Mathematics - 2017-09-16 (page 1 of 9)

it's actually the floor of $3\left(\sqrt{x^2-3}-2x+3+3\operatorname{floor}\left(\frac{x}{3}\right)\right)^{‌-1}$ but I'm looking for a more elegant form

Dodsy

D: sorry to hear that faust

glad you made a turn around.

Faust

end of last year the chair of the math department invited me to go into any honours program i wanted in the math department

Dodsy

12:42 AM

but faust

Faust

so dont be too worried about ur first year just work on the material and stay away from girls.\

Dodsy

HA girls.

Jasper

When you make a turnaround, at some point your instantaneous velocity is zero, lol.

Dodsy

My gf is enough for me.

@Jasper very deep

Faust

@Dodsy that seems like a contradiction Western and Ontario

Jasper

12:43 AM

@Faust I don't agree. I think love is the greatest inspiration in the world.

Dodsy

sigh.

I can't believe you haven't heard of it.

:(

Faust

i live in a little box

Dodsy

you're a country bumpkin?

Faust

mm no im just odd

i cant name 7 actors

Dodsy

brad pitt?

Dustin Hoffman?

Faust

12:44 AM

even if you let me name musicians as well

Dodsy

Selena Gomez?

Faust

i have heard of brad pitt

Dodsy

sad dude.

Faust

but i am rather knowledgeable of many real world things

not just biology chemistry and physics but mechanics electrical plumbing etc

i can fix basically anything even electronics

do i enjoy movies? yes

Dodsy

Do you know what edamame is.

Faust

12:47 AM

do i give two flaming shits what the actors are called? defiantly not

cheese?

peas?

im out of guesses

japanese sword?

Dodsy

beans, you were close.

Faust

they any good?

Jasper

I like Mr Bean.

Dodsy

ya they're really good

you boil them and salt them

then eat the insides out :o

really tasty

Faust

did you know that boiled peanuts are Delicious?

3

Dodsy

12:51 AM

no :o

Jasper

@Faust Yes, indeed.

Faust

@Dodsy if your ever in flordia and see a sign for boiled nuts you should stop its def worth it.

Jasper

Boiled peanuts are often served in Chinese restaurants as an appetizer.

Dodsy

I am not huge on peanut

I don't often enjoy peanut in butter form.

nor do I like peanuts in my foods.

Faust

yeah i dont really like peanuts eithier

but boiled peanuts are ftw.

Dodsy

12:55 AM

hm

Daminark

Peanut butter is the best thing that exists

Though I'm not fond of peanuts directly

Dodsy

I'm the exact opposite.

Faust

i dont mind the odd deepfried breaded PB&J sammich

gotta get hot enoug to melt the peanut butter though

Dodsy

When I was a kid my mom would make me pb&j for lunch and it would always be smooshed

Daminark

1:15 AM

I have it without jelly

In fact sometimes would just have a spoon of PB

Faust

i had a dog that fond of peanut butter in a similar way

it got run over by a tow truck.

Ted Shifrin

You kids still here?!

Daminark

Also @Balarka I figured out the problem from yesterday

The one about finite $T_0$ sets

It's easier to show that there's an open singleton and then look at opposite topologies

Ted Shifrin

Love peanuts in Szechuan and Thai :)

Daminark

@Ted so it seems. I don't have school right now so I'm not doing too much

Ted Shifrin

1:23 AM

Well, we know you're a lazy bum, Demonark.

Faust

@TedShifrin i left and did some GT then came back stuck on some graph theory hw

For every pair of integers k and l, where $ 2 \geq k \geq l $, construct a connected
graph $G_{k,l} $ that has a dominating set X of cardinality k as well as a minimal
dominating set Y of cardinality l, but no dominating set of cardinality less than
k. Explain why X and Y are minimal dominating sets, and why $G_{k,l} has no
dominating set of cardinality less than k.

can anyone dicipher that

Daminark

'Tis true, though I have been trying to do a bit of k-theory and finite topology so there's that :P

Ted Shifrin

How can the minimal dominating set have greater cardinality than a random dominating set? So what's a dominating set?

Faust

im assuming that $ K_{k,l} $

Secret

in The h Bar, Sep 9 at 12:56, by heather

no, i'm not going to just solve a problem where you haven't really put any effort in to make it understandable to others.

Faust

1:25 AM

uh

Ted Shifrin

Oh, $X$ ends up having to be minimal. Well, that's obvious, then.

Daminark

Dominating set for a graph is a set such that all the other vertices are adjacent to something in it

Ted Shifrin

Good for Heather.

Faust

$K_{2,5} $ has a dominating set of cardianality 2 and a set of cardinaltity 5 i think

Ted Shifrin

This is just language, Faust. I don't think there's anything substantive.

Oh, duh, $k\ge \ell$. I was reading it backwards.

Faust

1:27 AM

no i wrote it like a retard

Ted Shifrin

You have something wrong, Faust.

Daminark

Wait I think that's a typo, since $2 \ge k \ge l$ is... quite restrictive

Probably $2\le k \le l$

Ted Shifrin

Uh huh.

Faust

yeah

@Daminark got it

Ted Shifrin

That's what I figured. And then minimality should say $X$ must be minimal if $Y$ is. But how can $k<\ell$?

I don't know no graph theory.

Faust

1:28 AM

is $K_{k,l} $ an example?

Daminark

Minimal just means you can't remove vertices from it

In contrast to minimum

I think $K_{k,l}$ works

Faust

@TedShifrin then you know more than i do

Ted Shifrin

I truly know none.

I never took it and I never taught it.

Faust

im trying to take as many diffrent branchs of math as possible

Daminark

Good choice

Faust

1:30 AM

i got Number theory, graph theory, abstract algerbra, analysis and geometry this semester

Jasper

Harris, Hirst, Mossinghoff: Combinatorics and Graph Theory is what I recommend as a text.

Daminark

But yeah okay we just need to guarantee that you can't find a dominating set with cardinality < k

Faust

if its complete

bipartite

thats fine

do i need every set or just one?

Daminark

"every set"?

Faust

i dunno i know nothing about graph theory

every graph?

Daminark

1:33 AM

They're asking you to find a graph for any $k,l$ such that you have a dominating set of cardinality $k$ and a minimal one of cardinality $l$, and so that no dominating sets have $< k$ vertices.

Jasper

When someone asks: Do you know X theory?, just say: Yes, it is the theory of X.

Daminark

$K_{k,l}$ has those two sets you want, so all you've got left is to show that if you have a dominating set, it has at least $k$ elements ($k$ is the smaller one)

Faust

how do i do that?

Daminark

Wait a second

Wait I think that's wrong actually

For $K_{k,l}$ there's always a 2-dominating set

Choose one vertex from each side

Faust

hmm

K

Daminark

1:36 AM

Because we're talking about the complete bipartite graph, you choose $p_1$ from one side and $p_2$ from the other side

Faust

$K_{2,l}$

Daminark

So given a vertex, it has to be connected to one of them

Well now you've lost information on $k$

Faust

hmm ok

Daminark

I think what you need to do is not be complete, just be connected

Faust

like a tree?

Daminark

1:37 AM

Maybe that'd work

But the point is to create a bipartite graph with a side of $k$ vertices and a side of $l$ vertices

Then put just enough edges such that each side is a dominating set

But such that you can't just choose a tiny subset from each side and get everything

Hmm

Oh wait not connected actually

Here's an idea

I'm not totally sure if this'll work

Faust

it says connected

Daminark

Oh frick okay that messes up my idea actually

That's merpy

Faust

lol

Daminark

What I had in mind was to choose $k-1$ vertices and connect them in a 1-1 fashion to $k-1$ (of the $l$) vertices on the other side, imagine the ladder but without the side support

Faust

hmm

Daminark

1:41 AM

Then connect the last one to all of the remaining $l-k+1$ vertices

What about just a path?

Oh that doesn't work for any $k$ and $l$

Faust

yeah i was think about intersecting two paths one of length k and one length l

but it didnt quite work

Daminark

Okay I am gonna take the intersection of our ideas

Okay so, to be able to picture this, draw $k$ vertices on one side (vertically) and $l$ on the other

Then look at the bottom $k-1$ vertices on each side

Faust

ok

Daminark

Okay actually let's label them to make life better

Say

Call the $k$ vertices (bottom to top) $v_{1,1},v_{1,2},\ldots,v_{1,k}$

Faust

k

Daminark

1:47 AM

And call the $l$ vertices $v_{2,1},v_{2,2},\ldots,v_{2,l}$

Now we're in good shape

So, draw the path that goes $v_{1,1}$ to $v_{2,1}$ to $v_{1,2}$ to $v_{2,2}$ and so forth

This path will terminate at $v_{2,k}$

Faust

were these vertices connected in the first place?

Daminark

Nope, we're building this graph from scratch

Faust

ok thought so

Daminark

But yeah, then connect all the remaining vertices on the $l$ side (meaning $v_{2,k+1}, \ldots, v_{2,l}$) to $v_{1,k}$

I'll send a picture of the graph I have in mind for $k=4$ and $l = 8$ so you get what I'm doing

Faust

ok

i can visulaize it pretty well

im just not great with definitions specially when they aint in my textbook

Daminark

1:52 AM

Oh okay, that makes sense

But yeah so, I'll let you double check this but I'm pretty sure this graph does it

It's connected

Faust

got it?

Daminark

Yup

Faust

i have to grab the gf from the hospital

Daminark

Oh, I hope she's okay

Faust

(she a RN or w.e and is off in 10 minutes)

ah she fine

she works there

anyway ill be back in 30 or so prolly

Daminark

1:54 AM

Oh okay, phew, I thought she was there because she got hurt or something

user2860452

what's the coolest mathematic topics to learn right now?

Daminark

Aight, I'll email you. See you around!

Faust

dif geo is cool

user2860452

and what's the most influential research in mathematics nowadays?

Daminark

It's hard to order things linearly

PDE is the largest area of research, I think

In part because that's more easily applicable to the sciences, so gets more funding and whatnot

More generally, analysis

Number theory is also quite big, and is responsible for why a lot of algebra exists

As for the coolest, it depends on what you like. I'm into stuff like algebra (esp number theory), topology, and discrete math, and I'm not into geometry much at all as of now

On the other hand, Ted loves geometry. So try out a bunch of things and see what resonates with you the most @user2860452

user2860452

1:58 AM

The problem is I like all of them

.-.

but I don't have time to learn all of them

Daminark

What level are you at right now? High school, undergrad, etc?

user2860452

freshman

undergraduate

Daminark

Ah, so you won't likely have time to learn everything but you can get through a reasonable amount as an undergrad, to at least get a general feel

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$Mathematics$ Mathematics