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Home » Mathematics » High School Pre-Olympiad (Ages 14+)
 
Proof contest
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Temperal
Navier-Stokes Equations
Navier-Stokes Equations

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#141
I'm interested.

PostPosted: Wed Jul 02, 2008 10:37 am  Back to top 
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#H34N1
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


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#142
Can I join?
_________________
I lost. Why do I lose so much?
Latest stupid mistake(s): 2^4\neq 8.
More combo help please kkthx[url]. Epic fail.....

PostPosted: Wed Jul 02, 2008 10:40 am  Back to top 
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Temperal
Navier-Stokes Equations
Navier-Stokes Equations

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#143
#H34N1 wrote:
Can I join?

what do you mean, "join"?

PostPosted: Wed Jul 02, 2008 5:41 pm  Back to top 
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Ketvoman
Hodge Conjecture
Hodge Conjecture

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#144
Maybe make an easier proof contest at the High School Basics level.

PostPosted: Thu Jul 03, 2008 12:53 pm  Back to top 
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#H34N1
Birch & Swinnerton Dyer
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#145
Temperal wrote:
#H34N1 wrote:
Can I join?

what do you mean, "join"?


I thought it had already commenced so I thought I had to ask before submitting proofs.
_________________
I lost. Why do I lose so much?
Latest stupid mistake(s): 2^4\neq 8.
More combo help please kkthx[url]. Epic fail.....

PostPosted: Thu Jul 03, 2008 6:27 pm  Back to top 
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Math4tots
P versus NP
P versus NP

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#146
I'm interested too

PostPosted: Thu Jul 03, 2008 11:27 pm  Back to top 
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1=2
Birch & Swinnerton Dyer
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#147
Eye aim interested.
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Hmm... apparently quoting Disney movies gets me muted on FTW. Razz

PostPosted: Fri Jul 04, 2008 6:27 am  Back to top 
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timwu
Yang-Mills Theory
Yang-Mills Theory


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#148
Any update...?

PostPosted: Fri Jul 04, 2008 8:43 am  Back to top 
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binomial_4eva
Yang-Mills Theory
Yang-Mills Theory


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#149
im interested

PostPosted: Fri Jul 04, 2008 8:45 am  Back to top 
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Temperal
Navier-Stokes Equations
Navier-Stokes Equations

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#150
#H34N1 wrote:
Temperal wrote:
#H34N1 wrote:
Can I join?

what do you mean, "join"?


I thought it had already commenced so I thought I had to ask before submitting proofs.


1) it hasn't commenced
2) even if it had, you don't have to "join", you just submit your proof to the latest problem.

PostPosted: Fri Jul 04, 2008 10:24 am  Back to top 
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Poincare
Navier-Stokes Equations
Navier-Stokes Equations


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#151
I'm in.
The message is too small. Please make the message longer before submitting

PostPosted: Mon Jul 07, 2008 10:49 am  Back to top 
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1=2
Birch & Swinnerton Dyer
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#152
This is not a sign up thread like in G&FF. All you need to do to be included is to submit a solution for the current problem, which is not posted yet.
_________________
Hmm... apparently quoting Disney movies gets me muted on FTW. Razz

PostPosted: Tue Jul 08, 2008 6:07 am  Back to top 
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Temperal
Navier-Stokes Equations
Navier-Stokes Equations

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#153
The fact is that chess64 didn't want to continue it because of lack of interest, so expressing interest is perfectly legitimate, 1=2.

PostPosted: Tue Jul 08, 2008 7:29 am  Back to top 
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Lulze
Poincare Conjecture
Poincare Conjecture


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#154
Hm. When do you think the next problem will be posted?

PostPosted: Thu Jul 17, 2008 11:57 pm  Back to top 
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chess64
Birch & Swinnerton Dyer
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#155
Okay, maybe I'll post a problem tonight. I'll start easy.

PostPosted: Fri Jul 18, 2008 9:31 am  Back to top 
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RightAnnihilator
Hodge Conjecture
Hodge Conjecture


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#156
A word on difficulty. I suppose problems should not contain phrases like :

Quote:
It is well known that for all positive integers a,b, and reals c > 1, |a^c - b^c| > c.


It's especially not well known to anyone who lets a=b, and even then, I doubt it's well known :/ Maybe stick to things that don't require such a dismissal.

Cheers!

PostPosted: Sun Aug 10, 2008 8:44 pm  Back to top 
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analytic
Poincare Conjecture
Poincare Conjecture

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#157
when will the next problem be posted? maybe

PostPosted: Mon Aug 11, 2008 3:00 am  Back to top 
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Bugi
Birch & Swinnerton Dyer
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#158
t0rajir0u wrote:
chess64 wrote:
Since some people are wondering: n \in \mathbb{N} means that n is a nonnegative integer.

In Eastern Europe, maybe. Generally the American (and Western European, if I'm not wrong) standard is that n is a positive integer.


I am from Serbia but n \in \mathbb{N} means that n>0 and n is integer. But m \in N_0 means m is nonnegative integer.

By the way, I wanted to join. When will the new problem be posted, chess 64?

PostPosted: Fri Aug 15, 2008 1:21 am  Back to top 
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1=2
Birch & Swinnerton Dyer
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#159
Bugi wrote:
I am from Serbia but n \in \mathbb{N} means that n > 0 and n is integer. But m \in N_0 means m is nonnegative integer.


To clarify: \mathbb{N} means positive integers, \mathbb{N}_0 means nonnegative integers(or the whole numbers), \mathbb{Z} means integers, I'm pretty sure that \mathbb{Z}_- means negative integers, \mathbb{Q} means the rationals, and \mathbb{R} means the reals. In the occasional problem, \mathbb{C} means the complex numbers(or imaginary numbers), where they are in the form a+bi where a and b are real numbers, and i=\sqrt{-1}.

Also, to join, submit a solution to a current problem. This has not started yet.
_________________
Hmm... apparently quoting Disney movies gets me muted on FTW. Razz

PostPosted: Fri Aug 15, 2008 2:21 am  Back to top 
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Altheman
Birch & Swinnerton Dyer
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#160
Problem 3:

Definition: Let S be a nonempty set and let \triangle be a binary operation on S. The pair (S,\triangle) is said to form a group if the following hold:

i) If x,y\in S, then x\triangle y\in S (closure).
ii) If x,y,z\in S, then (x\triangle y)\triangle z = x\triangle (y\triangle z) (associativity).
iii) There exists a unique element, e\in S, such that for any x\in S, e\triangle x = x\triangle e = x (identity element).
iv) For any x\in S, there exists an element x^{ - 1}\in S such that x\triangle x^{ - 1} = x^{ - 1}\triangle x = e (existence of inverse).

Prove: if a finite subset, H, of a group is closed under \triangle, then H is also a group!



This is a very beautiful problem in my opinion! I will give a hint in a week (on 8/23/08).
_________________
-Alex
Altheman's Problem Column
Last edited by Altheman on Sat Aug 16, 2008 2:45 am; edited 2 times in total 
PostPosted: Sat Aug 16, 2008 1:23 am  Back to top 
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