OK, going to nip this one in the bud right now. I'm assuming you've been talking to whomever it was who PMed me to try find out my specific rank this year.

I am under no obligation to give out my rank and/or percentage to whichever random stranger rudely asks me for them over private message.

This said, the class lists are public. They are put up outside the Senate House, and published online in the university reporter, I think sometime in September. I am not trying to conceal my grade when I know both of those things happen.

I am, however, greatly enjoying the attempts to cast aspersions on me because of it, especially as those people doing it are going to look even more stupid when the class lists are put online in the university reporter and they find out what class I actually got.

Reply 3184

newblood

19

Original post by DJMayes

I have, thank you.
OK, going to nip this one in the bud right now. I'm assuming you've been talking to whomever it was who PMed me to try find out my specific rank this year.
I am under no obligation to give out my rank and/or percentage to whichever random stranger rudely asks me for them over private message.
This said, the class lists are public. They are put up outside the Senate House, and published online in the university reporter, I think sometime in September. I am not trying to conceal my grade when I know both of those things happen.
I am, however, greatly enjoying the attempts to cast aspersions on me because of it, especially as those people doing it are going to look even more stupid when the class lists are put online in the university reporter and they find out what class I actually got.

I have no idea what you got...I was just teasin him;

my apologies :hat2:

Reply 3185

Renzhi10122

11

Original post by DJMayes

I have, thank you.

OK, going to nip this one in the bud right now. I'm assuming you've been talking to whomever it was who PMed me to try find out my specific rank this year.

I am under no obligation to give out my rank and/or percentage to whichever random stranger rudely asks me for them over private message.

This said, the class lists are public. They are put up outside the Senate House, and published online in the university reporter, I think sometime in September. I am not trying to conceal my grade when I know both of those things happen.

I am, however, greatly enjoying the attempts to cast aspersions on me because of it, especially as those people doing it are going to look even more stupid when the class lists are put online in the university reporter and they find out what class I actually got.

Oh, are they still up now? Or do the class lists get taken down after a while?

Reply 3186

Eisenstein

1

Is there a summer of maths thread?

Reply 3187

Smash50

8

Original post by Eisenstein

Is there a summer of maths thread?

Nope, you should make one :biggrin:

Reply 3188

Renzhi10122

11

Original post by Mladenov

Problem 74**

Let

a,b,c

be positive real numbers. Then we have the following inequality:

\displaystyle \frac{a}{(b+c)^{2}}+ \frac{b}{(c+a)^{2}}+ \frac{c}{(a+b)^{2}} + \frac{2(ab+bc+ca)}{(a+b)(b+c)(c+a)} \geq \frac{3(a+b+c)}{2(ab+bc+ca)}

.

Spoiler

Was just browsing along, and saw that this was unsolved...

Solution 74**
Algebra bash:
Multiply out by

2(a+b)^2(b+c)^2(c+a)^2(ab+bc+ca)

*Page of algebra*
We'll use bracket notation here so that

[a_1,a_2,a_3]=\sum_{sym}x^{a_1}y^{a_2}z^{a_3}

End up with a degree 7 inequality that needs proving:

2[6,1,0]+[5,2,0]+2[5,1,1]+[3,2,2]\geq 3[4,3,0]+[4,2,1]+2[3,3,1]

By Muirhead's,

2[6,1,0]+[5,2,0]\geq 3[4,3,0]

and

[5,1,1]\geq [4,2,1]

reducing the inequality to

[5,1,1]+[3,2,2] \geq 2[3,3,1]

By Schur's,

x^4+y^4+z^4+x^2yz+xy^2z+xyz^2 \geq x^3y+xy^3+y^3z+yz^3+z^3x+zx^3

Setting,

x=a^{\frac{5}{4}}b^{\frac{1}{4}}c^{\frac{1}{4}}

y=a^{\frac{1}{4}}b^{\frac{5}{4}}c^{\frac{1}{4}}

z=a^{\frac{1}{4}}b^{\frac{1}{4}}c^{\frac{5}{4}}

, we arrive at

a^5bc+ab^5c+abc^5+a^3b^2c^2+a^2b^3c^2+a^2b^2c^3 = \frac{1}{2} [5,1,1] + \frac{1}{2}[3,2,2] \geq [4,2,1] \geq [3,3,1]

by Muirhead's as required.

(edited 8 years ago)

Reply 3189

Star-girl

12

Where is und? He's been slacking with the OP. :colonhash:

Reply 3190

Star-girl

12

Original post by DJMayes

...

Hey. Is there anyway we can start re-cataloging the problems and solutions on the first page without und (I noticed he hasn't been here for a while)? Or did we give up on that after problem 256? :tongue:

Reply 3191

Bushido Brown

14

Original post by Star-girl

Where is und? He's been slacking with the OP. :colonhash:

I haven't seen that guy post in years lol.

Reply 3192

username937760

16

Original post by Star-girl

Hey. Is there anyway we can start re-cataloging the problems and solutions on the first page without und (I noticed he hasn't been here for a while)? Or did we give up on that after problem 256? :tongue:

This is nothing to do with me whatsoever.

Reply 3193

und

OP

16

Original post by Star-girl

Where is und? He's been slacking with the OP. :colonhash:

The original method of cataloguing the problems and solutions was very time consuming. Someone at some point wrote a script to do this automatically but it needed improvement and I am not sure what happened with that.

Even if we were to collectively update the OP, which in theory shouldn't be too time consuming, bear in mind there is a strict character limit for posts, which does not play well with all those links. The first post is already out of space.

Anyway I hope you are having a nice summer!

Reply 3194

MathMeister

10

http://www.bmoc.maths.org/home/bmo1-2010.pdf

For q5 is one solution to the functional equation f(x)=x ?
I hope it's the only one or it's 3 pages for nothin' lol :/

( I put the solution back into the equation and using the properties of the eqn- I got it back - so surely it's true?)
Ty :smile:

Reply 3195

Renzhi10122

11

Original post by MathMeister

http://www.bmoc.maths.org/home/bmo1-2010.pdf

For q5 is one solution to the functional equation f(x)=x ?
I hope it's the only one or it's 3 pages for nothin' lol :/

( I put the solution back into the equation and using the properties of the eqn- I got it back - so surely it's true?)
Ty :smile:

f(x)=x is not a solution. You probably put it back in wrong, cos you should get xy=x+y+xy => x+y=0, contradiction. Oh, and there is more than 1 solution, gl.

Reply 3196

MathMeister

10

Original post by Renzhi10122

f(x)=x is not a solution. You probably put it back in wrong, cos you should get xy=x+y+xy => x+y=0, contradiction. Oh, and there is more than 1 solution, gl.

Huh ;/ Darnit i must try again lol

http://www.bmoc.maths.org/home/bmo1-2011.pdf - q2 - is (s,x) = (10,5) a solution?
Is there more than 1 solution? Cuz I tried putting in x values at the end and none others factorised.
( I used the fact that y-6 = (y-2) -4 to factorise in the first place and then it became trivial ..

Reply 3197

Renzhi10122

11

Original post by MathMeister

Huh ;/ Darnit i must try again lol

http://www.bmoc.maths.org/home/bmo1-2011.pdf - q2 - is (s,x) = (10,5) a solution?
Is there more than 1 solution? Cuz I tried putting in x values at the end and none others factorised.
( I used the fact that y-6 = (y-2) -4 to factorise in the first place and then it became trivial ..