/sci/ - Science & Math

First for clear thinking and many nice proofs.

>watch professor leonard lecture on partial fraction decomposition for integrals before taking the actual lecture in class
>Class professor immediately goes into non-factorable denominators and on a tangent about polynomial functions of degree 5.
Why do I even show up.

Working on Basic Mathematics. Am I doing it right? Finished all the exercises on addition, gonna move on to multiplication tomorrow. Having fun so far.

talk me down from wasting time looking at modular exponentiation as a matrix

Is a mathematics major worth it if I really don't give a single fuck about money and just want to spergmaxx my research career?

>>14489605
expanded post:
[eqn]\begin{pmatrix}x^3\\x^2\\x\\1\end{pmatrix}^T\begin{pmatrix} 2&3&4&1\\1&1&4&4\\3&2&4&1\\4&4&4&4 \end{pmatrix}\begin{pmatrix}b^3\\b^2\\b\\1\end{pmatrix} \equiv b^x \pmod 5[/eqn]
holds for b = 1 to 4, x = 1 to 4, fixing b gives you an f(x) and fixing x gives you a g(b), it seems useless because f(x) involves computing the entire cyclic group for b anyway
x goes to 4 and not 0 out of convention of originally trying p(f(x)) and wanting to guarantee x^4 = 1

>finish shitty math undergrad (major gpa 3.1)
>somehow get into stats ms
>"oh neat this will be easier than my math undergrad"
>first semester is just all R coding

i feel like i made a mistake, but the money.......
wat do, i could probably do a shitty MS in mathematics instead if thrown that direction but am terrified of the lack of careers outside of research
maybe i should've just gone for education instead ;-;

>>14489724
What are you coding?
i listened one lecture data science and had the impression they already implemented everything there is under the sun. Only got to use it for your data set.

>>14489601

>no tensor algebras and multilinear forms, no exterior algebras, ignoring something like Gaussian elimination even though it acts as a baseline intuition for e.g. applying Hilbert's nullstellensatz when working with ideals, etc.
Recommend me a book with all of that please. I don't think Friedberg checks all boxes. Defining the determinant recursively is kind of uninsightful

>>14489625
It looks like the middle matrix encodes all of the mappings in the cyclic group. The left and right are basic ascending powers.

>>14489742
>i listened one lecture data science and had the impression they already implemented everything there is under the sun
They haven't.
But more importantly, R coding is usually more along the lines of "using things for your data set" than anything else.

>>14489865
if that is the case, why the row and column of p-1? they seem to appear across matrices of larger primes
also i don't have the patience to fire up sage, but these matrices can also be constructed over fixed elliptic curves where b is a point

When you were in middle school (or high school), were you ever shown a proof of the area of the square? Were you shown straightedge and compass constructions from Euclid or would those be considered too difficult? Personally I don't remember seeing any of that, though I do remember learning a tiring amount of information about triangles. I don't think I had so much as heard of the method of exhaustion before reading the introduction to Apostol's Calculus as a college freshman.

>>14489912
Can you calculate a closed-form for the middle matrix? That or a formula that describes each entry

>>14490337
there are actually a bunch of patterns that show up in larger matrices that are various differences of squares, cubes, etc., i'll work on it more rigorously if this becomes more interesting
b^(x+y) could be interesting because its equation yields (y^T)E*(b*(x^T))*E*b = (x^T)E*(b*(y^T))*E*b
the main reason to not waste time with this result is dlog on b^x would still involve iterating across the entire matrix and all of <b>

Is there some neat intuitive interpretation of ideals?
With principal ideals it's crystal clear, they just generalise multiples.
Where I'm struggling is interpreting an ideal generated by several elements. So far I've come up with:
1) Just a linear combination of the "spaces" of multiples. Not really what I am looking for.
2) Connection with Bezout's lemma. But then I discovered that it doesn't hold in every ring, only in Bezout rings, so that doesn't work either.
3) Reading on Kummer's ideal numbers is interesting but the interpretation still relies on the ideals being principal.
4) Use in unique factorisation. Still lacking something.

Can I force myself to enjoy math? I was never very interested in or particularly decent at it but I remember after returning to school from a week at science camp (no math, just earth science and being in nature type stuff) as a kid, I was intensely fascinated by math in class for around 2 weeks before regressing back to not liking math again. I'm wondering if I can recapture that feeling

>>14490405
nullstellensatz

>>14489601
>ass
>cum
>ass

>>14490408
Effectively already included in 2)

>>14489864
bump for book rec

Is there an english translation of the exposes of the seminaire cartan?

How to make money with math (boundary condition: without killing people)

I'm bad at mathematics and therefore literally worthless

>>14490405
>TA, what is the intuition behind that?
>why are we doing this?
>Can you chew this concept up for me and spoonfeed me?
>No, I can't just learn a new concept. I NEED to learn a simplistic version that is more intuitive for me and then get confused when it doesn't work anymore
>Is this like X?
>I HATE learning new things
>I hope numberphile has a hecking cool video for this, that is all I need

>>14490594
kneepad futures trading

>take joint csci/math class
>ta is a fucking retard who can't even recognize simplified fractions
My first experience with a class graded by a ta, are they all like this?

>something times 0 is no longer 0
Damn, my math class coming up with new rules

>>14491039
Inverse exponentiation

>>14491152
Would math break if it was just 0?

>>14490698
>NPC can only deal with algebraic/symbolic math and doesn't understand the need for intuition
How is life with aphantasia?

> On the surface of the planet lives a vampire that can move with the speed not greater than [math]u[/math]. A vampire slayer spaceship approaches the planet with its speed [math]v[/math]. As soon as the spaceship sees the vampire it shots a silver bullet, killing the vampire. Prove that if [math]v/u > 10[/math], the vampire slayer can accomplish his mission, even though the vampire is trying to hide.

Found this at math.utah.edu/~cherk/puzzles.html. It doesn't make sense. If v > u at all, then the spaceship can just get arbitrarily close to the planet and chase the vampire down. If the ship has to *search* for the vampire then this feels tougher than a "logic puzzle."

>>14491299
It's a physics problem. 10 is the gravitational downward acceleration. The projectile has to hit the vampire before it reaches the ground.

Heuristically doubt that. v and u are both speeds, so v/u is unit-less, not an acceleration.

Also, since we're talking vampires and spaceships, this might not even be earth

>>14491213
>NPC can only deal with intuition about math and doesn't understand the power of formal reasoning

>>14490337
upon shifting x to [0,.. p-2], the coefficients of the new matrix are:
[eqn]a_{ij} = (-1)^{i+1}[{(j+1)}^{i} - 1][/eqn]
reposted because i burnt out and typed the captcha in the message box

Anyone else read this? Pretty comfy.

>1 year into graduate math program
>developed anger issues, coworkers tell HR, at risk of losing job which is paying for the program.
>Snapped two weeks ago after paper grocery bag ripped, punched my wife in the stomach, she sobbed and cried on the driveway for 5 minutes.
>had intervention with family, must enroll into anger management classes and show improvement, or leave program.
Is this normal?

>>14492398
normal if you're on meth, otherwise you should lock yourself up until you figure out your issues

>>14492398
I don't think studying Mathematics is the problem.

why in a superalgebra is 1 necessarily an even element? it's clear to me why it can't be odd (since 1^2=1, LHS even, RHS odd, therefore 1=0), but why should 1 be homogenous in the first place?

>>14491039
Jesus Christ the state of these threads

>>14492398
>punched my wife in the stomach, she sobbed and cried on the driveway for 5 minutes.
Get your shit together nigger

Given the integral:
[eqn]\int_{0}^{1} x^{\frac{-9}{10}} cos(x)dx[/eqn]
We introduce the variable change [math]x = y^{p}[/math] and choose a [math]p[/math] to get rid of the singularity in the integral so that we can use scipy.integrate.quad() and scipy.integrate.quadrature()
[eqn]x = y^p \Rightarrow x^{\frac{-9}{10}} = y^{\frac{-9p}{10}}[/eqn]
I don't understand how to go about this. If I just do the simple variable substitution and choose [math]p = \frac{-10}{9}[/math] but then the value inside the cosine function becomes a singularity so we can't just do that.
If I just leave the p as is and substitute the variables then this is what I get:
[eqn]\int_{0}^{1} p\cdot y^{\frac{p}{10} - 1} cos(y^{p})dy \ \textrm{since} \ dx = p\cdot y^{p-1}dy[/eqn]
So then we have that [math]p\geq 10[/math] but the computer integration still fails even if I take values larger than 10.
Any ideas?

>>14492690
Why are you studying superalgebras if you get stuck proving this sort of stuff?
Assume [math]1 = a + b[/math], where [math]a[/math] is even and [math]b[/math] is odd.
[math]a = 1a = (a + b)a = a^2 + ba[/math]. Since [math]ba[/math] is odd we know that [math]ba = 0[/math].
However [math]b = b1 = b (a + b) = ba + b^2 = 0[/math], so we're done.

>>14492779
va

>>14492398
Are you black?

so um, I've got a bit of a tard question here.
I got my math degree at a 5th rate university and I somehow landed a gig at Cornell, and they said they would pay like, one class a semester.

I'm pretty sure that I am completely unqualified to take any mainline graduate math class there. Should I just yolo it and see where I land or is there a way to skill check myself before throwing myself into incinerator and wasting everyone's time?

>>14492779
Nevermind I managed to finally solve this.

>>14492779
>>14492945
I took [math]p=10[/math] and ended up with:
[eqn]\int_{0}^{1} x^{\frac{-9}{10}} cos(x)dx = \int_{0}^{1}y^{-9} (10) y^{10-1}cos(y^{10})dy[/eqn]
[eqn]=10\cdot\int_{0}^{1}y^{-9} y^{9}cos(y^{10})dy[/eqn]
[eqn]=10\cdot\int_{0}^{1}cos(y^{10})dy[/eqn]
[eqn]\approx 9.7718427[/eqn]
Which is also the value I get via the online integral calculator.

>>14491883
Simon Singh's books are all bangers.

>>14492922
Is this for a master's?

>>14492779
How come I can only expand this picture when I have my mouse on the edge of it?

>>14493223
because of the tex code used in the post. html bug

>>14493050
>Is this for a master's?
it would be just to take classes
I know I'll never be PhD material and even then, I would have to suck more dicks at Cornell then all the there are phone scammers in india for one of them to raise an eye at the idea

>>14492788
fuck you, weeb

>>14492448
>on meth
I drink espresso all day every day, would that have a similar effect to meth? I've gone to a few therapy sessions but its too early of a stage to really get into it.

>>14492881
French Canadian.

Maybe its advanced linear algebra getting to me.

>>14489742
I mean, yeah, but using ggplot2 and dplyr for everything under the sun is a far cry from doing a t-test or even evaluating a density function. I think I'll just shut up and try to learn it but all I've done so far is edit example code to finish exercises lol

in short, I came expecting prooving thing, not "manipulate object and do test 20 times over" but I guess that'll be the entire first year or so ;-;

>elliptic curve factors an integer in reasonable time because... uh it just does ok

if [math]V=\langle b\rangle[/math] is one-dimensional, how to show the Clifford algebra [math]\operatorname{Cl}(V,q)\cong\mathbb{K}[x]/(x^2-a)[/math], where [math]a=q(b,b)[/math]? since [math]1[/math] and the image of [math]b[/math] in [math]\operatorname{Cl}(V,q)[/math] generate the algebra, it makes sense there's a surjective homomorphism of [math]\mathbb{K}[x][/math] onto [math]\operatorname{Cl}(V,q)[/math] which factors through [math](x^2-a)[/math]. how to show the factored homomorphism is an isomorphism?

What schools in the US are good for Set Theory? (Besides the obvious ones Berkeley, Madison, etc.). I want to go into foundations but I highly doubt I'm gonna get into a tier 1 university.

Genuine question, is there something off with University of Arkansas math department?
It seems strange that living nowhere near Arkansas, I've met so many PhD graduates from there.

>>14494893
The result follows immediately from a dimension count of the domain/codomain

>>14495035
i know the dimension of [math]\operatorname{Cl}(V,q)[/math] *should* be 2, but how could we prove the above w/o this result?

>>14495069
It's unavoidable that you are going to need to use the definition of the Clifford algebra.

If you want to show injectivity directly, you are going to need to write down what an arbitrary element of the Clifford algebra looks like. This amounts to picking a basis, which gives you the dimension for free. So you may as well just use a dimension argument.

>>14493801
If it's not too difficult practically (getting to classes, etc), then of course. Your grades won't matter, and you get the opportunity to go to a top math department and learn something new.

>>14495069
[math]K[x] / (x^2 - a) \to Cl (V, q)[/math] is surjective, as you've already pointed out, and injective as a map between [math]K[/math] vector spaces, since [math]K[x] / (x^2 - a)[/math] has two dimensions and [math]1[/math] and [math]x[/math] have different images.
Injective as a map between vector spaces implies injective always, naturally.

>>14495101
the problem is in the source i'm reading the dimension formula and injectivity are proven by decomposing an arbitrary Clifford algebra into a graded tensor product of such elementary ones, which are a priori assumed to be 2-dimensional, so doing it at as you suggest would result in circular reasoning
>>14495174
>and 111 and xxx have different images.
but how do we know that? why can't it be that x=1 and the algebra is 1-dimensional? i guess the crux of my question is how, proceeding from the definition of a Clifford algebra (quotient of tensor algebra), to show that 1 and a non-zero vector x are linearly independent

Are numbers... outdated?

>>14495213
If [math]\lambda \cong b \mod b \otimes b - a[/math], where [math]\lambda[/math] is any multiple of the identity, then [math]\lambda - b = v \otimes (b \otimes b - a)[/math]. Left side has gradation 0 plus gradation 1, right side has gradation n and gradation n + 2. They trivially can't be equal.

>>14495253
>right side has gradation n and gradation n + 2
Actually a bit trickier than that but I'm sure you get the concept.

>>14489025
Suggest an actually good introduction to tensors for mathematicians, please no weird physics shit.

>>14489025
>Be in grad school
>PDE class
Its functional analysis
>Numerics class
Its functional analysis
>Optimal control class
Its functional analysis
>Control theory class
Its functional analysis
>Image processing class
Its applied functional analysis
>Machine learning algorithms for comms/mathematical methods of signal processing
Its also functional analysis

Its functional analysis the end all be all of applied mathematics?

hello math gods.

how do i use to solve for x and y? the wall in my house is too tall for a ladder unless i get something specialized.
i could find a really long stick and some string but it would have to be an extremely long stick and this is a perfectly acceptable alternative.

>>14495253
>>14495261
so, just to be as thorough as possible: since [math]V[/math] is 1-dimensional the ideal generated by [math]v\otimes v-q(v)\cdot 1[/math] is equal to the 2-sided ideal generated by [math]b\otimes b-q(b)\cdot 1[/math], so if [math]x=1[/math] in [math]\operatorname{Cl}(V,q)[/math], then [math]b-1=y\otimes(b\otimes b-q(v)\cdot1)[/math] would hold for some [math]y\in T(V)[/math], but this would mess with the grading
correct?

>>14495314
pardon, meant to write [math]x=\lambda\cdot1[/math]

>>14495314
>>14495337
wait a sec, [math]T(V)[/math] is not commutative, how do we know [math]b-\lambda\cdot1=y\otimes(b\otimes b-q(b)\cdot1)[/math]? shouldn't it be something more like [math]b-\lambda\cdot1=\sum_iy_i\otimes(b\otimes b-q(b)\cdot1)\otimes z_i[/math]? what do we do now

>>14495300
reposting b/ i fucked up the angles, oops.

>>14495349
>>14495314

Not OP, are these topics you would bump into in a linear algebra course?

>>14495297
>algebraic topology
It's algebra
>algebraic geometry
It's algebra
>homological algebra
It's algebra
>algebraic number theory
It's algebra

Is algebra the end all be all of pure math?

>>14495149
wouldn't my failure possibly ping the professor or the department's average GPA? I mean I doubt it would even matter, but I know some graduate departments that are tyrants about keeping out anything less then a 3.0 average

>>14495404
You just wasted perfectly good bait for no reason.

>algebraic topology
It's category theory.
>algebraic geometry
It's category theory.
>homological algebra
It's category theory.
>topos theory
It's category theory.

Is category theory the end all be all of pure maths?

Why algebra books don't have a single limit or integral in them?

>>14495401
split into a rectangle and a square. then use tangent function.

>>14495505
>square
i meant triangle

>>14495505
>>14495507
ooooohhh thanks, i think i got it. i vaguely recall this in 11th grade...

Is the study of p-adic numbers (topological, algebraic, analytical, geometric) an active field? Is it as relevant to number theory itself as it is for other fields?

>>14495430
I doubt it. Most professors enjoy having people in their classes who try hard.

The mentality that you're guaranteed to fail isn't the best though. Sure, it's Cornell, but they accepted you because they thought you had a chance there, might as well try and learn something out of it. Your classmates might honestly feel similar, imposter syndrome is real.

>>14489025
>Go to undergrad with absolutely brilliant class mate
>Dude got perfect scores in all of his class
>Once even witnessed how he read an entire book on set theory like a novel in about 2 weeks
>Got invited to do a phd in set theory and logic at a top american uni
>Refuses to learn any practical skills whatsover such as programming or data science
Is this mans career basically over already? Or does someone as smart as him has an actual chance at making a professorship?

>>14496387
don't be jelly, man, the guy's good as long as he stays outside of the univalent club of autists
and even if he wouldn't, he doesn't neccessarily have to play around with constructible models, there are plenty of open problems for him

>>14496387
>set theory and logic
>practical skills whatsover such as programming or data science
These are not mathematics.

>>14489601
Abbreviate "ass" as "assoc. prop." and "cum" as "commun. prop." before you turn this in please

>>14496545
Don't have anyone to turn it in to, except you, baby. Thanks for the (You) though, helps me keep going!

By the way "comm." stands for commutativity so "commun. prop." doesn't seem right.

I miss old /mg/. Nu-/mg/ is trash.

>>14496991
Tell us ancient one, what was it like? What was it like in ye olde /mg/?

>>14496991
I MISS THE OLD EM-GAY
TOP OF THE TOPOS EM-GAY, MATHEMATICAL FOCUS EM-GAY
I HATE THE NEW EM-GAY, NO ANITRANNY EM-GAY
FILLED WITH FOOLS EM-GAY, RIGHT OUT OF SCHOOL EM-GAY
I MISS THE SMART EM-GAY, THE PHD EM-GAY
I GOTTA TO SAY AT THAT TIME I'D LIKE TO LURK EM-GAY

>>14495149
Don't listen to , >>14496117
please fuck off and don't waste our time. If you're really from a 5th rate institution, imagine being the only guy with down's syndrome in a class at your alma mater. That's exactly what's going to happen to you here. No one will have patience to deal with you, no one will have time to hold your hand to wipe your ass with a trivial proof.

Just
fuck
off.

I've been putting in a consistent 3 hours minimum of mathematics study daily for the past year and a half, no breaks. When do I hit the "mathematical maturity" milestone where I evolve like a fucking pokemon? 10000 hours? I will have less than 5000 hours of mathematics after completing a 4 year degree.

>>14497594
I was going to call you a gatekeeping faggot, but then I read his post again and saw that its for graduate studies.
I don't want to be mean like you, but he should prepare himself at the least for possible failure. If he can't make it at a top school grad program well hey, he gave it his best effort you know.

>no one will have the time to hold your hand
Well, that is for them to decide isn't it? And right now, they decided to let him in.

>>14497375
It was about the same

>>14492398
Dude WTF, what's wrong with you?

>>14496427
Im not jelly, i really admire him, hes not only smart but an amazing person and a really good friend, and Ive long come to terms with the fact that there are people out there not just smarter but actually much smarter than me.
I would just sincerely hate to see him crash into a wall after he's done with his phd just because the word "python" is not written on his cv

>>14497594
They should obviously come to terms with the fact that they'll get blasted, but it already feels like they know that lol. Doesn't mean that they shouldn't try. >>14497600
Exactly.

>solving integrals by immediately noticing if they're divergent, infinite, doing u-sub in my head
Progress feels good. power level increasing. What killed me yesterday is today's warmup.

>>14497600
>Well, that is for them to decide isn't it? And right now, they decided to let him in.
No, they didn't. He got in via the trash shoot by landing a gig. I'm guessing his job is paper pusher or more likely janitorial.

Don't sugarcoat it. Don't try to put lipstick on this pig of a profession. Professors gatekeep all the time. That's 1/5th our job. He needs to
fuck
off.

>>14497975
If you're so angry about it go work somewhere else. According to you, your employer does not respect you or your field.

>>14497595
It's a leap of faith.

>>14496387
idk his career path seems pretty set to me

>>14498424
Carlos!

Are math professors NPCs? I mean who the fuck wants to see huge ass technical proofs on the blackboard? We can all read this shit in a textbook much faster. If your lecture doesn't provide intuition on the topic then it's a waste of time and financial resources.

>>14495297
you aren’t in a math program.

>>14498808
This is the worst rping accusation I've ever seen. There's literally nothing weird about his post unless you're a computer scientist undergrad who feels that graph theory is being underrepresented. Even if you're an applied mathematician who does something that doesn't really use FA like integer programming you'd still be aware of the importance of functional analysis.

>>14498011
I fucking am. Worked 15 years on getting tenure, I get it and it wasen't worth it. During those 15 years I could have been at my most productive, but I get handed the shit detail, teaching freshmen how to wipe their ass and graduate students how to wash their hands.
>>14498588 is fucking right, I don't bring my intuition into the lecture because its pearls before swine and they don't pay me enough.

Listen, >>14492922, I don't hate you. Props on you for realizing you're a guppy cleaning up the messes of whales. Takes a big person to admit that. But stay out of our way, its one less student we have to chew the finer parts of this discipline and vomit into their mouths.

>>14498885
A bit egotistical don't you think? I only have a masters, but my entire time in school consisted of half asses lectures, and the actual learning done while hunched over a desk reading books and papers on a laptop. Outside the last stretch (I did research option) where I had some marginal assistance, professors were fairly useless.
Maybe that comes out wrong, but what I'm trying to say is that no one expects you to give anything more than the bare minimum to students as it is. If you were unable to perform at your best, you can't really fault having to teach classes for that.

>>14489601
1. Funny abbreviations;
2. Congratulations on your efforts to Lear mathematics. You are doing great and I hope you go far.

>>14491717
OT but the thumbnail of your image made me think you were a based navelchad and expanding it made me feel betrayed. Thank you.

>>14490407
imo the trick is to realize that math can be used to engage with any other field of study

consider it a road to understanding, and it makes it easy to pursue

Teaching myself all of math following
https://www.youtube.com/watch?v=pTnEG_WGd2Q
does /mg/ agree with his recommendations?

Aight /mg/ I need help understanding this very basic construction with manifolds. I am having a hard time wrapping my head around partitions of unity and using these to construct smooth extensions of functions. Why is it that I can use these functions to extend a smooth function f from an open set U to the reals using its restriction to a closed set K to get an extension to all of M? I understand I can get an open cover using U and M\K and that I get a partition of unity, but it's hard for me to visualize this. Do I then just get 2 smooth functions from each open set that I can use to weight f? I feel stupid.

If I apply my math skills to trading, will I get rich quick?

>>14498863
no i'm saying that by the classes he listed he isn't in a real math program. he's an applied math/CS guy. neither are real math. I like pointing out when people are pretending to be something more prestigious or important than what they are because it's funny and their behavior is embarrassing.

>>14499647
Are you a complete idiot or something?
How am I "pretending to be something im not" read my post you absolute twerp.
Also, kill yourself tryhard gatekeeping faggot

>>14498885
Shut the fuck up, just shut the fuck up.
Youre just propping up your own ego and importance at the expense of a poor fellow that might just have gotten the biggest opportunity of lifetime, you called him a guppy but youre a soulless faggot rat yourself.

To the Cornell anon, please pay no mind to the naysayer tards itt, I got started with math at the end of my bachelor's in EE, I started by taking analysis, when I asked for some tips here I had a bunch of idiots come out of the woodworks to tell me how much better thet where than me and how I was going to fail as a lowly engineer. I ended up acing all of my math classes and double majoring, im now doing a masters at a top uni and its going very well.
Moral of the story, seize the opportunity, try hard, learn a fuck ton. Good luck

>>14489025
Is anyone here heard of/planning to register for the
upcoming 2022 IGMO?

What should I brush up on before my Masters? I was thinking of reading some analysis.

is Euler's identity beautiful?

>>14499647
kys retard
>is functional analysis the end all be all of APPLIED MATH

>>14500075
no

>>14499647
Okay, LARPer kid. Name one nontrivial mathematical result you discovered on your own.

>>14500075
no, but [eqn]x \in \mathbb{Q}[/eqn] iff [eqn]e^{2xi\pi} \ncong S^1[/eqn] isn't bad

>>14501518
*forgot to make it the set of integer powers of that exponential but you get the point

>>14501518
>>14501554
hmm, you mean a number is rational iff that exponent doesn't generate S^1? i can see one direction i think (if it's rational, then the subgroup generated by it should probably be finite), how do you show the other direction?

>>14501728
i'm sloppy and handwaved a bunch of analysis results so don't take that result as necessarily correct
for instance how can integer powers map 1-1 to S1

>>14501518
>>14501554
Forgot to ask for a closure too.

>>14497595
You'll know when you know.

>>14499614
Disagree, the video is quite clickbaity, specially the FINISH since every one knows that math never ends. Also the topics discussed in the video aren't even that advanced. It helps if you want some initial recommendations, but I'd say they get short very fast.
This site is filled with charts, some are quite memey, but any chart is partially useful in the beginning, just remember to change it when you feel like it. If you go to uni, take your time to check the math sections in their libraries, since they are generally filled with good textbooks.

I have a BS in Comp Sci done. Should I add a BS in Math too? Is it worth it?

>>14502036
only if you enjoyed calculus 2 and didn't take some kind of numerical computing course

>>14502106
for my degree they have us take
>discrete math
>linear algebra
>combinatorics
>calc 1 and 2
I can do
>math minor in 2 courses
>math BA in 5 courses
>math BS in 8 courses

>>14502133
>linear algebra without matrix conditioning
>no numerical integration or finite element methods
>nothing to explain fft, much less any differential equations
ya no

>tfw you finish a proof of something that confused you for month

>>14499687
Looks like the competition is starting up...

>>14496991
>I miss old /mg/. Nu-/mg/ is trash.
Same, I even miss the Yukari poster, if you can believe it. At least he talked about math.

>>14499635
Trading is not about math. In fact your mathematical models are worthless here, as they (wrongly) claim you can never beat the market (a fucking martingale lol). Trading is about collecting relevant information as soon as possible, before it becomes news, and acting as soon as possible. Ideally you're an insider.

>>14502612
What about jobs that hire if you know "mathematical finance" then?

>>14489025
I hate math. I have pretty good mathematical intuition and a strongly analytical mindset, but I just can't handle mathematical notation, on a purely psychological level. As soon as I see it, my eyes glaze over and my mind stops trying to interpret the information. It just looks like a schizo symbol salad and the mere thought of trying to decipher it, immediately tires me. Why do you little sinkers always use single letter variable names? Why do you use such obtuse syntax and rely so heavily on operator overload? Why does mathematical notation look like a fucking APL program? Unfortunately, I find myself in a position where I need to get through a bunch of books full of your stupid notations. How can I cope with this?

>>14502678
>I have pretty good mathematical intuition
What kind of rotations are possible in 4 dimensions which you can't reproduce in 3 dimensions?

Why have you not gotten a $300k+ job in machine learning or quantum computing yet?

>>14502691
Because I reject the industrial-technological system.

>>14502686
ones lacking a fixed axis from two pairs of complex eigenvalues
babby's first linear algebra

>>14502702
>complex eigenvalues
Algebraist cope. Not a valid answer when asking for intuition.

>>14502706
the eternal analyst
spends his days reducing his arguments to less than nothing until one wonders whether they truly existed at all

>>14502686
1D -> 1 plane -> 1 rotational DOF.
3D -> 3 plane -> 3 rotational DOFs.
4D -> 6 planes -> 6 rotational DOFs?
If you're asking for an intuitive answer, there it is. I could probably sit down with a piece of paper and figure out a rigorous one but either way you sound like a fag and I don't like you.

>>14502720
>1D
I mean 2D.

>>14502720
rotations of odd dimension are guaranteed at least one fixed pole somewhere on the surface
even dimension has no such guarantee (2d has every point on the surface move if the rotation is nontrivial)

>>14502726
Don't know what you're on about, but I just checked and I was correct.

>>14489864
I just used my professors script :^)

>Fall down seven times, stand up eight
Thoughts?

>>14502158
>for the minor I would take calc 3 and a stats class
>for the BA I would take the previous 2 courses plus diffy q, a proofs course, and abstract algebra
>for the BS I would take the previous 5 courses plus two topology courses and complex analysis

>take complex analysis
>turns out its not complex at all, just tedious
can we call it tedious analysis now?

>>14503060
That's why it's called anal.

>>14502678
You should see some code that mathematicians produce...

>>14502678
same

do proofs exist in the platonic realm or do only the results?

>>14503154
>>14503258
>>14502678
Faggots

>26
>never learned calculus
>want to learn math
It's over isn't it

>>14495950
someone.. please.. im such a motivated aspiring mathematician that i dont want to lose myself in some dead research area

>>14504086
No, it's not. The best time to enjoy math is after college. Nothing ruins love for math as much as institutionalized learning.
Learn math and learn to take your ego out of it. Your progress on most things is inversely related to your ego investment.

To most people on the Internet, everything you do is "shit" anyways. Most people who have nothing but negativity are brainlets. It's teenagers in their angry phase or people who have never grown up. The brightest people were always encouraging. Listen to people like that and do not believe anything is too old.

>online math quizzes every week, worth barely any points, but still worth SOMETHING
>me, obsessed with winning and points
>spend upwards of 5 hours every weekend on these fucking quizzes
>problems aren't even fun, just super computation intensive

>>14504242
It probably still was good exercise.
There are different things that motivate different people. There is also healthy competitiveness.
But then there are also people who think too much about impressing other people. Then what happens to your goals in the cultural direction we are in now? Suddenly, everything is relative, we cannot tell women from men, facts do not exist.
Does anyone here really want to build their future and their goals on such a thing, on such a capricious thing as what society and others value? That's like building castles made of sand.

To hell with impressing other people. Do math because it's beautiful. And, as a bonus, there is nothing second to that has ever made people great. Sure, there was the notorious competitiveness of people like the Bernoulli brothers and mathematicians sending each other challenges. But deep underneath I am convinced that the primary motivating factor for them was a deep awe for the beauty of math.
https://web.archive.org/web/20080329153035/http://curvebank.calstatela.edu/brach3/brach3.htm

People who just want to inflate their ego, for e-penis, always run out of motivation eventually. If you compare yourself to someone worse then yourself, you hamper yourself. If you compare yourself to someone better than yourself, you become depressed. Quit that nonsense and stop seeing math as something to inflate your ego with, or something purely for a pay check. If you cannot see the beauty in math, quit now. If you can, do math no matter what.

>>14504270
what the fuck does sex or gender have to do with absolutely any of this

What is an ectomorphism in math? When I try to search it on the internet all I get is this pseudoscientific body type theory.

bros help how do i get a whiteboard for cheap

>>14502649
Thats just using your insider information to make correct calls

>>14504599
Check govdeals if you're in the US. Surplus sales in general are good.

>>14504599
Depends on what you're after. You can probably get a handheld whiteboard (which you can then perhaps mount on to something with minimal tooling) for cheap online.

>>14504824
no no no, i need a behemoth. the window i've been using (~2.75 by 3.25 forearms) does not cut it at all

>>14489025
Help pls
I have that [math]u \in L^1(a,b)[/math] with [math]u(x) = \int_{x_0}^{x} v(t)dt[/math] for some fixed [math]x_0 \in [a,b][/math] now I need to show that the weak derivatice of u is v, but without using the fundamental theorem of calculus on u.
Now, I quickly get that
[math]\int_a^b \phi'(x) \left( \int_{x_0}^{x} v(t)dt \right) dx = \int_{x_0}^x v(t) \left( \int_a^b \phi'(x)dx \right) dt = 0[/math]
Am I misremembering fubinis theorem or something?

How do you find a suitable N in the analysis of convergent sequences that aren't defined by closed formulas?
For example in 1/x, for a given ε, N>1/ε ensures the series is bounded away from the limit at a max of ε.
I don't see how you could derive such an N if the sequence doesn't have a closed representation.

>>14505535
You can try and get an upper bound on the distance from a proposed limit in terms of something like 1/N which you can then use to prove there exists N where it is less than epsilon away. It's hard to be more specific without an example really

When a female mathematician says she's interested in knot theory, that means she's a bondage slut, right?

>>14505800
No, it means she'll tie someone's dick into a knot
in so many ways the guy will beg to just have a
knot polynomial computed for that. It's the ultimate kink.

>>14505149
Your second expression doesn't even make sense. You can't integrate to x, when x only gets defined inside the second integral.

I'm new in /sci/, this is what i've learned so far:
>best math field is category theory
>real numbers don't exist
>in fact, infinity also don't exist
>axiom of choice is wrong
>set theory is wrong, homotopy type theory is superior
>euler's identity is bad
>0.999... is not equal to 1
Am I missing something?

>>14506042
Probability is always 50%. Either it happens or it doesn't.

>>14505886
What?
By the way I already solved it, if anyone wants the solution ill post it

>>14506161
Post it, please.

>>14506161
>What?
His post is very straightforward and on point, have you tried rereading it?

>>14506195
Note that, first w.l.o.g you can set [math]x_0 = b[/math]
[eqn]u(x) = \int_{x_0}^x v(t)dt = \int_a^b v(t) \mathbf{1}_{\{t \leq x\}}(t) dt[/eqn]
Then:
[eqn]\int_a^b \phi'(x)u(x)dx = \int_a^b \phi'(x) \left( \int_a^b v(t)\mathbf{1}_{\{t \leq x\}}(t) dt \right)dx \\
= \int_a^bv(t) \left( \int_a^b \phi'(x) \mathbf{1}_{\{x \geq t\}}(x) dx\right)dt\\= = \int_a^b v(t)(\phi(b) - \phi(t))dt\\
= - \int_a^b v(t)\phi(t)dt[/eqn]
Typed this on my phone on the train so if anythings wrong then whatever

[eqn]|\{(x,y)| x^2 + dy^2 \equiv 1 \mod p\}| = p - \left(\frac{d}{p}\right)(-1)^{\frac{(p-1)}{2}}[/eqn]

ew, what book do i need to look in to find this result?

>>14506336
>anythings wrong

>w.l.o.g you can
Not really a wlog you can handwave away without an explanation.
Sign's wrong on the very first equation, [math]\displaystyle \int_{x_0}^x v(t) \ dt = - \int_a^b v(t) \mathbf{1}_{t \leq x} (t) \ dt[/math], doesn't really matter because the signs cancel out on both sides.

>>14506365
That's just a simple application of quadratic reciprocity, so any elementary number theory book will do.

>>14506375
>doesn't really matter because the signs cancel out on both sides
I dont see how you would have the minus sign there on the first equation
The ansatz works wlog as u is only really defined from x0 onwards, so who a is doesnt really matter as long as its less than x0

>>14506375
Actually I fucked up too, it's [math]\displaystyle \int_{x_0}^x v(t) \ dt = - \int_a^b v(t) \mathbf{1}_{t \geq x} (t) \ dt[/math].
>>14506408
>I dont see how you would have the minus sign there on the first equation
[math]\int_a^b[/math] goes from left to right. Since [math]x \leq b[/math] (since the function domain is [math](a, b)[/math]), [math]\int_b^x[/math] goes from right to left. To pass in the indicator and flip the direction of integration you need to flip the sign.
>The ansatz works wlog as u is only really defined from x0 onwards, so who a is doesnt really matter as long as its less than x0
Lad did you actually completely forget about how integration from right to left works?

>>14506443
Why are you trying to reverse the order of integration?
The indicator function is not doing that here at all
Your formula does not hold

>>14492398
If you're a mathematician you will know that simply depends on how normal is defined.

>>14506387
i guess, but group order on a curve throws me for a loop
also i keep forgetting there's only one class of two-dimensional conic mod p

>unit ball is non-compact
>unit ball is contractible
>no non-trivial, locally finite, translation-invariant measure
What are some more geometric things we take for granted in finite dimensions but break down in infinite dimensions?

>>14506675
*unit sphere is contractible

>>14506675
Isometries (maps [math]T: V \to V[/math] such that [math]\| Tu \| = \| u \|[/math]) aren't necessarily bijective.
Vector spaces can be made topological vector spaces in multiple ways.
The orthogonal complement of the orthogonal complement isn't necessarily the original space.

>>14506737
Pls explain what topological vector spaces are
A vector space for which you define a topological basis?

>>14506744
A vector space equipped with a topology compatible with its algebraic operations.
That is, addition of vectors and multiplication by a scalar are both continuous.

what did i do
>>14506365 has p +/- 1 elements, but the order of single elements under clock addition can be p^2 - 1

>>14505149
I maintain that your second expression doesn't make sense, the expression should've been [math]\int_{x_0}^bv(t)\left(\int_t^b \phi'(x) dx \right)dt[/math], but your proof idea does work:
[math]\displaystyle \int_a^b \phi'(x)\int_{x_0}^x v(t) dt dx = \int_a^b \int_a^b\phi'(x) \mathbf{1}_{\{x_0\le t\le x\}} v(t) dt dx=\int_a^b v(t)\mathbf{1}_{\{x_0\le t\}}\int_a^b \phi'(x) \mathbf{1}_{\{t\le x\}} dx dt = \int_{x_0}^b v(t) (\underbrace{\phi(b)}_{=0}-\phi(t)) dt[/math]

ignore >>14507202 i'm stupid and chose an invalid point

Anons, can someone help with this log. This comes out to a cubic equation and my prof said that we don't have to solve cubic equations, just quadratic.

I don't have have to solve for x, just have to get the left and right side to be equal.

I have been trying to solve this since yesterday, please help.

>>14507495
>we don't have to solve for cubic equations
>i don't have to solve for x
what's the problem?

>>14492398
get a head scan, you might have a tumor or something wrong with your mind

This theorem seems way too strong to me, the sequence (-1)^n for example has two obvious subsequences which tend to 1 and -1 respectively, but the sequence oscillates at infinity.
Am I missing something? Did the author just forget to say that it's specifically concerning monotonic sequences?

>>14508013
Looks like it's just a badly formulated "if every subsetquence tend to b"

On second thought, the theorem sounds entirely like a tautology, given the premise directly implies that the sequence also has the limit.
The book also doesn't look math-academia credible, given that it denotes \infty as a "limit" too.

>>14508036
Not quite a tautology:
If every *convergent* subsequence has the same limit, then the sequence is convergent. The premise doesn't require that every subsequence is convergent. If the limit is finite, then the result seems intuitive to me

>>14507495
>2log6(2x) on the first line
????

>>14507495
Do you see that all of them have base 6? 6^log_6(x) = x

Do math questions go here or /sqt/?

I'm a brainlet who only studied math up to basic calculus and whose stats classes were a complete joke, stuff that should've been taught in high school instead. With that in mind, what path should I take until I understand Gibbs' inequality and information entropy? It seems to be stats but I'm dumb.

>>14508662
Post in whichever, no one really cares anymore.

>>14507495
Everything seems correct so far...
You're gonna have to solve the cubic, anon.

>>14508662
Depends on whether the question is stupid.

>>14508734
>>14508762
Well i think im stupid for even wasting time with this but idk about th question itself. Okay so im trying to prove

[math] \eta(-\frac{1}{\tau})=\sqrt{-i\tau}\eta(\tau) [/math]

by first showing they have the same logarithmic derivative and then showing the constant they differ by is just 1. I know there are several ways to do this and the most obvious one is to use Eisenstein series which i have done but just out of curiosity i tried explicity computing the logarithmic derivative of both sides and unless i did something wrong it seems like they differ by a constant of [math] 1/ \tau^{2} [/math], so they are not the same. The weird thing is that it shouldnt be a hard derivative to compute as its just a product, but im not getting it.

So basically all i want to know is what is thess expressions:

[math] \frac{(\sqrt{-i\tau}\eta(\tau))'}{\sqrt{-i\tau}\eta(\tau)}[/math]

[math] \frac{(\eta(-1/\tau))'}{\eta(-1/\tau)}[/math]

are but not in terms of Eisenstein series.

Of course i mean Dedekind eta function where tau has positive imaginary part.

>>14508839
Why are you using the formula for the logarithmic derivative instead of the product property of the logarithm?
>inb4 'the product property doesn't work for complex logarithms'
An integer multiple of [math]2 \pi i[/math] pops in, yeah, but it vanishes when you take the derivative, no?

>>14508013
The theorem is exactly equivalent to the following proposition

"If every convergent subsequence of (a_n) converges to b, then a_n converges to b".

That's the correct proposition. The sequence (-1)^n does not satisfy the proposition's hypothesis.

I believe the ambiguity in the theorem's redaction relies on the phrase "..then IT tends to b..", as it can be understood that "IT" refers to (a_n) and not the aforementioned subsequence.

>>14506675
meds

>>14509042
The reason why I (>>14508036) said it sounds tautological is that the sequence itself is a subsequence of itself.

Let's have a look at the contraposition:
>If a_n doesn't converge to b (say 777), then not every convergent subsequence converges to b.

Well okay, if a_n is known to be convergent, then this is literally trivial.
If I don't know if a_n is convergent, then the theorem doesn't help me as to establish the if-part, I need to establish the conclusion (what a_n converges to)
If I know that a_n is not convergent, then the theorem is not interesting.

So it seems like a bullshit theorem to me

Just found out I'm a brainlet. I don't have the spatial intelligence to understand Boy's surface.

>>14489724
That's how it should be. Ideally you should be proving things and working on the basic fundamental algorithms side by side, but first semester graduate statistics is mostly paper derivations with simple code because it's catering to a very wide audience.

Either way, the majority of your work will be coding. That's what you do in all the applied maths essentially. Proofs typically are seen more as tools for justifying techniques and algorithms and less as their own thing if that makes sense. Although, you should be in at least one pure theory course and typically you have to take a sequence of theory (which typically doesn't much coding), but the real meat (and where the money and employability is) is coding and understanding why and how algorithms work and when to use them.

You will continue to code entirely in R and if you don't like coding I don't know what to tell you. Personally I find it to be pretty beautiful and the best way to actually learn statistics which relies heavily on theorems associated with many observations.

>>14492922
You're gonna be fine. Graduate math is honestly easier than undergrad despite what you may think. It's just work.

You probably noticed in undergrad that while your later classes were more work, the path to knowledge seemed much clearer. It just keeps getting clearer to the point that my graduate classes (which are objectively more complicated than my undergrad classes) are nothing compared to what I had to go through for some of my undergrad work. A lot of times you're entering these undergrad courses with maybe a match at the beginning, in grad school you typically at least have a torch. It also takes longer to study more complex topics, so you have plenty of time to chew and digest (especially if you're only doing a class a semester).

>>14495297
Yeah more or less. But there's good reason for that. Most of these courses are computation focused and functional analysis is very translatable into matrix theory which a computer can handle.

In most applied math you're ultimately trying to make your problem discrete and in some type of matrix form so that you can actually solve problems.

Lol. Some of these are devious and I can imagine the fun someone had making traps for people to fall into...

>>14496387
That's a very weird choice since he will have to program at some point. Programming is just a tool you use, just like writing. Tell him he should learn at the very least to write better papers. If he has a visual simulation of anything he's working on, his paper is going to have much wider appeal.

Also, he's in threat of having his work become forgotten. Personally, I find math without practicality to be pretty disposable. It's the first type of math to be lost because there's no value in preserving it. It's better to spend your efforts on work that will have some clear use either now or in the future. It also makes your work much less likely to be recreated needlessly.

>>14509346
just realized its sec^2(x) and a much simpler problem.

>>14502678
Meh, it's pretty straightforward. I guess some authors like to go hard on autistic notation, but that's normally more so because they're trying to be as general as possible.

There's a lot of basic texts in any of the fields that will hand hold your way through the notation as long as you're aware of the very basics.

You might just be a midwit too.

>>14504599
Go to Home Depot or Lowe's and buy a melamine sheet. They are huge and cost probably about 30 bucks. Lowe's and HD will even cut it to your desired size.

They may smear a little but those suckers will last you ~2 good years.

>>14509311
Where are the major humps for undergraduate and graduate math majors? I get discouraged real easy and don't have friends or a support system for this, so I rely on math sorcerer motivational videos I put in a playlist... its just good to know I'm not the only one suffering at a certain stage or class, and I need to know what semesters to keep clear for one big bad course(I've heard abstract algebra is one of the hard courses)

Me thinking about the Ruliad.

>>14509377
Abstract Algebra and Real Analysis both were very difficult for me when I took them. They opened my eyes to many other problems later though, but at the time it was a lot of struggling.

Similarly, people tend to struggle in Calc 2 or 3. I didn't have the best spatial reasoning at the time so Calc 3 was difficult for me.

There was nothing more difficult than my physics courses though. Math Physics and Quantum Mechanics made my head spin, not necessarily because of interpretations or any bull like that, but because you had to just learn so many mathematical techniques and 'tricks' and ways of thinking in such a small amount of time.

Again, the biggest issue with undergrad isn't that the classes themselves are complicated, it's just that you haven't built up any tools when you enter them. Grad courses are much simpler even though the topics are more complex because you come in with so many tools already at your disposal. You'll find the hardest courses to be not necessarily complex, but the courses that you just have no tools for. Like if you've never programmed before and take a graduate computational methods course, you are going to struggle, but if you have programmed before, you'll find that the pace is nice and enjoyable.

>>14509377
calc 2 is designed for engineers and makes you memorize so many formulas that you don't want to do math anymore, kind of the same for diff eq, depends on your university i guess
abstract algebra is fine and only bites people when they expect it to blend into another math course they take that semester and slack off on it
analysis courses are the foundation of a math degree but the work is so routine that you forget a lot of the results because nothing feels like a priority

>>14509234
A shame. Maybe if you apply yourself, you'll be able to grasp Boy's Hole.

Elements of Algebra or Gelfand for algebra?

Weird how we try to get people interested in math by telling them about the applications, yet that's not what interesests most of us.

>>14509379
>Stands in your way.jpg

>>14509311
I dont know what your experience with math classes is, but mine is that it only got harder.

That said, I'm at an institution where the professors, in general, will pass everyone that at least turns in all assignments and does all the tests, without regards for final grade. That's because they expect the prelims to filter you, so its a quick way to bypass the 'crying graduate student in their office begging for a B so they can continue to be a part-time instructor' scenario.

>>14508759
>>14508219
>>14507586
Thank you, frens. Apparently the question was wrong, since we don't have cubic equations for the midterms.

>>14510543
Don't ignore ples

Can every graph be embedded in R^2 if we allow self-intersection?

>>14511401
No, consider the graph with no edges whose vertex set is all subsets of the real numbers.

>>14511455
kek

>>14506737
>The orthogonal complement of the orthogonal complement isn't necessarily the original space.
if we're talking about hilbert spaces, then this is always true for closed subspaces. in fact the orthogonal compliment of the orthogonal compliment is the closure of the original space. if we're not talking about hibert spaces, idgaf, get a life,

Serge lang try not to mention category theory in preface challenge — difficulty impossible

>>14505800
> knot
> kNOt
Take the sign anon she's not interested in you

>algebraic """"geometry"""
>the textbook contains no pictures

what is system T and how can i use it to prove the consistency of arithmetic?

still remember the absolute scenes on /mg/ when godel announced his incompleteness proofs back in the day
the memes about hilbert were mental altho some went a bit too far

>>14510832
yeah lol
i'm not this extreme anymore but i remember going through a hardy-esque phase where I had an aversion to anything even remotely applied

if [math] f=f(u) [/math], is [math] \frac{d}{du}log(f(-1/u))[/math] equal to

[math] \frac{f'(-1/u)}{f(-1/u)} [/math]

or

[math] \frac{f'(-1/u)}{f(-1/u)} \cdot \frac{1}{u^{2}} [/math]?

>>14512203
the second one because the chain is e(f(g(u)))

>>14510543
Serge Lang. Then Gallian when you get filtered.

>>14489724
Fuck prestige, learn2code and get the money.

surface integrals are mad hard on the lowk

>>14512712
fr fr bruh no cap that diffy calc be hella hard fr

>>14492398
All men should be sterlized and forced to work in labor camps

>>14492398
I acted the same way after two days of nofap
>>14513790
Never forget, woman, I could collapse your trachea with one hand if it pleased me

always feel bad for transient states on markov chains
poor fellas, they will never be visited infinitely often :(

let [math]X_1,X_2[/math] be independent random variables distributed exponentially w/ parameters [math]\lambda,\mu[/math]. i'm trying to calculate the conditional expectation [math]E[X_1|X_1+X_2][/math] and the answer i got looks kind of ugly and unexciting:
[math]E[X_1|X_1+X_2]=g(X_1+X_2)[/math], where [math]g:(0,\infty)\to\mathbb R,\,g(y)=\frac{ye^{(\mu-\lambda)y}}{e^{(\mu-\lambda)y}-1}-\frac{1}{\mu-\lambda}[/math]
in comparison, the previous exercise had Poisson variables instead of exponential ones and the answer i got was very clean. is this right by any chance or did i do something wrong?

How do I into vectors???

>>14515392
it's a module over a field

>>14515392
I would focus on the definition of vector space. The axioms are intuitive - eventually you'll see the intuition of working with the 2-tuple elements and how every operation generalizes.

it's been 5 years since i've done given up my hobby of maths for gardening, and now ii can't remember how to do most problems, and i'll have to relearn almost everything from scratch.
feel bad man

The binominal theorem is sort of cool.

>Lin. Alge and DE class
>class starts with 27 students
>we end with 7
>professor jokes about them being retards and failing
Apparently my class was a filter class even though it wasn't necessarily difficult.
what's the next filter class and how should I prepare for it?

>>14514416
I just did the calculation myself, and I got exactly the same answer, so you're probably correct.

>>14515985
Linear Algebra isn't a filter class
you probably just have one of those professors who make things hyper difficult to inflate their own ego

>>14515985
>how should I prepare for it?
Take the pre-reqs. If you need to do anything else then you don't deserve to get through the course. You'll figure out the things you need as the course processes and spend the extra time to fill in missed gaps

from a pure maths background, how do i into theoretical computer science?
i'm interested in the abramsky, hyland, plotkin etc. kind of stuff. seems fascinating to me and more pure and beautiful than many of the things we preoccupy ourselves with in maths departments

>>14516315
cool, thanks. weird that the answer was this "ugly", my thinking was that since the exponential distribution is the continuous analogue of the Poisson distribution, the results should reflect that

https://www.youtube.com/watch?v=0ylE4SJ4Mrc

>>14495404
>Algebraic geometry
>It's algebra
Topkek

Is talking about higher dimensional shapes math? I find this topic very interesting.

For dust thou art, and unto dust shalt thou return.

>>14517472
Higher dimensions can become weird though. I'm currently training my spatial IQ to gain more intuition of higher finite dimensions, but ultimately I want to get into infinite dimensional geometry. Gotta deepen my knowledge in algebraic and differential topology, cobordism theory and surgery theory.

>>14517601
>but ultimately I want to get into infinite dimensional geometry.
Why? Infinity doesn't even exist in reality.

>>14517611
I don't care about pointless ontology. Hilbert space has some intrinsic aesthetic in my point of view.

>>14503884
Only the results, in the intelligible world there is no dialectic because everything just is. Instead of having to prove something you would just see the whole thing and all its properties as part of it at once and it would be so self evident that the thing you would normally have to prove just melts into the object and becomes part of the definition. If you have an object, then everything you could possibly prove about it would be instantly apprehended since its definition and all its properties would be one and the same, since everything in the Platonic realm is pure being with zero becoming and divine Intellect apprehends the intelligibles perfectly without having to actually think about them. It’s like, if you were to see the color green and then try to “prove” that what you are perceiving greenness. Only a lower lifeform that could measure wavelengths but not actually perceive color would have to prove that it is seeing green.

>>14517850
profound

>>14517850
deep

>>14517850
Don't care 'bout yo goddamn 'ntology crap, m'kay?

>>14517880
>>14517867
It’s basic Platonism, in fact, I don’t even believe it, just answering the question

>>14516788
it is when they use axler
DE shouldn't be though unless it's a higher course

>>14517956

I must admit, as an interloper, that in spite of your clarifying you don't believe in platonism my reflex is to argue against the absurdities of platonism. Bah. I'd be a horrible teacher.

>>14517974
Is Axler's book hard?

Finally understood what a cyclotomic polynomial is. How come I never found any textbook who said "it's the polynomial whose roots are nth roots of unity but not kth roots for k<n"?

>>14518497
Because the word for that is “primitive” root of unity, and your book probably defined that and used it in defining cyclotomic polynomials

>>14489025
Do I need to read about the history of the idea to understand game theory at all? I know about Blaise Pascal etc. and it would be nice to know about John Nash's contributions to the tradition.

need mathemathic to predict quality of a product needed to gain X amount of sales

do i multiply or do i add the value
also how do i figure the miniscule value of each elements

>>14518697
>need mathemathic to predict quality of a product needed to gain X amount of sales
use a huge multilayered neural network that analyzes sales, shapes and marketing of certain products, it's an undecidable problem so you can't make a single algorithm to do that.

>>14518960
>neural network
this isnt /g/
>undecidable
Well how about assessing existing market? I ve done my own research so i just need some sort of affirmation to double check my findings... i could be entirely wrong but no other way to know.

>>14519096
dude you can't predict the quality of a product with an algorithm it's too complex

>>14517976
what are the absurdities of platonism? please enlighten me, for i am a platonist myself

>>14519350
Platonism is a tautology: alone the fact that Platonism exists is a proof of its validity.

>>14517974
axler's book is simple. you are just a retard.
linear algebra should be struck from the standard undergraduate curriculum anyway

I know this belongs in /wsr/, but I am looking for two specific books for someone. "All You Need About Mathematics - Jan van de Craats" and "Mathematics that Work Volume I by Dee Gee". I have searched through and through for PDFs of the English versions, but I could not find anything. Ideas ?

What help you really understand compactness? I can use it in arguments but it still seems a bit mysterious to me.

>>14518697
Well you probably have a list of 'quality' and a list of 'sales' right? The simplest model is an ANOVA model or a linear model of Sales ~ Quality.

You could also look at the problem as looking at the distribution of 'Low Quality' sales, 'High Quality' sales, 'Mid Quality' sales, etc.

Now if there are more terms you're looking at then just a wrapped up quality term, you'll potentially need a more complex model. Either way you should look into regression with indicator variables.

>>14519303
He's not trying to predict quality of a product. He's trying to predict sales GIVEN quality of a product. He probably already has some way he is categorizing quality (maybe by star ratings or some shit like that).

Even if he's doing the inverse problem, it's likely pretty easy. Hell, it's probably a pretty straightforward regression problem using Amazon ratings and sales

What's the dual of the free group on n elements? (i.e. Hom(F_n, C*))
I'm talking about the regular free group, not the free abelian group (for which it's trivial).

>>14517996
he's myopic and teaches with the intent that you go into functional analysis without providing any useful concepts for wider fields

>>14519885
oh, I misread the problem sorry about that.

Are there any describable mathematical objects that can't be described by an axiomatic system with a finite number of axioms and symbols?

Why?

[eqn]\sum_{i=1}^{n}i = i_{n} *i_{\frac{n+2}{2}}[/eqn]

anyone here know/is themselves an unironic intuitionist?

>>14520535
Yes you can describe Z_2 with finitely many axioms and finitely many symbols

>>14520419
Can you explain how that isn't just expecting an author to spoonfeed your lack of supplementary research?

>>14521183
Which books provide the supplementary knowledge?

>>14521202
Measure theory is a must for functional analysis, they are highly interrelated. I even had to study functional analysis just to really understand what was going on in measures. Secondly, I don't see what's blocking you from jumping into harmonic analysis if that's the application you mean.

>>14521202
>>14521218
Not him, but thought you meant there were other books that provided applications of functional analysis to other fields.