ChapterZero

Does it annoy anyone but me when they aren’t paid on time? I realize I don’t need to be paid on time… after all, I still live with my parents, it’s not like I would starve without reliable income… but I find it very rude and suspicious that I’m not being paid in a timely fashion. Last month, I wasn’t paid until near the very end, for that month, and the month before. Does that mean I’ll have to wait for another two months before I’m paid again? And just what the hell is going on here? I should be paid in the same time frame as every other employee of the department, and I know that they (whoever “they” is that is responsible for paying me) wouldn’t screw around with the whole department like this. So it’s insulting to me, and the other proctors, who also haven’t be paid yet, to treat us as unimportant peons. Although that maybe what we are.

I’ve been considering dropping my electrical engineering major, and just sticking to the math part. For several reasons:

• I would be able to take more math courses– a lot more, instead of just the minimum required for the degree
• I would have a lot more free time, which means even more time to dedicate to math, and even some time for computers and web design.
• No more stupid projects and report writing!
• No more spending 8 hours in the lab a week.
• No more 3 hour homeworks once a week

But some of those things above are what makes me want to complete the EE degree, just to say I did it. Plus, I want to be able to apply math, not only use it.

There is a reason I hardly ever post to math newsgroups: not only is the forum not the best for getting explanations, and frustratingly slow to use, but most of the time, I don’t get answers for my questions. At least this time, I discovered mathsolve.com, a site that is sort of like what I had in mind when I started mine, except community oriented. I’ll try to promote it at school, certainly among the UH math enthusiasts (aka the math club), and submit a couple of proofs of my own. Maybe I can convince Rob, the guy running it, to use some CSS– cause right now, it doesn’t look that inviting.

But a good idea.

I just got out of my circuits and systems class, in which I paying no attention. Instead, I was fiddling around trying to find the inverse laplace transforms of some functions. It all started when a guy asked me what the ILT of is; it took me a short while, but I soon worked it out by using division to rewrite it as and taking the term by term inverse to get . I originally tried using the derivative rule, that , but I started confusing myself. Then I was intrigued, and tried generalizing the division process to help me find the ILT of a function in the form of a polynomial in over . This led me to consider the inverses of , which turned out to be the -th derivatives of , from the derivative rule.

Near the end of class, I started trying more exotic functions like and , , which I suspect don’t have ILTs. I had the thought of expanding them into Taylor Series and using the term by term inverses, but is that sensible? I mean, does the linearity of the transform extend to cover infinite sums? I suspected not, just because that would make life too simple And after checking the Internet just now for the conditions under which an IFT exists, I think I was right for suspecting so; certainly, doesn’t have an IFT, because it doesn’t satisfy the two necessary conditions:

• 
• is finite

I just spent 15 minutes searching for a blog on math. I didn’t find any, although I found a couple of blogs with one or two arithmetic/mathematical philosophy related entries. This just serves to point out how lacking in diversity the blogging community is. The majority of us post on any of three things: technology, news, or ourselves. I don’t think that is intentional, which would be fine; I think it’s the result of laziness. Except for the news buffs, who live for that stuff.

What’s the point of blogging about yourself? Who cares? And yet we still do it.

So it seems rather promising to me that there is no prominent math blog… that is what I can shoot for as a realistic goal of my site.

This is the first in a series of entries on complex analysis. I’m posting as I read the book, Applied Complex Variables by John W. Dettman. So far, I’ve only read up to page 22, but it seems to be a good book; I like the style: definitions and statements followed by proofs. I also like the cheap printing… seriously; it gives it a certain ambience.

Curves and Regions

simple Jordan arc

A simple Jordan arc is a set of points defined by a parametric equation , , where and are continuous real-valued functions such that implies that

simple smooth arc

A simple smooth arc is a Jordan arc defined by a parametric equation , , where and are continuous, and .

simple closed Jordan curve

A simple closed Jordan curve is a set of points defined by a parametric equation , , where and are continuous real-valued functions such that if and only if , or .

Jordan Curve Theorem

Every simple closed Jordan Curve in the complex plane divides the plane into two disjoint open sets. The curve is the boundary of each of these sets. One set ( the interior of the curve) is bounded and the other (the exterior of the curve) is unbounded.

simple piecewise smooth curve

A simple piecewise smooth curve is a simple Jordan arc whose parametric equation , , has piecewise continuous derivatives and , were .

simple closed piecewise smooth curve

A simple closed piecewise smooth curve is a simple closed Jordan curve whose parametric equation , , has piecewise continuous derivatives and , where .

connectedness

A set in the complex plane is connected if every pair of points in can be joined by a simple Jordan arc lying entirely in .

domain

A nonempty open connected set of points is a domain.

region

A region is a domain together with all, some, or none of its boundary points

simply connected domain

A domain is simply connected if every simple closed Jordan curve lying in has its interior lying in .

I hate Halloween– it’s such a pointless holiday. Sort of like Easter, it’s just an excuse to eat candy and take a couple of days off from life. On second thought– that would make it a good thing, right?

I guess I have to examine my dislike for Halloween more closely. Part of it stems from the fact that people encourage their kids to go around begging for candy. I wouldn’t feed my kids candy, much less allow them to go begging for it! With all the chubby little tykes around, from gorging on pure sugar and fat diets, you’d think that we’d outlaw Halloween. At least here in Houston, the fattest city in the US.

But of course, that’s not all. Then there’s this whole supernatural thing going on, which I find totally stupid. If you’re going to pretend that witches, ghouls, and such are real for one night, why not be scared of them for just that night? The world is at the point where we need something to be scared of every now and again. I wish we could experience Halloween as the ancient Druids did Samhain. That would maybe shock the arrogance out of us, turning monsters into play things.

If there is some element of humor to be found in Halloween, it would be the reaction of zealous Christians to it. KSBJ, a Christian radio station I listen to sometimes, was encouraging people to attend ‘fall festivals’ as a family, as an alternative to trick or treating. What a crock!

And where did the phrase “trick or treat” come from?

Glad it’s over, that’s all.

I haven’t been going to church for over 6 months now. At first, I stopped because I was sick of church, and pretending to agree with every inane idea that people could claim was in the Bible, and most of the insipid ideas that a “good Christian” holds dearest. And since I’m not really close to any of the people in church, and being around some of them gives me a feeling of nausea brought on by an overwhelming sense of hypocrisy, I was glad to be able to spend my Saturdays on more constructive pursuits.

My parents have been rather cool about not forcing me to go to church. They realize that forcing me to go would accomplish nothing, an obviousness that I would not have expected them to acknowledge. At first, they tried wheedling me, but they gave that up rather quickly. Now they leave me be, at least for the time being. I suspect that they think– hope– this is just a phase. That’s pretty standard: they close their eyes to everything they don’t want to accept about me, and label it a phase.

But now, the hard part is beginning; the part that makes me think churches and cults have a lot more in common than the former are ready to admit. Random people from church call for my parents, and when I answer the phone, they ask why I haven’t been to church, and admonish me to “put God first.” Palpable disappointment wafts over the phone line, in what I presume is an (unconscious?) attempt to shame me back into church. Worst of all is my aunt, who says she doesn’t want to see me not make it to Heaven. This whole process seems like a muted version of withdrawing from a cult.

It all leaves me thinking, why does anyone care if I go to church? My parents care, I think, partly because they do want what’s best for me, but also largely because they want to think of themselves as successful parents. The people at church care, I think, because there is a dwindling youth population. There is no one who wants me to go to church solely because it is best for me; the closest person to that is my aunt, but even she has ulterior motives. Which is all to be expected: no one *is* capable of caring about someone else without biases.

Which means the decision is up to me. And I’ve made it, and sticking by it. Succintly, and simplisticly, I put it this way: church blows. If God wants me there, he can tell me himself. But that’s not going to happen now is it?