terms of pi.

If one were to draw the area where x/y is even, it’s pretty clear from the get-go that we will have something like the following:

square

 

I looked at the problem from the viewpoint of lines (x/y = 1/2, x/y = 3/2, …). This results in the following series from summing the area of the triangles (don’t forget to divide by 2):

\frac{1}{4} + (\frac{1}{3} - \frac{1}{5} + \frac{1}{7} - \frac{1}{9} + \cdots)

Luckily, the series at the end is basically \frac{pi}{4} from the arctan series expansion. Thus the answer is \frac{5 + \pi}{4}.

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My Petty Revenge

I was finishing up my workout at Noyes tonight on the mat. Doing stretches and cool down stuff. Well, I got thirsty and decided to go have a drink. Note that my towel, notebook, and workout gloves are still on the mat.

Then while I was gone for 2 minutes, this girl decides to come steal my place on the mat. I didn’t want to be rude because I can do abs back home but wanted to give her a piece of my mind.

Good thing that I had a small fart in my loaded up just for the occasion.

Take that.

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Ideas

The desire to build is strong with me, but I never got the training (same with drawing too). I guess that’s why the Arduino is sitting there, collecting dust. I wish there’s just labs where we build stuff here at Cornell.

But anyways… ideas:

  1. App where it shows the approximate location of buses as markers on Google maps using time data, and not GPS (too expensive). I think this should be fairly doable in the grand scheme of things.
  2. Clock where the hour is given by the shape of the polygon displayed. I see glimpses of coolness here, but can’t put my hands on it.

 

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Magic, Math, and Cooking

For the past few days, I’ve been just existing. I’m not wasting the day in anyways though. The day was spent shopping at Wegman’s Wednesday, while yesterday was spent cleaning the entire house.

Even without classes, I still feel that I’m not accomplishing much. I want to be great at math, start being decent at magic, and great at clarinet; also P90Xing on top of all that. That’s over 4 hours right there.

Am I over-exerting myself in expecting mastery in such diverse hobbies? Probably.

Will I keep on trying? Of course.

Lets just hope I don’t die this semester.

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Dreams

Had two dreams recently that was pretty weird…

  1. I had to hide in a hut when a comet shower was going on… which turned out to be a bunch of meteors striking the Earth. I think I was with a few REU folks… and then I had to dodge a rolling ball of fire.Influences: RTW II videos and the actual comet shower.
  2. I bitched about someone in front of a large group. I don’t bitch to people in large groups….

 

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Take It Back to Square One

After a long program like my recent REU where I hung out with a group of awesome people for such a long time that I forget the outside world, I reminisce about past groups. I think back to my MAO conventions where I flirted with love, jump back in time to the All-District concert with Dr. Green cheering us on during Maslanka… but I always feel sad afterwards that my memory of them is incomplete.

I wish I kept a consistent journal throughout my years to see how I developed. Sometimes when I clean my room in Tallahassee, I would find a little unicorn book where I wrote notes in third and fourth grade. Runescape notes dominated the pages (and a crush for a Megan Morris? … who is this girl?).

Hopefully I can start writing about my feelings/notes on daily life on here more. After all, I am spending a good amount to have this website and domain under my name.

Well. Back to square one.

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Project Euler #1

Add all the natural numbers below one thousand that are multiples of 3 or 5.

Besides the obvious solution by looping from 1 to 1000 and considering each number, this problem can be solved with some simple PIE counting.

Sum up all multiple of 3’s and 5’s with an arithmetic sequence, then subtract the multiple of 15’s due to overcounting.

Hopefully these type of posts will be much more interesting (for me too) as the questions get tougher.