@SimplyBeautifulArt Whew! Thanks for covering for me! :P

@Riker No hat?

for me? I've got 16 of them >_>

I've got oprah's hat in chat rn

it's just kinda sneaky

I've got the jester now though

(was just waiting for cache to update)

@Riker I see now! lol

:D

@Ovi I don't know of such books. Such stuff are always ad-hoc, and Michael appears to be some country's trainer for IMO, so no surprise.

@Ovi what level of problems are you looking for?

Olympiad etc,.?

@LastIronStar Easy Olympiad or less to start with, but I'd like to work my way up

@Ovi Be ready for an overload: artofproblemsolving.com/wiki/…

:D

They also have a forum where people post questions, that too is another resource.

@Ovi: Hmm can I move this olympiad thread to SBA's room instead?

@user21820 Yeah should've just asked there in the first place sorry

@Ovi No problem; I'll move it in a while.

← 11 messages moved from Logic

@SimplyBeautifulArt: If you have any other recommendations for algebraic stuff, I'm sure Ovi would love to hear!

Yes!

@Ovi: I did olympiads before, but it's mostly learnt by experience because there is no systematic approach.

@user21820 Hmm ok, though I would at least hope that there are some tricks that can be useful more often and should be known?

@Ovi If it were about inequalities, there are a couple of standard techniques. But if you're asking about just algebraic manipulations, there simply aren't many general techniques, because of the intrinsic nature of algebra. For instance, have you seen the algebraic general solutions of the cubic and quartic? The first step of reducing to depressed form can be vaguely motivated by saying that we want to reduce the number of free parameters. But beyond that it is thoroughly ad-hoc.

I have once asked some people whether they could motivate these algebraic substitutions via Galois theory. They didn't give me an answer. Galois theory in fact motivates a different kind of solution via Lagrange resolvents.

@user21820 I think you need to be a room owner to see history?

@user21820 @Ovi hm, I imagine someone from the main chat would know better.

@SimplyBeautifulArt @LeakyNun could see deleted comments in my room. Can you see this for example?

@amWhy :P

@user21820 nope

Still can't see it

I edited it to ping him. Let's see whether he can or not. I asked him about a previous one. If he can see this one then you and he clearly have some difference.

:P

Maybe Leaky is secretly a mod on some site x'D

@SimplyBeautifulArt Can't be, right? Their ◇ shows up everywhere.

Anyway I got to go a while.

Did you check the crude backlog? =)

@user21820 I will in a bit/probably after school

@user21820 Hmm that is a bit sad :(. But aren't inequalities just about using those same algebraic manipulations to bring your problem in the form of a known inequality?

@Ovi No. Because for inequalities we have some non-algebraic techniques such as Lagrange multipliers.

And power-mean inequality. And smoothing. And lots more.

@user21820 Ok thanks I will look these things up when I get back, I have to go now

bye!

=)

Bye!

@user21820 I cannot