Maths Uni Chat

ILU2

caps

Did you ever finish that book? (the green one by george E.Andrews)

I dunno I try to understand combinatorics by picturing it.

"Choosing" is very easy to picture

No, but to be honest I still don't like the proof on the page 7 but understand it. One day I will finish the book.


I find if there is extra information like if you choose this you have to choose this, then yeah I can't seem to follow the reasoning.

Even then choosing doesn't give out any information and is linked to the bionmial coefficients which the proofs I don't fully understand.

Nah, that is inefficient. The best bet is learning the theory and if you can't do that picturing or better skecthing it. That way you don't need to do the calculations.

You mean the integration. Which, one but looking at it in one minute.
a, i, ln(coshx)+c
ii. let u=sinx-cosx, then the result drops out.
iii. This is hard if you don't know a trick. But, you need the top to look like the bottom so, just add 3 and takeaway 3(obviously have to have same denominator).
iv. That actually looks tricky, I would say break up. I would break it up into complex numbers, but you probably haven't seen that technique. You can then just integrate around a real part or a complex part.

b. i. let u=lnx and dv=1 dx.
ii. let u=4-x^2
(in both case check for sigularities. )

It's a bit of a crazy proof. I'm only doing 3 subjects at A2 at the moment (essentially 2, FM + physics) so I might as well do some reading...

analysis or number theory? which to start first?

Exactly what I was after <3

For iii though, how does doing that trick help?
can you cancel the top bit then and have 3/denominator and intagrate that.

wouldnt iv be partial fractions?
and both b have singulariates, what to do then?

No, but to be honest I still don't like the proof on the page 7 but understand it. One day I will finish the book.


I find if there is extra information like if you choose this you have to choose this, then yeah I can't seem to follow the reasoning.

Even then choosing doesn't give out any information and is linked to the bionmial coefficients which the proofs I don't fully understand.

+1 for the hating of Number Theory. I've never even attempted to study it, but I still hate it...not entirely sure why. Same goes with Combinatorics.

Hmmm, I couldn't get the proofs without some sort of "picture" though. Like

$\binom{n}{r}+\binom{n}{r+1}=\binom{n+1}{r+1}$

Take a group of n people + 1, choose r+1 from it. You can take r+1 from a group of n and not choose the +1 or you can take r from the group of n and choose the +1. Or ginger as our lecturer called him iirc. Very easy argument to understand.

Elsy the caps was so that ILU would be in capitals.

What's wrong with Combinatorics? It's pretty and I completely disagree with those people saying that you can't visualize it... I can't visualize algebra but combinatorics? Pictures are usually one of my first steps to trying to solve a combinatorics problem...

By the end of the year I will have done more modules in combinatorics than in algebra.

What the hell, that isn't a picture. Thats just wordss....

Not in my head its not

Okay, its a movie not a picture.

Anyway, reasoning from pictures that just stupid. Hence, why combinatorics isn't a real branch of mathematics. Because, real mathematics i.e. the bourbaki ways say you shouldn't reason from pictures hence having no pictures in their books.

Real mathematics isn't what Bourbaki says.

Real mathematics isn't what Bourbaki says.

Yeah, it what Grothendieck says it is. Anyway, he would never draw a picture or reason from pictures.

What's wrong with Combinatorics? It's pretty and I completely disagree with those people saying that you can't visualize it... I can't visualize algebra but combinatorics? Pictures are usually one of my first steps to trying to solve a combinatorics problem...

By the end of the year I will have done more modules in combinatorics than in algebra.

No it isn't

Yes it is.

Adding more, abstraction should be the goal in mathematics. But, combinatorics is not abstract, hence stupid.

amen

maths can be whatever I want it to be