super_elmo, posts by tag: math - LiveJournal

Oh man. This is too awesome, you guys.

The departments of math, physics, and computer science at my school are having a mixer.

The theme is awkwardness.

***

Sister: Wanna hear my great idea for a reality show?
Me: Is it that you have to lose a lot of weight while becoming a famous chef?
Sister: No. It's making Michael Steele and Joe Biden live together.

Things that were fun about today:

1) I wore my favourite shirt--it's black and it says "Start a revolution... stop hating your body", and it magically makes me feel awesome--and my favourite underwear.
2) I woke up early to go grocery shopping and got to take a lovely walk though my quaint neighborhood in the early-morning autumn air.
3) I figured out the answer to a ridiculous math problem that I'd previously had no idea how to do. Then I went to ask my teacher if it was right, and I got to go in the very fast elevator in the math building. I love very fast elevators; they will never stop being exciting. You can feel yourself getting heavier as they accelerate upwards, because guess why? GENERAL RELATIVITY, that's why.
4) It was show-and-tell day in my Physics of Music class.
5) I was practicing the piano for a bit and I finally got the Arpeggio of Ridiculousness in Fur Elise to sound okay. We'll see if it sticks.
6) It was lighting levels day for the play I'm working on. Lighting levels is where you sit in the theatre in the dark and decide how the lights should look for each scene. It takes a really long time, but omg the lights are going to be SO PRETTY. The designer did a fantastic job with everything, and to be honest I'm a bit jealous, but this is supposed to be a list of positive things, undertaken specifically, in fact, to take my mind off this, so I'll try not to think about it anymore.
7) I was told on two different occasions that I'm a good stage manager and coach. I sure hope those people weren't just being polite.

The other part of this post is a math question. I have to prove that any prime besides 2 that's the sum of two squares is congruent to 1 modulo 4 (in other words, ∀x[Px ∧ x = y² + z² --> x = 2 ∨ ∃q(x = 4q + 1)], where Px means x is prime). I HAVE NO IDEA WHY THIS IS. Do you?

EDIT: I got it. Here's why:
If x and y are both even, then the sum of their squares is even and therefore not a prime except maybe 2.
If x and y are both odd, then the sum of their squares is still even and not a prime, either.
If x is even and y is odd, then x=2m and y=2n+1, so x² = 4m² and y² = 4n²+4n+1, so their sum is one more than a multiple of 4.

This is another one full of freaking out about math, posted in the vain hope that some omniscient logician will hug me and make everything better, so I expect most of you will scroll past.

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Oh God. I'm taking Mathematical Logic this semester, which has some of the most vicious algebra I've ever encountered. I have this vague memory of math involving numbers. Those were the good old days. I've had entire assignments in this class that do not involve a single numerical value, just lots of fun made-up symbols related to set theory.

Here is why this is so terrifying: my school has a place called the Math Help Desk, which is a big room with chalkboards for walls and lots of tables, and it's staffed by grad students and advanced math undergrads, and they will help you with your homework for free. It's a great place to go and study--there are always floating snippets of conversation about everything from Bernoulli ODEs and bivariate distributions to properties of logs and matrix algebra, and you can procrastinate by helping first-years with their calculus, and you can watch the tutors getting way too excited about how to prove commutativity of addition, and you'll sometimes run into a classmate and get to work with them on an assignment. I've been relying on this place for two years of being a math student, and even as the material in my classes got more and more complicated, the tutors have always been able to help me without breaking a sweat, often smiling fondly at my ignorance. It amazes me--is there anything these people don't know?

Well, it's finally happened. When I ask them about my assignments for this class, they just shrug apologetically and back away. None of them have taken Logic. They're nearly clueless about it.

I am all alone in the world.

Alone, and really screwed for this assignment.

I donated blood today! A few highlights:

1. I read a release form that told me that if I test positive for HIV, several government agencies would be notified, in accordance with state law, and that if I wanted a list of who and why, I should just ask. But the nurse didn't know of any such list. I am quite curious as to who is keeping a register of people with HIV and what they intend to do with that information.

2. One of the questions was about whether I have ever had sex with someone who has hemophilia. Hemophilia is a genetic disease. I asked the nurse about that, too, and she said she was pretty sure hemophilia is sexually transmitted. What? (Then she looked it up and guessed that receiving clotting factors increases your chance of contracting HIV. Scary.)

3. I also got nervous when I was reading about the HIV test because (we did a problem about this in class!) in a typical population, 60% of positives will be false positives, so you should always test twice, and it makes me sad that they would throw out perfectly healthy blood, tattle to the government, and scare people to death for no reason. I wanted to ask about double-testing, but I didn't because I'd already asked lots of questions and I didn't want the nurse to get suspicious that I was engaging in risky behaviors (don't I wish).

4. Free cookies and doritos.

5. I bet if some person from the Olden Days were whisked forward in time and learned about some of the advances in medical technology, they'd be horrified. I mean, there are people who think harvesting organs and things sounds like something out of a sci-fi novel (and, okay, they're right). But instead of de-sanctifying and commodifying human life, I think it does the opposite: no matter how many cool machines and stuff you have, or how many millions you spend doing creepy experiments, the only things that can produce real human blood are real human people. I like it. It's a comfortingly personal aspect of what some think is over science-ization.

Here is the score.

Things that have killed me: Radii of convergence of series solutions. Partial fractions. Particular solutions when you use the annihilator method.
Things that I have killed: Laplace Transforms. Inverse Laplace Transforms. Exact equations and integrating factors. Newton's law of cooling.

In all, I think I lost.

But now there will be no more math until September. Or, if I am feeling uncharitable when I'm deciding my schedule next year, there may be no more math EVER. Which is a scary thought. We're in a violent love-hate relationship, and I don't know if I can stand the emotional abuse. But I could never leave it.

But that is not what I have come to complain about. I am now deciding whether to go to New York for the weekend to visit my extended family for the Seders, and I am oscillating like the general solution of a second-order Euler equation with a coefficient of x for its y' term (which is a lot, since the roots are imaginary and there's no exponent so it's just the trig functions). In other words, I don't know what to do.

Pros: My family will be happy with me. I will get to see my aunt and uncle and possibly my awesome cousin. New York is fun. I don't want to be bored this weekend. This is really an ideal time to go because my next exam isn't until the 24th.

Cons: I actually only know a very tiny fraction of these relatives. It's $65 and 11 hours on a train, each way. I don't want to leave Montreal when the year is wrapping up and I'm so busy with flat-hunting and studying and saying goodbye to my friends for the summer.

Help me, faithful friends, and try to avoid the calculus spewing out of me.

Okay, physics-types, help me out. Special relativity is not making it into my brain.

How does the fact that light has no mass cause the Doppler effect not to work on it? Why does it still look just as fast when you're traveling at .99c as when you're stationary?

When two people pass each other in spaceships, why does each think time has slowed down in the other ship? How can two things both be slower than each other?

Why does your mass increase when you speed up? Look,
A = F/m
F = m(v/t)
F/m = v/t
Ft/m = v
So shouldn't velocity and mass be INVERSELY related?


It used to make so much sense. But with this chapter, even the professor who looks like Chuck Norris in our educational videos couldn't make me get it.

One: New icon from the movie Everything is Illuminated, ostensibly based on the book by Jonathan Safran Foer but actually only similar to it in the most insubstantial ways, considering that it took out about 2/3 of the storyline and changed who the main character is. This is sort of an unfair analysis, so read the book yourselves and then challenge it.

Two: Got 75 speaker points in debate yesterday, even though we lost to probably the two worst pairs in the entire city (and beat someone who won state last year; go figure.) I am tempted to post funny debate-quotes from the incredibly sucky pairs but I'm not sure they would mean much to you. I think I'll do it anyway later, hah!

Three: I am a competent person. I am not as absentminded as I pretend to be, and when I act modest, it's not 'cause I don't know I win at life. And you know what else? I like math and science. Some people in fandom blow it off because they're no good at it, but I am. I'm good at math. I get A's in calculus, even under a tighter-than-normal scale. I'm not going to pretend to dislike it anymore. ( Collapse )

Earthquake kills more than 3,000 in S. Asia [AP Wire]. Special triple-chocolate brownie cake points (a la jennuine's recipe) go to India for unexpected generosity to their long-time enemies. Let us follow their example.

What I learned today:
1) The instantaneous rate of change for any real x-value a in the function f(x)=bx^2 when b is a real number is 2ba.
I apologize that there is only one item on this list; it's Saturday. In penance I will prove the above statement. Ready?

Assume that the instantaneous rate of change m at any point (a,f(a)) equals the limit as h approaches 0 of [f(a+h) – f(a)]/h when a is any given x-value, a+h is another x-value, h is the interval between them, and f(x) is any given function. (This equation is the one used to find average ROCs between two points in a function, which is essentially what we will be doing, only that the two points we are working with in this case, a+h and a, are actually the same point being used twice and only pretending to be different. The interval between them, h, will be zero, which is why they're the same.)

(To make things simpler for me, and because I like the letter P and it gets slighted in math, we will use (P) as shorthand for lim_(h-->0). This is sort of unmathematical; sorry.)

If (P) [f(a+h) – f(a)]/h = m (inst. ROC), and f(x)=bx^2, then m=(P) [b(a+h)^2 – ba^2]/h. (Here, we substituted (a+h) and (a) in for x in the second equation.)

m=(P) (ba^2 + 2bah + bh^2 – ba^2)/h. (We used FOIL and the distributive property to clear the parentheses in the first part of the numerator.)

m=(P) (ba^2 + 2bah + bh^2 – ba^2)/h. (The terms ba^2 and –ba^2 canceled each other out to equal 0.) So, P=(2bah + bh^2)/h.

m=(P) h(2ba + bh)/h. (We reversed the distributive property to factor h out of the numerator.)

m=(P) h(2ba + bh)/h. (The h in the numerator and the h in the denominator canceled each other out to equal 1.)

So, m=(P) 2ba + bh, or, m=lim_(h-->0) 2ba + bh. (Are you still following?)

In order to solve a limit, we plug in the number that h approaches every time h appears in the accompanying equation. In this case, the number that h approaches is 0.

So, m=2ba + b(0), or just m=2ba. In English, that means the instantaneous rate of change for any x-value a in the equation f(x)=bx^2 when b is a real number equals 2ba. QED. (Do I get to say that? Or do you have to be a physicist?)

Effectively, this means that when you have a parabola, the slope at any given point is just the coefficient of x^2 in the equation, times the x-value of the point, times two. (i.e. The point (5,75) in the function f(x)=3x^2 has a slope of 30 because 30=5*2*3.)

(Take that, calculus. I will eat you.)

(I learned some new HTML on Thursday, but I'll spare you that, even though it is almost as fun as math and perhaps even moreso if you play with background colours. It feels weird, having everything I have learned about HTML in the last four years translated into about ten pages of a single textbook. I am officially no longer any smarter than anyone in my computer class. Having entered the class actually knowing how to use a computer no longer sets me apart. [OMG seriously, did I tell you we learned that you can have TWO PROGRAMS OPEN AT ONCE? And you can change by CLICKING ON THEIR NAMES ON THE BAR AT THE BOTTOM? I bet you didn't know that, huh? Incredible.])