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Tips for math proof.

Hey.

I'm doing some Maths revision, as I've got my GCSE exams coming up in a few weeks. I was hoping for some tips on mathematical proof. I understand proof when I'm shown it, but can rarely produce it myself.

What is the minimum that you can explain? And can you simply say that (for example) "due to the proven Circle Theorem, bla bla bla.."? Or must you prove everything?

Here's an example that I was hoping that you lot could give me an example on:

Prove:
2n - 1 = an odd integer

Now, I wouldn't really know how to *prove* this. I could explain it: 2 multiplied by any number is always an even number, 1 subtracted off an even number always resorts in an odd number... But, that's not enough 'proof' surely?

Regards;

Mike McCracken

That is a good explanation but consider what it means to be EVEN.

An even number is divisble by 2 with no remainder. Apply the test

Try (2n-1)/2

(2n-1) / 2 Distributing the division

(2n)/2 - 1/2

n - 1/2

Know 1 is not divisible evenly by 2 therefore (2n-1)/2 = n R1
so 2n-1 is not even

mlmcc

InteractiveMind

ASKER

You see.. that makes great sense, but I would never have thought of that. lol. :-(

When you're given something that you need to mathematically prove, what is your first step? (ie: what do you look for, or think?)... Or does it *completely* differ on the question?

Thanks very much Michael.

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Mike McCracken

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Harisha M G

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aburr

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InteractiveMind

ASKER

Thank you all.

mathbiol

InteractiveMind,

I can think of a few things that might be getting in your way:
1 logic
2 a negative belief about your mathematical abilities (this is very common)
3 not enough tools, i.e. not knowing enough facts from the area of math your proof is in
4 lack of experience with doing proofs

Have you tried this? Start with an assumption p, and see where it gets you, in other words, what inferences you can draw from it. When you reach some conclusion that looks nice, call it q. Voilà, you've made your own theorem p implies q. And you know how to prove it.

You could do this with non-mathematical ideas too, for practice.

The best way to read a math book is with pencil and scratch paper handy. Whenever the author presents a proof, see if you can convince yourself of the conclusion before reading the author's proof.

Often the first thing to do when making a proof is to write down any definitions you think might be relevant. You might also find it helpful to make a sketch or consider an example, as ways to develop some intuition about what's going on.

Good luck with your exams.

mathbiol

InteractiveMind

ASKER

Thanks very much, mathbiol :-) That's actually very useful.

Mike McCracken

GLad i could help

Good luck with the exams

mlmcc