Mathematics - 2017-12-22 (page 1 of 7)

Akiva Weinberger

00:00

'cause logarithmic derivative

Ted Shifrin

You can't be sure? OK, sure.

So double verification.

Secret

$d$ is the differential operator (I only saw a single d there)?

Akiva Weinberger

So you only need to prove it for something with one root and no poles

'cause you can multiply and divide stuff together

And, uh, I guess you can assume that root is at zero?

And you can always write it as $z^k$ times some analytic thing

and we can ignore that analytic thing

so we just need to prove it for $z$, really

And then that's just knowing how $\int1/z\ dz$ works

The "enter" key and the period key on the keyboard do the same thing

Secret

.

(is befuzzled)

Clarinetist

@TedShifrin I think this is where I'm stuck: so we know that $q \perp 1$. Cool. But what does this do with $\log p$? AFAIK there's no relationship between $q$ and $p$, other than that you're moving from the maximum point $p$ in the direction of $q$

Akiva Weinberger

00:03

They serve the same function

They end sentences

Secret

I see

Akiva Weinberger

The "enter" key is more versatile, though

as it can end clauses as well

Ted Shifrin

It means that $\log p \perp q$ for all $q\perp 1$. What does that tell you? @Clarinet

Secret

mobiles don't have that, though ,which is why when I am on mobile, my messages will become very short

because you cannot linebreak on mobile to get past that word limit

Akiva Weinberger

I'm not linebreaking, I'm legit starting a new message each time

You can copy/paste from Notes if you really need to, though

Secret

00:05

yup I know, I am just saying whatever that first comes to mind when I read the messages

Akiva Weinberger

Why's it called the argument principle, I wonder?

Ted Shifrin

Same reason angle is called argument when you write $\text{Arg}(z)$.

Akiva Weinberger

> The argument principle can be used to efficiently locate zeros or poles of meromorphic functions on a computer.

Ooh, cool

Ted Shifrin

DogAteMy: Did you ever email my former student at Yale?

Clarinetist

@TedShifrin If $\log p \perp q$ and $q \perp 1$... then I see that the integral is equal to $0$ (already given)...

Akiva Weinberger

00:07

One moment

Ted Shifrin

Quantifiers are important, Clarinet. for all $q$ with $q\perp 1$ ...

Think about subspaces in $\Bbb R^n$.

If $x\perp w$ for all $w$ with $w\perp v$, what do you conclude?

Clarinetist

@TedShifrin Forgive me if I'm wrong on this (it's been too long), but intuition is suggesting that $x$ is a linear combination of $v$, perhaps with a constant vector added to it

Ted Shifrin

Say what?

Clarinetist

@TedShifrin Okay, I'm digging out the linear algebra text

Ted Shifrin

Draw a picture. You have a one-dimensional subspace (spanned by $v$). For all $w$ orthogonal to that, $x$ is orthogonal to $w$. How can that happen?

(What's going on is $V^{\perp\perp}$ for subspaces $V$, in more generality.)

Clarinetist

00:11

Right, and the orthogonal complement of an orthogonal complement is equal to the original subspace

Akiva Weinberger

@TedShifrin Yes

Ted Shifrin

Well, it's true in $\Bbb R^n$ and it's true for closed subspaces in Hilbert space. So what do you conclude here, @Clarinet?

DogAteMy: Did he answer?

Akiva Weinberger

Not yet, I emailed him pretty recently so he probably hasn't seen it yet

Ted Shifrin

Ohhhh ....

If I counted correctly, he should have one more year at Yale, DogAteMy.

Clarinetist

@TedShifrin Well... $1$ and $\log p$ must be in the same subspace...

Ted Shifrin

00:14

Right, @Clarinet. In other words, $\log p$ must be ... ?

Clarinetist

@TedShifrin A CONSTANT! o_o

Ted Shifrin

Finally!

Clarinetist

Wow

Akiva Weinberger

Oh. You prove Rouche with homotopy?

I probably knew that at one point and forgot it

Clarinetist

@TedShifrin Thank you for your patience and help with that. If I ever wanted to actually learn this stuff in the future... do you have a suggested text?

Akiva Weinberger

00:16

(That's the one where $|g|<|f|$, and $f$ and $f+g$ go around the origin the same number of times)

Ted Shifrin

One can, DogAteMy. One need not.

@Clarinet: I have a bit on calculus of variations in one section of my diff geo notes, but there are classic texts. Fomin & somebody ...

Bennett

You know how $(-1)^{n/2}$ generates alternating signs for even $n$. Is there a way to do the same for odd values of $n$?

Akiva Weinberger

'cause $f+tg$ is a homotopy between them and the winding number is homotopy invarient

Ted Shifrin

I guess Olver wrote a book, too, Clarinet.

DogAteMy: You'd better be careful where the hypothesis comes in.

Clarinetist

@TedShifrin K, so the same as the MSE recommendation. I'll have to buy it sometime

Thanks again

Akiva Weinberger

00:17

The hypothesis is needed to show that $f+tg\ne0$ for $0\le t\le 1$, right?

Ted Shifrin

Could be :P

Adeek

@TedShifrin I was wondering do you know why adjoint operator is useful other than for proving things ?

Clarinetist

@TedShifrin This also explains why $p$ can't have infinite support... no constant over will integrate to $1$ over $\mathbb{R}$!

Adeek

I heard they represents useful things in physics

Clarinetist

It makes so much sense now!

Adeek

00:18

as like observables and stuff

Ted Shifrin

@Clarinet: So wait. Doesn't that mean there is no maximum?

Clarinetist

I had been wondering for the longest time why everyone said "if you restrict to the set of all probability density functions in $[a, b]$, you get..."

Ted Shifrin

You don't mean infinite support. You mean that our functions are defined only on a finite interval.

Clarinetist

(well, "everyone," meaning every source I found online)

@TedShifrin Heh, yes

What I mean to say is that the random variable cannot have support over $\mathbb{R}$

Ted Shifrin

Karim: That's self-adjoint, I believe.

Meow Mix

00:21

hi

Adeek

oh yeah

Ted Shifrin

@Clarinet: I cheated, actually. I used compact domain to get $\perp 1$ earlier.

heya @Meow.

Clarinetist

@TedShifrin Well, thank you again. Now after two weeks... I finally managed to finish Ch. 1 of this machine learning text. It's been a humbling experience. Grad-level stats, some hard probability questions, time series, Fourier analysis, and ending with calculus of variations in this one chapter of exercises

Ted Shifrin

Well, learning can be exciting.

Adeek

Learning is awesome

I wish life is just books and one can learn everything

Eric Silva

00:23

learning sucks

Adeek

nooo

Clarinetist

It's really exciting because I've never used Fourier analysis or time series or calculus of variations before doing this set of exercises

Ted Shifrin

you don't mean that, Eric.

Eric Silva

lol

Clarinetist

so it's a good excuse to learn them

Eric Silva

00:24

calc of variations is dope

skullpatrol

Understanding is the reward of learning.

Ted Shifrin

You should have been here to help Clarinet, Eric. He was stuck with me.

Eric Silva

ah

im not great at CoV, i know the bits that have come up in my geo and PDE journeys

Secret

1

Q: 100% of the real numbers between 0 and 1 are irrational

I've once read a proof about this and I'm trying to remember how it went. We want to show that if we randomly select a number x from the set [0,1], then P[ x is irrational ] = 1

Ted Shifrin

Someone posted a totally unintuitive yucky plane diff geo question on main, Eric. There must be something elegant/interesting about it. Look at it.

Clarinetist

00:26

I really wish I had done grad school in math. Stats is interesting and is very practical... but it's just not the same

Eric Silva

ive been meaning to spend some dedicated time learning some, but i guess i probably know a bit more than normal :)

Ted Shifrin

Eric: You should look at Griffiths's little book on moving frames and CoV. I already mentioned it to you.

Eric Silva

this is a weird question

Adeek

Eric are you doing geometry?

Eric Silva

oohh i should omg

Secret

00:27

hmm... I have no idea how one can query about how evenly the irrationals are distributed in some interval [a,b] since uniform distributions are not defined in the reals

Eric Silva

geometry is my muse my dude

Ted Shifrin

Yeah, it looks totally yucky when I write it out, @EricSilva, but maybe there's something interesting going on if you approach it right.

Rumplestillskin

Can anyone provide me with a sanity check: If I have a homogeneous system of differential equations with non constant coefficients. What does it mean if the determinant is zero?

Adeek

good that more people are doing geometry than bunch of algebraists haha

Ted Shifrin

What determinant, @Rumplestillskin?

Eric Silva

00:28

hmm maybe, ill draw some pictures and see if i get anywhere

Daminark

Gotta bring my algebraist friends to chat to compete @Adeek

Rumplestillskin

@TedShifrin how do you mean?

Secret

there's also the extra complication that every interval contains uncountably many irrationals, thus even if some of them have less irrationals, it is still uncountably many, thus basically it is quite intuitively even

Daminark

:P

Adeek

hehe @Daminark

@Daminark watch ted's lectures

Ted Shifrin

00:29

I'm asking what your question means, @Rumplestillskin.

Eric Silva

algebra is good too

it's just not as good

Adeek

yeah exactly

Secret

but then, the irrationals in the cantor set are not evenly distributed because clearly the middle third of the interval [0,1] has no numbers in it

Rumplestillskin

Ah excuse me. I have a system A x = 0. where x is a vector of first order derivatives. A is a matrix. The determinant of A is zero and I need a sanity check to verify whether this mean we do/don't have a solution. @TedShifrin

Ted Shifrin

Don't you mean $dx/dt = Ax$, @Rumplestillskin?

Secret

00:32

@LeakyNun Are the irrationals "evenly distributed" in the reals, in that pick any interval [a,b] where a=/=b I am guaranteed to find uncountably many of them?

Rumplestillskin

Nope the system is A x = 0 where x = [df/dx dg/dx dh/dx].... This is okay right?@TedShifrin

Ted Shifrin

@EricSilva: I think that guy got the question from a Brazilian text.

Daminark

@Eric and @Adeek kek

Ted Shifrin

Terrible to use x in both places, @Rumplestillskin. Can you please start at the beginning of the problem, not the end of it?

Rumplestillskin

:) @TedShifrin this is of course not the real problem this is just it's form. The real problem is quite large. But it's a homogeneous system of linear differential equations with three unknowns a' b' c'. This is my x vector. where prime indicates derivative with respect to xi. the coefficients of a' b' c' make up the matrix A. The determinant of A is zero.

Eric Silva

00:36

his name sounds brazilian as hell

Ted Shifrin

Yeah, and the author of the text is Keti Tenenblat, who's been in Brazil forever. I know her from my Berkeley days. Chern mentored her for a few years.

Clarinetist

Well, @BalarkaSen isn't here to hear my hypothesis testing rant :P

Eric Silva

hmm i cant seem to find the text he mentions

Adeek

oh she is turkish @TedShifrin

Ted Shifrin

And you're asking about $Ax=0$, @Rumplestillskin? In linear algebra, this will have lots of solutions when $\det A = 0$. Write down some simple examples. You'll get the corresponding subspace of solutions with $a', b', c'$ ...

Adeek

00:38

I am part turkish and greek

Clarinetist

Generalized inverses! Wooooo

Ted Shifrin

@EricSilva: The name of the text appears on her Wiki page. I know some books that are more advanced.

Small world, Karim :P

Adeek

yeah haha

Eric Silva

oh i see i was looking for it under the english title but maybe there isnt a translation

Ted Shifrin

I don't think there is.

Rumplestillskin

00:40

Yes that's what I thought. We have an infinite solution space for det(A) = 0. @TedShifrin

Eric Silva

no problemo there

Ted Shifrin

Seems so to me, @Rumplestillskin. Do a simple example.

And she does moving frames, ERic ... :P

Eric Silva

good stuff

Ted Shifrin

She and Chuu-Lian Terng did some stuff on PDE and moving frames years ago.

Eric Silva

ima take a look at this text

Ted Shifrin

00:42

Can you find it in Portuguese?

Eric Silva

yup

hmm the problem is just the last problem in the section on Frenet Formulae

Ted Shifrin

it doesn't seem like it's amenable to vector approaches

Eric Silva

this problems is mega unintuitive to me

Ted Shifrin

me too

the $1/\kappa$ gives a horrendous differential equation ...

Eric Silva

yup

Akiva Weinberger

00:50

@Secret Yes

Every interval contains uncountable many irrationals

Notice that every interval $(p,q)$ with $p,q\in\Bbb Q$ is isomorphic to $(0,1)$, in the sense of the existence of a bijection which sends rationals to rationals and irrationals to irrationals

and notice that every interval $[a,b]$, $a<b$ contains an interval $(p,q)$ as above

Adeek

@TedShifrin getting a lot of emails from students about TA duties

few students didn't put their name on the last assignment and I am trying to figure out who

students are careless sometimes

Secret

one thing I don't quite know how to formulate (or whether it is sensible at all) is how to find whether a given set of number "bunch" at some location of the number line because of the difficulty introduced by infinite cardinals. for example the harmonic series in [0,1] is countable, but it has a limit point at 0. The cantor set is uncountable, but there are intervals where there are no numbers thus the irrationals are effectively concentrated at the pseudoboundary and the interior.
I am not sure if there's a mathematical quantity that captures this

Ted Shifrin

sometimes?

Adeek

altough I am not organized at all but I was never careless though

atleast with my assignments

Eric Silva

A student in a class I TAed once emailed me his pset despite living two doors down from me

Secret

00:56

@AkivaWeinberger It is known every real is an accumulation point, but does that guarentee the "bunching" is uniform in some way?

Eric Silva

@Ted I think I've lost interest in this curve question

Ted Shifrin

I like to write comments (in red) when I grade, so .pdf homework sucks. I have to print it out and it never prints well unless it was TeXed to start with.

me too, @EricSilva.

I was just curious if you saw something I didn't.

Eric Silva

nah

Akiva Weinberger

@Secret The fact that every $(p,q)$ is isomorphic to every other should imply that it's uniform

Eric Silva

tried to take a derivative and got bored

Ted Shifrin

00:57

I like my exercises better :P

Akiva Weinberger

Just a linear transformation between them

Ted Shifrin

LOL ... but you bore easily.

Eric Silva

true lol

Secret

I see, never thought I can use isomorphisms to check that

Eric Silva

I like to write comments in TeX so i like when students send me TeX files

but not everyone TeXs

Ted Shifrin

00:58

Mostly not.

Secret

my dreams always lead to these weird questions that otherwise I never thought about

it is good I can actually learn from them

Eric Silva

if i were teaching I would maybe offer a tiny bit of bonus points if people TeXed, just because of how much easier it makes my life

Ted Shifrin

I like(d) to grade papers away from computers, relaxing lying back in a chair ... so ... blah.

Akiva Weinberger

@TedShifrin Curve question?

Eric Silva

that's fair

nitsua60

01:01

@TedShifrin I like to grade while sitting in on colleagues' classes

seems to make it a little more bearable

Ted Shifrin

I'm sure they appreciate that

Adeek

@TedShifrin if I grade near the computer I know I will procastinate

Ted Shifrin

DogAteMy: This nutsy question.

Adeek

I just shut down all electronic devices and grade so I can be effient.

efficient *

Akiva Weinberger

@TedShifrin The distance between Q and T probably ends up being a nice expression (I hope)

Ted Shifrin

01:04

Yeah, that part isn't so bad, DogAteMy.

As I indicated in my various comments.

Clarinetist

Ah, grading. Haven't done that since my undergrad. One of my professors, when he graded his first exam (not for my class), accidentally spilled beer all over the students' exams. I can't remember if they were still readable

Ted Shifrin

LOL ... sure he did.

Eric Silva

i feel like beer is a bad grading drink

Ted Shifrin

I chose martinis.

Secret

Huh. I knew your name looked familiar. I've been using your text, along with do Carmo's "Differential geometry of curves and surfaces" for supplementary reading (although I haven't done as many problems). It is really good indeed! — Matheus Andrade 2 hours ago

Still find it amazing that we have a book author hang out regularly in chat

Eric Silva

01:07

i feel like i would need something really hard to get through the nonsense

Adeek

Hey @TedShifrin just sanity check If we compute $\|T\| = sup \{ |(Tx,y)| : \|x\| = \|y\| = 1\}$ then it is true that $\|T\| = sup \{ |Re(Tx,y)| : \|x\| = \|y\| = 1\}$

yeah it is true

Secret

Eric: How's vodka sounds to you?

Ted Shifrin

I prefer gin to vodka. Speaking of which ... it's time for it.

Clarinetist

I had plenty of wine last week after my experimental design final

heh

So glad that class is done -_-

Some festive holiday music for you all:

Zee Avi-Frosty The Snowman

►

Akiva Weinberger

What's "experimental design"?

Clarinetist

01:13

@Akiva Good question. Do you know what a variance is?

Akiva Weinberger

Wait, is this [experimental design] final or experimental [design final]?

Clarinetist

[experimental design] final

Akiva Weinberger

@Clarinetist No. Something statistics-y?

Like a standard deviation

Clarinetist

@AkivaWeinberger Pretty much. So the square of a standard deviation is variance. The idea behind experimental design is that you want to perform an experiment: i.e., you have some units onto which you want to perform various treatments. How do you design your experiment so as to minimize the variance of your estimates? This is desired because you want your estimates to have as little variability as possible

Rumplestillskin

@TedShifrin Thanks this is exactly what I thought except colleague of mine is quite adament this is not the case! So I was doubting myself!

Daminark

01:17

@Eric Probably depends on what type of nonsense. It's half cringy and half funny

Eric Silva

i wasnt serious

Daminark

Lol but yeah at some point I'm gonna try to learn how to write comments on pdfs

Akiva Weinberger

@Clarinetist Ohh. Designing experiments, not making designs in an experimental fashion

Clarinetist

@AkivaWeinberger By "estimates," I mean quantifying the impact of your treatment

@AkivaWeinberger Yep, that's correct

Akiva Weinberger

I was thinking of, like, the phrase "experimental music"

Clarinetist

01:20

Has anyone listened to that vid I put up??? :o

Akiva Weinberger

I can't right now

Secret

@Clarinetist Very different to the cheerful version we often heard

Clarinetist

@Secret Yes, it is! I think it's a very interesting take

Secret

In other news, it seems pdf with vertical asymptotes are rarely used

despite for some of them, a lebesgue integral exists for such functions

Clarinetist

Yeah, I can't think of one time where I've seen a PDF with a vertical asymptote

Secret

01:31

but again, had it not because of the dream last night, such question will probably never came into mind which showed how I am so used to thinking pdfs must be lack of vertical asymptotes always (well it is the case in physics)

Last night dream claims the irrationals has the following distribution on the real number line:

I am guessing my brain probably spend too much time thinking about complex systems and the notion of criticality since that complex system symposium in 11-13 dec

Akiva and I then worked out a few minutes ago that such claim is false, though

Anyway, I think if there's a place where unbounded pdfs were used, it might look something like a mix of exponential and hyperbolic and starts or asymptote at zero because that is the most physical scenario I can think of

Ted Shifrin

oh no .. it's @orbit

Secret

(The other lines are numbers that are labelled in the dream, but the dream have gave no elaboration of them and the actua labels are so cluttered that one can only remember show much from a dream. (meaning I don't recall their exact positions except they form a cloud clustered near the base of that graph))

Clarinetist

Fascinating

The last vivid dream I had was maybe a week ago. Before that, 4 years

ish

skullpatrol

:O 4 years!

Secret

I can remember nearly all my dreams as I have dreams almost every single night (those night where I don't have dream I will see blackness or I won't aware I have been asleep). Idea dreams like the above (and with such rich amount of not too wrong math content) remains rare, though

Clarinetist

01:39

Yeah, it was weird to have such a vivid dream last week. My music theory professor became an optometrist. Was telling his students to look through a microscope in class to test our eyes

Ted Shifrin

I think I've caused my former students some nightmares.

Clarinetist

I think it was because I woke up in the middle of the night - my wife was up at 2am with the lights on

Ted Shifrin

Oh sure, blame it on her.

Clarinetist

:P

Eric Silva

@TedShifrin lmao

Secret

01:40

Usually, dreams tend to be easy to remember when you are being jotted awake when fast asleep.

Ted Shifrin

thanks, ERic

Secret

For me, the outcome is mixed

Clarinetist

I've had - not really vivid dreams about missing a class that I enrolled in for an entire semester and failing it

It was usually a history or English class

Ted Shifrin

I think most grad students dream about sleeping through their qualifying exams or thesis defense.

Clarinetist

Thankfully I haven't had that one ^

Secret

01:42

I have fail the exam or fail the test dreams on biology, english, chinese and sometimes maths

Ted Shifrin

I must be too well-adjusted.

Secret

they usually are a warning, meaning I have something important I need to do that I keep procrastinating away from

Eric Silva

I feel like I'd be paranoid about that

Ted Shifrin

you, paranoid, Eric? Hard to believe!

Eric Silva

I sometimes fall asleep at inappropriate times

Clarinetist

01:43

My wife is deriving the unit circle in preparation for Calc. I next semester

(i.e., the $\sin$, $\cos$, and $\tan$ values)

Eric Silva

I've missed things because of it before

Clarinetist

Weird to think I did that 9 years ago

Ted Shifrin

I am teaching precalculus this year, Clarinet. I think I have those down.

Is she a teacher or a student?

But we've moved on to complex numbers, then vectors and linear algebra.

Clarinetist

Fun. No, she's a student. Studied music back in her undergrad, going back to school to do CS

Ted Shifrin

Ahhh.

Secret

01:44

As for nightmares, I had 5 nightmares in the past 8 years which felt like they are actively trapping you in them and preventing you from escape even if you have reality warping abilities

Clarinetist

The one thing that I'm glad my Pre-calc teacher did was make us derive the unit circle values using the 30-60-90 and 45-45-90 triangles using only a pencil and paper. Told us that he didn't want us using calculators at all

skullpatrol

@TedShifrin wow! Professor you are moving fast?

Secret

@Clarinetist how does one derive e.g. sin 15 from drawing those triangles, since it is one of the standard questions using common trig values

Ted Shifrin

This is the AoPS syllabus.

Totally agree, Clarinet. And I showed my kidlets how to double the 30-60-90 triangle to figure it out.

Not standard, Secret, not at all. In fact, I've never learned that at all.

But one gets to double/half-angle formulas.

I personally don't believe in half-angle formulas.

Clarinetist

Yeah, I would say use the half-angle formulas with the unit circle if you really want to do that

Ted Shifrin

01:48

I don't believe in half-angles. :)

Just apply double-angle.

Clarinetist

Oh. Why does that make so much sense? Lol

Secret

back in my high school days, we received questions like deriving sin 75, cos 75 wihtout calculators, but by that time we have compound angle formulae. I am not sure if one can do that purely geometrically though

Clarinetist

I think too much priority is placed on memorization

Ted Shifrin

I totally agree.

Clarinetist

I didn't learn trig at all in high school. I had to relearn it from tutoring in my undergrad

Ted Shifrin

01:50

But the AoPS course didn't make them memorize much besides what I approve of.

Should know law of cosines, law of sines, addition formulas.

Fawad

$\theta^{..}$

orbit-stabilizer

@TedShifrin hello. I passed all of my math courses!

@Clarinetist what's the machine learning text you're going through called?

Fawad

What it means 2 dots on theta?

Ted Shifrin

heya @orbit. Congratulations. But I didn't think there was any doubt.

orbit-stabilizer

Perhaps the second time derivative?

Clarinetist

01:51

@orbit-stabilizer Machine Learning by Sergio Theodoridis

Secret

What are the contents in your precalc courses? It will be interesting to see how that compared to australia's

Ted Shifrin

@Secret: The course I'm teaching is not a typical high school or college course. Totally not.

Fawad

orbit-stabilizer

@Clarinetist why did you choose this specific text? It's not standard

Clarinetist

@TedShifrin I'm surprised how many textbooks don't describe the law of cosines in words. Whenever I tutor it, I say (a side)^2 = sum(other two sides ^2) - 2 * product(other two sides) * cos(opposite angle of your side)

Students, in my experience, seem to think that there are three different formulas

Secret

01:52

@Fawad that's indeed $\frac{d^2 \theta}{d t ^2}$

Ted Shifrin

Um, I guess I've never done that, Clarinet.

skullpatrol

Four students, right? @TedShifrin

orbit-stabilizer

@Fawad theta is the angle, you're looking at the second derivative of the angle w.r.t time

Ted Shifrin

Yup, skull, but that's because the school just opened and high school level kids are too busy. The elementary classes are damn full.

Clarinetist

@orbit-stabilizer Because I've read all of the standard texts, and I hate them. They are terrible to learn from, IMO

Fawad

01:53

@Secret orbit is saying wrt to time

orbit-stabilizer

@Clarinetist like what?

@Fawad secret made a typo

Secret

sorry typo

Clarinetist

@orbit-stabilizer Let me give you the list of all of the ML books I've at least skimmed through:

Ted Shifrin

Oh, I see your point, @Clarinet. I only write one formula.

Clarinetist

@orbit-stabilizer I've read the following:

Machine Learning: A Bayesian and Optimization Perspective (Theodoridis)
Pattern Recognition (Theodoridis)
Pattern Recognition and Neural Networks (Ripley)
Pattern Recognition and Machine Learning (Bishop)
Foundations of Machine Learning (Mohri et al.)
Understanding Machine Learning (Shalev-Shwartz, Ben-David)
Hands-On Machine Learning with Scikit-Learn and Tensorflow (Geron)
Machine Learning (Flach)
Make Your Own Neural Network (Rashid)
Modern Multivariate Statistical Techniques (Izenman)

orbit-stabilizer

01:55

Oh, you don't like ESL?

Or Hands on Machine learning with scikitlearn and tensorflow?

Clarinetist

@orbit-stabilizer Nope. I think it's way too handwavy and is rather misleading in its preface for its prerequisites

skullpatrol

Professor, I saw "common core math for kindergarteners" the other day :-D @TedShifrin

Ted Shifrin

OMG

orbit-stabilizer

I found the Hands On book good for actually writing code.

I have only done the first chapter, but I found it really helpful.

Clarinetist

@orbit-stabilizer For the TensorFlow one, yes, that's the best one for code. Completely agree there. I needed a theory-driven text

Its theoretical discussions, IMO, are pretty good, but not where I needed to be

orbit-stabilizer

01:56

Yeah, totally agree there haha

Clarinetist

In my grad class, I'm going to be expected to know the "by-hand" details of these algorithms. Starting it in a month.

orbit-stabilizer

I'm surprised you find ESL hand-wavey, I thought it was a pretty standard text for intro ML

Have you taken a look at this?

ece.uvic.ca/~agullive/Mackay.pdf

Daminark

So it turns out open mapping theorem makes max modulus quite easy

Clarinetist

@orbit-stabilizer Yes, it is. But I imagine most of the people reading it don't really know the details behind what it says. I've actually tried doing the algorithms by hand using what's in ESL and it's insufficient

Most of the people I know reading ESL have only skimmed it for a high-level understanding

Daminark

Though my complex prof said he prefers the way he did it since it works for harmonic functions

Clarinetist

01:58

@orbit-stabilizer Yes, I have that book. Haven't had a chance to really read that one

Ted Shifrin

To me ESL = English as a Second Language

orbit-stabilizer

ESL = The Elements of Statistical Learning

web.stanford.edu/~hastie/Papers/ESLII.pdf

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$Mathematics$ Mathematics