Hi there, I need to take over a little complicated proof (perhaps not too complicated  :roll:) , but the thing is that Im in oxide, I will like to  see sugestions for brief introductions to math proofs, and exersices, for see if I can prove the thing.

I have proved my problem more heuristically (if Im not wrong is trusting more in my sense... than in math :D), but I need a correct math proof and I will be more happy.
Posted on 2005-06-20 09:53:43 by rea
Ok, I have finded a resource, perhaps a little common http://mathworld.wolfram.com/topics/FoundationsofMathematics.html from there perhaps I can start like a guide...
Posted on 2005-06-21 00:45:50 by rea
I think the simplest proof is still prove by induction. There's alot of ways to prove by induction, but as of now I cannot give you an example yet. I will try to find an example qn and prove it if you require the proof.
Posted on 2005-06-21 02:23:04 by roticv
MathWorld is a very good resource. Perhaps if you give a better idea of what you want to prove. Different problems require very different approaches to proving them and it would take a long time to try and develop some familiarity with them all.

P.S. I gather you wish to do this yourself and not be just given the answer. Thats a great attitude to have and I can understand therefore that you mightn't want to post the problem in case someone else goes and does it on you, but some extra info on the problem will make it much easier to help.
Posted on 2005-06-21 05:13:29 by Eóin
What I have  now is a conjeture or hipothesis http://mathworld.wolfram.com/Conjecture.html http://mathworld.wolfram.com/Hypothesis.html but being that, I only have made some little numbers that aparently backup the conjeture, but that not make it true...

And not only that I whant to prove it true or false, but I think will be funny if I say some like "hey I have found xyz" but being a conjeture if later proved not being tru, then I will fill a shock for not to see it...

Then hope that you understand this, I have two ways, prove the conjeture to be true or false (I dont know in what become a conjeture if is true) and terminate the program and prove it with morenumbers than  4-5 diferent numbers...

Also tought is suposed that I know the proof by induction, apart from havent practiced my math skills, I dont see clearly how to do... lol, hope I will practice something :)..

Now I know in what will turn http://mathworld.wolfram.com/Proof.html it will turn in a theorem
Posted on 2005-06-21 09:04:59 by rea
Really the best way to learn how to prove things is to practice practice practice. Personally I was only able to learn by seeing examples done and then trying similar problems myself. MathWorld is a great resource but many of the example proofs are very complicated and not an ideal source for learning.
Posted on 2005-06-21 10:18:22 by Eóin
That is what I was thinking... tought it is fun to have a place like that, I have learned something that I dosent grasps... the things about theorem, axiom and suchs...


I have followed some things there, I understand some, but some are very complex....

Do you know of a resource, where I can follow examples??? (I will search ;))
Posted on 2005-06-21 12:37:04 by rea
The only sources I'd know off hand would be 2nd level math books. But I'll do some googling and see if I can find anything.
Posted on 2005-06-21 13:28:37 by Eóin
Well about the only resource of math questions I could find are the past papers form irelands state exams, heres the link.

Start with the math junior cert papers. Questions such as "express blah in terms of ...", or "show such and such" and of course "prove such and such" are the sorts you should practise. Try the leaving cert questions if you find the junior cert too easy.
Posted on 2005-06-21 21:26:30 by Eóin
I have finded a book about math logic: http://www.tylerwilson.com/330text.pdf

I dont understand completely the page... :roll: but I will try to get what you say.


I have a question, the algoritm seem fast be itself, but from the start I know that I will need generate the Pow set of some results, now I see that I will need generate the pow set of a set with 1,030 elements, the results, that will be 1,060,900 can be cuted a half, perhaps more, but anyway, I need generate them...

And like I have see a way to generate them, is give a bit per each element in the set, and start counting up, in fact, I will need a representation of 1030 bits and start counting, that is a very large computation for get the results require of at less 32 registers of 32 bits... and count from 0 to the high posible.. and that will be a messs!!!!!!, if Im not wrong, and like I have watched at start, this part is by far more the more complex (in calculation time) from all the algoritm... :(, this break the fast thing that the rest of the algorithm is...

In fact not only beak it, but destroy it...

:(.

perhaps I should look a workaroud.... but I dont see how... :S.
Posted on 2005-06-22 10:36:31 by rea
Then, the only way around is that I proof the first annotation (the source of this algorithm) for see if have sense try to optimize some steps... more than before seem the only reasonable thing.

:(, that calculation make me sad.... have stoped a very interesting thing :S.
Posted on 2005-06-22 10:39:23 by rea
Rea, I'm getting a bit confused overall. I think it's gotten to that stage where I'll need to know exactly what you're talking about so you'll really need to describe the problem / algorithm and what you're trying to prove if I'm to be of more help.

Eoin
Posted on 2005-06-22 11:00:05 by Eóin
Im working in a little thing about prime numbers, I have watched something, then I do some operations, that in fact are very fast, but over the results I need to apply a pow of the set of the results, after this pow of the set, the results can be cuted a half or more...

I have calculated for short primes and composites and the algo seem to work ok, even can calculate composites, thought like I say you before I not have a math proof that show if the observation is true or false.

But for some numbers (the numbers that I have prooved), the pow set is a little short, and because that, I havent watched before the complexity of this step... :S.


Op1, Op2, ... are the operations
R1 is the results of Op1, R2 are the results of Op2
Ok, here is a description without describe the operations...

gived n prime or composite, I apply Op1

Op1(n) is very fast (even for very large numbers) the complexity is by far less than n....
Op2(R1) This is the operation of Pow over the set R1. The complexity of this operation break the fast of the other operations..
Op3(R2) This operation can discard much of the results in R2. It should be fast like R2 (or n gived by #R2)
Op3(R3) This operation are only divisions for test the results in R3, if none divide, then n is prime, if some one divide, we have finded a factor.

The thing is that Op1 is fast, but it give a plenty of results... and than is showed by Op2 that is the pow of the set gived by Op1...


Op2 will make me sad, or I need see a way for Op1 give less results... :S...
:(.
Posted on 2005-06-22 11:19:50 by rea
I take it you want to prove that after these four operations that you can be sure that a number is definitly prime or not. Well I imagine it could prove quite tough to do this rea.
Posted on 2005-06-22 11:32:40 by Eóin
Not only prove that is prime or not, but in case to be not a prime, give one of the factors :).

Like you see, the only not descrived operation is op1, and in fact is what I need to give a proof, the rest of the operations are for calculate it in computer, but like I see now, from a practical point of view, the observation that generate Op1 will have no sense, because Op2... :S, perhaps the observation can be of some sense in a mathematic way in case to be true, but not more than that.. :S...


hehe, now Im happy, I see that I can delete Op2 in some cases, but I need first prove Op1 and a slight modification :)
Posted on 2005-06-22 11:46:24 by rea
I am quite confused by your phrasing and spellings (I suppose that English is not your first language), so I need to clarify some stuff.

Is you algorithm/method a way to determine whether a number is prime or not by generating a set of number that supposingly able to divide the number if the number is composite? Else, the number is prime.

Btw when you are talking about "the complexity is by far less than n", do you mean that the time complexity is better than O(n).

Haha. Let me publish Victor's bullshit prime number theory.

All prime numbers except 2 and 3 are in the form 6n ? 1 where n = 0,1,....
Posted on 2005-06-22 12:24:28 by roticv
Yes, english is not my first language, tought I think the majority of the time persons taht know well the language can understand what I write... also my spelling is in the floor I guess... :).

Im not good at algorithm notation and proofs, taht is why I not say what is the exact algorithm, because a guy taht I know say me, "perhaps you take much cannubis" in spanish :D... then is also for that Im so restricted at specific things...

About the above question, if Im not wrong is...

O(n) mean if n = 5 there will be no mre than 5 iterations... but can be 4,3,2,1 iterations... if that is, then yes that is what Im talking, the "exact" (because my math skills) I only know and see that is by far much less than n... I have not calculated it, but I supose how to calculate it....

What I know about this things, like you see, the operations are "exclusive" or they are not inside other... then Op1 is much less than n but Op2 is by far the more complex operation and that will break the complete algorithm (the porpuose), because the other ones are related to n being the count of the anterior results.


I will try make a proof about Op1, because it will not have sense continue (try optimize the algorithm) if the results that I see are only a small subset of good results... like I say before I have a nice Conjeture :). But for the moment is far from being a theorem... that is why the topic is math proof, when I have the proof, I will publicate the algorithm, other case no.

By the way, how look the algo is already publicated, but the specific is not...


I will put the rest of the day, week and perhaps more in try to make the proof...
Posted on 2005-06-22 12:40:05 by rea
Only for not let.. I have finded other resource, there are some links to online books.. and is a very extensive site.

http://metamath.org/ select your prefered mirror, also read the first pages for explanations about the site and some things, like follow the .gif verion or Unicode one...

Tought is complicate because Im not mathematician (is writed like that?) I will see what I can learn.

If you dont find them... the referenced books (in the first page) are http://www.mathsci.appstate.edu/~jlh/primer/hirst.pdf and http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf
Posted on 2005-06-25 11:45:53 by rea