Topics to think about.

Conversation started Jan 16, 2017 at 19:56.

Simple Art

Jan 16, 2017 19:56

Say, does anyone have introductory problems that are easy enough to be interesting to a broad range of people?

but with a lesson to be learned in the problem?

Astyx

Introductory to what ?

SteamyRoot

That sounds very, very broad

Simple Art

Idk

Introductory to anything that doesn't require a lot of pre-reqs

For example, I asked this question:

Krijn

@SimpleArt $\sum_{i = 0}^n F_i^2 = F_nF_{n+1}$ where $F_i$ is the $i$-th Fibonacci number

Simple Art

Approximate this sum with +/-0.1 error for all n

$$\sum_{k=1}^n\frac1{\sqrt k}$$

@Krijn Thanks, I might do that :3

Krijn

Jan 16, 2017 20:01

Or $\sum_{i = 1}^n 2i = n(n+1)$ has a nice visual proof

Simple Art

@Krijn I think more advanced

SteamyRoot

Building on that, prove that $\left( \sum_{i=1}^n i \right)^2 = \sum_{i=1}^n i^3$ ?

Krijn

sarcopsy

You can motivate some simple group theory stuff with counting problems I guess?

Krijn

Draw $n \times (n+1)$ dots

Then look at the triangle with 1, 2, 3, $\ldots$, n dots

Astyx

Jan 16, 2017 20:03

Numbering the maximal amount of regions you can form with $n$ straight lines ? How many are bounded ? How many triangles do they form ?

Krijn

The other triangle is also the same triangle and they hold $\sum_i i$ dots both, so $\sum_i 2i$ dots in total

Simple Art

I ask this because I've recently made a small chat room full of random people, and I've decided I'm going to have some questions and try to get them to touch on a lot of random topics.

@Krijn Gauss :-)

Krijn

@SimpleArt Close, but simpler than his method

Simple Art

But I seriously think I can introduce harder concepts than that @Krijn like the gamma function.

Mhm... maybe I should ask them how to define fractional values of the factorial :D

Astyx

It requires quite a lot of pre-reqs to some extent

Simple Art

Jan 16, 2017 20:05

@sarcopsy I'll have to learn that XD

@Astyx The gamma function?

Astyx

Yes

These are not so random people I figure

Simple Art

I think they all know calculus/integrals, and we're not going to do anything crazy

@Astyx Oh no, they are random :D

Astyx

The amount of people who know calculus/integrals is not that big

sarcopsy

Isn't it a compulsory thing?

Astyx

That does not mean much

Simple Art

Jan 16, 2017 20:08

What's compulsory? Learning? Probably

@TheGreatDuck Hi totally random person :-)

Ah... anyways...

TheGreatDuck

well yeah I am very random right now. Incredibly eratic.

Simple Art

lol

TheGreatDuck

dont get in my way right now. I'm in the process of purging my inappropriate questions.

sarcopsy

@Astyx and @SimpleArt I guess.. haha

Mike Miller

@PVAL-inactive A bit aggressive.

Cameron is very nice.

Simple Art

Jan 16, 2017 20:09

The camera?

PVAL-inactive

Whats aggressive?

Simple Art

Cameras

Krijn

So, at university I work in a room with 4 other Masters students and sometimes I need to look up a silly definition, like "automorphism". Out of shame I will google it on my phone instead of my laptop because the others will think I'm hella dumb. Today we found out that all five of us are doing this.

PVAL-inactive

@Mike What's aggressive?

Simple Art

@Krijn XD

SteamyRoot

Jan 16, 2017 20:10

@Krijn everyone does it

Astyx

I've no idea what an automorphism is

Balarka Sen

@Krijn I do it so very often

Simple Art

@PVAL-inactive Me saying cameras

Astyx

I always look it up too

Simple Art

@Astyx :P Have you taken real analysis?

Astyx

Jan 16, 2017 20:11

Sure

Simple Art

lol

I haven't

PVAL-inactive

@Mike Cameron is unbelievably nice.

TheGreatDuck

@SimpleArt gonna lose about 100 rep but I think if the questions have sat dead for this long unanswered they should be deleted. (referring to questions from last year).

Astyx

@Mike I've read you were going to Cambridge ?

SteamyRoot

@Astyx Do you know about groups and group isomorphisms?

TheGreatDuck

Jan 16, 2017 20:12

i figure more than 50 questions is a bit... excessive

PVAL-inactive

He's usually in his office all day available all the time and always willing to discuss things.

Astyx

I sure do @SteamyRoot

Simple Art

@TheGreatDuck Nah, don't delete

You are probably referring to products and integrals?

TheGreatDuck

just random silly questions

Simple Art

No, don't

SteamyRoot

Jan 16, 2017 20:13

Oh, okay.

TheGreatDuck

like "why does the multiplication operator change shape"

Simple Art

that like ruins the system

Just leave it mate...

TheGreatDuck

if they're unanswered it doesn't matter...?

Simple Art

@TheGreatDuck :|

I come across plenty of unanswered questions

and they can still be of value to me

And I broke 800 rep today finally

TheGreatDuck

what? I cannot clean up old questions that I find no longer useful to me personally and that in a lot of cases attracted downvotes?

Simple Art

Jan 16, 2017 20:14

Hm, what do you guys think?

Balarka Sen

Tim Burton on Kevin Smith (after Smith jokingly accused Burton of stealing the ending of Planet of the Apes from a Smith comic book): “Anyone who knows me knows I would never read a comic book. And I would especially never read anything created by Kevin Smith.”
Kevin Smith on Tim Burton (in response to “I would never read a comic book”): “Which, to me, explains fucking Batman.”

Astyx

Lol

Mike Miller

@PVAL The proof by Lagrangian.

@Astyx I'm here for this week.

Simple Art

You know what

TheGreatDuck

manbatbatmanbatmanmanbat

Astyx

Jan 16, 2017 20:17

Oh is it only one week ?