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23:02
Hey Zach! Long time no see!
Heya @Meow
so tired
whats up
Also hey @Fargle, @Semi, @Ted, @arctic :P
23:03
Hi @Dami, how goes it you nerd?
Oh, hey, Zach. Nate was worried about you.
Hey @Akiva!
Rehi Demonark, @Fargle, tern, DogAteMy.
did he think you ate me?
Not much, @Meow, just listening to music and taking notes from Artin. You?
23:03
It goes well, finished classes for the quarter
Heya @Ted.
playing sm64
LOL, I don't know about that, Zach. But I'll be missing for a month, so good to say hi/bye to you!
All that's left is exams next week... :(
Hibye. Europe trip?
23:04
Has your doctor checked to make sure you don't have mono or something, Zach?
Yup.
Not yet, i haven't seen a doctor about it
I'm sure you'll have a lot of fun on your trip! :)
Damn, Demonark. That means you've learned all you can learn for this year.
Parents say it's my diet
Oh goodness. My fingers are crossed for you that it isn't mono.
23:04
Your diet does suck, from what I know, Zach.
Wait what's wrong Zach?
But it's worth having your bloodwork checked.
I had mono my senior year of high school. Was out of school from November until after Christmas. Wouldn't wish that on almost anyone.
(here's lookin' at you, 45)
@Ted Ah, there's still the bootcamp, and the void between the school year and bootcamp is a nice time to do... something
Maybe that would explain his having no stamina, @Fargle.
23:05
@Fargle almost
Yup, Demonark, learn forms and integrals and work lots of my problems.
@Daminark I reserve my derision for a select few people, usually those unduly in a position of power...
Oh that's what you meant by 45
I was not sure for a sec
why are you shit-talking the number 45. he's not even prime. if anyone deserves it, its 37
or perhaps 42, he gets so much attention
37 isn't an even prime either
23:07
i mean, "meaning of life"?
contemplates truly ignoring Demonark
Actually I've gotten "elected" as the chair of the search committee for even primes in math club :P
I believe 45 may be exceeding 37 by a long shot, Zach.
quickly counts backwards in presidents
I don't know what president number 37 is
23:10
Nixon.
I just know that the number 37 is a total loser
57 is my favorite number
While we haven't found any even primes
I like 5.
It's a prime divisible by 3
Which gives me hope
You like ketchup that much, Demonark? I thought you knew something about good food.
23:11
4 is my favorite number. I have like a whole list of reasons.
ketchup is good
Oh I dislike ketchup
Oh wait
Lel
@Ted I forgot one of the formulae for surface area on a math test so I derived it using calculus
Hopefully I did it right
Those things are tricky.
I did something like that for a question that really shouldn't have required it
Like, on a placement test there was this question intended to be precalc, and it was something basic like finding the highest point of a circle or whatever
23:13
I remember once I had to use the Maclaurin series for sin because I didn't have a calculator for a calculus test.
But I didn't know how the equation of a circle looked
So I used calculus to find the highest point
(At least I think it was something like that)
@Fargle o lawd
Heh, @Fargle
Yeah, we needed an answer to two decimal places.
That's a bit dumb.
one of the kids in my math class asked "How do you do trig functions without a calculator"
23:15
I don't understand what's the point of that
I had done that independent reading but still didn't understand Taylor's theorem, so I just went out to the 7th degree term.
Here's a fun question: How does your calculator compute trig functions?
It does weird stuff
Agreed, except it was supposed to be practice for the AP test, which has a calculator only portion.
...I was just an irresponsible student who forgot my calculator.
23:16
calculator only?
nothing else?
My immediate guess would be via Taylor series but context in which you asked it makes me wonder
I mean then it doesn't really make sense that the AP test has a calculator only portion :P
CORDIC (for COordinate Rotation DIgital Computer), also known as Volder's algorithm, is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions, typically converging with one digit (or bit) per iteration. It is therefore also a prominent example of digit-by-digit algorithms. CORDIC and closely related methods known as pseudo-multiplication and pseudo-division or factor combining are commonly used when no hardware multiplier is available (e.g. in simple microcontrollers and FPGAs), as the only operations it requires are addition, subtraction, bitshift and table lookup...
Like, IB is a bit forgivable because they did some statsy stuff and you were meant to use distribution tools on the calculator which cut out quite a lot of work (though they still had dumb problems of, oh well you could just leave this in exact form but nah decimals)
Huh, this is interesting
Cordic is amazing. Along with most mathematicians, I always thought it was Taylor until I heard a lecture on Cordic.
Did I ever tell you guys my dumb linear independence question
Well it's like combinatorics kinda
23:21
Do tell
@Daminark Agreed
(And @Ted yeah, this is pretty dope)
But like, given any $n$ how many sets of 4 natural numbers less than or equal to $n$ exist, such that there exists no way to group the numbers into vectors that are linearly dependent
It's senseless, and it leans too heavily on computation as opposed to concepts, which is what passes for "useful applications" in a high school level course.
For instance
{1,2,3,4} is valid for $n\geq 4$
23:22
What I find funny about CORDIC is that it was invented in 1956.
But, {1,2,2,4} isnt because you can group it as [1 2] and [2 4] which are linearly dependent
Arguably that's not a set of 4 natural numbers :P
But it gives references to prior work in the Wikipedia dating back to Henry Briggs in 1624 and Robert Flower in 1771.
Well, not arguably, it isn't, but like, multisets so why not
I have a challenge for you all (perhaps some will burst into laughing). Calculate by integration techniques, without using properties of the binomial coefficient - without using the binomial coefficient at all -, the following simple integral $$\int_0^1 (1+x)^n \log(x) \textrm{d}x$$
23:24
@Semi Huh
@MeowMix I assume you mean pairing them into vectors in $\Bbb R^2$, because you could be a pedantic jerk (as I am wont to be) and just consider the vectors [1], [2], [3], [4].
Hi again chat
That's what I meant
Hm. Integration by parts would give $$\left[\frac{1}{n+1}(1+x)^{n+1}\log(x)\right]_0^1-\frac{1}{n+1}\int_0^1 (1+x)^{n+1}\frac{dx}{x}$$
Hi @EricSilva.
23:26
0 makes log a problem
@Semiclassical Maybe some blow to infinity there on those limits?
Yeah, I just noticed. Scratch that.
I mean yeah, so I'm wondering if maybe integration by parts is probably not a way to go about it because of that
@Ted just turned in my geometry final
Congrats.
I have a suspicion you did better than some of the grad students.
23:27
Only thing left to do is galois theory and move out of the dorm
Yeah at least one grad student failed apparently
Well, Feynman's trick is worth remembering i.e. partial derivatives of something like WITHDRAWN.
Bah, that version doesn't work.
@Semiclassical One only needs very simple tools. High school tools.
Tbh I think his geometry class was easier than my galois theory class
reads @Semi's message why would you take partial derivatives of the word "WITHDRAWN"?
Show that the random variable $U=X/(X+Y)$ has a uniform distribution on [0,1] when X and Y are independent random variables with the same exponential distribution.
Could someone help me with that?
23:29
I don't think anyone ever said that about my grad geo class, Eric :)
Also dayum @EricSilva
I think it's probably that my galois theory class is really hard
It's good for you, Eric.
And I just put in a lot of work out of interest too I guess
You're also less naturally algebraic, which skews things.
23:31
This is true
teach me geometry so i can teach you foliations
meh i forgot my vow of silence
@EricSilva you should consider replacing the geometry in the bootcamp with Galois theory!

*waits for impending storm*
nods condescendingly at a @Balarka
(Jk I actually want to do geometry tho)
no, Demonark, you all have an algebra course to take next year.
23:32
We basically did galois theory in disguise last year..
Whereas you won't learn the geometry stuff anywhere else.
what kind of geometry?
Differential geometry
Oh with the thing about Riemann surfaces and quintics? @EricSilva
Actually, I gave it some thought. My favorite number is the principal value of $\sqrt[12]{256}$.
arent there 12 of those
23:35
$\log(x)=\log(1-(1-x))=-(1-x)-\frac{1}{2}(1-x)^2-\cdots$ for $|1-x|<1$, so one could reduce this down to evaluating integrals of the form $\int_0^1 (1+x)^n(1-x)^m\,dx$. @Waiting
That has, however, a canonical meaning, Zach, as you know.
I thought I sprayed pedant repellant on the message before I sent it, @Meow. :D
Apparently not enough
I need that stuff. Where do I get it from?
@Daminark yeah
23:36
Hey, @Fargle. Have you dropped Ken an email?
Though if I had any sense I'd have done $u=1-x$ first.
@Semiclassical The way to go must be very simple.
@Balarka The engineering department?
The reason it's my favorite is that it's the canonical ratio of frequencies which make up a minor sixth interval in twelve-tone equal temperament, which is my favorite interval.
(Good work though Zach :P)
23:37
@TedShifrin I don't think I have. Should I have? Oops
I just suggested you should.
Neves will eventually start teaching undergrad curves and surfaces here @Ted, not till me and Daminark are 4th years though, but still glad we're finally getting one
@EricSilva Nice. Any reason why they swapped with dynamics?
He just finished his first year at Simon's Rock.
23:38
@Secret I posted a cute challange (for fun, of course) in chat
$$\int_0^1 (1+x)^n \log(x) \textrm{d}x$$
im gonna program something to solve this problem for me
I may. I just feel awkward communicating with anyone who taught at a school I failed out of.
Good, @EricSilva, although it may be off the deep end for my taste.
then look it up on oeis to see if theres any pattern
Idk its probably cause the book was kind of annoying and super imprecise all the time @Daminark
23:39
Don't worry about that, @Fargle. It was not an intrinsic thing with the school.
Ah, yeah that'd do it
@TedShifrin lol, you know what I mean.
Well, @EricSilva, some people find anything I write annoying.
@Semiclassical wow h8r
I think he would like to hear what math you're up to, @Fargle. I'm being sincere. Teachers like to hear from past students.
23:40
Your notes got generally good feedback from the boot camp though!
@MeowMix speak of the devil and he does appear!
Nate, I warned him you were worried. You should see his response.
@TedShifrin I know you are. I'll send him one. Besides, I didn't fail his class.
>_>
Lmfao I saw!
He didn't care at all!
@Daminark I might sit in when you guys lecture on Dynamics, I know zilch about that stutf
23:41
What a strange coincidence though
I almost went into dynamical systems. That was by far my favorite grad course my first year, @EricSilva (Charles Pugh).
I started checking obituaries with the name "zach"
It seems very cool and like it has loads of connections with lots of other things which is always a plus
Meh I am going to skip this chapter and move on with foliations w/o holonomy. Candel and Conlon, sorry to let you down, but I can't read this anymore.
Lots of analysis and lots of topology, Eric.
23:43
I want to take a class on it at some point, but I think we only ever do a second year grad course on Dynamics here
Those are like my second and third favorite things
Yeah, I'm pretty happy with the lineup of topics. None of these are likely things I'm going to take, at least at that level (Marianna's complex will assume undergrad level background)
And even some Riemannian geometry. Like the geodesic flow on a $K<0$ manifold is Anosov.
I bet I missed him and he won't be back for two weeks again...
Oh hey @Daminark
Missed whom, Nate? Zach is still here.
@Daminark get ready for Titchmarsh
23:45
waves Hai
It's old school
Sometimes old school is refreshing.
What exactly does that entail?
In this context
It reads like Hardy's books on math
I know at least one person had high praise for it so that's a plus?
23:47
Speaking of school Ted, not sure if I've already asked you this, do you miss teaching?
I haven't read anything by Hardy
If youve ever read any of those
@EricSilva If you're speaking of G.H Hardy, I will hear none of it!
Is the one person Brian
I was speaking of that Hardy :P
Definitely, Nate. That's partly why I waste time here. ... But I may actually get to teach really smart high school kids in September.
23:47
I have ready his book "A Mathematician's Apology" and it's such a bleak view of mathematics.
Surprisingly enough, no
I think I passed my job interview.
Nice @Ted! :D
@TedShifrin Wow that's awesome, Ted!
I mentioned it here. AoPS is opening a brick-and-mortar school about a half hour from me.
23:48
Oh weird, he's the only person I've heard praise that book. @Daminark, i didn't like it because I found it hard to read
Art Of Problem Solving?
@EricSilva Sorry I don't understand.
Yup. Kids all over take their courses electronically, but they have a few actual schools.
Oh wow cool.
@Dodsy its probably bleak because he was depressed when he wrote it iirc
I picked up a few AoPS books in high school and worked through them
drugged writing >>> depressed writing
23:50
The person who mentioned it is a 3rd year who did not do the bootcamp I think
I thought they were really hard
You mentioned that, I think, Eric. I sort of hate to have to follow someone else's book and lesson plans to the letter, but I can survive.
Eh, it's very much like "only young people can do math, math sucks anyhow, it's not really worth much, but I like it"
You know Danny?
that's the vibe I get.
23:50
Stoll? @Daminark
Yeah
I'm aware of him
@Dodsy I kind of agree with the last 3 sentences of your summary
He's the one who said Titchmarsh was good
@BalarkaSen Then you'd like G.H Hardy!
And you're back!
23:52
Lel @Balarka
His course of pure mathematics is kind of fun if you have a lot of time
@TedShifrin You learn number theory before calc at AOPS
Woah 325 bucks.
American too.
Not necessarily.
I need some of those AoPS books. Where do I get them?
That's like 600 bucks in monopoly money.
23:54
?
I was given a choice of precalculus, calculus, and tricky problem solving.
The price of monopoly boards does not suggest the conversion you state @Dodsy
@Ted which did you go for?
@TedShifrin if I wanted to enroll in every course offering it would cost me 6'700 dollars!111111111!!!
We'll see what they offer, Demonark. I preferred calculus. My talents aren't so much contest math, but I could learn something doing that with smart kids.
I'm sure you'll do great no matter what
I don't see how you couldn't get hired
being so successful and brave.
bravery is important. You're like beowolf or that other scottish guy.
23:56
@Dodsy One other option is that you can work with me on Laci problems and become a combinatoricist
@Semiclassical @Secret This simple integral that apparently says nothing (I mean it seems something unimportant, piece of cake for everybody) eventually is proving to be a cute little challenge (especially with the given requirements).
Well, just having taught college for 36 years doesn't necessarily mean one's great.
@Daminark Whose laci ?
Who's
@MeowMix young fellow, you shouldn't miss it $$\int_0^1 (1+x)^n \log(x) \textrm{d}x$$
23:58
@TedShifrin I would consider doing those courses to get better at mathematics.
Jack finds the product of three different prime numbers. Is it possible for the sum of the digits of Jack’s
product to be 18? Why or why not?

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