[Kisai]

I've been assigned some advanced questions for a mathematics course. The questions are of the type in which the method (strong induction) has to be followed, but the nature is that unless the idea of how to do the problem occurs to you (which is some non-intuitive conception of an algebraic description), you're not going to get to the part where you can even begin to work on the solution.

Consequently, I've been looking up these problems online. Once I get the conception, I can follow the answer and solve it myself. However, I feel like its cheating to skip the conception phase. But then I'm given only a week to solve a complex problem and not turning in anything because the idea on how to solve it, means I get the same score as someone who didn't even bother looking at the work.

These are the types of problem where a mathematician may or may not figure out to solve one of them in several weeks, much less a novice with a full workload in a week. It just sticks in my craw that I would like the time to actually solve the problem on my own, rather than research someone else coming up with a solution and aping their answer.

[reb]

your moral clarity is usurping your practicality, Kisai.

the prof dint say 'don't go online to see solutions', did they? if they are good at what they do, they realized you're going to have to dig around.

if you really feel icky about this, ask the prof for some further work to do on your own later, without a deadline.

[Latro]

Proofs are very different from every other kind of problem, in my opinion, because there's so much that has to go into them. Here's my vague outline:
Expand definitions.
Look back at what you already know that isn't given in the problem. (In this case, for example, what the principle of strong induction says.)
Figure out how the things that you're given are related. (This mainly has to do with proofs that are implications; for induction, this is mainly how the inductive hypothesis for n (or all k <= n) is related to the case for n+1).
Formalize everything.

This can be difficult. It helps a lot to have seen some similar proofs. For example, in using regular induction, much of the time you are dealing with things like sums. It is very useful, in dealing with subsequent proofs about sums, to see, in another proof, the trick of separating the (1 to n+1) sum into the (1 to n) sum and the n+1 term. Similarly, in dealing with situations where you need strong induction, it is nice to see examples that show which of the k <= n you need to know something about. For example, in Fibonacci sequence problems, you tend to need to use the previous two terms, but not all n of them. In real analysis, you'll pull tricks with the triangle inequality, adding and subtracting terms, and so on. Once you've seen these tricks, you start incorporating them into your toolbox, just like pure logic or algebra.

It is hard, though, but at the same time this is what you're learning about. The pure reasoning is probably not all that new to you, but the filling in the blanks is what is new and relevant to you. So it's best to try not to have someone else fill in the blanks.

This is coming from someone who's probably a semester or two ahead of you in mathematics; I'm taking real analysis I right now, and the proofs get harder, believe me.

[acyckowski]

The wheel was conceived a few thousand years ago, and you probably don't feel guilty about driving or riding a bicycle without having conceived it yourself.

One of the things I hated most about college was the never-ending cycle of re-proving the work of people who came before me. If it took the likes of Faraday years of experiment and reflection to make a groundbreaking insight, why do you expect me to do it for homework?

These kinds of assignments are the academic equivalent of hazing.

[ClydeB]

I have to agree with acyckowski. Problem solving does not necessarily equal reinventing the wheel. If you are feeling guilty about using research material in the pursuit of the proof, then cite your sources as part of it. And as a plus you're covered against any possible plagiarism accusations down the road.

[Anreader]

I'm probably not as mathematically sophisticated or up to date as you are, but... I liked to start from the end and work backwards when I did the last proofs I did. At least as a starting point.

[Kisai]

	Originally Posted by ClydeB To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I have to agree with acyckowski. Problem solving does not necessarily equal reinventing the wheel. If you are feeling guilty about using research material in the pursuit of the proof, then cite your sources as part of it. And as a plus you're covered against any possible plagiarism accusations down the road.

That's what I did. I feel a bit better.