Thank God for Maple

Yeah, it's surprising how much algebra some calculations use. Some of my past stats homework included several pages of algebra for one problem.

I'm glad for stats packages. There's nothing worse than calculating a 10x10 hat matrix by hand.

Author	Comment
CRAWLand1000 Registered User (1/4/02 1:47 pm) Reply	Thank God for Maple If you don't know what it is, it's a computer program that can do some symbolic mathematics: algebra, derivatives, integration, tons and tons of stuff. Some recent physics homework involved algebra. Lots of algebra. "Big deal," you say, "algebra's something you do in junior high." And I guess that there's not much that couldn't, in principle, be done by a highschool student. I've done problems with so much algebra that the work filled multiple pages. However, some of this work has such complicated algebra that the final answer's expression alone would fill a whole page. Without computer assistance, it would take DAYS to solve this stuff. Here's a concrete example. But first, to get you up to speed on the physics: Of course, if you'd grab a spring and move it up and down with your hand, you could move it with any speed you like. However, as soon as you let go, it'll vibrate with one and only one frequency, the natural frequency of that spring. When there's more than one spring involved, there are still natural frequencies, but there may be more than one. The example used in class was a triatomic molecule, like carbon dioxide. So, there's two masses out to the side and one different mass in the middle, and they're layed out in a straight line (unlike, say, water, which is a little bit bent). The bonds between the atoms act like springs. Well, if you solve the problem, you'll find that it can vibrate in two ways (or any "sum" of those two ways). One, with the center molecule motionless, and the other two moving in and out at the same time, same amplitude, but different directions (one moves to the left, the other right, then vice versa). The other, with the two side masses moving one way, with the same amplitude, while the middle mass moves to the other way, with a different amplitude. The problem we had to solve involved FIVE moving particles contected by springs. The first step in the problem is to expand a five by five determinate. A two by two determinate is easy. Three by three, not too tough. Four by four, getting pretty hard, especially when the entries are all expressions with variables instead of numbers, like in my case, so they don't simplify. Five by five? Forget it. Sure, it can be done, with pages and pages of algebra, but it's time consuming, and this is just the FIRST step of this problem. Fortunately, Maple does this problem for me. After you expand the determinate, you get a fifth degree polynomial equation. Well, you can easily factor out one expression to get a fourth degree polynomial. These equations can be solved "in principle", but it's even harder than the previous step. Maple factored the polynomial into two quadractic expressions. Quadractic expressions are easy to solve by hand, even when the coeffients are expressions, so I did that myself. This gives the four fundamental frequencies of the system. Then you have to find the ratios of amplitudes for each frequency. This could be done by solving 4 sets of 5 linear equations. Again, this in principle can be done, but it's not fun. Normally, high school won't have you solve more than one set of 3 linear equations (which is much easier than 5; once you get over 4, every additional equation makes the problem much harder), and even then all the coeffients will be normal numbers, while in my case they were all complicated expressions. Fortunately, Maple did this for me, too. So, one problem with 3 gut-wretching algebra steps. If you don't really understand what I was talking about, that's okay - the point I was trying to make was how complicated the math was. Does having a computer "do all the work" take away from learning, or "doing", physics? In my opinion, hardly. Only the first step in the problem was physics (finding the potential energy and kinetic energy matrix), and I easily did that myself. If anything, all the math steps following that would only serve to obscure the physics. There has been lots of math done before the age of computers to solve problems like this, but, frankly, I think it's worthless now. I LOOOOOOVE Flying Omelette!! Crawl and 1000
Facilitypro Moderator (1/5/02 1:06 am) Reply	Maple Yeah, it's surprising how much algebra some calculations use. Some of my past stats homework included several pages of algebra for one problem. I'm glad for stats packages. There's nothing worse than calculating a 10x10 hat matrix by hand.
Liontamer The Game Jerichoholic Ninja (1/5/02 11:41 pm) Reply	Re: Maple I used to use Maple all the time when I was taking math and computer science classes. I hated that program, but it did come in handy. It beats the hell out of SyStat (which I used for my Psyc classes). -'Tamer "Young lady, stars shine only in the sky, and stars which fall to earth never shine again." --Anubis, Dark Warlord of Cruelty
Crawl and 1OOO Registered User (1/1/04 12:18 am) Reply	I LOVE FO! I got an 'A' last semester in my Electrodynamics course. It's really math-intensive. Surprisingly, though, I didn't use Maple once. I did all the algebra and calculus by hand. I LOOOOOOVE Flying Omelette!! Crawl and 1000
Liontamer The Game Jerichoholic Ninja (1/3/04 3:26 am) Reply	Re: I LOVE FO! I used to like calculus before I had calculus 2 in college. That class is what turned me away from math. I guess it's a good thing though since that caused me to embrace pyschology, resulting in a publication this year of a journal article that I co-authored. -'Tamer "Young lady, stars shine only in the sky, and stars which fall to earth never shine again." --Anubis, Dark Warlord of Cruelty
Crawl and 1OOO Registered User (1/5/04 8:44 pm) Reply	I LOVE FO! I still like math a lot, in principle. I considered majoring in mathematics, but wimped out slightly by taking into account that physics might be slightly more useful, job wise. I'm not even sure what calculus 2 would have been (of course, it might be different from university to university anyways). I took very little calculus at the university level because, before my freshman year of highschool, I was really obsessed with math for some reason, checked a calculus book out of the library, and went through it all on my own. Off the top of my head, the only things it didn't cover were complex methods (which I later taught myself with a Schaumm's outline book) and differential equations (well, it had a couple, but nothing substantial), and we covered some of those in physics (such as Poisson's equation). To this day, I think Taylor's theorem is probably my favorite theorem in mathematics. I LOOOOOOVE Flying Omelette!! Crawl and 1000
Liontamer The Game Jerichoholic Ninja (1/6/04 11:53 pm) Reply	Re: I LOVE FO! Like I said, I used to love math and science in high school, but some experiences at the college level with boring classes or annoying professors turned me off on both a lot. Actually, I started to lose a little interest in science in high school. My advisor convinced me to take his AP Biology class and was very enthusiastic about it too. He would give me extra material to read and study and would discuss them with me. Unfortunately, when I returned to school for spring break, I found out that he had passed away. My heart was just never into biology as much after that. I loved math in high school, and I was very good at it regardless of which type of class (geometry, algebra, calculus, etc.). I even won my school's math award my senior year. I considered going into math or science in college, but the first physics class I took was more theory than calculus. Being math-oriented at the time, this just didn't appeal to me. When I considered math as a major, I didn't like the computer science classes that it would require, and I hated my calculus 2 class. I took a few psych classes and enjoyed them, and that's how I ended up a psych major. -'Tamer "Young lady, stars shine only in the sky, and stars which fall to earth never shine again." --Anubis, Dark Warlord of Cruelty
Facilitypro Moderator (1/20/04 12:42 pm) Reply	Re: Thank God for Maple Congrats on your first pub. Was it �Motion Parallax: Is it Presented Accurately in Textbooks?�
Liontamer The Game Jerichoholic Ninja (1/20/04 6:28 pm) Reply	Re: Thank God for Maple Yep, that'd be the one. It was meant to be the beginning of a series of article on motion parallax, but I'm not sure if the follow-up will ever come to be. I hope we do finish it though since I'd hate for all of those lab sessions that I ran to be for nothing. -'Tamer "Young lady, stars shine only in the sky, and stars which fall to earth never shine again." --Anubis, Dark Warlord of Cruelty

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