Theledge.net

This was sent to me at work as a replacement part from a vendor. Still sealed in the bag...

Since I haven't really had time to post, I figured I would take a quick opportunity to round out the end of the month with a post that illustrates the kind of thing I’ve been doing to waste my time keep me busy.

Here goes:

If our inner product is defined as and our basis is defined as our Gram-Schmidt process is as follows:

Obviously,

Once we have found a normalized polynomial in our basis we can generate an orthogonal polynomial.

Once we have an orthogonal polynomial we need to normalize it.

Again, now having two normalized, orthogonal polynomials in our basis, we can generate another orthogonal polynomial.

Again we need to normalize the polynomial:

Since we now have three orthonormal polynomials we can complete our basis:

Therefore our new, orthonormal basis is:

Several things to note:

• This is not what I am learning. This is something I learned a year and a half ago. This is something I am doing in order to learn other things.
• This was essentially part “a” of a five part problem.
• The assignment had five problems.
• We were given a week to finish it.
• These are the first couple of Laguerre polynomials. We used them to approximate a function. It was a terrible approximation.
• I’m not bitching. This is actually the class I am doing well in and that I enjoy.

Addendum to anyone who finds this by searching to solve a homework problem: I have no idea if this is right. I would not suggest using it.

I don’t talk to my daughter the way most people talk to their kids. I kind of figure this is because she doesn’t talk yet, but I might have the correlation backwards on that.

And really, I just don’t talk the way most people do. I just don’t seem to have the knack for “normal” conversation.

So I say weird things to my daughter like “What’cha doin’, babe?“ or ”What the hell did you think would happen?” or “You are looking a little ragged.”

And I tend to use the term “abused” pretty regularly with little Alphie. I use it when she is getting beat up by life and her constant need to move at top speed or when she whines about some small injustice.

I’ll toss out “Oh, you’re so abused!” when she screams at me because I made her sit down in her chair. Or I’ll grab her and hug her and tell her “You’re looking a little abused.” when she looks particularly disheveled and is looking a little neglected.

So today she had a fever at daycare and didn’t feel well. And that last comment was exactly what I said to her when I picked her up early.

She was eating some apple sauce, sitting at a table with the sole attention of one of her very kind teachers. And I mean sole attention, which is not easy to accomplish in a room of six toddlers. It meant one of her other extremely nice teachers was essentially being pulled to the ground and beaten.

So I walked in and gave Alphie a once over. It was apparent immediately that she had a fever. She was boiling hot, and flushed, and her hair was matted with sweat and tears. She had dried snot crusted around her nose, and her eyes were red and puffy.

And so I leaned in and gave her a hug and told her “You’re looking kind of abused.”

And one of Alphie’s teachers (the alpha one, if there is such a thing; the one neither suffocating under a pile of small children nor offering my daughter tender murmurs of comfort) swiveled her head in an instant and said “WHAT?”

And I, having no real understanding of how to talk to people and having some (perhaps misplaced) pride in my interactions with my daughter, told the lady “I told her that she was kind of looking abused.”

And, in response, my daughter’s teacher laughed.

But I still might try to avoid the word “abused” in the future, if only when we are at daycare.

The humor I quoted in my previous post reminded me of the story of the worst professor I have ever had.

It was shortly after I re-started college. I had tested poorly on a math placement test and had subsequently been placed in Pre-Algebra. I was somewhat distressed about the prospect of wasting a semester doing math that I actually knew how to do, but I was excited to be in school again so I had resigned myself to learning as much as I could.

This class was a large class. Not a 300-person, huge class, but a 30-person class stuffed into a small room. It was hot. The room had no windows. I tried to remain excited.

The professor walked in. He was youngish, maybe mid-thirties (I would have been twenty or so), clean cut, and appeared to be sane. He calmly announced that there had been huge problems with the placement tests, and that the school was going to use the first day of class to administer a second placement test and that some people would probably be able to test out.

I felt my excitement level raise a little bit.

He handed out the test and then sat down behind the front desk, facing the class, and did absolutely nothing for the next hour.

I took the test. It was easy. I breezed through it. I double checked a lot of my work. I felt good about it. I was the second person in the room to hand the test in.

A third person handed the test in a few minutes later. I tried not to be bored.

And then the professor addressed the room. Before a room that was quiet except for the scratching of pencils he spoke these words (as best as I can remember them):

So, I figure I need to tell you a little bit about myself. My name is Professor So-and-So. I’m thirty-eight, I am single, I don't have any pets. No birds, no dogs, no cats, no nothing. I teach Mathematics at two community colleges, alternating days, and I am a copy and review editor for a publishing house. I stand in front of students and teach all day, and when I am done I go home to an empty house and I sit and read.

I am just waiting to die.

And he said it with no humor whatsoever, and with complete seriousness. No smile, no irony, no hint of any real emotion.

He then sat back down and began grading the tests he had in front of him.

He graded them quickly enough that he was bored waiting for tests to come in. Except that he wasn’t bored, he was just blank. He didn’t express any emotion as he sat waiting.

I tried to do some homework, but I increasingly became concerned that I would be stuck in this class with a lunatic for a whole semester.

After the last test had been handed in and graded he asked for everyones attention and flipped through the pile of tests, calling the names of the people who had tested out. He asked them each to grab their things and leave as he called their name. He congratulated each in turn.

He did not call my name.

After he had finished he apologized to us all for having to be in the class and told us that he hoped it would be O.K. in the end. He then dismissed us.

I packed up my things, conflicted and concerned. The second to last thing I wanted to do in my whole life was approach this instructor and accuse him of making a mistake. The last thing I wanted to do was spend a semester in his class. I paused and watched as other people swarmed around him, asking him questions about homework and tests and policy. He didn’t smile at any of them. He answered all their questions, but he didn’t interact. He was just there.

As the crowd thinned I caught his eye and as politely as I could I said “Is there any way I could know how I did on that test? I felt really good about it, and I don’t know what I could have possibly missed.”

He grabbed the stack of tests and flipped through them as I told him my name. He wasn’t bothered or concerned. He found my test. I had scored a one hundred percent. He calmly said “I must have missed your test as I went through them. Sorry about that. Well done.”

I thanked him and fled.

I don’t really know if he was a bad teacher, really, but I am glad I missed the opportunity to find out. I don’t exactly feel bad for him. He was, obviously, cognizant of his life and he seemed a reasonable person. I can’t pity anyone who has that much control over his situation.

But I will never forget the feeling of confusion I felt when I heard him say “I am just waiting to die” and I looked up, the appreciation of humor creeping across my face, only to find that there was no humor there to appreciate.

Today was the first day of school for both Alphie and I. You can see that she was excited.

Ok, so she was more confused than excited.

She handled it well, though. She woke up a little earlier than she normally would (on her own, though, we didn’t have to tear her away from the joy of sleep), and was immediately bundled into clothes, handed a sippy cup, and wrapped in her outdoor wear.

We arrived at daycare just before most of the other children, and Alphie immediately ran for the paints. She roved around the classroom with a bottle of green paint and ignored me while I checked her in and organized all her stuff. Then I told her she was going to have fun today, that I love her and that I would pick her up later.

And I walked out the door.

I admit, I hovered outside for a couple seconds, peeking in through the one-way window, but she was completely oblivious to my sudden absence.

Actually, that is wrong. She was not oblivious to my absence because she saw me leave. She simply was unconcerned by my absence.

And as I walked out she met my gaze through one of the regular windows and there was a brief flicker of recognition but no trace of panic or concern. I headed out and got in the car and called Angie.

I can’t say it was hard to leave her at daycare. I won’t say it was easy. She is in good hands, and she seems to enjoy herself, so I can’t complain.

I went through the day with the usual feelings of dread that revolve around doing something new (feelings that occur ever semester) and only a mild tingle of concern in the back of my mind as to how my daughter was doing. My biggest hope was that she was not experiencing an emotional meltdown brought on by confusion.

As it turned out, she was not.

I made my way through my own day with the usual feelings of isolation I have when I am awash in a sea of people who generally could not care less about one another’s existence. My instructors seem like capable people, the material seems relatively interesting, and none of the classes seem to require obscene amounts of work. They all seem difficult, but I believe that is the way with mathematics.

I ate a crappy lunch of Subway in a quiet, out the way place near the security desk in the student center. No one but police and construction workers passed by, which helped to make the day feel a little less surreal. I don’t know if it is just the age difference, or if it is cultural, but college students (especially in large groups) make me feel as though my soul is threadbare. Hearing construction workers bitch and swear helped me feel a little more normal. The police who passed by were as alone as I was, so they didn’t say anything. The security desk is far enough out of the way that they didn’t need to swagger, though.

I had to force myself to sit down and work on homework after my last class, so that I did not rush from campus and grab my daughter early in a bid to return to a comfortable routine. I am glad I was able to manage to restrain myself.

When I arrived to pick Alphie up she saw me as soon as I entered the room. She was standing, facing the door, coloring at a small table. As I walked in she looked up, grinned, and said “Hi!” rather loudly.

She then went right on coloring. I talked with the teachers for a little bit, while Alphie ran around and pulled things out in what seemed almost like a frantic bid to stave off leaving. Her teachers said she had been wonderful, and that she had had a wonderful day.

Alphie meanwhile steadfastly refused to acknowledge that I was there to pick her up. She finally responded to me directly when I suggested we go wash our hands, which she loves doing, especially in the little sinks the daycare has.

Once her hands were clean and her coat was on she was ready to leave, and even walked out the door ahead of me, before I was entirely ready.

So she had fun. She even did a little piece of art to bring home for mom.

It was a good first day.