Prove it!

langfor6

Hi. I'm a computer science major. As I progress further into my curriculum, I've learned something very unsettling about my intellectual capabilities.

I can't do proofs.

Throughout high school, the only class I ever had where we did proofs was Geometry, and I did poorly in that section, moved on, and forgot about them.

I took a course in Discrete Mathematics last semester, and did well on everything but (you guessed it) proofs. I can sort of fumble my way to partial credit on mathematical and strong induction, but I'd hardly say I'm a master of it.

Now I'm in a class on algorithm analysis, and proofs are all over the place. I'm able to mechanically reproduce results on certain basic problems (proving something is O(n^2) for instance), but I'm still getting a lot of problems wrong.

I try to believe in the idea that I can learn something if I really try, but proofs just don't seem to be clicking for me. I think I could probably continue with my fumbling through them, picking up points where I can, but I don't like it.

Can anyone give me any general or specific advice on how I can get good (or at least better) at proofs?

enlightenedbum

General advice is a sort of thought process:

1) Where do you want to get to?
2) What do you know (in this specific case)?
3) What do you know (generally) that links 2 -> 1?
3a) Does it seem like there's an intermediate step that it would be useful to get to?
3b) (Academic situations only) What are we currently covering and can I get to somewhere that looks like that?

musanman

enlightenedbum wrote: »

General advice is a sort of thought process:

1) Where do you want to get to?
2) What do you know (in this specific case)?
3) What do you know (generally) that links 2 -> 1?
3a) Does it seem like there's an intermediate step that it would be useful to get to?
3b) (Academic situations only) What are we currently covering and can I get to somewhere that looks like that?

Often times when I have a proof I just can't see (and eventually you'll start to make connections and see them quickly) I just list out all the shit I know and what that tells me.

Eventually you should be able to make a ton of connections and get home that way. Proofs through induction were tough for me at first I recall, so I just did a bunch of them...I think what bothered me the most was that they seemed so flimsy when I first learned them. It turns out they were just elegant and I was thinking too hard.

Kakodaimonos

This helped me a lot.

http://store.doverpublications.com/0486284336.html

langfor6

musanman wrote: »

enlightenedbum wrote: »

General advice is a sort of thought process:

1) Where do you want to get to?
2) What do you know (in this specific case)?
3) What do you know (generally) that links 2 -> 1?
3a) Does it seem like there's an intermediate step that it would be useful to get to?
3b) (Academic situations only) What are we currently covering and can I get to somewhere that looks like that?

Often times when I have a proof I just can't see (and eventually you'll start to make connections and see them quickly) I just list out all the shit I know and what that tells me.

Eventually you should be able to make a ton of connections and get home that way. Proofs through induction were tough for me at first I recall, so I just did a bunch of them...I think what bothered me the most was that they seemed so flimsy when I first learned them. It turns out they were just elegant and I was thinking too hard.

I have that same experience with induction. It really does seem flimsy.

2868

Proofs are all I am good at mathematically. I have Dyscalculia so numbers fuck me. But I digress, this isn't about me.

The way I handle proofs is as if I were approaching an argument that I know the solution to. (A rhetorical argument, not a bar fight.) It just becomes a matter of gathering evidence, and winning the smaller arguments that constitute the proof.

Now that may not be helpful to you, but I am rhetorically minded, so it helped me a ton to approach it like writing a paper, or building a debate case.

Though I regret haven't done geometry since college, so I can't build an example for you.

Centurion

First of all, don't feel bad about it. In my experience, proofs are something that you need to have a knack for. Also, being able to do them is just about irrelevant outside of academia.

Second, some proofs are really fucking hard. There aren't many people who could have come up with a proof for Gödel's incompleteness theorem on their own. When I was doing linear algebra at the university, the finals would always contain one or two proofs that nobody out of >1000 students figured out.

Having said that, there are techniques that can help. For example, some times it's easier to disprove the negation of the hypothesis, instead of proving it directly.

Steel Angel

Centurion wrote: »

Having said that, there are techniques that can help. For example, some times it's easier to disprove the negation of the hypothesis, instead of proving it directly.

Computer science proofs in an Algorithms class are usually proof by contradiction. That does not make them suck any less, but you at least get partway there by identifying the negation.