/sci/ - Science & Math

>>11593150
Quit it.

>>11593164
>Quit it.
Quit what?

>>11593150
Based

What is the comfiest topic for self-study?

Threadly reminder that proofbooks are necessary for first semester undergrads and not a meme, get one of them and do all exercises.

>>11593193
>Threadly reminder that proofbooks are necessary for first semester undergrads and not a meme
Why not read a math book instead?

>>11593192
Logic, especially because it interlaps with analytic philosophy and linguistics so you can learn and create a ton of things, it's so cool and it will also make you have a better understanding of proofs and mathematics as a whole, it will open new doors in set theory and category theory as well

Threadly reminder to work with physicists.

What's a good book on (formal) combinatorics?

>>11593193
based

>>11593194
Because the new student who never had experience with proofs might feel intimidated. I, for instance, never really got the grasp of proofs until I did Velleman, then it gave me knowledge about how proofs really works and confidence

>>11593200
>Logic
>analytic philosophy
>linguistics
Wrong board for this trash

>>11593202
>What's a good book on (formal) combinatorics?

>>11593204
>Because the new student who never had experience with proofs might feel intimidated. I, for instance, never really got the grasp of proofs until I did Velleman, then it gave me knowledge about how proofs really works and confidence
Sounds like your first post should have said that proofbooks are necessary for brainlets. I've never met anyone who actually used one of those books, they must be tucked away in third-rate containment colleges.

>>11593192
In my experience, group theory. No other fields have books half as good as group theory. Can't say the same for ring or Galois theory though.

>>11593214
Not everyone who didn't have experience with proofs is a brainlet, you're being very rude. So your solution for people who didn't do any hard proof before is to just throw them into analysis?

>>11593192
Finite groups and maybe abelian categories. Not necessarily homotopy theory if the book is full of typos.

>>11593223
>Not everyone who didn't have experience with proofs is a brainlet, you're being very rude. So your solution for people who didn't do any hard proof before is to just throw them into analysis?
I had no experience with proofs and got through a few dozen math courses without ever reading a proofbook, as did all my colleagues.

>>11593227
Wow, congratulations, so? How does that help those who weren't as lucky as you and your colleagues?

Threadly reminder to use Anki if you want to keep up with the geniuses

>>11593243
>How does that help those who weren't as lucky as you and your colleagues?
I'm not concerned about brainlets in containment colleges. I'd suggest transferring into something less mathematical like economics, engineering, computer science or physics.

>>11593250
how do flashcards help with mathematics?

>>11593193
If proofbooks are necessary then why do they not appear in the official curriculum?

>>11593221
>>11593230
I didn't really understand your answer, but here's my attempt: I used the proved fact that W is the smallest subspace that contains X. Since L is a subspace that contains X, this means that L is contained in W. This proves the other inclusion
>Whenever you are dealing with a proof something that is minimal (maximal) with some property, you try to show that it is smaller (bigger) than any object with the said property.
I understood. Thanks!

>>11593251
Oh, how much self-love can a man have? You're honestly so sad to look at, thinking so highly of yourself and your companions to the point where anyone with a little difficulty in a subject is already unworthy to be in your special club. Well, guess what? No one gives a fuck about you, your 'intelligence', your colleagues and your little genius club, the best advice one can get right is to ignore your advices. Just imagine if Smale, who was a terrible student at first, listened to that shit you sprout.

>>11593282
>Oh, how much self-love can a man have?
I'm not a "man".

>>11593259
https://www.lesswrong.com/posts/8ZugMc4E5959Xh86i/how-i-use-anki-to-learn-mathematics
This should be mandatory read for math majors

>>11593150
How to into math?

>>11593287
>lesswrong
cringe

>>11593298
>Judging a book by its cover

>>11593250
How would you use them? I would probably write the assumptions on one side and the conclusion on the other.

>>11593277
Wait! Just to make sure you don't get any misconceptions, let's break this down into 2 parts. In general, if W is the smallest subspace containing X, and L is any such subspace, then it is W that is contained in L, and not (necessarily) the other way around. In fact, if L would be contained in W, then L would be at most as big as W, and the minimality of W would then imply L=W, as otherwise L would be strictly smaller contradicting the minimality of W. In the context of this proof, the inclusion of L into W is true. The proof is essentially just showing that L is a subspace, and then the minimality of W does the trick.

>>11593307
>it is W that is contained in L
Yeah, that's what I meant to type.
>The proof is essentially just showing that L is a subspace, and then the minimality of W does the trick.
That's what I wanted to hear. Thanks

>>11593317
No problem. The proof begins by noting that the minimal subspace of V containing S contains the set (!!!) L. The next thing to do is to show that L itself is a subspace of V. Just make sure you see where these facts arise from and you have a firm grip on that proof.

>>11593150
>lecturing to Vietnamese farmers about schemes and abelian categories
What was he hoping to accomplish here?

>>11593355
If you think about it, it is quite logical to talk to farmers about such matters. They have fields and sheaves already.

>>11593210
The cult around this book is incredibly undeserved. It's popular because Stanley has a ton of political influence and he has like 50 students with political influence, and you'll be forced to read it by your advisor if you work anywhere near algebraic or enumerative combinatorics.
It does have a lot of stuff in it that's not in other combinatorics books, but what people don't mention is that the unique content is not because Stanley is deeper than everybody else, but because the book is really mostly him autofellating over his own work and circlejerking his students. The entry for R. Stanley in the index of EC1 alone has legitimately around 100 fucking subentries. On naive average he's mentioning himself every 6-7 pages, not accounting for the fact that like 40% of the book is problem sets.

>>11593307
>How would you use them?
Memorizing theorems and proofs, read the link I posted >>11593287
Anki truly is black magic, my fren

>>11593396
There's also this one
http://cognitivemedium.com/srs-mathematics

>>11593387
What's your recommendation for combinatorics books?

What field of math is best for recreational purposes?
Speaking about prerequisites, I've finished IT major at university.

>>11593437
combinatorics, only prereqs are basic proof knowledge

>>11593437
Number Theory obviously

>>11593441
More specifically? I've learned basics of combinatorics in school and university.

>>11593446
Same question.

>>11593452
Depends, there are an infinte number of interesting problems in basic combinatorics. You could try studying one of the more "obscure" branches, like combinatorial matricies, but idk about those prereqs. All you would need for that is just basic combinatorics tho afaik

>>11593465
>Depends, there are an infinte number of interesting problems in basic combinatorics
Can you name some? Or better tell me where to find them.

>>11593396
>>11593414
Didn't notice the link before posting. I'll give it a read, as it seems there's no sleeping to be done tonight.

>>11593437
Hyperbolic geometry. Why? Because you can draw nice hyperbolic tesselations after that! Not much for prerequisites either. Just a bit of topology, and enough group theory to know how the Möbius group would act on whichever model you are using for the hyperbolic plane.

>>11593429
If you're the same guy asking for "formal" combinatorics, take a look at Aigner's Course in Enumeration. Same guy who wrote Proofs from the Book. It's still fairly heavy, systematic enumeration, and you should probably know basic counting stuff before you start, even though it's reviewed. There are dozens of good raw intro sources if you don't.
Also Van Lint/Watson is a really nice source to have for all the older-school stuff that the modern folk who keep generating functions in their porn folders are ashamed to admit exists.

>>11593468
You can check this out, http://www.openproblemgarden.org/category/combinatorics but really it is so easy to invent problems in this field. For instance, here's a problem I gave a friend of mine which turned out to be ass: Let's play a game with simple rules. At every turn give yourself a point.
Turn 1: Roll an n-sided die. Call that value [math] p_{1,1} [/math]
Turn 2: Roll an n-sided die twice, naming those two values [math]p_{2,1} \text{ and } p_{2,2}[/math]. If [math]p_{2,1}+p_{2,2}>p_{1,1}[/math], then you can move on to turn 3.
Continue this up, so for round k, you hope for [math]\sum_{i=1}^np_{n,i}>\sum_{i=1}^{n-1}p_{n-1,i}[/math]. What is the expected value for a game with an n-sided die?

>>11593150
Trying to get into topology a little bit, any good readings I should get into?

>>11593485
let me fix that broken line:
[/m a t h], then you can move on to turn 3. Continue this, so for round k, to pass you must have that [math]\sum_{i=1}^kp_{k,i}>\sum_{i=1}^{k-1}p_{k-1,i} [/math]

>>11593504
Munkres

>>11593510
And to answer for >>11593459
Algebraic number theory needs number theory and algebra, and analytic number theory (RH-type stuff) you need number theory, real and complex analysis, and probably some form of topology

>>11593510
Thanks, I got it. Sounds really easy (I bet someone has already solved it). That is more, you can get answer by running numeric experiment and then proof for known formula. I'll think about it.
And thanks another time for the link.

>>11593521
np

I could imagine doing an Anki walking trip to a nice park in my city and answeing the questions there. Thanks, nice anon!

anons, I come bearing bad news
I was a mathfag but went into a career instead of pursuing my PHD
Now I see it almost impossible to go back to school for it. I am currently doing my MBA and it's not hard but holy hell is it time consuming. Can't imagine an actually challenging topic like number theory
If you have the choice, go for it. You're going to regret it

Who needs sleep when you finally crack the problem you have been struggling with?

>>11593575
I'm thinking about staying for my masters and working through a PHD with night-classes
thoughts?

>>11593649
Depends. What industry? If it's something like comsci, then I can see it happening. But to that I just ask, why do you need a masters?

>>11593657
Well I want a PHD, I want to be a mathematician
my thinking is working through my PHD would offset some of the college debt. it'd also put something on my resume to fall back on if academia fails me as a career path
where I work during my PHD studies wouldn't matter the least to me, I'd take whatever would be paying the most.

>>11593664
Well unless your program requires it, I would skip the masters all together and carry on with your plan. That way, you don't waste 2 years.

>>11593680
Even if my school offers a masters with only a single year?
also isn't a masters more employable?

>>11593683
>Even if my school offers a masters with only a single year?
a masters in math? Or can you do something else like stats?
>also isn't a masters more employable?
It is but only if it's something valuable. A comp sci masters with a math undergrad is fucking employable anywhere. With a stats masters, you will have good luck as well for DA positions if you know some basic code. But a math undergrad and masters is still employable, but kinda doesn't add any value.

>>11593657
comp sci industry is really draining. Do you really think you can grind maff after programming for 9 hours

>>11593693
>a masters in math? Or can you do something else like stats?
I'll look into it. I'm not certain whether or not my undergrad major and masters have to be the same for the program
>a math undergrad and masters is still employable, but kinda doesn't add any value.
interesting. I'll keep that in mind

I'm already nearly a year ahead of schedule for my undergrad math degree. since there's some double counting on the classes if i go with an applied or pure math masters I'd likely be able to get it in a total of 4 years spent in college rather than the usual 6. I might be able to do similarly going with stats as you say, but I doubt the same can be said for something like Comp Sci

>>11593575
I tried to get a job in analytics after with a BSc in pure math, but never got one. Couldn't afford grad school and cost of living right away, so I had to just get a job. Finally going back after 4 years... I'm pretty nervous. Reading Rudin right now to get back into it and it's coming back quickly. Going to take Topology first. How fucked am I?

>>11593700
>after programming for 9 hours
that's why I say go for a huge corporate gig. It's not as pressing, and the hard work is contracted out to pajeets
Some roles I recommend would be project manager, scrum master, data analyst, business analyst, finance analyst. Math degree opens doors to all of them.
>>11593710
So I messed up my undergrad. I was really good at math and thought engineering was for me. damn did I hate it. Lost a year there since I didn't know how great a math degree was. Didn't take my first programming course until my sophomore year, and that was definitely my biggest regret in school. I didn't get to finish my minor in CS since I was just trying to graduate and make up lost time, but I took enough classes to make me employable (+my stats minor)
Turns out I fucking hated it lol but that goes without saying that it is very good skill to have. I still use it in my new career but I didn't ever want to imagine a world where I'd be coding the rest of my life
anyways, I got too verbose reminiscing. Sounds like you're on a great path. If you can finish the masters that quick, fuck it go for it. Land a comfy college job (know some stats/finance/programming) and then do your own thing. Don't give up. I miss school and I'm only doing MBA classes.

>>11593716
I got a pure math degree too. What other skills did you carry with you? programming? finance? Any internships?
I graduated with a data analyst research gig and internship, and went to work as a data analyst/admin.
good luck, and I wouldn't say you're fucked at all. There are lots of resources now that can help you.

>>11593720
>Sounds like you're on a great path
thanks
here's to hoping I don't fail any classes and blow it all
>(know some stats/finance/programming)
took a macroeconomics course, taking intermediate stats next semester, and I know Lisp, scheme, and C++ from my self study in highschool (used to think programming was neat, now i think CS is a meme)
how's that. I imagine macro is a bit abstract for finance and that programming lang set is a bit narrow, no? I have no idea what intermediate stats is gonna be like. probability and statistics felt like babby stuff here (nothing more complex than some binomial distribution, normal distibution, poisson, and bayes theorem), but some of my classmates were struggling, so maybe it's just intuitive for me (indicator functions are bizzare tho)

>>11593150
Ouch. Imagine growing up with the best nutrition in the world, and several generations of your family doing the same, and still finding out that half the junglegooks are taller than you

>>11593736
Here are your 3 most valuable skills for a graduating math major (take it from someone who has been in your shoes and now interviews candidates)
Excel is your #1 hands down. For any job. Know ifs, pivot table, charts, conditional formats, and index/match & Vlookups
SQL is your most valuable skill when programming skills. Then python
For finance, I would say know some basic accounting/terms.

>>11593769
thanks for the info m8
I'll try to pick up some SQL and python over the summer and sharpen up my excel skills
my school has linkedin learning courses free to access through our school emails, so I can poke around with all of those fairly easily through that

>>11587301
Path spaces fit into the fibration [math]\Omega X\rightarrow PX\rightarrow X[/math], hence if [math]X[/math] is path connected so that [math]PX\simeq \ast[/math] then you may apply the Serre spectral sequence to obtain either [math]H^\ast(X)[/math] or [math]H^\ast(\Omega X)[/math], given that you know the other space. This is useful for Eilenberg-Maclanes since [math]\Omega K(\pi,n) = K(\pi,n-1)[/math].
>>11587254
Get a good grip with Hamiltonian mech with Landau-Lifshitz first, then starting with Arnol'd after that is good. Guillemin-Sternberg may also be useful.

how do I git gud at drawing manifolds, CW complexes, graphs etc. ?

How does [math]S^1 = \mathbb{R}/ \mathbb{Z}[/math] compare to [math]\bar{\mathbb{Q}}/ \mathbb{Z}[/math], topologically and group-theoretically, apart from the obvious fact that they have different cardinalities?
What's [math]\pi_1 (\bar{\mathbb{Q}}/ \mathbb{Z})[/math]?

>>11594357
>what is the fundamental group of a nowhere connected space
gee i wonder

>>11594353
Good book.

Suggest me must-have books for university math for each year starting from junior to specalist.

>>11593727
4 years as a research assistant in mathematical modeling, which was most similar to a data scientist job and analyzing data before putting into model, had TA experience, can program in MATLAB, R, Python, and have taken MOOCS in deep learning. Have a few things on my github showcasing this. Still never got a call back.

>>11593205
>>>/g/

What's a good graduate level book on fluid dynamics?

>>11594501
>>11593262

>>11594631
https://link.springer.com/book/10.1007/978-1-4757-3665-6

>>11594942
definitely not

>>11594353
Do like all low dimensional topologists: draw a cryptic 2d schematic and tell the reader to use his fucking imagination.

>>11593150
how difficult is it to get accepted to a masters in math?

I will graduate college with a B.A. in math and a somewhat shitty GPA. (like 3.25-3.5 with a lower major GPA.) Some of this was my fault, but academia definitely fucked me over as well.

Thanks for recommending the Anki thingy. I will definitely make a deck or two this weekend.

>>11595226
Share the deck with us.

>>11593150
Would you guys go do cryptography for the NSA? They recruit at my school.

>>11595243
And then you will tell me I'm dumb.

>>11595249
No, I dont know if im dumber than you, but I am guaranteed worse at math than you.
Im just interested.

>>11595265
Yeah well I'll see if I can get anything done.

I'm gonna do Stewart's Precalculus because I've been away from math for a while and then his Calculus, I tried doing Spivak first but it became obvious straight away that I'd need to get acquainted with proofs and currently I need to have a basic grasp on calculus itself as soon as possible, so that's why I chose Stewart. Still, I want to do Spivak afterwards, so I downloaded the Book of Proof and How to Solve It. Which should I do first in preparation for Spivak?

>>11593192
Classical geometry

>>11595306
None. Do How to Prove It.

>>11595347
I meant Daniel's How to Prove it, not Book of Proof, sorry. My plan is based on what I read on the wiki.

>>11595391
I'd also recommend How to Read and Do Proofs by Daniel Solow

>>11594353
Cute book. Practice, practice, practice — anyone doing art as a hobby or as a living would tell you that. Maybe copy the pictures from that very book or look up tutorials on perspective drawing, etc. You could try asking for tips on >>>/ic/ but I'm not sure if they'd appreciate it; their sticky has some resources for beginner artists in general which may or may not be useful.
In the case of manifolds, try to understand how to gradually construct them in a drawing. Make a detailed list of the steps you follow and refine them, see e.g. here: https://matheducators.stackexchange.com/a/7909

>>11593307
Eh, more or less it's about being able to reduce a proof down to it's most essential ingredients and state them as simply and intuitively as possible, you don't actually need to use flashcards per se.
>>11593210
Check out Rota's stuff, the original combinatorics bible.
>>11594353
Learn about using shading to emphasis curvature and start drawing.

I am mathematically retarded and would like to read Rudin's Analysis.

I've tried time and time again, but my patience and my ADHD has made me quit over and over, that and the fact that I am retarded.

What are some books that could help me gain a greater understanding on math?

Please help me, honest question.

>>11595609
Btw. And I know this question has been asked, and will continue to be asked, countless of times. I already tried How to Prove it. Or at least tried to do most of it.

At the moment I was studying from pic related.

>>11595609
>>11595618
>I already tried How to Prove it.
Why did you stopped? It's a very entertaining book.
>>11595609
>my patience and my ADHD has made me quit over and over
Maybe try to motivate yourself watching online lectures, examples, or, the heart of learning mathematics: ask yourself questions. That kind of things keep me motivated.

>>11595618
start with spivak.

If you can't do spivak, then you obviously won't be able to do rudin.

>>11593437
Polytopes
Fancy geometric patterns

>there are people out there who have never eaten a Riemann surface of [math]\sqrt{z}[/math] of apples

I wanna review algebra and analysis this summer. What kind of plan should I do? I was thinking of going through the first 4-5 chapters of rudin and doing all the problems. But I don't really know what to do for algebra. Any suggestions?

>>11595618
>At the moment I was studying from pic related.
How is that book? The table of contents looks like dogshit, you're better off with how to prove it or spivak's calc

>>11595822
Its, quite literally, an expanded version of How to Prove it, nothing wrong with it. Plus it has a lot of exercises.

It was on pic related so decided to grab it.

>>11595889
Why are you using a computer science reading list to do higher math?
I would honestly just recommend the normal path of self-learning, Lang Basic Mathematics -> Spivak -> Artin Algebra/Munkres Topology and you're good to go

>>11595935
Because most of what I do involves programming. And my general interests are towards computer architecture, circuits, all that jazz.

This is just a list for that.

The sci wiki always recommended studying some Lin Algebra text before jumping into the sort of texts like Artin. How true is that?

>>11595822
>The table of contents looks like dogshit
What? It's basically first semester uni math. Very important stuff. What are you talking about?

>>11595774
A First Course in Abstract Algebra by Fraleigh. Underrated book. Exercises are tough.

>>11593437
group theory

Given a finite set of values, how does one derive a sine function which has a zero at only one of those values? I need a general equation (for a program), it's an obvious task for a specific case. The other zeroes of the sine don't matter to me, just that exactly one of it happens at one of the values and that no zero lies on the other values.

>>11596205
There are probably lots of ways to approach this. If you want to kill a_k, something like [math]\sin(\frac{\pi (x-a_k)}{\max{a_n} - \min{a_n}+1})[/math] should work.
This is zero at a_k, and the period is so long that the next zero to the right occurs at [math]a_k+\max(a_n)-\min(a_n)+1 > \max(a_n)[/math], and similarly to the left.

If I fucked up the exact math, the idea's still sound. Just make the period so long you can't have another zero in the interval of your set of values.

>>11596205
Let [math] v_1, v_2, v_3, \dots [/math] denote the values that you don't want to take the zero value and let [math] v_z [/math] be the one that should hit the zero.

Since [math] \sin(0)=0 [/math], the function
[math] f(t) := \sin(\pi \cdot \, (t-v_z)\, /\, T) [/math]
is zero at [math] t=v_z [/math].

Now you want to choose your period length [math] T [/math] such that all other [math] v_i - v_z [/math] are never an integer multiple of [math] T [/math] .

>>11596252
minor formal correction, my T is only half the period length

>>11593283
you are an egocentric loser with no real love in your life. good luck.

>>11596062
Generally, you do linear algebra as a first course in proofs because it's incredibly straight-forward and the proofs end up pretty much how you expect them to be. However, if you already have SOME experience in proofs, this is completely unnecessary and you can jump right into analysis or algebra.

>>11596252
I already had the same idea in mind, my problem was just that I didn't know any method to come up with the last step but >>11596251
now did something like that.
Thanks

>>11596491
No one cares if you had the same idea in mind. The point is that you couldn't do it. Period. You had to ask for the answer.

>>11596205
>>11596491
It's probably also worth pointing out that if your values are all integers or even rationals (which seems plausible in a computer application), then this entire construction is overkill and you can simply use [math]\sin(x-a_k)[/math], since sine of a nonzero rational is never even rational, let alone zero.

Do you prefer [math]\mathcal{P}(\mathbb{F})[/math] or [math]\mathbb{F}[x][/math] to denote the set of all polynomials with coefficients in [math]\mathbb{F}[/math]?

Is there any prime number (except 2) that is not of the form:
[math]\Pi_{i=1}{k} x_i + 1[/math] where [math]x_i[/math] is one of the prime numbers.

>>11596673
I meant
[math]\Pi_{i=1}^{k} x_i + 1[/math]

>>11596651
>P(F)
I'd say you're full of shit, but then again card(X) is a thing.

>>11596673
5.

>>11596681
5

>>11596693
>>11596694
2*2 + 1.
What I meant is the same prime number can appear multiple time.
Sorry I wasn't being clear.

>>11596698
>>take the prime minus 1
>factor it
Also, the empty product equals 1, so 2 actually also has that form.

>>11596673
>>11596698
>is there any prime that isn't equal to some other number plus one
no. no there isn't.

>>11596705
>>11596708
I just realized how retarded that question was after I answer the previous post.
It's literally an even number.
Fuck.

>>11593150
Retard here, struggling to understand lambda calculus notation. Are these written correctly?
[eqn](\lambda x.x)2 = 2[/eqn]
---
[eqn](\lambda x.3 \cdot x)4 = 3 \cdot 4 = 12[/eqn]
---
[eqn](\lambda x.25 + 4 - x)3 = 25 + 4 - 3 = 26[/eqn]
---
[eqn](\lambda x.x)y = y[/eqn]
---
So the parameter has to be applied only when the expression is within parenthesis?

>>11596764
Nevermind, finally found something that does not magically assume I know everything. https://calculushowto.com/lambda-calculus/

How the fuck there is a well-ordering for every set? That doesn't make any sense

>>11597013
oh goddD I'M CHOOOOOOOOSING ARGARGARGRHrgrrh

how am I supposed to learn math when I get filtered by professor layton puzzles

>>11593192
kkkrypto

Good morning /mg/! Did everybody notice this? http://www.math.uni-bonn.de/people/schwede/global.html

>>11597125
Have you tried actually studying? That could help, you know.

What's the /mg/ consensus on the best book for real analysis?

>>11597402
Spivak of Fuchs Fomenko, you choose

I'm studying Principles of Mathematical Analysis currently. I'm a bit ashamed to say I look up most exercise answers for hints. I can rarely complete an entire one on my own without looking up a hint or entire answer. Am I the only one?

>>11597454
Nah dude those exercises are fucked

>>11597454
You're definitely not the only one. Most of the reason Rudin has stayed so popular for so long is that the problem sets are really good, and part of that is that they're really challenging. The actual writing sucks.
You should be able to struggle through a good portion of them on your own eventually though. If you can't do at least like 40-50% or so of them without cheating, especially the earlier ones, you're either giving up too fast, not understanding the chapter well enough, or both.

deep yukarifag lore: banned from over 5 discord servers for posting shota

>>11596764
unironically learn haskell, it will help you

Are There any other good math Forums like sci but more focussed on math

>>11597915
do you not like it here with us, your fellow cu/mg/uzzlers?

>>11597949
Yes, but i want to See the World

https://www.strawpoll.me/19857145

>>11597971
Basically everything except for homework and anything related to 2d or Anime

>let
>consider
>take

I'm so tired of this bullshit

>>11598058
Given an arbitrary mathematical text, it is very likely you will see those words come up quite often. Indeed, they are commonly used as first words of sentences.

>>11598058
what is your problem mate

>>11598058
You mean English? Guess you do not really need it if you never go to England.

>>11598129
It is quite essential in Scotland, too.

>>11597402
Pugh.

>>11597402
>What's the /mg/ consensus on the best book for real analysis?

>>11597454
>I'm studying Principles of Mathematical Analysis currently. I'm a bit ashamed to say I look up most exercise answers for hints. I can rarely complete an entire one on my own without looking up a hint or entire answer. Am I the only one?
Rudin is a meme.

Can anyone give a nice summary of what Model theory is? How is it different from Proof Theory?

https://en.wikipedia.org/wiki/Model_theory
The introduction in this Wikipedia article doesn't really mean much to me. I know what a formal language is but beyond that I don't really know.

It seems to study something to do with what the symbols actually semantically mean? How is that possible when we ascribe the meaning ourselves?

>>11598361
>Can anyone give a nice summary of what Model theory is?
not maths

>>11598353
imagine unironically writing a 3000 page analysis textbook

>>11598366
"Model theory
From Wikipedia, the free encyclopedia
Jump to navigation
Jump to search
This article is about the mathematical discipline"

>>11598370
"From Wikipedia, the free encyclopedia"

>>11593150
Why do you keep doing this?
Why push political messages into every math general, did that ever work out well?

>>11598371
Yes, that site is indeed a good encyclopedia for general information about a subject.

>>11598374
>Why do you keep doing this?
>Why push political messages into every math general, did that ever work out well?
It's just a play on the last thread, and it doesn't seem to have derailed this thread. What's the issue?

Next one should be /mg/ maths general: 6 million edition

>>11598371
How can it be free when it has non-trivial related articles?

>>11598361
From an undergrad course years ago, I remember it being about studying for example how a theory can be modelled. You have the notion of a model which is a pair consisting of a set of whatever called the universe and a set of symbols which you interpret in some way, and then you can use the symbols and and elements of your universe to make all sorts of sentences. Depending on what each symbol means in your model, such sentences will be given a truth value, and this allows you to use those models as tools for studying theories. A theory, if I remember correctly, is a finite set of such sentences, and then you take your model and see which of them hold in it. If all the sentences are true, then you say that your model models the theory. Someone else can probably explain it better, I'm working on some faint memories now.

>>11598384
>it doesn't seem to have derailed this thread.
It DID derail the last thread, so there is no reason to repeat that...

It can't be that hard to not bait everyone who has an opinion on the subject of race to comment.
Just keep it explicitly mathematical, that really can't be too much to ask.

>>11598394
Thanks anon. You description combined with what I've read here makes a lot more sense than the Wikipedia link.
https://plato.stanford.edu/entries/model-theory/#Oth

>>11598407
That philosophy encyclopedia is amazing, it also has lots of good entries about set theory and logic

>>11598393
>tfw great grandpa dies and because he was a holocaust survivor you need to call the Israeli government so they can add him to the list of holocaust victims

>>11598374
>>11598401
don't start the off-topic posting if the thread has stayed out of it for more than half a bump limit
that really can't be too much to ask

>>11598407
No problem! Have a productive day and a nice weekend.

>>11598429
Meta discussion is technically on topic.

>>11598423
>tfw grandpa dies and because he was a holocaust perpetrator you need to call the Israeli government so they can remove him to the list of goyim who have to pay reparations

>>11598440

>>11598449
*of boards* not *of generals*

>>11596159
LOL the exercises are not tough. Good book though

>>11598444
>he thinks they stop collecting on death
you just called and informed them that you'll be paying your grandpa's reparations from now on

>>11593200
>Logic
>wildberger already formalized beyond belief thus mechanical
You should watch his latest videos lol

>>11597013
Just keep choosing the next element in the order bro

>>11598393
http://math.uchicago.edu/~drinfeld/Golden%20years/Fuchs.pdf

I'm building a math textbook collection (intended for math majors), but I need textbooks on the following areas:
>Differential Equations (ordinary and partial)
>Algebraic Geometry
>Graph Theory (or discrete math in general)
>Game Theory
>Functional Analysis
>Logic
>Complex Analysis (Ahlfors maybe?)
>Differential Geometry (Do Carmo?)
>Algebraic Topology
>Measure Theory
Can I get some recs?

my god why is everyone so obsessed with choosing textbooks

>>11598562
Low IQ and the desire to appear smart and waste time instead of learning something by reading it.

>>11598562
honestly I learn more from a book than from a lecture t b h

>>11598552
>Functional Analysis
Lax.
>Complex Analysis
Kodaira.
>Differential Geometry
Curves and Surfaces or muh manifolds?
>Algebraic Topology
Fuchs-Fomenko.
>Measure Theory
Cohn.

>>11598356
ur a meme, bro

>>11598486
Y-yes

>>11598361
Model theory is the study of mathematical structures. A model is a structure that gives an interpretation of a set of sentences in a formal language. For example the group of integers with additions is an model of the group axioms. Some questions that come up in model theory are given some model what extensions does it have? A theory is collection of sentences that is closed under logical consequence. Another question might be how many models does a theory have? One open problem in this area is Vaught's conjecture. A subset of model is definable if its members are precisely those elements of the model that hold for some formula in the language. What are the definable sets of a model? For an infinite cardinal k, is the model k-categorical, that is are all models of size k isomorphic? Some important results in model theory include the compactness theorem, which says that if every finite set of sentences has model then the entire set of sentences has a model. The Lowenheim-Skolem theorem, which says that if a theory has a infinite model then it has models of every infinite cardinality, in particular a countable one. The Morley categoricity theorem which says that if a model is k-categorical then it is l-categorical for every l>k. It is a really interesting field.

>>11596251
So here is the function I generated with the code for the prime numbers:

y = (x-2)/(1-2)*(x-3)/(1-3)*(x-4)/(1-4)*(x-5)/(1-5)*2 + (x-1)/(2-1)*(x-3)/(2-3)*(x-4)/(2-4)*(x-5)/(2-5)*3 + (x-1)/(3-1)*(x-2)/(3-2)*(x-4)/(3-4)*(x-5)/(3-5)*5 + (x-1)/(4-1)*(x-2)/(4-2)*(x-3)/(4-3)*(x-5)/(4-5)*7 + (x-1)/(5-1)*(x-2)/(5-2)*(x-3)/(5-3)*(x-4)/(5-4)*11

Here is the stuff with the sines (no idea why I thought it to be so important:

y = sin(f*(x-2))/sin(f*(1-2))*sin(f*(x-3))/sin(f*(1-3))*sin(f*(x-4))/sin(f*(1-4))*sin(f*(x-5))/sin(f*(1-5))*2 + sin(f*(x-1))/sin(f*(2-1))*sin(f*(x-3))/sin(f*(2-3))*sin(f*(x-4))/sin(f*(2-4))*sin(f*(x-5))/sin(f*(2-5))*3 + sin(f*(x-1))/sin(f*(3-1))*sin(f*(x-2))/sin(f*(3-2))*sin(f*(x-4))/sin(f*(3-4))*sin(f*(x-5))/sin(f*(3-5))*5 + sin(f*(x-1))/sin(f*(4-1))*sin(f*(x-2))/sin(f*(4-2))*sin(f*(x-3))/sin(f*(4-3))*sin(f*(x-5))/sin(f*(4-5))*7 + sin(f*(x-1))/sin(f*(5-1))*sin(f*(x-2))/sin(f*(5-2))*sin(f*(x-3))/sin(f*(5-3))*sin(f*(x-4))/sin(f*(5-4))*11

f is supposed to be calculated as you commented (pi/5), but it works for almost all frequencies and it approaches the polynomial as the frequency approaches 0.

I also tried out some other sequences and it works well for some (polynomials obviously, exponentials also for longer than expected), but for some like the primes it's shit beyond the already given input.

>>11598393
/mg/ maths general: most irrational number edition

>>11598841
Also, how would one approach generating a Taylor Series for any sequence (basically linear regression but not linear, rather for any polynomial)? You obviously can't take derivatives and simply using matrices feels a bit like cheating without understanding the intuition behind it.

>>11598845
Much needed:
/mg/: Amateur proofs disproval edition
/mg/: 0.999... = 1 (last thread) edition

>>11598854
what about /mg/: tropical edition

>>11598871
/mg/: Machine Gun Edition

>>11598845
>>11598854
>>11598871
We've already had those editions, maybe harmonic analysis edition, or atiyah-singer index theorem edition, or Yuno edition.

>>11598914
Harmonic analysis is one of those things I've always wanted to get into but never got around to putting in the effort. My uni has a cluster of harmonic analysts and some of them even collaborate/crossover with my group but I've never even taken a class.

>>11598933
Take one, it's a very interesting, albeit technical, subject, with a lot of interesting problems. I say interesting because it's actually quite shocking how broadly applicable harmonic analysis techniques are. From analytic number theory, ergodic theory, combinatorics, pdes, geometric measure theory, graph theory, and so on. Folland has some good books on this harmonic analysis, so does stein and tao.

>i will never make any meaningful contribution to mathematics
whats the point of going on bros....

>>11599075
have you ever thought about doing it just for fun?

On other boards, people give different answers to this one.
I'm curious to see if everyone in here gets the right answer though.

How was your week mathematically, anon? Mine was pretty good in the end.

>>11599088
1/2, the ball is either green or it isn't

>>11599102
[math]/thread[/math]

>>11599088
3/2

>>11599088
Has already been posted on this board you nigger

>>11599102
There's a 50% chance I've already ejaculated inside your mom
There's a 50% chance I've ejaculated inside your sister
Therefore there's a 75% chance I've creampied at least one of them

>>11598552
>DEs
Tenenbaum for computational ODE.
Strogatz Nonlinear Dynamics and Chaos for theoretical ODE (a second course).
Strauss for computational PDE + some theory.
Evans for the full PDE theory.
>Discrete math
I thought Rosen was quite good, though others dislike it.
>Functional analysis, complex analysis
Stein and Shakarchi. Should be them for Fourier as well, and even maybe for Real.
>Differential geometry
Do Carmo for diff geo of curves and surfaces.
Spivak calculus on manifolds for manifolds, differential forms, etc.
Guillemin and pollack for diff top.
Lee Smooth manifolds/riemannian geometry for the real deal.
>Algebraic topology
The common sentiment is "read hatcher until you realize it's shit, then you're ready to switch to fuchs-fomenko."
>measure theory
I recommend Stein and Shakarchi real analysis but there are other good options.

>>11599097
i just did all the assigments and read this week's lectures
too lazy to do work on my research problems

>>11599229
As a reward of your good work, take a penguin stream https://www.edinburghzoo.org.uk/webcams/penguin-cam/#penguincam..

>>11599097
Finished Baby Blue chapter 1 and Analysis Yawps associated chapters, working on exercises. I have a BSc in math but somehow avoided analysis, did algebra up to algebraic geometry during. Going to take a course in Topology this september before applying for a masters, 5 years after I graduated.

>>11599244
Algebra and topology are the choice of a thinking person. Any plans for the master stuff?

>>11599175
>nigger
Why the racism?

>>11599255
No plans yet. Had to work to pay off debt and my dad kicked me out upon graduating in a city with high cost of living, or I wouldve gone right after. I loved Galois theory and dreamed of working on the inverse Galois problem. I'm going to take it slow at first to get back into the groove, starting with topology! I gotta find a prof who will work with me as well if I end up going to the uni for an MSc that Im taking courses at.

>>11599244
>I have a BSc in math but somehow avoided analysis
this sounds crazy to me. My BSc in math had 4 semesters of mandatory analysis

>>11599244
>Going to take a course in Topology this september before applying for a masters, 5 years after I graduated.
That sounds nice anon, hope it goes well. Why the break?

If an object suddenly grew, what formula would you use to calculate the weight?

Say you had a glass marble with a diameter of .75in and a weight of 1 gram and it magically doubled to a 1.5in diamater, would it weigh 3 grams?

pls

>>11599325
>this sounds crazy to me. My BSc in math had 4 semesters of mandatory analysis
Analysis is irrelevant to most of mathematics, if anything you should have 4 semesters of mandatory category theory.

>>11593205
No, anon.

>>11599372
most of mathematics is irrelevant

>>11599319
The best of luck to you! It may take some time to get back in the game, but when it happens then it really happens.

>>11599097
bad, i am too lazy

>>11599603
Not motivated? Distracted by something? Really just lazy?

Doing engineering, thinking of doing a maths masters, im from europe and have taken calc1(derivatives, integrals, some series), calc2(multivar calc, thats all i think), complex analysis and differential equations(last sem and i dont really remember, residue theorem, then a whole bunch of dif eqs that i dont know the names, and fourier something, which was approximating a function via sins and cos but it had to be a set value out of some bonds), uh have also taken some mini discrete maths which was primes, gcd, gerator functions orso, and graphs at end, like djikstras and fork fulkerson, computational maths which was the typical numerical analysis, i think it should be the same everywhere, and now taking signals/systems where we are learning laplace and fourier transform (we are actually using tables lmao); so uh i thought manifolds were interesting when we learned about them in calc2, we only talked about implicit value theorem and inverse function theorem orso, because we could say that in a point in space we could approximate a function with several variables to a function with one variable, which seems very useful irl, also youtube how can we quantify a curve XD videos i guess, so i think thats related to geometry, but i want to do this more as a 30 day quarantine challenge orso and would rather learn new things, i would also have to learn algebra for a maths masters, so im thinking of either reading an algebra book(and actually doing the exercises, i never do that), or doing the same for some geometry book and get fucked by probably middle school geometry shit and then some linear algebra revisions, so what do and what book? thanks

>>11599631
>Doing engineering, thinking of doing a maths masters, im from europe and have taken calc1(derivatives, integrals, some series), calc2(multivar calc, thats all i think), complex analysis and differential equations(last sem and i dont really remember, residue theorem, then a whole bunch of dif eqs that i dont know the names, and fourier something, which was approximating a function via sins and cos but it had to be a set value out of some bonds), uh have also taken some mini discrete maths which was primes, gcd, gerator functions orso, and graphs at end, like djikstras and fork fulkerson, computational maths which was the typical numerical analysis, i think it should be the same everywhere, and now taking signals/systems where we are learning laplace and fourier transform (we are actually using tables lmao); so uh i thought manifolds were interesting when we learned about them in calc2, we only talked about implicit value theorem and inverse function theorem orso, because we could say that in a point in space we could approximate a function with several variables to a function with one variable, which seems very useful irl, also youtube how can we quantify a curve XD videos i guess, so i think thats related to geometry, but i want to do this more as a 30 day quarantine challenge orso and would rather learn new things, i would also have to learn algebra for a maths masters, so im thinking of either reading an algebra book(and actually doing the exercises, i never do that), or doing the same for some geometry book and get fucked by probably middle school geometry shit and then some linear algebra revisions, so what do and what book? thanks
what's the tl;dr?

>>11593192
Integrals. Just solve a bunch of complicated integrals using integration by parts and substitution etc. It will be hard but extremely rewarding and it will get better after the first 1000 problems.

>>11599631
>>11599638
TL;DR:
Doing engineering bachelors, want to do maths masters, want to study some maths as quarantine challenge XD, im probably interested in geometry but i would rather learn something completely new from the start; what do and what books?

>>11599657
Topology or group theory. Sound good?

>>11599657
>im probably interested in geometry
well then I've got the perfect reading list for you

>>11599325
Well I took an analysis course using an easier book than Rudin in second year. Rudin is third year analysis and to get the degree you can take it or an applied complex analysis course, and I took the latter. I did courses in Rings and Fields, Groups, Galois theory, and Algebraic geometry. So I avoided rigorous analysis and measure theory, which I regret. My brain seems more open to the ideas now.

>>11599680
forgot to add to tldr that i was thinking of algebra(more likely as i dont know shit so everything is new) or geometry(which would prob have to see some shit i learned in middle school + a review of lin algebra);
my school uses langs algebra, but online it says its a graduate book, so im guessing they dont do it fully / use as complementary.. what book should i use for abstract algebra?
>>11599688
shoo meme guy

>>11599713
I liked Herstein's book myself, but I have seen people praise Dummit-Foote a lot.

>>11593355
Deeper knowledge of cohomology theories made the vietcong invincible

>>11599617
dont know, has been like that for a while. sometimes i worry about having lost all my knowledge/skill. oh well, it will be alright.

>>11599733
>sometimes i worry about having lost all my knowledge/skill
I know the feeling. I have a basis for a resignation letter ready because of the crushing despair this causes sometimes. Eat your veggies and vitamin, iron too.

>>11599731
Dummit-Foote is a decent book for its intended purpose (catch-all text for undergrad algebra courses) but it's really bad for self-study. It's bigger than my old phonebook, there's literally thousands of problems (most of which are mediocre and boring) and there's no way for a self-studier to know which problems don't suck.

>>11599731
>Herstein
Youre talking about 'topics of algebra', correct? Im getting 2 books via google search

>>11599778
Yes, and it seems I am also recommending it, since >>11599776

>>11599776
Guy that wants the answers here, im looking to do the exercises, but i expect to fail/get stuck a lot, i probably want a book that i can find the solutions somewhere

>>11598562
Planing the best way of learning X is a good way of procrastinating while appearing to be doing something useful. It's common among language learners too

>>11598331
Fraleigh is an excellent choice for a first course if you're unfamiliar with proofs. Herstein is the definitive undergrad algebra book. Dummit & Foote, as others have pointed out, is good but very encyclopedic.

>>11598562
Because it's fun. Everybody likes windowshopping.
It can be, and often is, used as a procrastination device (I can't learn anything unless I use the one and only absolute perfect book, oh damn I read the first 10 pages on set notation but this other book looks better, guess I have to start over, repeat ad nauseam) but as long as you spend most of your time actually learning things, a little time spent shopping around for books doesn't hurt anybody.
In fact considering you're probably going to spend a few months with whatever book you use, it seems reasonable to spend a week or so thinking about what's available and what best fits your tastes/what you're looking for.

Good night, /mg/.

>>11599785
Alright thanks, see my youtube for daily updates (prob not daily)

How do I visualize GL(n,R), SL(n,R), GL(n,C), and SL(n,C) as smooth manifolds embedded into some higher dim. Euclidean space? In particular, how do I visualize their relations to each other? I am inclined to view GL(n,R) as two blobs floating in space, disconnected by [math]\det > 0[/math] vs. [math]\det < 0[/math], and SL(n,R) as a submanifold on the [math]\det > 0[/math] blob. But that can't be correct, because SL(n,R) isn't simply connected either.

And then I get totally lost when it comes to visualizing the complex groups.

>>11600139
>And then I get totally lost when it comes to visualizing the complex groups
Just don't bother.

>>11600139
>how do I visualize [math]R^{n^2}[/math] minus the zeroes of the determinant polynomial, the zeroes of the [ath]det ~ x -1[/math] polynomial and the same for the complex cases
Stare into Grothendieck's bald head until it reveals its secrets.

>>11600191
how was daddy alexander so smart

>>11600139
>and SL(n,R) as a submanifold on the det>0det>0 blob. But that can't be correct, because SL(n,R) isn't simply connected either.
Why can't it be correct? A submanifold of a simply connected manifold does not have to be simply connected.
It's probably honestly not a good idea to try and form a visual picture to rely on, because the only special linear group you can actually visualize ( SL(2,R) ) is the only one in the entire sequence with a goofy topology compared to the rest.

>>11600188
>>11600191
>>11600234
Hmm, okay, fair enough.

>>11593164
>>11593164
>>11593164
>>11593164

>>11593150
It is well-known that you can describe groups, rings, modules, etc. internal to any category using so-called finite product theories. This is generalized to finite limit theories, which also include internal categories, internal groupoids, etc. Any coalgebraic structure can be obtained in a straightforward way by simply dualizing.

What I want to know is if any work has been done in the "non-Cartesian" setting; i.e. replacing categorical products with an arbitrary monoidal product.

Currently learning about Hopf algebroids on the way to the E-Adams spectral sequence, for context.

>>11600446
dilate

>>11599354
>If an object suddenly grew, what formula would you use to calculate the weight?
volume times density gets you mass
>Say you had a glass marble with a diameter of .75in and a weight of 1 gram and it magically doubled to a 1.5in diamater, would it weigh 3 grams?
if it has the same density as the small form it should be 8 grams
[math]V_{sphere}=\frac{4}{3}\pi r^3[/math]
doubling r multiplies the volume by 8 (2^3)

>spent all day fucking around instead of working on an easy paper
why do i do this

>>11594528
wtf i have less qualificaitons than you and found my first job easy af and also get new offers regularly. do you apply exclusively to google or what

I am currently doing an applied math masters. I have published papers in statistics (Q2). I have taken measure theory, analysis, functional analysis, some discrete math and knowledge. Basically zero knowledge of topology, abstract algebra, geometry, number theory. Could I switch brances to mathematics? Could I get accepted with funding to a masters (or phd lel) in math?

>>11600941
yes, but in what? You don't do "mathematics" at masters/PhD level, you select an area of mathematical research you're interested in and you pursue in this particular field.

>>11600956
>You don't do "mathematics" at masters/PhD level
Depends where you are. In the USA your first year or so is usually spent grinding out the general-purpose "mathematics" analysis/algebra/topology trilogy, before you write your qual and immediately forget 85% of it

Good morning, /mg/!

>>11599877
Link?

>>11600745
All too relateable.

>>11601108
buddy it's 12:30 in the morning. Quarantines really messed up your sense of time

>>11601119
6:33 ante meridiem*

>>11601127
Don't know what that is, so it's not real. Go to bed

>>11601146
Nope, it's time to work.

>>11601150
At the [math]bear[/math] minimum you should sleep in till 8 or 10, c'mon

>>11601157
I wish I could sleep more than 6 or 7 hours a night.

>>11601164
Thoughts and prayers for you

>>11601173
Thanks.

Hello /mg/, I heard you guys got BTFO'd by a basic induction problem a few threads ago, so I thought I'd drop by and offer a chance to redeem yourselves

>tfw my circadian rhythm is about 24.5 hours
I actually went and got this formally diagnosed as a sleep disorder in high school. There's fuckall I can do about it, no matter what I try I just constantly loop forward in the time I can physically fall asleep until I'm going to bed at 11am.

>>11593150
>/mg/ maths general: anti-racism (second edition)

When I was kid, had a protected home and family. I didn't need to worry about the outside world. Didn't need to understand the fears of socio-economic jewery. I used to had sound sleep and dream lucid. I was like a aspiring mathematician reaching the omega point. It was like getting free from earthly boundings. It felt like I am finally the 'nobody'. The 'neutral'. The 'god'.

Couple of years later everything messed up. I was exposed to n g g r s and m z z y s. Keep myself barely alive is current goal. Socio-political condition is declining. Losing position everyday. Thinking about math is distant luxury.

Test
>11600000

>>11601552
Test #2
>>11600000

>>11598367
Imagine a 2200 page calculus text.

Is there an elegant Steiner construction of regular pentagon? (In theory given circle and its center you can perform every classical construction using straightedge alone.)

I know this is probably a brainlet question, but how can I prove the algebraic dependence of meromorphic functions on a compact Riemann surface?
Pic related gives a hint but it's not obvious by linear algebra, so there should be another analytic argument I'm missing here, I think.

>>11593283
ok anny mctranny

do you guys really have time to watch anime?

i dont know bros... i dont feel like doing anything

>>11593287
You should assume that everything on less wrong is false, unless proven otherwise.

Reminder, that this was started by a guy too stupid to figure out how to loose weight.

>>11599085
i dont find doing hard things/struggling fun

>>11601836
Not always, but now I think I could easily spend a few hours on that.

>>11601866
How to tight weight?

>>11601776
>it's not obvious by linear algebra
Are you super duper sure it's not obvious by linear algebra?
You have a map [math]z \rightarrow \{ f(z)^j g(z)^k \}_{j, k}[/math] which sends points in the Riemann surface to these matrices (which we'll interpret as vectors in the vector space of matrices, so [math]\mathbb{C}^{n^2}[/math] ). You want to show that there's a non-zero linear functional on [math]\mathbb{C}^{n^2}[/math] which makes the thing zero [math]d^2+2d[/math] times. I think you can even do it by picking random points where [math]f[/math] and [math]g[/math] don't zero and making the thing zero there.

>>11601881
>How to tight weight?
You mean "loose weight"?
Go outside and eat less then what you would normally eat.

>>11601898
But that is for losing weight. I want to tight or loose weight.

>>11601906
>But that is for losing weight.
No, that is for loosing weight, you know where your skin becomes loose, because you loost fat.

Yes, I know my english isn't perfect...

>>11601916
The good thing about this lock down is that it makes eating less a lot easier.

>>11593150

based good ol'

by the way, can mathematicians be called "order enforcement"?

>>11593192

it is category theory, sir

>>11601923
Well, for me it makes eating more and sitting around all day a lot easier.

>>11601883
That doesn't seem to work. You're basically saying that given d^2+2d points in a d^2-dimensional vector space you can find a non-zero linear functional mapping them all to zero. This isn't true in general (I think this is what you meant by saying you could pick values of z randomly)
Of course in our case we have more information about what our vectors look like but a proof of what we want in this case still seems absolute aids.
Let me know if I'm being a brainlet.

>>11601931
>it is category theory, sir
A good recommendation.

>>11601932
That's not nice.

Where are yukariposts?

>>11601942
>That's not nice.
That's why, over the last few days, I only ate lunch and skipped the rest.
The calories from that really should be enough...

>>11601946
Stay strong, anon.

>>11601949
Thanks!

>>11601941
My bad, I make a mistake earlier.
You see, the sum starts at [math]0[/math], so the vector space actually has dimension [math](d+1)^2=d^2+2d+1[/math].
Then you can choose [math]d^2+2d+1-1[/math] random points and make the functional annihilate them.

Huh

>>11596069
I'm comparing it to other books that I find better

>>11600876
what kind of job you got? i apply anywhere, for data analyst positions mostly.

>>11601964
God damn it. I'm retarded, but thanks for helping me out.
Here's another one. I promise this is the last one and I'm not gonna clog up /mg/ with any more dumb stuff.
I think I got it, except for the case in which [math]lim_{y \rightarrow \infty} f(x+iy)=\infty \forall x [\math] (to prove that the fourier seriers terminates on the negative side, and then the same using the other limit for the positive side)

Did /mg/ suddenly slow down by 60?
A weekend effect?

>>11602662
>Did /mg/ suddenly slow down by 60?
What do you mean?

>>11595306
>Book of Proof and How to Solve It
proofbooks = memebooks

>>11602662
zoomers post on here pretending to do their homework

>>11599644

that does sound comfy as fuck.

>>11601945
>Where are yukariposts?
She passed away (COVID-19)

>>11601945
(s)he is too racist to post in anti-racist breads

>>11602707
60%, only 1 thread per 3 daus.

>>11602379
well yeah mi position is called data scientist

>>11600988
yeah that was what I was thinking about, taking general purpose phd level classes before knowking what do I want to pursue

>>11602997
>60%, only 1 thread per 3 daus.
generals are a meme

>>11603055
Are such classes a US thing, or are they common everywhere? I don't have such in my uni (euro).

>>11597402
As an introduction Neil carothers

does this happen to anyone else?

I found a probality theory book at goodwill for $3.99, but it's not on any meme list. It's a good book though, it reads well, MIT authors, and it's short and it's perhaps most importantly not a pdf but a real book. but i always get this nagging feeling when I do shit like this that I should drop reading it, look up the best meme book and get it from libgen instead. i guess it's a form of perfectionism / me maybe trying to justify some form of procrastination

anyway im gonna stick with it, just wondering if anyone else has the same retardation

>>11603263
not quite
but I have two books on probability, two on PDEs, two on topology, and two on linear equations
They're each slightly different from one another in their approaches, target audiences, etc which I appreciate. I'm currently reading the two topology books concurrently and it's a very interesting experience.

>>11603263
>>11603319
i have 7 books total. (not on probability or math, just books in general). not too many but i know what they are about.

awesome we got another mass SHITMMIGRATION poster farting his shit all over /sci/. go back t redit you scientifically illiterate rube.

>>11595729
>never even tried to race a turtle but find that you will never reach it

>>11600446
Sure...
This seems like something where you wrote down a source category equipped it with a monoidal structure and then considered monoidal functors out to various targets, no need to restrict what kind of monoidal category you use as target.

Anything in particular you want to do with the E-based Adams spectral sequence?

why are PDEs so beautiful

>>11604837
wait, desmos has image export