/mg/ - maths general

[Anonymous No.14744148]

Formerly >>14699453 >>14714498

Talk maths.

[Anonymous No.14744155]

>>14744148
can somebody give me a physicslet-level explanation of Chern-Simons theory? preferably examples or pictures; i’ve seen the equations already and it does nothing for me

also Simons is rich so hopefully this knowledge is lucrative

[Anonymous No.14744161]

>>14744155
specifically the Chern-Simons three-form. whatever the math is there. forget i said “theory” i just care about whatever Chern and Simons (mathematicians) did

[Anonymous No.14744267]

>>14744155
sorry but physics (think) is too hard for mathematicians(hide behind formalism from think), try rephrasing your question in terms of sets

[Anonymous No.14744395]

Why are there no good combinatorics books?

[Anonymous No.14744398]

>>14744395
bc there arent any good combinatorics

[Anonymous No.14744413]

>>14744395
Applied Combinatorics by Tucker is pretty decent. There's also a really good section on it in Concrete Math by Knuth and team.

[Anonymous No.14744464]

>>14744155
Don't got any help for C-S theory but Simons always says the math gave him the intuitions for revising models, so I'd think at best you'd have keener eye lookin at datasheets after suffering with some manifolds.

[Anonymous No.14744512]

>>14744395
There are tons
>>14744155
Simons is rich due to insider trading kek

[Anonymous No.14744667]

In order to study measure theory and functional analysis, which subject should I go first with?

[Anonymous No.14744670]

>>14744667
principles of mathematical analysis rudin, walter

[Anonymous No.14744673]

>>14744670
I mean between both those subjects, Functional or measure, or they can be studied simultaneously maybe?

[Anonymous No.14744737]

>>14744673
it would be normal to study the basics of measure theory (Lebesgue measure and Lebesgue integrals and the basics of Hilbert spaces such as L2) before doing either. But after that point you could get started with either

[Anonymous No.14744741]

>>14744673
Measure Theory
L^p spaces are important for FA.

[Anonymous No.14744747]

>>14744667
Analysis 1-3 by Amann & Escher

[Anonymous No.14745485]

hit me with a book that has a decent section on multivariable calculus

[Anonymous No.14745544]

How do I get good at maths? I generally sucked and procrastinated throughout my school life in maths.
But, I'm trying to get my stuff together for college. But, it feels so hard to try maths. I get burnt out easily. Literally, everyone in my class is better than me at mathematics.

[Anonymous No.14745560]

>elliptic and modular functions can be defined as rational expressions of theta functions
Where can i learn about theta functions that take this approach? As in they are introduced before a general theory of elliptic functions.

[Anonymous No.14745592]

>>14745544
Practice and hard work, what kind of answer would you expect?

[Anonymous No.14745627]

>>14745592
But I'm doing something wrong if I simply don't understand the material in the first place. The practice part would come later.

[Anonymous No.14745643]

>>14745627
No, the understanding comes after practice. Always. Until you actually do the proof, the statement is unlikely to make any sense.

[Anonymous No.14745645]

>>14745627
Read easier books. Or simply other books. Different people have different taste in textbooks. Admittedly picking correctly gets easier as you learn more and learn what sort of presentation gels with you.

What sort of material are you having trouble understanding and what book are you using to learn that material?

[Anonymous No.14745663]

>>14744395
There are:
(Kluwer Texts in the Mathematical Sciences 19) O. Melnikov, V. Sarvanov, R. Tyshkevich, V. Yemelichev, I. Zverovich (auth.) - Exercises in Graph Theory-Springer Netherlands (1998)

[Anonymous No.14745705]

>>14745627
This is right. Listen to others advice, but believe in yourself.

>>14745643
"One should never try to prove something which is not almost obvious."-Grothendieck

Why are you putting practice above understanding? Math is not chess tactics.

>>14744395
You really should read concrete math by Knuth. Even >>14744413 mentioned them. The methods don't always work, but they're really powerful.

>>14745485
Sadly your best bet may be google and a book as reference.

[Anonymous No.14745728]

>>14745645
It's highschool level precalculus. I have two books recommended: College Algerbra and The Art of Problem Solving. But, I mostly just read the lecture notes given by the lecturer. Also, it's mostly not the books that are the problem, I don't understand it when it's explained in the class.

[Anonymous No.14745751]

>>14745728
Art of Problem Solving is hard to beat. I don't know who your teacher is, but I'd trust them over 99% of HS teachers.

[Anonymous No.14745776]

>>14745705
Math is a lot like chess. You wont beat a GM by learning every rule and every tactic of chess. it takes practce just like any other skill. Just the same you can know every definition and every theorem in real analysis, but that wont help actually proving something converges. The most obvious statements can have the most difficult proofs, and without practice all your understanding wont help one bit with an actual proof.

[Anonymous No.14745784]

I wish I was smart enough for maths

[Anonymous No.14745818]

>>14745776
>without practice all your understanding wont help one bit with an actual proof
Shows how much you understand.

Practice is very important, but there are many levels of thought in mathematics. No one level is sufficient.

>>14745784
Do pure math if you enjoy it. Talent doesn't make mathematicians life easier.

[Anonymous No.14745933]

>>14745818
You are just wrong. All the theory in the world wont help with something like
[math] \sum_{n=1}^{\infty}(-1)^{n-1}\frac{H_n^3}{n^2} [/math]
You can understand all there is to know about infinite series and harmonic numbers and anything else you think you need, and still you couldnt solve this. Only by practicing thousands of examples can one realize how to approach this problem.

[Anonymous No.14746198]

>>14744741
thanks anon.

[Anonymous No.14746204]

>>14745784
I am not smart enough for maths, but people either can't notice or are too polite to say anything. Just a B student.

[Anonymous No.14746241]

>>14745933
It converges by the Leibniz Criterion. Every freshman learns that even without doing exercises.

[Anonymous No.14746280]

>>14746241
I never learned this as a freshman. What course?

[Anonymous No.14746281]

>>14746280
Analysis 1

[Anonymous No.14746296]

>>14746241
Oh, you're referring the alternating series. I was unaware it went by another name and I got mind blocked. Also just read the post you're replying to, which I hadn't before I claimed I never learned it.
Yeah, sorry.
I covered this in calculus II as a freshman as well. Pic from textbook,didn't know it named after Leibniz, im not big on names or history.

[Anonymous No.14746451]

I'm finding baby Rudin's treatment of point set topology kind of unintuitive, any supplementary resources?

[Anonymous No.14746458]

>11 months since PhD
>still no post-doc
It is over, isn't?

[Anonymous No.14746466]

>>14746458
Just apply to the NSA and enjoy retirement at this point.

[Anonymous No.14746467]

>>14746458
Here's your post-doc employment

[Anonymous No.14746481]

>>14746458
I mean it's not like you can apply all year round. If you missed last year's deadlines, it's not very surprising. Now if you apply in Fall and don't get anything, you can start looking for work in industry. Better yet, start looking for work in industry in September, while you apply for postdocs

[Anonymous No.14746485]

>>14746451
Reminder that people who recommend Rudin have never read any other textbook and have massive inferiority complexes.

[Anonymous No.14746552]

>>14746241
>It converges
No shit it converges. But what does it converge to?
>inb4 who cares
Evaluating series are extremely common in analytic number theory, and theres no "understaning" behind it. The only way to know what to do is by doing it hundreds of times before.

[Anonymous No.14746566]

>>14746485
>Reminder that people who recommend Rudin have never read any other textbook and have massive inferiority complexes.
The below is an interview I had with a few friends who also knew Rudin well and were impressed by his research. (I went to read "Kiss Out", Rudin's work about the relationship between mothers and kids.) "I liked Rudin for his thesis research on the genetics of parenting and the role that women in the family play," said Susan.

Another friend wrote:

I would agree with the conclusion it has drawn from Rudin that the importance of children is not a one or two-sided problem. In fact, it makes me think that the issue should be a more complex problem, more complex than the one we're trying to discuss and not a single issue.

I understand how some people think that the main issue is the need for mothers to choose the mother that they want to have. But in order to get what is important, as in the case of some groups, that needs to be found first. The same needs to be expressed for men as for women!

This, I would suggest, is a big problem that people have all too often ignored. It is true that these people can be more helpful and kind to children, because they can understand the need to ensure they're getting all the answers they want. But it is also true that they can't ask what is actually the best way of doing things for

[Anonymous No.14746582]

Is there an introduction to Analysis I that is even easier than Abbott, kinda like an Analysis survival guide for non-mathfags? It should just teach you the absolute minimum you need, not try to show you the beauty of math or shit. Should teach you to do proofs too, but very gentle and with lube.

[Anonymous No.14746600]

>>14746582
Introduction to Real Analysis by Bartle is as handholding as it's gonna get short of the author coming to your house and tutoring you

[Anonymous No.14746619]

>>14744148
Anyone here done some learning theory?
If so, does the fundamental theorem of PAC learning extend to non 0-1 loss functions?
The proof I know for this theorem relies heavily on showing that the VC dimension of a hypothesis class of binary classifiers coincides with the VC dimension of the class of induced funtions, that is [math]\mathcal{F} = \{ \ell^{0-1}(h, \cdot, \cdot) : h \in \mathcal{H} \}[/math]
If I use anything other than the 0-1 loss the entire argument fails.

[Anonymous No.14746628]

>>14746485
My first class on the subject was with rudin and whilst the professor encouraged us to look into other sources and even made us compare proofs from different authors I still think rudin is the best way to go about it

[Anonymous No.14746634]

>>14746485
I've read parts of all the popular RA texts that go around here and they all hold your hand way too much, to the point where I'd prefer Rudin leaving me in the dark occasionaly

[Anonymous No.14746664]

>>14744395
while you could argue that there aren't any nice general books on combinatorics, perhaps because combinatorics doesn't really have "unifying organizing principles" or stuff like that (see also Igor Pak's blog post https://igorpak.wordpress.com/2021/07/03/the-problem-with-combinatorics-textbooks/ ), there are a bunch of nice books in various branches of combinatorics; say Richard Stanley's two-volume Enumerative Combinatorics, or Stasys Jukna's Extremal Combinatorics.

also want to mention two relatively recent books that are pretty cool: Yufei Zhao's Graph Theory and Additive Combinatorics, as well as Larry Guth's Polynomial Methods in Combinatorics.

[Anonymous No.14746668]

>>14744148
Abstract algebra book recommendations?

[Anonymous No.14746690]

>>14746668
https://alozano.clas.uconn.edu/math5210f16/
Textbook and syllabus.

[Anonymous No.14746712]

>>14746668
I liked Artin.

[Anonymous No.14746764]

>>14746668
I'm currently going through Aluffi - Chapter 0 and enjoying it a lot. Probably not a good first exposition to AA. On the other hand, I can at least vouch for it being a nice first exposition to category theory.

[Anonymous No.14746821]

>>14746668
groups rings modules auslander

[Anonymous No.14746873]

is geometric algebra a meme?

[Anonymous No.14747249]

>>14746873
Anything too far into the "pure" field is a meme. Its not "pure", its childish, trivial, and useless.

[Anonymous No.14747256]

Has anybody on here ever completed every single problem in a calculus textbook?

[Anonymous No.14747257]

At what point in your studies did you stop feeling like a complete fucking waste.

[Anonymous No.14747259]

>>14747256
Yes, but I had the answer book for Spivak to guide me through it for honors calculus I/II/III. I'm currently a junior, and this is my post >>14747257

[Anonymous No.14747297]

>>14746458
just curious, what have you been doing for 11 months since finishing your phd and now? I mean in the sense of what have you been occupying yourself with

[Anonymous No.14747300]

>>14746668
Personally I really liked Dummit-Foote. It's organised really well and proves almost everything.

[Anonymous No.14747310]

The document I’ve been using to type answers to the hartshorne exercises is finally at 100 pages.
I’m tired bros… but I must keep going

[Anonymous No.14747315]

>>14747310
Don't give up anon! We believe in you. Things will eventually be great.

[Anonymous No.14747406]

>>14747315
Thank you friend.
So far my favorite parts were part 5 and 6 of chapter 1.
The abstract nonsingular curves he defined is one of the coolest objects in math I’ve seen so far. I also really liked the proofs involving completions of local rings.

[Anonymous No.14747546]

I got my math bachelor's degree last year and I'm considering graduate school now, but my grades were pretty shit. Should I grind out a low tier masters program and try and get a better record in the hopes of getting into a good phd program? Is that common?

[Anonymous No.14747693]

I have to into differential calculus soon. What topics should I master before doing this. I got Stewart's percale book to prepare for this.

[Anonymous No.14747744]

Should I use certain texts to learn Mathematics, or does it really not matter all that much (at least in the beginning)? I'm self-studying the subject so there's no real need for rigor, but I find it fascinating to the point that I want to know Mathematics to the fullest extent I can-rigor and all. I've seen people argue that modern textbooks are rather lacking with regards to how they go about covering concepts as well as the poor quality of problem sets. I don't know how true that argument is, seeing as how I'm a mathlet.

So should I prefer to use whatever gets recommended, or can I get by with whatever text is available to me? If the main issue is with the problem sets found in the texts, can I just use a supplementary problem book and make due with that and whatever text I come across?

[Anonymous No.14747778]

>>14747693
Everything from pic related.

[Anonymous No.14747795]

>>14747693
Honestly just reads stewart's calculus. Unless you're completely clueless about even the most basic math you shouldn't be reading a precalc book, as just about everything they cover is also covered in calc texts.

[Anonymous No.14747814]

>>14744148
What is going on in this thread?
Its filled with early undergrads asking about calc and tards seething about baby Rudin.
Cmon, let's start some interesting discussion.
What are you working on/stuyding, anon?
In currently working hard on optimal control and mainly statistical learning theory for an upcoming exam.
Learning theory is pretty damn interesting, the theory is decently well fleshed out but there's a lot of obvious room for new results, specially when it comes to characterizing learning.
The current results have some rather restrictive assumptions and the main result doesn't encompass all possible scenarios.

[Anonymous No.14747951]

>>14747778
I'll start with Steearts Calculus and follow along with Chad Leonard. I was worried because I was told that people without a solid foundation struggle with Calculus.
Thank you, fren.

[Anonymous No.14747954]

>>14747795
>>> >>14747951

[Anonymous No.14747983]

>>14747814
>Its filled with early undergrads asking about calc and tards seething about baby Rudin.
What the fuck are you talking about, every thread is like this.
>What are you working on/stuyding, anon?
Yu Gi Oh

[Anonymous No.14747988]

>>14745933
The summation you linked is tedious indeed, but Concrete Math by Knuth spends is full of general methods to approach summations like this. No cleverness required, only understanding and a lot of patience.

[Anonymous No.14747993]

>>14747983
yu gi oh is the only acceptable card game

[Anonymous No.14747998]

>>14747951
not that anon but I'd say I only first developed strong foundations of math after I went through calc. Just do math and don't worry too much about whether you are "ready" for something.

[Anonymous No.14748009]

What is a set in mathematics? How can I tell if something is a set or not?

[Anonymous No.14748010]

>>14745933
The summation you linked looks very tedious, but very well I accept the challenge. Roast me when I fail.

I've barely solved any summations like this, but I understand what should work in principle.

[Anonymous No.14748035]

>>14748009
Cant you faggots just google?

>>14747983
>Yu Gi Oh
Why not something more fun like magic the gathering?

[Anonymous No.14748041]

>>14748035
>Cant you faggots just google?
I did, but google is not helpful in this case.

[Anonymous No.14748050]

>>14748009
Find a hobby

[Anonymous No.14748051]

>>14748041
Ok then there's two options:
1) youre a retard that thinks ZFC is "wrong" or something and yourr going to start posting your diahrrea here
2) youre a mega retard that doesnt understand basic definitions and youre going to post even more retarded questions here

If 2, work hard, become less retarded and come back later.
If 1, just fuck off to /x/ or /pol/ or wherever

[Anonymous No.14748059]

>>14748051
>1) youre a retard that thinks ZFC is "wrong" or something and yourr going to start posting your diahrrea here
Not the case.
>2) youre a mega retard that doesnt understand basic definitions
What basic definitions? That was literally my question.

[Anonymous No.14748066]

>>14748050
My hobby for now is foundations of math.

[Anonymous No.14748072]

>>14748059
>What basic definitions?
Those
https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory#Axioms
Using a search engine for 10 seconds could have given you them.

[Anonymous No.14748080]

>>14748072
Are you retarded? Have you even read the article? They don't define what a set is even in the slightest.

[Anonymous No.14748083]

>>14744148
I passed Trigonometry (pre calc) with an A about a year ago, and I can't remember a goddamn thing. Its irritating the hell outta me, but I would really like to have the concepts laid out in Trig to embedded in my day to day usage (computer programmer). Does anyone have any advice on how to properly internalize these concepts. Its very upsetting that I can't keep these things in my head

[Anonymous No.14748086]

>>14748080
That set of axioms is literally the defintion of a set.

[Anonymous No.14748093]

>>14748086
You must be an ESL. Please look up what the word definition means before using it.

[Anonymous No.14748094]

>>14748080
Took me ten seconds to find a long ass article explaining sets
https://en.wikipedia.org/wiki/Set_(mathematics)

[Anonymous No.14748107]

>>14748080
>They don't define what a set is even in the slightest.
Now it's time for you to sperg about how primitive notions aren't rigorous while ignoring the munchausen trilemma

[Anonymous No.14748123]

>>14748094
Nowhere in that article is the contemporary notion of a set defined. They just list a bunch of properties they wish to hold.
>>14748107
Nothing wrong with primitive notions as long as you understand what they refer to. After all, we all have to start somewhere. But there's a difference between primitive notion that nobody has a clue what it means and is unable to explain to others, and primitive notions that are clear, intuitively obvious and easily explainable.

[Anonymous No.14748151]

If some process now occurs "50% faster", does this mean that the speed increased by 50%, or time reduced by 50%?

[Anonymous No.14748216]

>>14748123
>>14748080
So option one of >>14748051 then.
Fuck off.

[Anonymous No.14748222]

>>14748151
>If some process now occurs "50% faster", does this mean that the speed increased by 50%, or time reduced by 50%?
These 2 are equivalent you fucking brainlet.

Oh for fucks sake, cmon lets talk about something interesting discuss with me any of the following:

>Functional analysis
>Numerics, specifically numerics of PDE but also could do numerics of signal/image processing (formal discussion of course)
>Systems theory
>Non discrete optimization
>Learning theory

I know my interests are completely applied but oh well I want to talk about the proofs, the theorems, etc

[Anonymous No.14748227]

>>14748222
Is "there are infinitely many primes" a definition of prime numbers?

[Anonymous No.14748233]

>>14748222
>These 2 are equivalent you fucking brainlet.
NTA, but
Let's say v=s/t where v is process speed and s is some fixed amount
if we increase v by 50%, we will get t'=s/v' = 2s/3v = 2t/3, so time increases by 66.6%
if we reduce t by 50% instead, we get v'=s/t' = 2s/t = 2v, so v increases by 100%
>I know my interests are completely applied
Maybe it's too early for you to do actual math if you don't know school-tier basics and act as a cunt to newbies

>>14748151
See above

[Anonymous No.14748236]

Base 10, your time is up!

[Anonymous No.14748238]

>>14748216
>>14748051
Is "there are infinitely many primes" a definition of prime numbers?
What about "2 is a prime number". Is that a definition of what a prime number is?

[Anonymous No.14748249]

>>14748151
>time reduced by 50%?
>>14748222
>These 2 are equivalent you fucking brainlet.

Lmao average /sci/ poster

[Anonymous No.14748283]

>>14747546
You sound like me 4 years ago. Thats what i did and it worked out. Just dont do bad at your low-tier masters or youre permanently fucked.

[Anonymous No.14748293]

>>14748222
>These 2 are equivalent you fucking brainlet.
Would you mind pretending to be an algebraic geometer the next time you post something retarded? Appliedfags are bullied enough here as it is.

[Anonymous No.14748299]

[math] \texttt{Retvrn To Tradition.} [/math]
[eqn] \mathtt{\sum_{n=-\infty}^{\infty}q^{n(3n+1)/2}(x^{3n}-x^{-3n-1})=\prod_{n=1}^{\infty}(1-q^n)(1-xq^n)(1-x^{-1}q^{n-1})(1-x^2q^{2n-1})(1-x^{-2}q^{2n-1})} [/eqn]

[Anonymous No.14748331]

What's the proper name for 360-gon? Trihectahexacontagon?

[Anonymous No.14748395]

Do real numbers require assuming actual infinites?

[Anonymous No.14748430]

>>14748395
The natural numbers require actual infinities

[Anonymous No.14748436]

>>14748430
How so?

[Anonymous No.14748451]

>>14748430
How does the concept of 3 require actual infinities?

[Anonymous No.14748499]

>>14748331
It's called a circle, anon.

[Anonymous No.14748503]

>>14746873
It's nice to know the basics. Helps build intuition. But overall it's a niche subject.

[Anonymous No.14748588]

>>14748436
>>14748451
Virtually every property of the naturals is proved via induction, which requires an inductive set (i.e an infinite one)

[Anonymous No.14748605]

>>14748588
>which requires an inductive set
No it doesn't.

[Anonymous No.14748612]

>>14748588
an partial ordering R in M is called inductive, if every chain in M to R got a supremum though

[Anonymous No.14748622]

>>14748605
It does in a rigorous environment, read the formalisation part of https://en.m.wikipedia.org/wiki/Mathematical_induction
>>14748612
Okay? We're talking about inductive sets

[Anonymous No.14748634]

>>14748622
>We're talking about inductive sets
so

[Anonymous No.14748640]

>>14748634
So I'm not sure what you're reply had to do with my post

[Anonymous No.14748642]

>>14748622
>It does in a rigorous environment, read the formalisation part of https://en.m.wikipedia.org/wiki/Mathematical_induction
No it doesn't, idiot. Read the section you linked. You can state induction in first order logic, where no completed infinity is assumed.

[Anonymous No.14748648]

>>14748640
an inductive set has an ordering. how could you deny that

[Anonymous No.14748655]

>>14748642
Lmfao

[Anonymous No.14748658]

>>14748655
>you can state induction in a theory that requires completed infinities, therefore induction requires completed infinities
Retard.

[Anonymous No.14748659]

>>14748642
You can state it but you need two extra axioms and the system has to be one in which the naturals are already defined, whereas it's a theorem in ZFC.
Not sure what your point is

[Anonymous No.14748661]

>>14748655
Read a few line below this.

[Anonymous No.14748666]

>>14748659
>Not sure what your point is
My point is that you don't need completed infinities to prove properties of the naturals, you retard.

[Anonymous No.14748670]

>>14748666
>>14748661
You need an axiom as well as an axiom schema if you don't want to use completed infinities, and I obviously don't need to tell you why that's problematic.
Any system that doesn't axiomatize induction requires completed infinity

[Anonymous No.14748675]

>>14748670
>You need an axiom as well as an axiom schema if you don't want to use completed infinities
Yes, you can state the axioms perfectly well in first order logic.
>and I obviously don't need to tell you why that's problematic
Because it's not.
>Any system that doesn't axiomatize induction requires completed infinity
That's just nonsense.

[Anonymous No.14748686]

>>14748670
Why is having an axiom schema problematic?

[Anonymous No.14748693]

>>14744148
>hence thus therefore

Is there any difference?

[Anonymous No.14748706]

>>14748693
The difference is in prose and rhythm. Its important that you dont sound like a robot when you write. Compare anything written by Hardy with your average american graduate text and you will see what I mean. Mathematicians have lost the ability to write and still wonder why people turn to older books.

[Anonymous No.14748708]

>>14748675
>That's just nonsense.
Provide a system that doesn't axiomatise the notion but which has induction then.
>>14748686
It's like responding to someone claiming that the definition of a real number requires the notion of cuts/cauchy-sequences with "no they don't! you can just assume that they exist!"
Pretty meaningless

[Anonymous No.14748713]

>>14748706
The only language a true mathematician needs to master is LaTeX.

[Anonymous No.14748719]

>>14748706
Mathematicians today are writing bullshit several times more complex than anything Hardy ever imagined. He wasn't a real mathematician anyways, just someone who coasted off others.

[Anonymous No.14748723]

>>14748706
As it should be, I'm reading your book to learn something, if I wanted to be enamored I'd read a poem instead

[Anonymous No.14748748]

>>14748706
>"muh beauty!1!"
Hey buddy, I think you got the wrong door. The philosophy club is two blocks down.

[Anonymous No.14748752]

>>14748748
Two blocks down and six feet under.

[Anonymous No.14748753]

>>14748748
he's an underage summerfag. He'll learn soon

[Anonymous No.14748872]

>>>/r9k/69769328

[Anonymous No.14748895]

Are there any names that own an intro course as hard as munkres owns topology?

[Anonymous No.14748908]

>>14748895
Rudin

[Anonymous No.14748918]

>>14748908
no

[Anonymous No.14748950]

>>14748895
Evans for PDEs

[Anonymous No.14748966]

>>14748918
Yes

[Anonymous No.14748996]

>>14745933
>>14748010
Okay lol you win. I give up.

This problem is akin to asking someone to multiply 371638272622 by 17382829911 by hand and saying it demonstrates understanding is secondary to practice.

It can be done, but all together is a huge test of patience.

You compute the summation by systematically computing the 25 summations below it, where each of those is expressed in terms of the summations preceeding those. All together this will take at least 30 pages.

[Anonymous No.14749015]

>>14748908
I prefer Amann & Escher. Soviet/Russian ones are really good too.
>b-but it's long
don't care.

[Anonymous No.14749041]

>>14748009
If something has curly braces around it, it's a set. You can even have only the curly braces and nothing inside them, that's the empty set.

[Anonymous No.14749046]

>>14749041
{how many elements does this set have?}

[Anonymous No.14749055]

>>14744148
pi r squared... native americans called it maize

[Anonymous No.14749061]

>>14749046
[math]\vert \{\textrm{how many elements does this set have?}\} \vert[/math]

[Anonymous No.14749067]

>>14749015
I don't like amann not because it's long but because it's often long for no good reason.
For example in defining the naturals the author brings up the ordinal construction and inductive sets and what not and then immediately forgets about it and develops the naturals via peano axioms.
It reads more like a formal treatise on analysis than a textbook intended to teach you.

[Anonymous No.14749074]

>>14748010
>>14745933
This computation is fucking FAT, but fun at least. Be back in 7 days.

[Anonymous No.14749152]

Any recommendations for complex geometry books

[Anonymous No.14749214]

>study point-set topology
>dont care about counterexamples

[Anonymous No.14749222]

>>14749152
any intro book like apostol calculus has the "geometry" of complex numbers anon

[Anonymous No.14749239]

>>14749222
That’s not what I mean by complex geometry. I’m talking about objects like complex manifolds

[Anonymous No.14749248]

>>14749222
>Open Apostol Calculus
>CTRL+F for [math]CP^n[/math]
>No result found
...

[Anonymous No.14749254]

>>14749248
>be mathematician
>search for cp
>get arrested

[Anonymous No.14749279]

>>14749152
i also recommed Ch7 of Chern differential geometry and Moroianu kahler geometry, though do note he leaves a lot of proofs to Griffiths-Harris

[Anonymous No.14749301]

>>14749279
Pdf seems kino, thanks friend.

[Anonymous No.14749304]

>calc II exam tomorrow
>final homework assignment is worth 1% of grade
>150 problems covering everything in the course
I've spent this whole week just doing this homework assignment and still have a few left. I can't leave points on the table...
At what point does math stop being "grindy"?

[Anonymous No.14749325]

>>14749304
>At what point does math stop being "grindy"?
At calc 2 desu.

[Anonymous No.14749330]

I'm having some trouble grasping conditional probability. It says that Pr(A & B) = Pr(B | A) * Pr(A), so Pr(B | A) = Pr(A & B)/Pr(A), given that Pr(A)>0. But what is the intuition behind this, and how did someone come up with this?

[Anonymous No.14749331]

>>14749325
Not if he still has diff eq and linear algebra ahead of him

[Anonymous No.14749341]

>>14749330
P(A) is the probability A occurs. P(B|A) is the probability B occurs if A is known to occur. By the product rule P(A)*P(B|A) is the probability both of these events occur. Let’s say we know A occurs 25% of the time, and 50% of the time A occurs, B also occurs. Then the probability they both occur is 12.5%, which is 50% of the 25% of the time A occurs

[Anonymous No.14749345]

This is without a doubt the most egregious case of Hatcher's dogshit authorship. There is so much detail packed in here that is completely swept under the rug which the reader has been given 0 means to unravel themselves.

I was able to find seven MSE posts asking for clarification on this example. Seven.

The fact that this terrible book is standard in algebraic topology is not just a shame, it's an act of laziness by all universities and professors who still use it.

[Anonymous No.14749348]

>>14749331
I guess that's true. At the very least you can expect Linear Algebra to be relatively more "highbrow" excluding all the retarded RREF and inverse calculation shit they make you do.

>>14749345
What do you suggest as an alternative textbook?

[Anonymous No.14749351]

>>14749345
just read rotman bro

[Anonymous No.14749363]

>>14749345
What are you talking about this is perfectly well exaplained.
If you can’t imagine the klein bottle as gluing two möbius bands together, just use the construction of those surfaces that comes from gluing together boundaries of squares.
Hell if you present it that way you can triangulate the space pretty easily and compute homology that way.

[Anonymous No.14749375]

>>14749331
Remaining:
Linear Algebra
Numerical linear algebra
Statistical Analysis
Multivariable calculus
Scientific computing
Combinatorics
Intro to PDE
Numerical methods for PDEs
Applied vector and tensor math
Abstract Algebra
complex variables
Real Analysis
Math Modeling with Diff Eq
History of math

[Anonymous No.14749385]

>>14749375
>numerical
>applied
>statistical
>modeling
If you don't like "grindy"... I've got some bad news.

[Anonymous No.14749388]

>>14749341
Also note that if A and B are independent, as in B occurs 50% of the time regardless of if A occurred or not, then P(B|A)=P(B)

[Anonymous No.14749391]

>>14749385
Oh... maybe it gets better once we use matlab more hhaha....
I wanted a CS degree but without the gay courses. Its applied/computational math.

[Anonymous No.14749472]

>>14749391
>Oh... maybe it gets better once we use matlab more hhaha....
Can you use matlab on your exams?

[Anonymous No.14749491]

>>14749472
No...

[Anonymous No.14749496]

>>14749391
Tbh I don't think those courses are necessarily grindy.

[Anonymous No.14749502]

>>14749363
>If you can’t imagine the klein bottle as gluing two möbius bands together, just use the construction of those surfaces that comes from gluing together boundaries of squares.
Of course I'm not talking about the easiest part. It's the neglecting to include a picture of said square, the immediate reduction to the shorter sequence which is not explained, the maps pulled out of nowhere (not explaining the nuance of orientation which is basically why this computation works), and worst of all the half-baked explanation of H1 which is literally a trick. The SE answer about that part alone is multiple paragraphs of necessary computation and explanation.

This is also the singular example given on the topic, and worse, the only place in the book the homology of the Klein bottle is computed, yet the final result is not even summarized or highlighted for reference.

[Anonymous No.14749516]

>>14748293
>>14748249
>>14748233
Welp sorry for the retarded post, read that wrong

>>14749375
Seems very based, bachelors?

[Anonymous No.14749524]

>>14749516
>Seems very based, bachelors?
Yes, at michigan tech.

[Anonymous No.14749554]

>>14749502
He does explain it.
“All the higher homology groups of K are 0 from the earlier part of the mayer vietoris sequence”
If you really need to be handheld, the higher homology groups of the circle are all 0, and A, B, and A intersect B are homotopic to a circle.
The explanation of H_1 isn’t a trick, him choosing a new basis is just an isomorphism of Z oplus Z so that the map we have becomes 1 maps to (0,2). You do this type of thing all the time when dealing with exact sequences.
If you have trouble understanding a proof just ask in sqt, but don’t pretend the author is writing a bad proof

[Anonymous No.14749598]

>>14749524
Damn nice, wish I could do stuff like that during bachelors.
Doing my masters in the same area but in europe.
How strong is your program programming wise?

[Anonymous No.14749599]

Why are PDEs guys afraid of talking about de Lebesgue measure and measure theory in general? Obviously they mention it but whenever a measure theoretic question comes they just kinda hind it. It is a basic tool I think most people have seen it.

[Anonymous No.14749609]

>>14749598
Um, I don't really know. I just picked Michigan tech because its in-state. I got into Umich as well which people talk up a lot, but I don't want to be anywhere near Detroit and the course names didn't sound as cool.

[Anonymous No.14749611]

How do I actually motivate myself to learn math? I enjoy it and I need to brush up on it as I'm going to be studying computer science but learning everything I knew before again is a drag

[Anonymous No.14749631]

>>14749599
>Why are PDEs guys afraid of talking about de Lebesgue measure and measure theory in general?
What are you going on about? Modern pde theory is based on Lp and sobolev spaces.

>>14749609
I meant as in computer programming.
Do they make you do a ton of computer programming?

[Anonymous No.14749637]

>>14749611
You need to make it a habit and pace yourself.
I just have a ritual for every day when I get back home, to study for 3 hours. I have a nice desk with all my books on a shelf, syllabus and checklists taped on the wall, stationary organized. Its a great zen zone. The only internet I allow myself during that time is math related content.

[Anonymous No.14749642]

>>14749631
>Do they make you do a ton of computer programming?
Not that I've experienced yet. Matlab is heavily used later on, but I don't think anyone in the math curriculum requires another programming language. I will still take up to algorithms/data structures, since I hear that is how you get a job. Well, I'll actually just do whatever my advisor tells me, I don't want to think about that, only the math.

[Anonymous No.14749656]

>>14749631
Yeah obviously but it is not like they discuss the definition of the Lebesgue integral or write things in terms of usual measure theory lingo. I get that it is usually not needed but it is also not terribly hard to do it. Usually Lp space is a space of functions with a norm and it is complete and the properties for integrals you want are satisfied but I mean the texts and courses seem to avoid going over it. Hell I think brezis just defines as a closure to avoid it altogether.

[Anonymous No.14749665]

>>14749375
damn, I'm very good at maths (at least so far), but how the hell are you capable of keeping all that stuff in your head?

I passed Trigonometry (pre calc) with an A about a year ago, and I can't remember a goddamn thing. Its irritating the hell outta me, but I would really like to have the concepts laid out in Trig to embedded in my day to day usage (computer programmer). same thing happened to me with algebra a year and a half before that. any advice on how to properly internalize and solidify these concepts in my head? I get worried that I won't be able to apply this knowledge to future projects just because they get so easily memory hole'd

[Anonymous No.14749667]

>>14749656
They dont go over basic measure stuff because
1) youre supposed to know that already
2) PDEs are older than measure theory and have their own lingo
3) like you said its not terribly important
Formalism is only good when necessary.

[Anonymous No.14749677]

>>14744148
What do you guys think of lie superalgebra?

[Anonymous No.14749720]

>>14745728
>"College Algerbra"
Is that the one by Kaufmann and Schwitters?
Absolutely can commend that book. Broken down very well and linearly introduces concepts to things.

[Anonymous No.14749725]

>>14749667
>Formalism is only good when necessary
Well here is kinda my issue. The properties we like about Lp spaces and Sobolev and whatever basically come from measure theory. If you don't understand this you basically can only use pure functional analysis and whatever you know from calc. For example, the duality in Lp spaces for conjugate p,q is a deep result but the hardest part about the proof uses measure theory. So what we end up learning will not have a lot of wiggle room. And the problem is that I don't think most people have seen the proofs of these things.

[Anonymous No.14749747]

Just recently got back into self studying math and am at conic sections. I've done decently well with basic algebra type shit and I want to know where to go from here and where to end up. I did some basic calculus with differentiation and integration for polynomials but that's really it. There was a practice site I found and I did decently on it, was fun. Where do I go from here?

[Anonymous No.14749759]

>>14749637
That's good advice, thank you anon. I appreciate it

[Anonymous No.14749768]

>>14749554
>If you really need to be handheld
It's unfortunate that people still think like this. Explaining and handholding are different. Strang ILA is an example of way too much hand holding. There is an in-between, and those are the best textbooks. Hatcher is infamous for lying on the opposite side of that spectrum, as I'm sure you have heard before.
> You do this type of thing all the time when dealing with exact sequences
Which is precisely why the author should explain it. Exact sequences are introduced earlier as though they are a brand new concept. He builds the long exact sequence from scratch. This should tell you he's not assuming them as prerequisite knowledge. But then in actual practice he doesn't explain basic computations involving them. His writing is purposefully terse and cryptic when it needs to be the most to be clear, and rambles on and on and on when just a simple definition/theorem would suffice.
> If you have trouble understanding a proof just ask in sqt, but don’t pretend the author is writing a bad proof
I understand the proof in its entirety, with no help from the book. Once I found out what needed to be done, and saw how simple it was, I was bothered, as should be anyone, with how Hatcher could not be fucked to write a couple extra sentences. All I'm saying... seven SE posts for such a basic example speaks for itself.

[Anonymous No.14749803]

Its possible learn advanced geometry facts without using coordinates?

[Anonymous No.14749811]

>>14748293
you and him are the same
you will never make any discovery that would impact our worthless species anyway
it's funny seeing a human mocking his own kind without realizing they both require the same waste product to survive

[Anonymous No.14749875]

>>14749665
Uh, well I'm not there yet. Those are the courses I have left, and I'm about to enter my sophomore year this coming fall term. It really isn't that much though. I'm set to get an A in Calculus II if I get above an 83 on this final. I got a 100 on the series and power series exam. I don't really memorize anything besides the occasional "one weird trick!" which seems to be common with big integrals, before exams. Same with series expansion for a few tricky series I knew would take too much time to derive during an exam.
I mean, all the stuff I listed that I have coming up is just more of the same, just in increasing detail. What I did absolutely forget was all of C++. I took two courses to meet some elective requirements, got a A and a B because I worked in group projects, but I just didn't care about it and I probably couldn't even do the very first example now lol.
As for your trig stuff, you will still use it all the time every day, so its hard to forget... Maybe the product-to-sum and sum-to-product identities will make you stop and think about them for a bit, but everything else just becomes intuitive after a while.
So I guess.... just actually care about it(so you like to remember it) and then do it every day, or you'll end up like me and my now wasted semesters in C++
I'm just an undergrad though. I hope someone way past us gives us a comment too.

[Anonymous No.14749893]

>>14746467
Wrong. I'd sooner kill myself than go to Australia

[Anonymous No.14749944]

Any faggot here has any clue if there's some -free- courses available to transition into mathematical finance coming from a pure math background ( AG, HT, ST )?

[Anonymous No.14749997]

>>14749341
>By the product rule P(A)*P(B|A) is the probability both of these events occur
But what is the intuition behind that rule? Why is the probability that they both happen the product of the first one's probability and probability that second one happens given first one happened?

[Anonymous No.14750013]

>>14749997
Because if two events are dependent, it means we can extract information about one’s probability if the other one happens, and we need to factor in that gained knowledge. Note that by symmetry you could do this from both sides, but arrive at the same answer. Put one more way, think of each multiplication as a restriction to that event. Multiplying by P(A) restricts us to those events where A occurs. In the space of events in which A occurs, the probability B occurs is no longer P(B), it’s P(B|A)

[Anonymous No.14750017]

I have just come to accept that my worse decision in life so far has been to study Math. Trying to justify studying this crap for anything other than mental masturbation is cope.
>b-but muh le abstract skills
>muh reasoning skills
I should've studied Mechanical Engineering because I like cars but I was too depressed to remember and just picked the most edgy option.

[Anonymous No.14750022]

>>14750017
Nice. I only studied math because it was one of the few degrees offered that I could complete entirely online, from home, without ever stepping foot on campus.

[Anonymous No.14750023]

I'm new here and haven't done math since high school. I'm reviewing pre calc material now, but should I learn calculus alongside it or just go in depth on pre calc? And when I start, should I use Stewart's book or Spivak?

[Anonymous No.14750054]

>>14750022
If you think about it it's similar to me. I couldn't see myself putting effort into a career where you couldn't do everything with a paper and pencil. I had a good experience in the local Olympiads and thought, hell why don't I make this my living? Just paper and pencil.
I guess I was just being dramatic, I find dreadful the following. It's a sea of definitions and theorems, but the applications are thin. It's easier to forget shit you don't even use. I would actually find my program EASIER if the courses were more crammed together than spread out through semesters.

[Anonymous No.14750061]

>>14750054
>. It's a sea of definitions and theorems, but the applications are thin.
Should have gone for applied math. Applied chads win again. 90% of the fun, 100% of the money.

[Anonymous No.14750104]

>>14750023
Having a good grasp of how polynomials work, how to add, subtract, multiply, divide, and factor them, and knowing what they look like on a graph helps a lot with everything in calculus. Knowing exponential functions and trigonometry is important too, since any calculus book will have lots of example problems with them.
If you wanna follow the memes, use Spivak, but if you wanna go for something easier, you can use Stewart or Larson. The concepts are the same, even though the presentation is different.

[Anonymous No.14750107]

>>14750061
I couldn't have chosen that, but my current program is a mix of applied, pure and even physics. The only universities that offer Applied Math are pretty far from where I live. I could have done it if I was working and renting but damn, would that have been hard. But probably good for health.
Anyways can't keep crying over spilled milk, I will study Applied Math in graduate school if I even care about additional education. "Applied Math" usually denotes a subset of what actually is Applied Math? Like it's more Applied Analysis rather than "Applied Maths" in general

[Anonymous No.14750167]

>>14750017
>mental masturbation
Yes, and?

[Anonymous No.14750172]

>>14750023
Spivak is very, very hard for beginners.
If you're not interested in pure math then you shouldn't even bother, something like Stewart or Thomas would be more appropriate

[Anonymous No.14750188]

>>14750172
You can just read spivak alongside whatever book is used for your course (probably stewart).

[Anonymous No.14750203]

>>14750188
Why read Spivak at all if you can read an easier book on Calculus that covers the same stuff instead?

[Anonymous No.14750212]

>>14750203
The same reason you read 3 books on the same topic for every course. Different ways of explaining the same thing assist in comprehension. Spivak also has better problems, and the solutions manual is cheaper.

[Anonymous No.14750231]

>>14750212
>The same reason you read 3 books on the same topic for every course.
I don't. I read one book and expect it to have everything I should have to know. If I don't understand something, my natural instinct is to go down, not up on the complexity scale.

[Anonymous No.14750258]

>>14749330
Draw a venn diagram, if you have 2 sets A and B that are not independent nor mutually exclusive, the conditional B | A is asking you to only consider the entire set of A and its subsets, which in this case would only be A&B and A&B' (the set A isolated from B, or A not including B). From Pr(A | B) is just a first principles problem, the total probability of A&B being Pr(A&B) divided by the total probability of Pr(A). If you're not sure about the first principles reasoning, think of an urn problem. You have n objects in an urn, k of them are red and the remaining n-k are blue. If you want the probability of drawing 1 red object, it would be the total amount of red objects divided by the total amount of objects, that is, k/n. From there, the reasoning for the product rule Pr(A&B) = Pr(A)*Pr(A | B), is more of just an algebraic result that stems from the aforementioned first principles.

[Anonymous No.14750262]

>>14750017
That sucks, hope things get better for you. /gioyc/ is on >>>/adv/ btw.

[Anonymous No.14750387]

Why do analysis books take the existence of the supremum as an axiom? It should be a theorem, it arises from the order in R and the Zorn's Lema.

[Anonymous No.14750393]

Well, this semester was the first time i've ever felt lost in the career, and it was for topology. Nothing has ever compared to that subject in complexity. I've studied analysis, abstract algebra, functional analysis, EDO's, but nothing comes even close to be as hard as topology is. Maybe topology showed me that I am not as good as thought for math.

[Anonymous No.14750411]

>>14750387
What do you mean they take the supremum as an axiom?
Do you mean that every subset of R with an upper bound has a least upper bound? In that case it does not follow from the ordering of R and zorns lemma. If all you needed was an ordering and zorns lemma, then Q would have this property and it doesnt.
>>14750393
What exactly was the issue? Most of point set topology should be covered in an analysis class. What topics did this class cover?

[Anonymous No.14750430]

Looking for mathemathical examples or application that can be used to know the value of an image like the amount of traffic it will garner or sales it ll gain

Doesnt have to advanced ones but probably modern enough to be used in webs recently so one can know pleasing aesthetics for the web design or similarly

[Anonymous No.14750442]

>>14748222
>applied "mathematician"
>arrogant and ignorant
Imagine coming to fucking 4chin to stroke your ego thinking you are hot shit because you took an undergrad PDE course, and not only not being able to answer simple questions, but actively discouraging it. Maybe l*ddit will be more up your valley, you can farm upvotes there for sounding smart.

[Anonymous No.14750458]

>>14748222
Discuss this
>>14750430

[Anonymous No.14750550]

>>14745933
Ask me how I know you're Indian

[Anonymous No.14750626]

>>14750550
You dont

[Anonymous No.14750632]

>>14749656
>>14749667
>>14749725
I dont get your complaint.
Most modern treatments of pde absolutely do treat the measure part of it carefully and most books I know either reference a book on measure theory or even have an appendix on it (Evans for example)
The proof of things like p,q duality in Lp spaces is not the object of a course on pde even if the result is used there.

[Anonymous No.14750633]

>>14745784
>I wish I was smart enough for maths
I wish retards stopped blaming some mythical "talent" or "predisposition" or "genes" for lacking skills like mathematics, playing musical instruments, languages, or drawing.
You spend time and put in effort, you get results. That "talented" musician, or "talented" painter, or "talented" mathematician, or "talented" polyglot (his parents were linguists!) have put hundreds or likely thousands of hours to get where they are.

I've already said it before, the concept of talent is one of the most destructive ideas that somehow survived in the digital era.

[Anonymous No.14750635]

>>14750633
yeah

[Anonymous No.14750648]

>>14750633
This. I had a friend in high school who was apparently "talented" in math and always got better grades than me, and now, in university, I'm better than him. Why? Because his "talent" boiled down to his parents teaching him "advanced" mathematics at an early age and at a certain point he'll have to, just like me, learn new stuff.

[Anonymous No.14750655]

>>14750442
>only not being able to answer simple questions, but actively discouraging it
Nigger this board has /sqt/
This thread is for the discussion of mathematics
Stop being such a drama queen faggot
Also, please do seethe at the fact that all appliedchads will work in problems way more interesting than anything you ever will and will actually get paid for their work
Faggot

[Anonymous No.14750657]

>>14744148
she's literally me

[Anonymous No.14750660]

>>14750655
uh-oh meltie

[Anonymous No.14750662]

>>14750458
You want an algorithm that given an image Outputs a score that estimates the amount of "traffic" it can generate?
How are you measuring this popularity/traffic?
Do you have a database of popular and unpopular images?

[Anonymous No.14750668]

>>14750662
>How are you measuring this popularity/traffic?
>Do you have a database of popular and unpopular images?
Wow, apparently it takes an "applied" "mathematician" to figure out that you can solve this by maximising a popularity score through supervised learning based on already labeled data.

>>14750655
Take your meds, anon. And don't forget to brush up on 3rd grade maths so that you, too, would be able to reply to simple questions.

[Anonymous No.14750673]

>>14750655
>fucked up solving a simple high-school problem while acting cocky
>shits out an incoherent schizo rant the next day
Yikes, buddy.

[Anonymous No.14750682]

>>14750662
Ok so i need popular and unpopular images. Thats done... then what do i do with it?

[Anonymous No.14750683]

>>14750662
>how do i measure traffic
Thats the question. Naturally the format would end with =T(equals T) but i m not a math wiz either.

[Anonymous No.14750686]

>>14750655
Learn to take the L my man. Everyone is laughing at you not because you made a mistake (that's normal), but because you ALSO arrogantly dismissed the question and felt like you needed to flaunt the fields you allegedly are knowledgeable about. Nobody likes people like you, learn from it and be better.
>Nigger
>drama queen faggot
>seethe
>Faggot
Nevermind.

[Anonymous No.14750715]

>>14750686
>Everyone is laughing at you not because you made a mistake (that's normal), but because you ALSO arrogantly dismissed the question and felt like you needed to flaunt the fields you allegedly are knowledgeable about. Nobody likes people like you, learn from it and be better.
Fuck ton of projection here.
I didnt "flaunt" the fields I am knowledgeable about. Bunch of dudes here doing much harder/interesting stuff. I just wanted to discuss topics beyond very basic questions, so I listed topics I can actually engage in discussion beyond basic remarks.
H
Point is, how can this general still draw any interest if every thread is undergrad homework questions + baby Rudin seethe + schizo shit about infinity ?
Why do you even entertain all this shit when this board actually has a thread for questions?

[Anonymous No.14750873]

Discord was the end of /mg/.
There's many math discords that have better math discussion while also having 4chan style shitposting as well as coomer and anime images.

I'm not hating on on /mg/, but I'm kinda surprised why this thread still makes 100 posts per day.

[Anonymous No.14750882]

This is the most autistic shit I have ever seen https://us.metamath.org/mpeuni/areacirc.html

[Anonymous No.14750883]

>>14750715
>Point is, how can this general still draw any interest if every thread is undergrad homework questions
Well for one, we don't have enough educated people to discuss more sophisticated topics, especially when self-proclaimed experts like you are obnoxious cunts.

[Anonymous No.14750893]

>>14749875
yea, I guess we both are coming at this from different ends. I've been extensively learning the c++ library, coupled with Win32. there's alot to memorize (obviously), but the concrete results help fuel my resolve to continue. I was hoping that I could somehow utilize graphics programming - or just programming in general - to facilitate the learning of trig, calc, etc. but I wouldn't know where to start with that either. You are probably right that I need to 'care more' about maths to get better at it, but I do have a concern and need to be better, I just don't know what I can utilize to properly practice and internalize these concepts in the same way I can for coding up a project in c++

[Anonymous No.14750894]

>>14750873
where can I find these discords?

[Anonymous No.14750895]

>>14750662
Bump

[Anonymous No.14750897]

>>14746668
Get Langed

[Anonymous No.14750916]

>>14750873
What such discords do you know, partner?

[Anonymous No.14750920]

>>14750882
kek yes, but metamath also found some shorter proofs to theorems previously proved. If anybody cares about this. It's also nice they they allow one to choose ones own axiom systems and logic. It's hella ugly and all in one ridiculous file, but it has its perks.

[Anonymous No.14751037]

>>14750883
>especially when self-proclaimed experts like you are obnoxious cunts
Nice strawman
Ive never claimed to be an expert

[Anonymous No.14751058]

>>14750895
You said you had a database of images tagged as popular and unpopular, as >>14750668 said, your problem can be solved by training a classifier, I suggest one of the many famous CNNs out there such as resnet.

[Anonymous No.14751075]

>>14750883
>experts like you are obnoxious cunts
Expertbros, we're clearly unwanted here, maybe we should go to reddit after all.

[Anonymous No.14751357]

What are some "lost arts" in math that everyone used to know?
>root extraction
>elliptic/special/hypergeometric functions
>solvable polynomials

[Anonymous No.14751360]

>>14750668
>>14751058
Yeah this seems like it but problem is that cant actually compare directly nor is there a proper way to do this either despite importance of the subject or its generality.
>CNN,resnet
Can i instead do this manually? I guess it wont be as precise but maybe a sort of entry to learning data analysis since i have no set future anyway lel

[Anonymous No.14751445]

>>14751360
>Yeah this seems like it but problem is that cant actually compare directly nor is there a proper way to do this either despite importance of the subject or its generality
What do you mean by "comparing directly"?
Do you want to compare the probability of an image being popular with that of another? Then the cnn approach allows you to do this
Do you want to estimate popularity in absolute terms (eg with a probability of 0.9 this image will have a popularity score of ie 10 with) ? If so then maybe setting up the problem as a regression task could be the correct way to go.
In any case this is absolutely a machine learning problem.

>Can i instead do this manually? I guess it wont be as precise but maybe a sort of entry to learning data analysis since i have no set future anyway lel
You can do whatever you like however keep in mind coming up with architectures that generalize well is vey hard and in fact a major field of research in the area, thus for a specific task that you want to solve using something premade will almost surely (terminology intended) always be better.
If you want to mess around with building your own architecture id suggest doing it with a toy dataset such as mnist or fashion mnist and then trying different things out. Ive done exactly this with pytorch and its pretty fun and straight forward, its specielly fun if you start messing around with implementing your own version of gradient descent for trainng.

[Anonymous No.14751454]

>>14751445
Oh I should mention that if you want to train neural nets then you should absolutely gain access to an nvidia gpu first, either by using a cloud computing service or by using your own rig. Otherwise its painfully slow and also just fries your poor cpu

[Anonymous No.14751568]

My hunch has always been that indicative conditionals in natural language are expressing that the consequent is probable given that the antecedent is true. Turns out that this would go terribly wrong https://en.wikipedia.org/wiki/Lewis's_triviality_result
Thoughts?

[Anonymous No.14751581]

bros... I'm having some difficulties in accepting the axiom of choice. Reading the statement outloud makes me say "it's obvious", but it's consequences are very awkard and make me cringe. Using weaker versions of it seems like a big cope, and I don't think you can justify it just because of weird developements, it feels artificial to restrict yourself in such a way, so you end up doing choice or don't. Is there a nice resolution to this, or am I stuck with having the spectre of banach-tarski haunting me?

[Anonymous No.14751611]

>>14751075
kys tranny

[Anonymous No.14751651]

>>14751445
>>14751454
K i ll have to rethink this first
Thank you belly much

[Anonymous No.14751787]

>>14748238
As you seem to understand a set is a primitive notion so it has no mathematical definition. However the idea behind a set is simply that of a collection of objects. I don't see how this is difficult to understand. Alternatively if you use class theory, a set is defined as:

x is a set iff there exists some y such that [math]x\in y[/math] holds.

[Anonymous No.14751820]

>>14751581
imo the "paradoxical" part of Banach-Tarski is a result of infinity, not choice. If you accept a set can be duplicated by splitting it into infinitely many parts, accepting it can be done in finitely many is not that big of a leap (unless you've been conditioned to intuitively accept the cardinality paradoxes).

You could become a finitist but accepting the axioms is more fun and interesting, and works incredibly well for all physical applications.

[Anonymous No.14751909]

Is there a formula for taking the average between expectation and reality?

Let's say I buy three hard drives. The manufacturer claims there is a 1% risk of failure, per drive, per year. A year on, exactly one has failed.

Probably, the manufacturer lied and the real failure rate is higher? But by how much?

Probably, the answer is more than 1%, and probably, it's less than 33%. How do I calculate it more exactly?

Intuitively, if I buy say a million drives from them, and 25,000 fail, then I can safely assume the failure rate is ~2.5%. But how can I generalize this to smaller numbers? Is there a formula?

Reading about it online, I found Bayes' rule. That's great, but it requires me to have some kind of prior for how unreliable the manufacturer's data is (variance?). Is there a simple rule of thumb to calculate this if you don't have it?

(Assume drive failures are 100% independent and a static property of the hard drive model. Not asking specifically about hard drives, it's just an example.)

[Anonymous No.14751939]

>>14744148
im self-studying pure math and i just finished a book that was hard. Ive never felt so accomplished, ive found the key to happiness

[Anonymous No.14751948]

>>14750167
Cool if that fills your soul, I have bigger aspirations and I'm not so smart to have it not taking a lot of my time

[Anonymous No.14751956]

>>14751939
What do you mean finish? You did a few exercises after each section/chapter? Personally I avoid exercises

[Anonymous No.14751989]

>>14751956
Trust me anon, try not to avoid them. Also try to reconstruct every proof you go by on your own. You'll see so much stuff you failed to understand.

[Anonymous No.14751997]

>>14751956
i did all the excercises. They not only come well if you solve them but they also are good as worked examples if you look up the solution

[Anonymous No.14751999]

>>14751989
This. Sure, you will take "longer" but better to take 3 months for a book and then fully understand every single thing than to have a vague idea of the topic after reading through it all in a week

[Anonymous No.14752011]

>>14751909
The drives have a binomial distribution with p=.01, so for n samples the expectation is np and the variance is np(1-p). Then you can calculate how likely your sample distribution is compared to the expected distribution, and if it is significantly different (people usually look for 5% likelihood as default) then you start calling bullshit

[Anonymous No.14752026]

>>14752011
Sure, I get that, but how do I calculate the "real" value of p based on that information?

Also, how do I handle say 3 drives x 1.2 years? n = 3.6?

[Anonymous No.14752053]

>>14751939
What book?

[Anonymous No.14752065]

>>14752026
Sorry I missed your per year part. That changes the distribution but not the theory. I think it’s by the central limit theorem that the sample mean will converge to the statistical mean as n goes to infinity, and the variance is essentially a measurement of how fast that is. As n gets large the samples have to tend towards the mean, and if they tend towards some other number then that other number must be the mean. Disregard my last variance but your variance should be easily calculable

[Anonymous No.14752070]

>>14752053
introduction to topology by bert mendelson. Ik it may not be hard for the smarts around here but im retarded so lol

[Anonymous No.14752071]

need help fellas.
solving this easy integral, and i get the same expression twice, and the correct answer is only one of the expression because it repeats itself? is that a thing? im missing something right? theres no way you just erase an expression because it repeats itsellf...?

[Anonymous No.14752073]

>>14752065
Sure, but what I'm asking is how to get the statistical mean.
If my amount of samples is very low, it should be basically the same as the prior.
If the amount of samples is very high, it should be basically the same as the observed value.
How do I weight between the two? Can I use Laplace's rule here?

[Anonymous No.14752076]

>>14752065
Depending on what you mean by ‘per year’, the distribution you should use is the exponential distribution, assuming how old a drive is doesn’t change that 1% chance (i.e. if the drive has survived 3 years, it’s still a 1% chance it fails this year)

[Anonymous No.14752081]

>>14751989
>Also try to reconstruct every proof you go by on your own.
I always do, it's just that I don't get why would I want to solve some exercises. They seem hard and not interesting results

[Anonymous No.14752083]

>>14752073
But you either trust their statistic or you don’t. If you trust it, then the mean is their stated mean. If you don’t trust it, then the only mean you could guess is the mean of your samples. It’s impossible to guess which way to move your sample mean without taking more samples

[Anonymous No.14752106]

>>14752083
Well, no. For example, let's say that there are ten different hard drive factories - A, B, C, D, ..., J. And the average across all of them is 1%. I know that all of my drives are from the same factory, but I don't know which one, or the failure rate per factory.

How do I interpolate between the observed value (33%) and the stated value (1%)?

[Anonymous No.14752142]

>>14752081
Because failing to do them will strengthen your grasp on the concepts and help you uncover what you are lacking. Once you can actually prove stuff on your own, it won't be hard to reconstruct some of these proofs after you completely forget them.

[Anonymous No.14752150]

>>14752070
Very nice anon, no need to call yourself retarded.
Any ideas what subjects you’d like to look into next?

[Anonymous No.14752196]

>>14752150
id like to read about abstract algebra, because the group part of topology seems really interesting. Will probably buy the abstract algebra book by Gallian

[Anonymous No.14752200]

>>14752070
bro, you self-studied topology, at least at some 'basic' level. That's a world of difference between being smart and retarded. You did it, congratulations anon, I'm proud of your success despite I don't even know you.

I wanted to self-study topology at some point, but I needed analysis (instead of the basic calculus ofcourse) and I took other detours into stuff I found interesting to study, and it's been years since that lol. I hope to have the timke, energy and motivation to keep this way for as long as I can.

[Anonymous No.14752235]

>>14752200
thanks

[Anonymous No.14752244]

>>14752106
It seems to me you’re basing it on outside information like how much you trust the manufacturer or how the manufacturer operates. You can factor that in however you want but you’re assuming things you don’t know, such as “the manufacturer is lying but only a little bit”

[Anonymous No.14752479]

With the set [math]P(x)[/math] being the set of polynomials on x. and [math]d(P_m,P_n)=|{m-n}|[/math] a metric where [math]m[/math]. and [math]n[/math] are the degrees of polynomials respectively.
Is there any interesting application to this?

[Anonymous No.14752482]

What does the world of modern combinatorial study look like?

[Anonymous No.14752495]

>>14752479
I can think of it implicit in some ideas like minimal polynomials, but it seems too simple and narrow in scope to be of much interest

[Anonymous No.14752503]

>>14752495
>it seems too simple and narrow in scope to be of much interest
I see. I was thinking about a topology induced by the metric [math]d[/math] but it's all that I have, I haven't studied topology yet so I'm just shooting blind about this.

[Anonymous No.14752712]

Have any of you been following the letters to the editor in the AMS notices? Back in January, there was a letter from Richard Stanley, mathematics professor at MIT, complaining that most of the survey articles in the magazine are incomprehensible pretty much everyone. The continued into another letter in the May issue, and it remains unanswered.
From where I'm standing, the elephant in the room is the idiocy of Notices in general. Most articles have nothing to do with Mathematics, and are just political or social issues on diversity and inclusion. The few articles that are published there, don't seem to have been looked over for any coherence with the rest of the content published alongside it, and only exist to keep it "math themed", as nothing else is.

[Anonymous No.14752722]

>>14752712
provide links

[Anonymous No.14752748]

>>14752722
https://www.ams.org/journals/notices/202201/202201FullIssue.pdf?cat=fullissue&trk=fullissue202201

Original letter from Stanley is here.

https://www.ams.org/journals/notices/202205/202205FullIssue.pdf?cat=fullissue&trk=fullissue202205
Retired professor echoing the sentiment here.

You can review most of them here,
https://www.ams.org/cgi-bin/notices/amsnotices.pl?thispage=collectionnav&article_id=fullissue&article_type=gallery&gallery_type=fullissue

and see that besides a few math related articles, its mostly LGBT or diversity content.

[Anonymous No.14752792]

redpill me on the surreal numbers.

[Anonymous No.14752858]

>>14752792
A subclass of games.
https://en.wikipedia.org/wiki/Surreal_number#Games

[Anonymous No.14753003]

>>14748283
thanks, that gives me some reassurance. Did you have any good references? I made no lasting impressions with my professors, I'm not sure how I'll find some letters of recommendation

[Anonymous No.14753241]

>>14751909
>Is there a formula for taking the average between expectation and reality?
Hoffdings inequality?

[Anonymous No.14754044]

>>14752748
>and see that besides a few math related articles, its mostly LGBT or diversity content
Why in the fuck has everything become infected with this cancer? Growing beaurocracy ? Costless way to make your company/org appear more modern and hip? Like, seriously, why the fuck, virtually every single company/institution out there has a diversity statement these days and constantly puts out related stuff.

[Anonymous No.14754102]

>>14752479
That's not a metric. It's only a pseudometric.
https://en.wikipedia.org/wiki/Pseudometric_space

[Anonymous No.14754161]

>>14754044
>Why in the fuck has everything become infected with this cancer?
Spic-nig industrial complex

[Anonymous No.14754792]

>>14754102
oohh of course, my bad.

[Anonymous No.14754813]

is NBG+Boffa's anti-foundation axioms still a conservative extension of ZFC?

[Anonymous No.14755263]

are urelements ad quine atoms the same in terms of functionality?
what are the differences?

[Anonymous No.14755270]

>100% on calc II final
>97% final grade for Calc II summer term
pfff, easy. Now I know to believe 4chan instead of reddit on how difficult things actually are.

Bad news: It seems Muji no longer carries the 5mm grid B5 notebooks, and I only have 6 left. The only ones I can find are $10 on amazon.
Any other stationary autists have preferred materials for math? I also use an pentel orenz nero 0.2mm mechanical pencil and the ZE31 clicraser.

[Anonymous No.14755276]

>>14755270
I take notes with scraps of literal trash

[Anonymous No.14755283]

>>14755276
Badass.
If I'm not in a comfortable chair with noise cancelling headphones on, using my ideal mechanical pencil (wiped down so it has no body oils on it) on grid B5 paper, with controlled lighting (I use a screen bar light), and a filled mug of coffee, I am just not in my optimal zone and its not worth forcing myself to work in discomfort.

[Anonymous No.14755302]

It is generally accepted among modern mathematicians that the square root of 2 exists. However, there is a fringe group of mathematicians called finitists who argue otherwise. In this article, I will use algebra to show that the Square Root of 2 does indeed exist.

Algebra is all about the properties of numbers. Let's start with a number:

We start with 1. Then we know that 1 squared is 2 and so 22 = 4. We can just add 12 and 22 together to get 12. We can do the same thing with 92 and 42 to get 16. In general, the number we get when we add all the numbers we found by multiplying together will be bigger than the number that we started with. A number that equals the number we started with is called a normal number. We can continue to do this process, continuing to add numbers that have been found. Eventually, we will get to the number we started with. Now, what is a normal number? Some people say that the number we will eventually get after all this is no square root of 2. But the square root of 2 is a normal number.

So the square root of 2 exists. But just to be sure, let's check what is actually a square root of 2. Suppose you try to show me that 2 is a square root of 2. If we look at the proof that 13 + 22 = 4 and then divide that by 3, we see that 23 - 32 = 1. Then 22 - 12 = 23. Therefore, if we can do the same thing with 32 and 42, we see that 32 - 12 = 23 + 12. In other words, 32 - 13 is a square root of 2. But what is the square root of 2?

We can define a number that is not a square. We can find the square root of two. It is simply the smallest number that is the square of the square

[Anonymous No.14755321]

>>14752792
Excuse the popsci taste but this video is a good demonstration https://youtu.be/ZYj4NkeGPdM

[Anonymous No.14755910]

what do topologists even do?
like, most other fields work on all sorts of various topologically-flavored objects
but... what do you do with topology alone?

[Anonymous No.14755943]

>>14755302
>we know that 1 squared is 2
>We can just add 12 and 22 together to get 12
Huh?

[Anonymous No.14755981]

>>14755321
This video is great, felt like I was being thrown off a cliff in a good way

[Anonymous No.14755985]

>>14755910
kneepads

[Anonymous No.14756002]

>>14755321
holy shit

[Anonymous No.14756007]

>>14755321
Apparently the youtuber had died :(

[Anonymous No.14756009]

Do you think optimization is a good research area?

[Anonymous No.14756027]

Why isn't there a site like https://www.econjobrumors.com/
but for math bros like us? why are we relegated to one thread on one board on 4chan?

[Anonymous No.14756045]

>>14756009
As far as I know both discrete and non discrete variants are very active very interesting fields.
Specially with the current popularity of machine learning

[Anonymous No.14756233]

>>14756007
Yes, it's true, by suicide just before New Years 2022.
He also had a music channel where he does jazz
compositions on piano.

https://twitter.com/omaitzen

[Anonymous No.14756246]

Finding closed form solutions is mental masturbation
Numerical solutions are the only useful solutions

[Anonymous No.14756860]

what branch of math will make me cum?

[Anonymous No.14756873]

>>14756860
The one you build an intimate relationship with.

[Anonymous No.14757037]

Don't have the financial stability to go into a PhD program. I can't ask this anywhere else, but would most other mathematicians think less of me for going the masters to industry route?
I could do a thesis option of course.

[Anonymous No.14757341]

>>14757037
Why would they think less of you? More importantly why do you even care what anyone thinks?

[Anonymous No.14757598]

>>14756860
Algebra
Genuinely makes me feel like I want to cum.

[Anonymous No.14757649]

>Solve every question correctly
>Teacher doesn't like how i write math, despite everything is justified
>Grades goes down form 93% to 72%
How do i learn to write math properly? I mean, when i'm doing a proof i try to justify everything but the teachers always find something to criticize my work.

[Anonymous No.14757766]

>>14757649
Examples?

[Anonymous No.14757819]

>>14757766
Once i was making some proof about convergence of funciton. I wrote [math]\forall \epsilon>0 ...[/math] insted of Given [math]\epsilon > 0[/math] I got two points less in that question.

[Anonymous No.14758126]

>>14757819
This seems like a minor thing. Sure, I'd take off a point, but not 2.
The only solution is to just read a lot of proofs to see how people write.

[Anonymous No.14758135]

>It's hard to know where to start with “baby Rudin.” There is probably no more well-known, respected, loved, hated, and feared text in all of mathematical academia. Steven G. Krantz claims it’s one of the books that made him a mathematician; “It was easy to say, and often true, that anyone who could survive a year of Rudin was a real mathematician.” Vladimir Arnold, one of the champions of the “organic” approach to mathematics, reportedly called the book (in comparison to the lectures of Vladimir Zorich) “Bourbakian propaganda, stripping and sterilizing analysis of any soul or meaning beyond the symbols.”

>“Bourbakian propaganda, stripping and sterilizing analysis of any soul or meaning beyond the symbols.”

Who was in the right?

[Anonymous No.14758336]

>>14757649
>>14757819
It seems like you’re in an “introduction to proofs” class and the professor is trying to tell you to write in sentences instead of informal shorthand. Or you are using things as synonyms when they aren’t. Either way the way to learn how to write math is to listen to your professor