serious-discussion

[worn garnet]

Speaking of which anyone here follow TCS research ?

[dapper badge]

Ate too much :(

[primal seal]

Story of my life; a walk helps

[meager sonnet]

a tiny bit

[tender tulip]

Random shit that forms a topology:

[eager reef]

Lots of things do that

[tender tulip]

Lets say we have a partially ordered semigroup (K,<) such that
xy < x and xy < y. Then consider a subset P of K such that if xy is in P, then x or y is in P.

Now, for any element x in K, let V(x) be the set of elements of P that are greater than x, then the set of all compliments of a V(x) is a topology lol

I think,

[surreal sapphire]

do you have an interesting example?

[tender tulip]

Spectrum (prime ideals) of a ring. I didn't realize this til later

[compact tartan]

that sounds kinda like a generalization of zariski

[tender tulip]

I know, the prime condition is specifically chosen to make V(x) union V(y) = V(XY)

[compact tartan]

I'm thinking of the semigroup of strings with u < v when v is a substring of u

I wonder if that yields anything interesting

[tender tulip]

now that I think about it this is a semigroup morphism

Lots of random things form topologies in the right contexts

[compact tartan]

you can make a topology out of any set of sets

(subbasis)

[fading tusk]

we select a subset S of 2^[n] such that every element appears with probability 1/2 independently. What is the probability the topology induced by S is discrete?

[fresh patio]

If I simplify an expression, the original version and the simplified version can't result in different results for the same input, right? I mean they're the same expression technically

[lavish kayak]

Yeah and no.
Some simplification enlarge the image

I.e. (x^2-1) / (x-1) is not the same as x+1

[fresh patio]

Yeah but algebraically plugging the same value into both versions should yield the same result provided the simplification was done correctly

[river moon]

nope, $f(x) = \frac{(x-1)^2}{(x-1)}$ is not the same as $g(x)=(x-1)$ for $x = 1$

[fathom swallow]

Transparent_Elemental

[river moon]

in simplifications like that you always assume you aren't dividing by zero, which doesn't always hold

moreover in inequalities you have to consider the signs and such

[neat lintel]

I feel like my current complex analysis class is less abstract than classical analysis.

The professor is a mathematical biologist, so I guess that makes sense.

[storm sage]

That's often the case since complex analysis is more applied- or engineering-geared

[neat lintel]

I was not expecting that, since it has so many applications in algebra, geometry, and number theory.

[storm sage]

It has so many applications!!

[neat lintel]

It does!

I really love how he started the first day of class by basically saying that the i^2 = -1 definition is stupid and we should use matrices instead.

[storm sage]

LOL

[neat lintel]

So we used I = [1, 0, 1, 0] and i = [0, -1, 1, 0] and then derived everything manually.

[storm sage]

there are so many fun definitions of complex numbers

the nice algebra-based way is to say C = R[x]/(x^2 + 1)

[neat lintel]

I think it makes a lot more sense and its more extensible than just saying i^2 = -1 by definition.

[storm sage]

so you're basically saying C is like R but you extend it to have a number x such that x^2 + 1 = 0

[neat lintel]

Oh, field extensions?

[storm sage]

yup

[neat lintel]

Interesting.

[storm sage]

or C = R(i) (but that's not a definition of C)

[neat lintel]

I don't have much exposure, so I figured that was a quotient set.

[storm sage]

It is! It's a quotient of polynomials in R by the ideal generated by x^2 + 1

[eager reef]

your name man eric

[storm sage]

this essentially means that you "send x^2 + 1 to 0"

[eager reef]

lmao

[storm sage]

LOL

[eager reef]

the tone is just

you know these memes "emily you're so quirky"

[storm sage]

LOLLLL

[tender tulip]

i also feel like complex analysis is much more “stable” in terms of the structures

[neat lintel]

It looks like my professor is going to introduce paths in the Calc III way and not the topology way.

[tender tulip]

because the prominant definition of a complex function, differentiable with Reimann Cauchy, forces smoothness

Along with algebraic closure

[storm sage]

homotopic paths are important in complex analysis

[neat lintel]

I expected a little more topology.

[tender tulip]

just makes it very nice

[neat lintel]

But no topology course is required for this one.

Though it shouldn't stop us from learning.

[storm sage]

there will prob be some introductory topology

[tender tulip]

I mean you’re working with topology it’s just not abstract

[storm sage]

once you start talking with "spaces with holes in them"

like the domain of 1/z

[neat lintel]

Right, with classical and complex analysis.

[storm sage]

this turns out to be important

[tender tulip]

anytime you work with any union of balls (heh) it’s topological, cuz it IS the topology

[storm sage]

for the cauchy-goursat theorem

[neat lintel]

Open sets play a big role.

[tender tulip]

actually is the basis of C’s topology balls or annuli

i assume if it’s based off of R then it’s annuli.

[eager reef]

im not sure if i agree with this

[neat lintel]

It looks like we've defined a continuous function in the traditional VVF way from Calc III and not as having to take place in an open subject of C.

[storm sage]

it turns out that if you have f being analytic on its domain D, then any two line integrals of f are equal to each other if the paths are homotopic :)

[eager reef]

it feels more smooth

[neat lintel]

He's doing things very differently from the book.

[eager reef]

i agree

[tender tulip]

yes

[storm sage]

what's VVF?

[eager reef]

but like

[neat lintel]

Vector-valued function.

[eager reef]

there's really weird stuff happening

[storm sage]

ahh

[tender tulip]

many functions and series are smooth except for the boundary of convergence and the like, where shit can get funky

[eager reef]

which i wouldn't call a stable structure

[neat lintel]

Saying f(x + yi) = u(x, y) + v(x, y)i

[eager reef]

necessarily

[storm sage]

okay yeah you often equate f : C -> C with f : R^2 -> R^2

[tender tulip]

often weird fourier series reside on these disc-boundaries

[neat lintel]

Just with some weird differences.

[storm sage]

but complex differentiable functions are more special than R^2 differentiable functions

[neat lintel]

Like how z^n or z^(1/n) work.

[neat lintel]

Holomorphic is the term, right?

[storm sage]

yeah exponentials and logs are interesting

[neat lintel]

I think all derivatives are guaranteed.

[tender tulip]

mmm reimann cauchy

[storm sage]

I don't love the term holomorphic because some authors use it to mean different things, the two standard definitions are
f is holomorphic at x <=> f is complex differentiable at x
f is holomorphic at x <=> f is complex differentiable in a neighborhood at x

[neat lintel]

Yeah, the second one is what I was familiar with.

[storm sage]

I don't think the book I used even used the word holomorphic

[tender tulip]

Reimann cauchy makes the jacobian a scaled orthogonal matrix, right?

[neat lintel]

It seems like the field is very fragmented.

[storm sage]

correct, the jacobian is of the same form as a complex number

.
[a -b
b a]

[tender tulip]

Actually is C* isomorphic as a group to a semidirect product of U(2,R) and R*

*SU(2,R)

[storm sage]

wtf

[tender tulip]

Wait no

I’m an isiot

*idiot

[storm sage]

let me parse that sentence

[tender tulip]

The isomorphism itself is e^(x+yi)

[storm sage]

are you asking if each complex number can be represented in polar form

[tender tulip]

i am an idiot

[storm sage]

z = Re^itheta

[tender tulip]

i thought of rotation and scaling for a second without remembering that polar form is a thing

[storm sage]

Lol

[tender tulip]

i was thinking of purely Matricies

[storm sage]

I think (C*, ×) should be isomorphic with S1 × R^>0

[tender tulip]

SU(2,R) is isomorphic to T
Z(GL(2,R)) is isomorphic to R*

i just did a circular loop of trying to explain reimann cauchy lmao

[storm sage]

what is SU?

[eager reef]

special unitary

[tender tulip]

Special ortho

[storm sage]

Oh

I've always written SO oops

[eager reef]

those are different things

[tender tulip]

i may have gotten it mixed up

my loop of reasoning

[storm sage]

SU(2) is isomorphic to the group of unit quaternions? interesting

okay SO(2) is isomorphic to the circle group

I see

oh by T you mean the circle group

[tender tulip]

complex function -> reimann cauchy -> jacobian is a scaling and a rotation -> direct product of SU(2,R) and Z(GL(2,R)) in GL(2,R) -> isomorphic to the direct product of T and R -> isomorphism is angle and radius -> oh shit polar form -> oh wait that’s the complex numbers

[storm sage]

ohh the T is for torus

[tender tulip]

i use T for circle group, i keep forgwtting that’s not general, fuck

[storm sage]

I mean wikipedia uses T

[tender tulip]

epic i am justified

By wikipedia

[vivid halo]

https://twitter.com/kittegory/status/1293952869478141952/photo/1

the homotopy category is a homotopy category (@kittegory)

MathOverflow, where an answer to the question “how to remember the formula for the inverse of a 2x2 matrix” starts with

Likes

760

Retweets

135

Twitter · Aug 13, 2020, 4:49 PM

this is how the current conversation feels

[amber fog]

typical stackoverflow

[open aspen]

Whats the difference between math stackexchange and mathoverflow?

[untold sage]

I've never heard of mathoverflow

[bright hill]

@neat frost have you done multivar yet?

or is that what calc4 is about?

[severe swallow]

its amazing whenever you're not the one asking the question

so basically math stackexchange

[untold sage]

Wdym

[bright hill]

so basically all of stackexchange

^fixed it for you

[open aspen]

TeX stack exchange helped me once

[severe swallow]

usually you google questions online and whenever a link to these sites show up when someone else posed it. It often has a satisfactory answer. but sometimes.. there is no answer and that's when shit gets real

[open aspen]

You just have to commit to acting like the answerer is a gift from God and you're lucky they deigned to help you

The latter being actually true, the prior maybe not so much

[neat frost]

No. Calc3 is multivar

[vivid halo]

mathoverflow is for more "advanced" stuff

usually this leads to a lot of arguing whenever someone posts something too advanced for mathstackexchange but too basic for mathoverflow

[worn garnet]

See some of the juicy crypto stuff coming out :)

[bright hill]

you haven't done calc3 and you wanna do calc4?

[storm sage]

most of it was me going on a wikipedia rabbithold looking up what each term in miz's answer meant

but then I got distracted by random cool math facts

[bright hill]

bruh, so I'm not alone??

[storm sage]

LOL

[bright hill]

I thought I was goin insane

(also, my main source was walfram lol)

(nice and concise)

[neat frost]

No?

Oh I see what you mean

I can sign up for calc4 next sem

I’m doing calc3 this sem

[bright hill]

do you know what book you're gonna be using?

[neat frost]

We don’t use books.

[deep mango]

Based

Still dont get wtf "calc 4" is

[bright hill]

I see

welp

I'm working through spivak on manifolds atm if you wanna prepare ahead

[neat frost]

I had a syllabus at some point

Idk where it went

[neat frost]

Yeah… no lol

I’m not taking calc4

[bright hill]

calc4 is calc on manifolds?

[neat frost]

Idk

I assumed you were assuming that when you said “prepare ahead”

[bright hill]

I thought calc3 was calc on manifolds

[neat frost]

Oh

[eager reef]

Wait till you hear about calc 5

[little vine]

Calc 4= differential equations

[deep mango]

Calc 4 = functional analysis!!!!

calc 4 = calculus of variations

[floral sedge]

Hey, I’m in my last year of English a levels (American AP) studying maths further maths and computer science, I kinda wondered what the difference is between the level of maths im at now and degree level maths? The lecturers keep saying “people don’t like degree level maths” but no one can explain what the difference is so I hope someone here can maybe elaborate for me, sorry if I interrupted any convo going on here

[bright hill]

I'm assuming "degree level math" means the math you do to get a degree in math

but the difference is that everything is now proof based

[floral sedge]

I was looking at computer science and maths joint course, so the modules are similar to that taking in a maths course, I just don’t do As many of them

[bright hill]

every theorem, corollary, lemma every fact is rigorously proven before being declared as "true"

while ap calc, for example, serves to foster intuition, in higher level math intuition is useless without rigorous proofs to accompany it

[teal lion]

Either that, or you’re supposed to prove it yourself

[floral sedge]

Right that makes sense when I think about it

Did that take you a while to get used to? Is it like a different subject or just a different style

[teal lion]

It took me a couple months to really get going

[bright hill]

it's totally different imo

[teal lion]

I think it is incredibly different

Analysis vs Calculus case in point

Most people find analysis very difficult at first

I find analysis difficult too

[floral sedge]

I’ve heard that, is it real analysis? All I hear is people saying how hard it is 😂

[teal lion]

Real analysis is just analysis over the reals

[storm sage]

I wonder if any universities have calc 5

[teal lion]

Analysis is the study of stuff with metrics generally

[storm sage]

I wouldn't say intuition is useless without rigorous proofs to accompany it

mathematics is the art of making good conjectures sometimes

[teal lion]

ryc probably has a better definition

[storm sage]

but wrong intuition is useless, and actively harmful

and the way you figure out what's right/wrong is through proofs

[floral sedge]

That makes lots of sense, how would you say is best to get an idea of if I’ll like it? I’m really scared of picking s course that I rlly enjoy now and hate it for 3-4+ years

[surreal sapphire]

real analysis is the study of real functions up to sets of measure 0

you can try to read some mathematics book

[storm sage]

what does this mean...

[surreal sapphire]

its a joke 👀

[storm sage]

well yeah but I wanna know what the joke means 😭

[deep mango]

analysis is kind of just the general, extended study of continuity, differentiability, and integrability on the reals

[surreal sapphire]

like, you can disturb a real function on a set of measure 0 and steal treat it as the same, e.g. when integrating

[storm sage]

ahh

I see

but not when differentiating :(

[surreal sapphire]

who would do that

[deep mango]

you could be broader and call analysis the study of ordered groups

[floral sedge]

Wdym by Ordered groups? The first bit made sense to me

[teal lion]

Example?

Of an ordered group that isn’t naturally something else

Are you talking like group limit completions and stuff?

[deep mango]

a group is a set with an addition or multipllication operation with some properties, and an ordered group is a group where you can compare elements with a > sign

(so, like the integers or the reals)

[deep mango]

it's always just Z, Q, or R, but the point is that the interaction between the additive structure and order structure is what's important

[teal lion]

Oh

That’s boring

[deep mango]

you need that interaction to be able to define, say, a metric which is valued in some set

analysts don't waste time with generality

we don't need it

we study difficult problems in very specific settings

[teal lion]

I like proving, simple, general problems

[deep mango]

(specific relative to other kinds of math)

[teal lion]

That inevitably lead up to something powerful

[storm sage]

analysts don't waste time with generality

you could be broader . . .

Lol

[teal lion]

To use on specific stuff

[deep mango]

you could, but no analyst is

is the point

[teal lion]

The rising sea and all that

[deep mango]

any analyst would tell you this

[dapper badge]

Could you elaborate on what you mean by "inevitably"

[teal lion]

“End up”

[storm sage]

inevitably means you follow the flow of the book, and everything magically works out, no worries about how it works in research

[floral sedge]

I think I understand what you’re saying, is AI an application of analysis? Cause it uses metrics to evaluate how well they do? Or am I way off

[surreal sapphire]

all my research projects end up successful, wdym

[storm sage]

"How many moves do you look ahead?" "Only one, but the right one."

~ Some chess player

[dapper badge]

It's just that like

[teal lion]

“I found 50 ways not to derive this functor”

[dapper badge]

Some people spend a long time coming up with important (counter)examples

[deep mango]

different kind of metric, but AI is an application of optimization theory which is in many ways part of analysis (at least very very closely related)

[surreal sapphire]

reject generality, math is a collection of interesting examples

[dapper badge]

Real

[deep mango]

anti-shelah

[teal lion]

Reject specificity, embrace generality

[deep mango]

like for example the thing that always gets me most excited in math is weird constructions

[storm sage]

Embrace

[deep mango]

that exhibit some kind of pathology or unexpected behavior

i think a person who does analysis is more liable to like that kind of thing

[teal lion]

The thing that gets me excited is generalizations that apply to everything

[storm sage]

ryc is giving me "behold, a human" vibes

[deep mango]

for me, if i see something that generalizes and applies to everything, it immediately loses my interest

but i understand the appeal for sure

[teal lion]

I don’t like wonky functions

I want to deal only with the beautiful

I also hate math comps

most problems are terrible

[storm sage]

like all the ones I write!

[teal lion]

Just weirdly specific stuff

[storm sage]

You have a strange definition of beautiful

the topologist's comb is beautiful 🥺

[teal lion]

That isn’t a definition, it’s an instance

The converse does not hold

[storm sage]

the weierstrass functions are beautiful

[teal lion]

No

They’re boring

[storm sage]

you're just wrong

[teal lion]

they’re just a random thing constructed to allow us to come up with better conditions to describe things

[deep mango]

they're real objects

[teal lion]

I know

[storm sage]

well

that depends on your definition of "real"

[teal lion]

I mean, i wouldn’t want to study the function itself

[deep mango]

they arise naturally from several short chains of inquiry

yeah that makes sense

[teal lion]

Just try and generalize to bigger and bigger classes of functions

[storm sage]

wittgenstein cursing at you from his grave

[teal lion]

to classify functions by how differentiable they are

[teal lion]

But I like Wittgenstein

[storm sage]

Lol I recall one famous anecdote where he said the best way to appreciate a museum is to pick one painting in it and spend the whole day studying it

[teal lion]

oh that’s true

I agree with him

[storm sage]

I don't

That might be nice for a second visit

Or a third

But definitely not for the first visit

[teal lion]

He never said for the first visit

[storm sage]

(Also is the museum free entry?)

[teal lion]

mine is

[storm sage]

(If not, then I probably wouldn't ever do this lol)

[teal lion]

it’s more a center for the arts

Actually

[bright hill]

you think generalizations are the goat but you also think pathological examples that break the rules are boring

but the two things are always intertwined

don't you see the contradiction there?

also

wasn't the weierstrass function the catalyzer for a serious study into fractals or smth?

and that in turn made rise to holomorphic dynamics?

[teal lion]

You’re proving my point

It’s not the weierstrauss function itself that’s interesting

It’s how you generalize it

How it fits into the broader context

[storm sage]

Sad Weierstrass function noises

[bright hill]

the researchers that worked on the issue would surely disagree

since they wouldn't study the function if they didn't find it interesting

[teal lion]

the weierstrauss function is the necessary tool to study the broader whole

I know the researchers would disagree

I don’t want to research weierstrauss functions

[teal lion]

I also don’t see the contradiction. If a pathological example breaks the rules, you aren’t thinking generally enough

[bright hill]

if you don't care about the specific examples why the hell would you give a fuck about all encompassing generalization

[teal lion]

what do you mean?

[bright hill]

generalizations aren't formalized for masturbatory reasons

they serve to solve specific problems

[teal lion]

theories are meant to solve problems, but it’s not about working on the problem

it’s about seeing where the theory takes you

[bright hill]

the theory would take you nowhere without a concrete destination in mind

[teal lion]

Also, is the cursing really necessary?

[teal lion]

You don’t need a destination, just a starting point

and the destination will make itself concrete as you go along

[bright hill]

see the second meaning

[teal lion]

I’m not referring to masturbatory

I’m referring to the swearing

also, it’s a bit mean to call me excessively self-absorbed for wanting to study certain things

[bright hill]

I clearly meant self indulgent

[teal lion]

they come hand in hand

when they are excessive

[bright hill]

can we please stop attacking my language and start paying attention to my argument?

[teal lion]

You just sound like you’re yelling.
In my personal experience, studying things in extreme generality will, due to being general, apply to more things than specific things

[bright hill]

I can't think of a destination other than solving a specific problem tbh
(sry for the delay, I was busy)

[stone ferry]

If you ignore the other definition, this sentence is quite funny

[tawdry radish]

@bright hill

[bright hill]

that's what I thought the first time I heard the word lel

[stone ferry]

It also could either mean:

1. generalizations are not formalized, because formalizing them would lead to inappropriate activities.
2. generalizations are not formalized, because the people trying to formalize them are "busy".

[bright hill]

that's mainly the reason I used it, hardly as an attack on serge's character

I apologize if it seemed like so

[spiral saffron]

Hey! Somebody can ELI5 me on imaginary numbers please?
I understand they are used to work with negative square roots right.
But what's that deal with circles? and z=?

[solid snow]

haha would be quite hard to explain this to a 5 year old

basically you know the unit circle is sin^2x + cos^2x = 1 right?

[spiral saffron]

nope x)

do you mean sine?

sin is a religious thing rigt

[solid snow]

sin is sine

would be a tad more difficult to explain this topic now since i would have to explain the unit circle

but anyways

the unit circle is defined as a circle with radius 1 about the origin

[spiral saffron]

unit circle?

[solid snow]

yes

[spiral saffron]

what is that x)?

[solid snow]

just said what it was

[solid snow]

yes

[spiral saffron]

what 's the relation with angles?

is sin always vertical measure? (oh no nvm)

[solid snow]

any right triangle you create with a radius of that circle will have a hypotenuse of 1

in this case it is

[spiral saffron]

i'm dumb x)

[solid snow]

$\sin(\theta)$ here is $\frac{opposite}{1}$

[fathom swallow]

josemom2

[solid snow]

which means that the opposite (vertical component) is just sine

likewise for cosine

[spiral saffron]

where is the opposite?

[solid snow]

the side opposite to theta

[spiral saffron]

if the triangle has the same values?

/\

[solid snow]

?

sine and cosine are defined based on the sides of a right triangle here

[spiral saffron]

equilateral i mean

[solid snow]

no

if you don't know trig this whole concept might be a bit above your head for now

and i guess also taylor/maclaurin series of sine and cosine because that's where euler's formula comes from

[bright hill]

  /|
 / |
/__|

triangle ^

[little vine]

[bright hill]

what?

want a right triangle?

there

[little vine]

[spiral saffron]

so trigoometry is more about circles than triangles?

[solid snow]

it's about triangles

right there in the name

trigon ometry

triangle measure

it has to DO with circles but it would be weird to say that it's solely about circles

[neat frost]

Circles are just a special case of triangle after all

[spiral saffron]

yup I like this one

[spiral saffron]

but what's the angle of a circle?

a radiant?

who invented it?

[neat frost]

Oh no I was shitposting

[solid snow]

Slurp 😭

[bright hill]

that shitpost doesn't even make sense

[solid snow]

No mate

[bright hill]

slurp, shitpost better smh

[solid snow]

A radian is equal to a “rope” of the circle’s radius laid out on its circumference

Or an arc of that same radius w/e

Different flavors

$\pi$ radians draws a semi circle

Or halfway

[fathom swallow]

josemom2

[solid snow]

180 degrees

[untold saddle]

Like someone from this server tried to offer their services as a math tutor can i report that or no?

[deep mango]

if they're bothering you, feel free to DM @polar panther. you don't need to if they aren't bothering you

[bright hill]

[little vine]

Woohoo

Huh

[storm sage]

Lol

easy

get good

[bright hill]

I just saw the rules for differentiation an hour ago, they look deceivingly similar to their one dimensional counterparts but I can't put them in my head for the life of me

[storm sage]

They are very similar! Except the derivative is a matrix

:p

[untold saddle]

What do I do when no helper has gotten to me in an hour?

[storm sage]

That's basically to be expected, there's no hired helpers or anything here

It's all just volunteer

[untold saddle]

fair, I'm just trying to see if I can communicate to use a the number in the percent rather than the percent itself. ie use 20 instead of .2 for this problem

[spiral saffron]

Hey what are some social media math accounts you love?

[fervent pebble]

can anyone think of examples where lots of different people define the same thing in math different ways

like defining N to include 0 vs not including 0

[bright hill]

integrals

[solid snow]

LUL

[bright hill]

there is a bajilion definition of integrals

[fervent pebble]

nono not equivalent definitions

[bright hill]

not all definitions of integrals are equivalent

[storm sage]

"increasing" in intro calculus books

similarly, "decreasing"

[fervent pebble]

hmm how do you mean

to both

[storm sage]

some books define increasing to mean the derivative > 0, some books define it to mean if x2 > x1, then f(x2) > f(x1), some books define x2 > x1 => f(x2) ≥ f(x1) instead

[bright hill]

some functions are lebesgue integrable but not riemann integrable

[bronze wedge]

most definitions of integrals are generalizations of past ones. cant think of one thats not a generalization

[storm sage]

there is no consistency as to whether points with derivative 0 should be included in the region where the function is increasing (they should be in certain cases, but definition 1 doesn't capture that)

[bronze wedge]

so really they are equiv

[bright hill]

like f(x) = {1 if rational and 0 otherwise}

[bronze wedge]

yes - but the lebesgue integral is equivalent to riemann when we restrict ourselves to riemann integrable functions

[bright hill]

well, all numbers are naturals if we restrict ourselves to integers bigger than 0

[storm sage]

well that's different

naturals including 0 is not a generalisation of naturals excluding 0 lol

[solid snow]

Is complex analysis actually easier than real

Lmao

So I’ve heard at least

[storm sage]

Depends on the class

And the instructor

[solid snow]

Maybe by the point you’re at complex it seems easier than the first time doing real?

Could be that too

[storm sage]

Lol I did complex analysis without touching real analysis

😎

[solid snow]

Same lol

Not really

I just touched a part of it before ever touching real

[bronze wedge]

one good answer to @fervent pebble question is the strantonovich/ito integral

they do not agree

but you can convert between the two

Ito is used in analysis

Strantonovich is used in geometry

[bright hill]

don't you think "B is a generalization of A" means
$$A\Rightarrow B$$
but
$$B\not\Rightarrow A$$

[storm sage]

fourier transform is always defined differently

[fathom swallow]

DarQ

[bright hill]

?

[bronze wedge]

also true - probabilists like to have the characteristic function w/out the pi term

[solid snow]

Contour integration too cool man

[wooden flax]

who even is a probabilist smh

[bronze wedge]

[bronze wedge]

if you are working on a manifold, it is much easier to define the strant int

[bronze wedge]

the main advantage of the ito integral is the ito isometry

which allows you to take a very functional analytic approach to stochastic analysis

[zealous garden]

I want to learn these integrals because they sound cool, what will I need to knock out to get to that point

[bronze wedge]

you just need measure theoretic probability and real analysis

[zealous garden]

sounds like a Season 6 episode

[burnt dune]

p easy

[bronze wedge]

what was your previous profile pic?

i cant remember lol

[burnt dune]

a picture of mee and a friend holding a pyramid of giza

[zealous garden]

yeah we're in the last arc of season 5 rn

[burnt dune]

no srsly

analysis is very easy

only the hard parts are hard

when u get to study locally continuous stuff

haha

[zealous garden]

I've come to see that analysis has a range

[burnt dune]

yea analysis is the study of thing that have ranges

haha

[velvet dagger]

"only the hard parts are hard"

[zealous garden]

is it wrong?

[tender grotto]

is there a name for the study of recursive functions and iteration

like finding fixed points and stuff

[burnt dune]

like i meant like

there is a certain vibe you get

before even reading in details

u know this shits hard

and u get this only in analysis for me

once u see the word "gelfand" and those sword notation u know ur done for

[little vine]

Give it a try

I'm assuming it's free

I used Stewart Calculus and have no complaints. You can probably find a cheap hardcover older edition on thrift books.com

[meager sonnet]

dagger???

[burnt dune]

yea this one

the anti christ

[zealous garden]

you mean $C^{\dagger}$

[fathom swallow]

wraithlord_kohomology

[meager sonnet]

operator algebras?

[burnt dune]

yup

[tender grotto]

anyone?

[fervent pebble]

tbh if it's calc any textbook out there is fine

[leaden torrent]

Generatingfunctionology

This is a joke answer but there's actually a textbook named that all about this

The honest answer is that "recursion" is too broad a technique to attribute it to a specific field

You really need to pick a specific context for it

It's like trying to mathematically study "inductive proofs"

(in fact, discrete recursion IS induction, so...)

Generatingfunctionology is a very fun read btw, I read it casually

Probably above the level you're thinking of tho

But its quite light

[tender grotto]

ah ok its in the context of sequences and series, like using iteration to approximate solutions

ill look into that book tho ty

[leaden torrent]

If your goal is to approximate, then this is touched on in numerical analysis

But I am not aware of whether that subset of numerical analysis has a name

It probably does, I know very little applied math

[storm sage]

if it's a recursively defined sequence then it sounds like you could be interested in dynamical systems?

[tender grotto]

ooh that seems like it

is there any simple intro books to it

[storm sage]

If you find any then let me know lol

[modern owl]

I love Math

Yes, Gaz

[neat lintel]

When $\lim_{x\to-\infty}$ it approaches -1

@neat lintel

[fathom swallow]

Gaz

[neat lintel]

so for every asymptote of -constant^x it is -1?

[neat lintel]

No that would be 0, for $a^x+b$ the asymptote will be b

[fathom swallow]

Gaz

[neat lintel]

b is in this case 0

ohhh it is smth we need to remember

i seee

thankyou!

[neat lintel]

@tough trench

You here

[tough trench]

Hi

[neat lintel]

You want to calculate the force in the horizontal direction

[tough trench]

no its on a slope

Theta=53

[neat lintel]

Wait can you show me the question again

[tough trench]

Sec

It's Google translated from arabic so there might be a bit of confusion

Oh wait I just

the force is the one applied at a 53 angle

Shit

I'm dumb

I'm sorry for wasting time

[neat lintel]

Don't apologise, that didn't even cross my mind. Saying sorry should be reserved for when you hurt someone else. Saying sorry for minute things is unnecessary and will only make you feel worse about yourself.

I think people apologise too much in general

[neat lintel]

This is also unnecessary

You're not dumb

[raw bison]

Hello

Where I go for help

[neat frost]

#❓how-to-get-help is a good start

[raw bison]

Thanks

[true urchin]

I regret being exist

[neat lintel]

Most relatable post

[true urchin]

nocap

[neat lintel]

Tfw can learn problem solving but can't solve my own problems

[true urchin]

I put the fun in dysfunctional

[vale plover]

biggest pet peeves when buying a used book or checking out a library book?

mine's dog-eared pages

[bronze wedge]

Things like this

Or the book feeling greasy

[vale plover]

marginalia or limited highlighting in a used book isn't ideal but at least it makes the book cheaper without damaging the book too much

dog-eared pages really ruin the longevity of a page though

plus it's kinda fun to see what other people think is important

[bronze wedge]

lol I was kinda weirded out and decided not to do problem 1.5

[distant goblet]

I usually check out the nice ones that people don’t like to use

[fading moon]

is there a machine learning channel here?

[bronze wedge]

No

we don't have a channel for OLS w/ constructed regressors

[teal glacier]

@placid finch u alive?

[placid finch]

no

[teal glacier]

hi

pls help

in 20 mins

i need halp

[teal glacier]

wait is this like a joke or are u not free LOL

[fading zealot]

What do you guys think about Matt Parker ocassionally call 2 and 3 “sub-primes” because they “do not follow many patterns the larger prime numbers follow”?

[next schooner]

it is dumb

[neat frost]

I prefer to call 2 and 3 “2 and 3” but idk about you

[mild urchin]

Does anyone have any advice on how to best engage with a tutor?

Im mostly selt taught (have some basic analysis, type theory and algebra under my belt) and am going to be meeting with a tutor on a regular basis starting soon.

[mint canopy]

Do the homework they set

[bright hill]

Good morning slurp!

[lavish kayak]

Obviously the resident genius didn't even consider the questions you thought were easy

[neat lintel]

oop

[mint canopy]

#latex-testing please

[neat lintel]

sorr

[neat frost]

Good morning!

[willow finch]

they wrote nothing because they became speechless from seeing how easy they are

[neat lintel]

where should I start if I want to self study mathematics?

[brittle socket]

Where are you at

[neat lintel]

I´m mostly familiar with algebra, trigonometry and basic derivatives

[bright hill]

If you're comfortable with high school math I think the canonical starting point should be linear algebra

And if you find difficulty with proofs or expect yourself to find difficulty with proofs the discrete math

[mild yew]

Can anyone explain oilers cat theorem to me

[bright hill]

You can ask for book recommendations for both subjects in, well, #book-recommendations

[solid snow]

DarQ 😭

[bright hill]

What's wrong?

[neat frost]

Starting point is discrete math

[bright hill]

I didn't start with discrete math

[neat frost]

Exactly.

[ripe wasp]

what's in discrete math

i never studied it as well

[solid snow]

I guess like “technically” it makes more sense to do la before calculus and all that

But have some fun with calc

[bright hill]

It's differs from uni to uni

[bright hill]

Oh

Forgot Americans don't teach calc in HS

[solid snow]

They do?

[bright hill]

In AP classes

[solid snow]

Ap at least

[bright hill]

So calc isn't highschool stuff technically

[dusty wagon]

[solid snow]

Ap is serviceable for the methods of calculus/a decent overview of it

[dusty wagon]

USA Education Systems seems kinda flawed

Don’t they also have to do like 2 years of Gen Ed courses in uni

[solid snow]

Depends on uni

[dusty wagon]

I only had to do a single gen ed course luckily and took ‘Life in space’ lol

Tldr ‘yes, but no’

[bright hill]

Intro to proofs, maybe some graph theory, first order logic etc etc

[brittle socket]

Ah that reminds me of my country where there are stupid general education modules you're forced to take in uni

[neat frost]

They do, not just in AP

At least I think they do

Or every American I’ve talked with is in AP

[solid snow]

No they don’t really

Ap is where you get calc

[brittle socket]

I tried Rosen last time and it was way too boring for me so I tried Enderton (Set Theory)

[solid snow]

Or international programs from cambridge or ib

Like a levels and stuff

[neat frost]

Oh then I guess Occam’s razor failed me

[bright hill]

The idea I get is that discrete math is uni's way of thing their student what they should've been taught in HS + some useless stuff to practice proofs or w/e

[solid snow]

I know a friend who’s high school had a calc 3 class but it wasn’t ap or anything

It didn’t count for university credits

[dusty wagon]

Iirc we did limits, derivatives, integrals, linear algebra and probability in HS

[solid snow]

So kinda a waste

[neat frost]

What kind of linear algebra tho

[neat frost]

Set theory too

[dusty wagon]

Introduction of vectors and matrices, operations and the determinant. Nothing further than this

[bright hill]

Every self learner ever be like:

[neat frost]

But it’s purpose is to create a basis for all your other math courses and to introduce you to formal proofs yesh

[solid snow]

I probably should have skipped the counting chapter in book of proof

😭

[neat frost]

Like vectors as in column/row vectors or the idea of more abstract vectors as well?

[bright hill]

That's what I meant by first order logic

[solid snow]

It’s neat and all but kinda useless ig

At least for me rn

[neat frost]

Oh I see. But I wouldn’t argue that that should be taught in HS?

[dusty wagon]

Yeah more as a way to list numbers, we didn’t introduce vector spaces

[brittle socket]

Oh boy this reminds me of one time I checked one of my local unis modules and vector spaces are only introduced in like Linear Algebra II bruh

[dusty wagon]

I vaguely remember giving a presentation on the Eigenbavlue problem in HS when everyone had to do a presentation

But I could be wrong, long time ago

[bright hill]

Oh, grass, u in HS?

[dusty wagon]

Lol what

It is a topic for the first lecture of a LinA 1 course

[brittle socket]

Bruh

LA II

LA I

[dusty wagon]

Hmm kinda unnecessary splitting of topics

And concepts

[brittle socket]

Exactly like bruh

[dusty wagon]

Just do it rigorously from the beginning

[bright hill]

What math major learns about determinant in their second year??

[dusty wagon]

Fr lol

[neat frost]

Yeah we learn about determinants in third year

[dusty wagon]

Engineers learn all of this in first semester btw

[ripe wasp]

what does first year cover then...

[bright hill]

Bruh

[neat frost]

Do I need to add the /s for you DarQ?

[dusty wagon]

I think I learned about complex numbers 1 week before graduation

[brittle socket]

Probably not here

[bright hill]

It wasn't at all clear you were shitposting but w/e lel

[neat frost]

Well DarQ

I get it

[brittle socket]

idk bruh

[neat frost]

We can’t all be as amazing as me

But at least try

[neat frost]

Tbh yeah this was all covered in my first course in uni which was about a month-long course

What’s the syllabus for LA1?

[dusty wagon]

NGL I’m very glad I live and study in Europe. American elite unis seem very tempting and cool but way too hard to get into, while the regular unis seem to have kinda a bad rep?

[bright hill]

Slurp's reading comprehension is at an all time low

[brittle socket]

"Sample study plan" lmao

[neat frost]

Ohh I thought this was LA2 for second year. Oh that’s standard for LA1 ig, but weird they take it only in second year

[bright hill]

How many stem courses do you guys take per semester?

[neat frost]

This is not the worst mistake I’ve made

[dusty wagon]

4-6, but among them no ‘non-stem’

[neat frost]

Give me some credit, at least I knew it was an LA course

[ripe wasp]

bruh

[brittle socket]

Yeah this is exactly why Im kinda a little put off local unis here

They have a shit ton of compulsory GE mods too bruh

[bright hill]

GE?

[tight comet]

wine tasting

[brittle socket]

General education (modules)

[bright hill]

Tf are those?

[tight comet]

do you really think that it's good to do 4 years of the same thing?

[tight comet]

I told you, wine tasting

an example:

The primary aim of the module is to introduce students to the nature of infectious diseases and their impact on human activities. At the end of the module, students will be able to understand the interactions between microorganisms and human, and the position and role of human in the living world.

[brittle socket]

dumb modules :p

[tight comet]

ah yes "everything I hate = dumb"

[eager reef]

Id hate general education as well in uni

Fuck that

[tight comet]

I think the appropriate thing is to consider if you're actually generally educated

[eager reef]

What do you consider generally educated

[tight comet]

this lmao

[eager reef]

This isn’t worth taking a Uni course about

[dusty wagon]

I don’t go to uni for a specific Major to get generally educated

I can read interesting stuff in free time

[surreal sapphire]

this is also kind of a historical question, people used to go to university to become generally educated (mostly rich people who didnt need to work anyway), but today this changed and universities more and more just prepare you to work in industry

[tight comet]

It's not about whether it's interesting. It just leads to further specialisation but a lack of any generic awareness

[surreal sapphire]

so one really has to ask if general education is important

ofc we live in a democracy, so one can argue that its in everyones interest if people know things outside their field

[tight comet]

Why the fuck would you get vaccinated if there is no mathematical proof it works?

[surreal sapphire]

but im unsure if university provides this

what

[dusty wagon]

Luckily (?) I wasn’t prepared for industry at all lmao

[eager reef]

What are you saying man

HAHAHA

[surreal sapphire]

there is no mathematical proof of anything in medicine

[honest veldt]

That was so outta left field lmao

[tight comet]

EBM is at most statistical

[bronze wedge]

You can't prove something about the real world

[tight comet]

My point is then everyone who reads no statistics will have no say nor any relevance in concluding anything about public health

[dusty wagon]

Does beer help counteract headache

[bronze wedge]

No

lol

[eager reef]

Does the headache stem from a hangover

[dusty wagon]

Yeah

[eager reef]

Then yes

[surreal sapphire]

what is it called in english

[eager reef]

Getting drunk again cures the hangover

[surreal sapphire]

Konterbier

counter beer?

[eager reef]

Was looking for a word as well

Lmfao

[surreal sapphire]

[eager reef]

Bruh

[dusty wagon]

Lol

[surreal sapphire]

https://en.wikipedia.org/wiki/Hair_of_the_dog interesting

[eager reef]

Konterbier is way better

[dusty wagon]

They should just call it counter beer

Do you sometimes feel grossed out after eating too much food

[eager reef]

You mean like

Getting nauseous

?

[dusty wagon]

Nah more like ‘ew, food’

Or ‘wtf did I eat’

Kinda like post nut clarity but with food

[eager reef]

Not really

[sleek wing]

I can relate

[eager reef]

I just eat whatever suits my diet plan

[dusty wagon]

You have a diet plan?

I just eat what I want to or have at home

[eager reef]

Yes

[sleek wing]

I just eat what I want when I want and make sure it’s below 2300 calories a day

[dusty wagon]

For workout?

[eager reef]

I am a gym person so I track my macros

Plus i have issues with eating a lot

So i have to make adjustments to what i eat when I’m bulking

Otherwise I can’t reach my calories

[dusty wagon]

Ah yeah I used to do that too but 1 month ago I kinda stopped going to the gym after an accident, it’s healed now but can’t really find the courage to get back even though I was actively going for more than a year

[eager reef]

2300??

Wtf

Are you like giga cutting

[dusty wagon]

Gained 3 kg in the 1 month off because I didn’t adjust my eating

[surreal sapphire]

lol

[vivid halo]

That's pretty normal lol

[surreal sapphire]

when i cut i aim for 2000

[eager reef]

I eat 3.300

On a cut I eat 2600

[dusty wagon]

I mean depends on height and weight

Pure calorie numbers make no sense stating without context

[eager reef]

And body fat percentage and shit

Yeah true

[sleek wing]

Big man

[eager reef]

Not really

[surreal sapphire]

but i probably dont work out as much as you lmao

[sleek wing]

I eat 2600 when bulking and 2000 when cutting

[surreal sapphire]

im at like 2500 kcal for maintenance

[eager reef]

I have an active lifestyle plus gym 6 times a week

That boosts tf out of your calories

[sleek wing]

This is the main factor probably - I only go to the gym 2-3 times a week

And cycle 2-3 times a week as well

[eager reef]

It’s kot really

A generally active lifestyle

Makes more difference

[surreal sapphire]

i actually lost some weight tho, i have to start regaining

[eager reef]

You don’t burn a lot while weightlifting

[surreal sapphire]

from a few hiking tours

burning 1000 kcal a day

[eager reef]

Holy

[surreal sapphire]

if you hike 30km a day

[sleek wing]

The biking definitely buns a few hundred calories though

[dusty wagon]

https://tenor.com/view/mujikcboro-seriymujik-gif-24361533

[eager reef]

Yeah exactly

That’s why I was wondering about the 2300

[vivid halo]

Walking burns a surprising amount of calories if you're walking a few miles every day

[eager reef]

Yes

[surreal sapphire]

ye, also if you traverse lots of height difference

[eager reef]

My main cardio while cutting is walking

[sleek wing]

I think my metabolism is just bad for burning calories

[dusty wagon]

Any good shows on Netflix

[eager reef]

Ah okay

Im the opposite

[sleek wing]

Yeah lucky

[eager reef]

Nah

Bulking is hell for me

[sleek wing]

I wanna eat 500 chicken nuggets in a day too

[eager reef]

I pretty much have to eat every meal to a point where I physically can’t eat another bite

[dusty wagon]

,w chicken nugget calories

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Theta#9545

[dusty wagon]

,w McNuggets weight

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Theta#9545

[eager reef]

But I still don’t think 3.300 is that much for a bulk

[sleek wing]

There’s 840kcal in a box of 20 mcnugs

[bright hill]

Bruh

[eager reef]

I have friends who go up to 4K and more

[sleek wing]

10k dirty bulk year round wya

[eager reef]

Im not that tall either

[vivid halo]

Friend who literally cannot put on weight because Adderall makes your metabolism insane

[eager reef]

Im like 187 cm

[sleek wing]

I’m 183cm

[eager reef]

What’s your weight

[dusty wagon]

I’m 177

[surreal sapphire]

not that tall

im literally 183cm as well

[sleek wing]

87kg

[dusty wagon]

And 71kg rn

I’m smol

[eager reef]

Your metabolism is weird then

[sleek wing]

body fat probably around 16-28% atm

*18

*48

[vivid halo]

I should use my apartment gym more

[eager reef]

Okay

[dusty wagon]

Quite a stretch

[eager reef]

Well

[sleek wing]

I did actually mean 18 fr

[eager reef]

Im 85 at a bit lower BFP

[sleek wing]

Lucky

[dusty wagon]

I remember when I could see my AB muscles

Now it’s fat

[sleek wing]

Same

[eager reef]

I don’t care about abs tbh

[dusty wagon]

It’s really nice being lean and muscular

Looks good

[eager reef]

The goal is to look insane in tanktops and wifebeaters

[sleek wing]

Ottermode gang rise

[dusty wagon]

Nah looking good naked is most important

[sleek wing]

The most important is being able to PUNCH through SOLID BRICK so if you are being PURSUED you may ESCAPE WITH EASE

[surreal sapphire]

the goal is to not die immediately once i stop working

[dusty wagon]

Rente at 75 incoming

[surreal sapphire]

also like

i used to be tired all the time

[dusty wagon]

I’ll probably die with 70

[eager reef]

good point

but like

im just not satsfied with how big i am

so i keep bulking

used to be a pretty skinny kid yk

[sleek wing]

Same

[eager reef]

but you're pretty jacked then wew aren't you

[dusty wagon]

I was fat kid maybe that’s why I prefer lean now lol

[eager reef]

16-18 bfp and 87 kg at 183 cm height

[sleek wing]

I’d say kinda jacked lol

[eager reef]

definitely

[sleek wing]

My pull muscles are shit but my push are fucking cracked for some reason

[eager reef]

makes your calories more surprising

[eager reef]

aesthetics wise or strength wise

[sleek wing]

Strength

[eager reef]

ah

[bright hill]

[sleek wing]

I can bench plates but can barely deadlift 2.5 cause my back gives out

*2 plates

[bright hill]

How tf am I supposed to satisfy this shit??

[dusty wagon]

My pull strength is insane I do +30kg pull ups for reps

[eager reef]

that is insane indeed

[eager reef]

my back extensor is kinda weak as well

[bright hill]

I'm gonna STARVE

[sleek wing]

And don’t even get me started on my stabiliser muscles I’m such a wobbly bitch

[eager reef]

benching and deadlifting is also a lot about leverages and proportions tho

[bright hill]

How much is 2 plates?

[eager reef]

100 kg

[sleek wing]

100kg

[eager reef]

sniped

[sleek wing]

~220lbs iirc

[bright hill]

On each side?

[eager reef]

no

overall

[sleek wing]

no good god

[dusty wagon]

I used to train pull ups at the beginning of every workout though 5-6 days a week

[sleek wing]

bar (20kg) + 40kg on each side

[eager reef]

i recently had to swap stance again for deadlifts

so its around 160 kg now

[bright hill]

I deadlift more than wew?

[dusty wagon]

For DB bench my PR was 36kg per hand for like 6 reps, so slightly above body weight

[eager reef]

knee issues while doing sumo

[sleek wing]

I've been trying mixed grip recently and it's been helping but my god my form just gets fucked as soon as I go over 110kg

[eager reef]

mixed grip is kinda

questionable

[sleek wing]

I have the strength to do more but it will come with a risk of DEATH

[eager reef]

i dont like it too much

[bright hill]

Oh, I'm kinda cheating with straps then

[eager reef]

yes

[bright hill]

[eager reef]

straps dont count

[dusty wagon]

I’ll get back to gym tomorrow

Probably lost all strength bruh

Like 1.5 months of inactivity

[eager reef]

my bench is around 2 plates as well

[bright hill]

My grip is weak af doe

[sleek wing]

yeah I don't have straps

[eager reef]

train it

[sleek wing]

or chalk

[dusty wagon]

I do exclusively DB bench BB hurts my right shoulder

[eager reef]

i use chalk

and hook grip

[bright hill]

Chalk is for snobs anyways

[sleek wing]

I absolutely hate how it makes my skin feel

[bright hill]

Fellas

[eager reef]

nah

[bright hill]

Don't be snobs

[eager reef]

first 3 sessions will feel bad

after that you'll slowly gain everything back

[dusty wagon]

Or mathematicians

[dusty wagon]

Yeah

[eager reef]

actually not even slowly

[bright hill]

Shit, didn't see this message

[eager reef]

its just 1.5 months

[sleek wing]

anyway darQ how much you curl

[eager reef]

i dont know how much the ez bar weighs here

[dusty wagon]

I gained a surprising high amount of fat during the inactivity tho like 3kg

[eager reef]

they can differ a lot

[bright hill]

I don't curl

[dusty wagon]

Based

[eager reef]

cringe

[bright hill]

Prolly 30 or smth

I should focus more on my biceps lmao

[dusty wagon]

Kg?

[eager reef]

i do like really strict curls tho

[bright hill]

Ye

[eager reef]

i lean forward a bit and stretch my arm fully

[sleek wing]

my standard workout:

walk in the gym
load 400kg onto the bar
3x3 sets of rack pulls with an hour rest period between each set
leave without unloading the bar

[eager reef]

for a better resistance path

[eager reef]

dude i was deadlifting a few days ago

didnt find a single 20 kg plate

looked over to the leg press

some mfer

took all of them

[sleek wing]

[eager reef]

to film 2 half reps

and then leave without re racking

[sleek wing]

lmfaoooooo

[vivid halo]

[sleek wing]

hero move

[eager reef]

told him hes an asshole

he didnt like that

[sleek wing]

dude I haven't used a leg press in so long I forgot how much I like that machine

[eager reef]

leg press fucks my knees

[dusty wagon]

Same