why does this happen every term

[wallwalker]

I just spent about an hour staring at math homework and trying to figure out how I was supposed to solve a particular problem. After a while I gave up because staring at it, and rewriting it every way I could think of, wasn't actually helping me learn anything. As usual, I'm close to tears as a result. (I'll probably be fine, once I talk to the professor tomorrow before class. I hope.)

The real problem is that this class shouldn't be taught over a five week term. Period.

These proofs using the Fibonacci algorithm are killing me. I know what I'm supposed to do; I know that I'm supposed to be rewriting f(sub)n as f(sub)n-1 + f(sub)n-2 in some form or another in order to manipulate the equation so that I can use the inductive statement to replace part of it, so that I can eventually get to the statement I need to prove... but there are so many ways to rewrite these equations, and at this point I'm just getting to the point that it's more complicated than it was in the first place. (It doesn't help that when the professor tried to do this in class, he showed us how to start, then ended it when it didn't look anything like the statement we were trying to prove because we ran out of time.)

Specific specifics: Show that (f sub n+2)^2 - (f sub n+1)^2 = (f sub n) * (f sub n+3) for all n>=1.

The basis case is easy! I just... can't get anywhere with this induction proof.

*sigh* At least the bit of number theory that we're studying makes more sense than this.

Comments

[flarewerk]

Ugh, I'm really sorry your coursework is so frustrating. I'd offer to help, but the stuff under the cut might as well have been the eldritch love child of the Necronomicon and the entire aired run of Mister Rogers' Neighborhood -- bizarrely compelling, yet impossible to comprehend.

[wallwalker]

That's all right. It'd be easier if this was a course required for more than two major programs (Computer Science/Engineering, which most people consider one plan with a few minor differences between them, and Mathematics.) At least lots of different people have to learn, say, Calculus. This makes most Calculus students boggle.

And yes, I know what you mean. It'd be easier to read if I could type it as it appears in the book - but I can't remember how. I'll check the markups later.

[yohjideranged]

You know, I don't know why some schools insist on teaching these kinds of things in five weeks. I think it just makes it more difficult on everyone involved. Oh, to be sure, students are learning...but alongside what they learn in the mathematics, they are learning deep frustration, self-doubt, and sometimes outright anger.

As for your specific specifics...it looks like gibberish. Equations like that should not exist. *nods*

[wallwalker]

This equation is basically the classic example of a recursive function. (In other words, magic, as far as most beginning computer science students are concerned. How can a function call itself in its own definition? It boggles the mind.)

My professor said the same thing. He was telling us that the only reason that this course is so short is because the campus wanted to start Interstitial terms in May and August, which are ten or so days long! And since this course is only 3 CH, it got cut to five weeks. I have a few very pointed things to say about that in my course evaluation, when that comes around. Not about the professor, though; none of this is his fault.

[novel_machinist]

If you like, I could give some of the problems a try and break them down for you? Do you want them to be in programming language or would like

F_n = F_(-1/2-sqrt(13)/2), F_n = F_(1/2 (sqrt(13)-1))

work? It's been a LONG time, but I think my wife and I could probably get back into gear with it.

[wallwalker]

Hm. Maybe - let me see if I can find them online, that would be easier to handle than trying to type them out. (And something like that would be fine - I take programming foundations next term, actually. So I could probably understand them from my own experience, but it wouldn't be as easy for now.