Calculus homework in the 21st century

In the early 20th century, a student studying mathematical analysis (calculus) in college would probably sit with paper and ink, computing a few dozen integrals. In the middle to late 20th century, mathematical software became available that was able to compute these integrals, and in the late 20th and early 21st century, this functionality became available to students in the form of TI-89 calculators. Still, though, high school teachers and college professors almost always required the students to "show their work", rendering the automated integration technique useful only as a way to check the answer.

This changed very recently with the release of Wolfram alpha. Here is an example of it doing integration for you, with both words and equations. One needs only to copy the text into LaTeX and turn it in. Impressive, huh?

Actually, while the functionality of the Wolfram Alpha search engine is indeed impressive, this is not the impressive part. Here's why. Software uses algorithms for numerical approximations when numerical computations are required, but algebraic manipulation is pattern matching, just like it is done on paper. To a first approximation, a computer solves an integration program just like we do. These algebraic computation systems have been developed for a long time, and the algorithms are accessible in full to someone who is willing to spend some time on it. All that is left is to print the steps.

To calculus teachers reading this: please don't deny students access to this resource. Just don't allow computers on exams.

A package from Hungary - not

On application, Budapest Semesters of Mathematics asked for six addressed labels, and then sent me a letter with the address handwritten, I wasn't sure what the labels are going to be used for.

Today, a rather curious package arrived in the mail. On the box was printed "Budapest Semesters in Mathematics, and a tiled design with a comical interpretation of state seals. A stamp read "Magyar border control 335 (210) Magyar Vizem 2001 Check Point". Another stamp: "2001 Budapest, 01.09/18 Ferihegy 1". I don't know where BSM got those stamps, but one thing is clear: the package was addressed from the North American Office, it did not arrive from Hungary.

Inside the box, a curious assortment of souveniers. A picture says it all.

Looks like a reminder: get the forms in ASAP. And do your math homework.

Post mortem midterme physica

It happens like this: you take a midterm with three problems on it, realize that you can only confidently answer one of them, somehow manage the second, realize at the last five minutes how to do the third (and have a little time left to start it). Then the bell rings, you turn in the test, and walk out of the classroom feeling this close to declaring a third major.

Well, what did I expect? I expected a Lagrangian problem, and there was a Lagrangian problem. I excepted a Frobenius method problem, and there was a Frobenius method problem. I didn't know what else to expect.

It was, of course, a solution of Laplace's equation with given boundary conditions. A Dirichlet problem. Something that was covered in math, and in Physics on the Friday before I left for Toronto (which I'll write about later). What's the problem? I left for Toronto, completely forgetting Friday's lecture on this exact same problem.

Somehow, I managed to remember the first few steps: separation of variables, boundary conditions; and then ran out of time.

Why I am feeling good about this test is to me a mystery.

In memoriam cultorum

No, I'm not being serious. Just a little angry. And yes, I will reappropriate the funds, though at the moment I will not say to what cause.

Two loops made of plastic, two pieces of steel,
Their future together, their lives intertwined,
Left last week abroad and will never return,
Left last week abroad and are now left behind.

For over a decade they were at my back,
For over a decade I held them close by,
I saved them from teachers, I lost them and found them,
Yet failed today - from an airport guy.

And was denied also for them a transport.
The couple's bright future was now deferred.
As if by misfortune they came on my way,
And I - to a place that consumed them away.

And as by misfortune they came at a time
When I could no longer nor could yet provide.
I know now, I have to look toward my future
To let survive others, whose lives come beside.

Then, find a good cause, you, unpaid mailing fees!
Help more than a pair of scissors to breathe!
This Autumn, this August, to Europe I fly
To find me new partners, new friends, a new life!

A gem inside the cube of ice

(I wrote this a while ago, experimenting with repeating lines.)

In my backyard there sits a cube of ice.
I move it not, disturb it not, and pray
There be a gem inside the cube of ice.

The frost upon it's surface is a vice.
The grass around the cube is dead and gray.
I wait, ice may sublime, so be my price.

The more I look at it, the less precise
The thought becomes, but still it does not sway:
There is a gem inside the cube of ice.

I hesitate to break or melt the ice,
For if I haste, much more will melt away!
I wait, ice may sublime, so be my price.

I think about it, yet seek no advice,
For though the cube looks terrible today,
There is a gem inside the cube of ice.
I wait. Ice may sublime. So be my price.

Not ready (or) What's next?

What did I feel that day when I returned
To that green house in the woods downstream
My friends, for whom not long ago I yearned,
Were there, and greeted me. As in a dream,
They've not foresaken threads weaved once together
And I was welcome once again there-in,
And all was good, as it at first had been.

But what? Be in my face that mud had splattered,
As if some pressure was released from down the drain.
I, being marked with some internal stain -
A curse, that witches of Macbeth have muttered,
Among my friends, was lonely once again.

Discouraged, worried for no reason from no cause,
Doubting that I'll come thither soon, I went away
Back then, in high school, what an introvert I was!
Now, once again I'm feeling happy on my own,
And know I've not become less like a stone.
My introverted self just did not sway.

I write these lines, and wary of my future,
Where will I fit in now, where can I stay
While having friends, and not to run away
From things unseen, unheard, and unimagined?
Can I come back to my old group of friends,
Who took me in so easily, so simply,
Without distancing myself and running thence
Because of ghosts that haunt the house and make minds tense?

I would come back, be not the ghosts inside.
I would play spades again, my friends beside.
But now, my companions are my texts,
And I am with them, wondering: what's next?

Back and just in time

I am back from Moses Lake where, to my surprise, the NCS team did not place first in MiC Masters. But that's not the point.

The point is, as I realized on the two-day-long trip, my end of spring quarter this quarter will not be any less busy then last quarter. The draft for the MATH 336 term paper is due this Friday, and the code for my CS project: a week from next Wednesday. This serves as a reminder: we're approaching the third-to-final week of Spring quarter. Ouch. No wonder I decided to take some recreational reading along on the trip: Bewersdorff's Galois Theory for Beginners.

I'm not complaining. I could have two research projects to do this quarter, that is, if I stayed in chem. I could have other honors stuff to do, that is, if I were taking an honors civ and not a "survey of linguistic method and theory." And, finally, I might actually have a chance at a 4.0 in physics if I do just as well on the next exam as on the first one.

What's coming? Studying in the library as before, but also typing up the paper and working on the CS project. Not sure how I will consolidate the two. Of course, regular weekly homeworks, inconveniently all due on Friday. No lunch, and you'll probably not see me this week except in class. (I'm exaggerating.)

1st week - followup

Today marks the end of week 1 of the experiment which I have started this Monday afternoon. I have spent two of my lunch breaks: Tuesday and Wednesday, in the math library and must say, the results are very satisfying. I started on my MATH 336 term paper and am progressing quickly through the project. Somehow I have managed to find time, and I should say, a significant amount of time, to do research.

In fact, I checked out two books today: an introduction to Galois theory and a heavy graduate text on elliptic curves. Both are relevant to my paper, as well as to the broader study of elliptic curves.

Finally, to all my friends who paged me in Google chat that Monday, to one who called me to ask what have been the problem, thank you for being there for me. Thank you.

I only wonder if anyone is reading my blog now that it has moved out of Facebook. Huh?

Notice

Dear students, faculty, and staff of UW Seattle,

I take no pleasure in summing up that the recent few weeks of events surrounding my immediate friends have been, in the least, highly disturbing. In the last two weeks, the social strain on me has become more and more unbearable. As much as I would hate to withdraw from my present social lifestyle, I currently see no plausible alternative. As a result, the following take effect immediately.

1. My primary (and only) Facebook account, is hereby deactivated until further notice. All Facebook communication channels are deactivated as a result. Also:
2. All instant messaging / chat interfaces are disabled.
3. I will no longer frequent the RC except when I deem it necessary.
4. My Facebook blog is moved to my public blog at http://itolkov.blogspot.com.
5. I am accessible by e-mail via all public aliases (@g, @u, and @cs) anytime.
6. If you would like to meet one-on-one, I will be on the second floor of the Math Research Library (PDL C306) from 11:30 to 12:15 every day except Fridays. I am completely open to meeting there.
7. All prescheduled meetings with other students are hereby canceled. The only exception is the meeting with CR and BM - you know who you are.

I would like to thank everybody who helped me out this year. I would especially like to thank the RC group for recognizing me and letting me in. It is unfortunate that my relationship with the RC community had to proceed this way. Please understand that I do not intend to disappear, and will be glad to resume contact. I hope that what I said about you is true and that I will see you all in the nearest future.

I've posted a copy of this message on my blog at http://itolkov.blogspot.com. I'd be glad to read your comments there (anonymous comments are turned ON). Bear in mind that I wouldn't see your comments to the copy of this message on Facebook.

A PGP-signed copy of this message can be found here: http://stu.../itolkov/temp/notice9511.zip

Nothing stated herein is intended to impact my academic performance at UW. THIS NOTICE IS PUBLIC.

Again, I hope to see or hear from you soon.

Best Regards,

Igor Tolkov
University of Washington, Acad 6.0

A light no more

A lighthouse shines afar atop a cliff.
Raschelle inside awaits the coming rain.
Inside the castle, though the walls are weak,
She sits, sure that together they'll sustain.

Clouds gather, heavy torrents, gusts of wind,
Bombard the wooden roof, and seep below.
In Rachel's fear, courage intervened,
Preparing for what weather may bestow.

And miles away, where showers came and went,
But never caused destruction in their way,
I saw the waining light and did lament:
"Raschelle, wherefore did run you hence, away?

"Why did you leave behind our sunny town,
Out for the abyss where two oceans meet,
Where, day or night, you could astray and drown,
And perish there amongst the fiery heat."

I cried this out, and saw the light no more,
The hurricane so strong, the lantern bent
And plummeted unto the rocky floor.
And all the structure in it's shadow went.

And you, Raschelle, there lie disdainly tossed,
From one sea to another 'till one take
The body of a life untimely lost
And bury it far down beneath the wake.

Soon will ascend the heavenly canoe
Yet no other light will shine so true,
Than yours, which flew away to raging seas
And there, amongst the waters, came to peace.