/mg/ - Math general

[Anonymous No.9781931]

What are you studying, /mg/?

[Anonymous No.9781950]

>>9781931
studying Teichmüller space while laying mein kampf next to it

[Anonymous No.9782121]

>>9781950
Teichmüller was so fucking based.

[Anonymous No.9782123]

>>9782121
you can't say based when he literally gave his life to hitler

[Anonymous No.9782134]

>>9782123
I can't?

(I am 90% memeing by the way)

[Anonymous No.9782136]

>>9782134
no u can always give your life to hitler if you have all your heart :)

[Anonymous No.9782147]

>>9782136
I am afraid that the time for giving your life to Hitler has passed and there is now nothing in the world giving your life for (I am not convinced of the wirth of giving your life to Hitler).

[Anonymous No.9782744]

Should I worry about working through a more classical textbook on Algebraic Geometry before diving into a modern text like Hartshorne?

I find I can never really get excited about studying the more classical stuff. Modern abstraction and formalism just seems to make everything seem cooler to me.

Probably the best would be to study a modern text and supplement it with more classical material to better understand the intuition and motivation behind the abstraction.

[Anonymous No.9782746]

>>9782744
>Should I worry about working through a more classical textbook on Algebraic Geometry before diving into a modern text like Hartshorne?
No.

[Anonymous No.9782761]

>>9782744
You certainly could, but I think if you dive straight into a modern treatment you're going to come away with the impression that algebraic geometry is algebra.
Maybe that's not bad, depending on your tastes and why you're studying it in the first place.

[Anonymous No.9782773]

>>9782744
>Modern abstraction and formalism just seems to make everything seem cooler to me.
>>>/lit/

[Anonymous No.9783234]

Can I use hyperbolic geometry to transform a nonconvex set into a convex one?

[Anonymous No.9783258]

>>9781931
>What are you studying, /mg/?
d-differentiation

[Anonymous No.9783459]

>>9782744
You shouldn't worry unless you have some type of brain damage which prevents you from developing intuitions about the objects you're working with without knowing and studying in depth how things were done a long time ago. The classical material is actually best understood using modern language, especially if you are learning it for the first time and you haven't picked up various bad habits yet.

[Anonymous No.9783466]

Ah ... That feel when finally got my paper in pure math accepted in a good journal

[Anonymous No.9783496]

smoothed particle memedynamics

[Anonymous No.9783672]

>>9783496
u talking to me?

[Anonymous No.9784526]

Is homotopy type theory a meme?

[Anonymous No.9784536]

>>9784526
>homotopy type theory
Why are you posting about this in /mg/?

[Anonymous No.9784538]

>>9781931
Algebraic Biology

[Anonymous No.9784542]

>>9781931
Studying black holes!

[Anonymous No.9784552]

Biochemist here. The little math I learned sparked my interest.
Is it possible to learn undergrad math autodidactically?

[Anonymous No.9784581]

>>9784526
A boring one. If you are trying to do something foundational, enjoy your dry stuff, and if you want to learn homotopy theory, try getting into it via topology and then categories instead of that shit.

[Anonymous No.9784675]

>>9784552
Yes.
Solve textbook problems or problem sets obtained online from undergrad courses to ensure you are actually learning the material.
If you can do the problems then you can be certain you aren't just deluding yourself into thinking you know the material. Note: looking up the solutions and "understanding" them isn't even remotely the same as finding the solution yourself.

[Anonymous No.9784693]

>>9784552
>Is it possible to learn undergrad math autodidactically?
If you actually have the motivation to do it, yes.
The key point is that you do exercise after exercise, if you just read the book you learn nothing.

[Anonymous No.9785036]

>>9784552
basic order you'd need, you'll obviously have covered many of these already
Differntiation > Integration > Series (Taylor etc.) > Ordinary Differential Equations > Vectors > complex numbers and methodology > vector calculus

the depth of statistics depends on the discipline, but those subjects would get you started on most of the maths required for any physical system.

the number of starting points and routes for pure mathematics is pretty crazy though.

[Anonymous No.9785042]

>advanced linear algebra
>probability
>"measurement and integration theory"

I don't know how to translate those names, but you got the idea. I've done real analysis and topology already but the course is getting more and more difficult.
I'm honestly not sure if I'm still doing it because of the challenge or because of my love for mathematics.

[Anonymous No.9785059]

>>9781931
Top fucking kek this is the whiteboard I have in my room.

[Anonymous No.9785066]

>>9785036
>Differntiation > Integration
yikes...

[Anonymous No.9785067]

Why would you care about differential forms if there are many interesting manifolds that are not orientable? Measure theoretic approaches let you generalize theorems and actually has a proper geometric intuition.

[Anonymous No.9785068]

>>9785059
>scribbling random stuff from Lee and basic QM shit to appear smart on a Cantonese urban cycling forum
Yikes.

[Anonymous No.9785073]

>>9785068
Yeah talking shit on /sci/. The purpose of the whiteboard is to write stuff like small proofs and definitions that I want to understand and look at them all day to digest them.having them written there it’s the first thing I look in the morning and keeps me thinking about it.

[Anonymous No.9785077]

>>9785067
Differenital forms serve more purposes than just defining a volume measure.

[Anonymous No.9785080]

>>9785073
>literally all algebraic symbol pushing
>not one single geometric drawing of tangent bundles and their pullbacks
>"""intuition"""
Yeah sure, I believe you.

[Anonymous No.9785088]

>>9785080
I don’t give a single fuck if you do anon. Read my answer again and try to understand what I’m writing. PROOFS AND DEFINITIONS. Diagrams and geometric drawings are for paper.

[Anonymous No.9785093]

have you had your daily dose of category theory on windows /mg/?

[Anonymous No.9785094]

>>9785093

[Anonymous No.9785095]

>>9785077
Could you further further explain that? As a way to write down many equations and laws elegantly, I understand the appeal, as actually doing all the measure theoretic work seems pretty tedious and hard, but what exactly, besides the algebraic simplicity, makes them useful?

[Anonymous No.9785099]

>>9785088
[math]{\mathbb{S}^n} = {\sum ^\infty }{S^n}[/math] brainlet

[Anonymous No.9785101]

>>9785088
>proofs, which is more significant, on whiteboard, which is less permanent
>intuitive drawings, which is a once/twice look-over thing after the right picture is in your head, on paper, which is more permanent
Good job whipping that up drawing in the past 3 minutes btw, though I'm not sure why you'd write down the definition of a section on paper right after you said definitions go on the whiteboard?
>[math]\mathbb{S}^1[/math] for the circle [math]S^1[/math]
Yikes.

[Anonymous No.9785114]

>>9785101
I don’t know what you’re trying to prove, this system worked for me for the last 4 years and is still working. I didn’t draw this now, I had a thread about it one or two months ago as a matter of fact. If someone would want to seem smart in an anonymous forum (which is fucking retarded) he would have drawn diagrams and geometric drawings, in which case you would have responded the same way. I won’t keep this going because I respect the thread and it’s purpose and I’m not in the mood for arguing with an anon whose opinion means nothing to me. I just found it cool that another person saved the drawing a friend of mine did (it was hitler’s birthday, also 4/20).

[Anonymous No.9785120]

>>9785114
Yeah don't worry I'm just fucking with you, mostly.
>I respect the thread and it’s purpose
Lmao. Enjoy your stay, newfriend.

[Anonymous No.9785121]

That was a pretty gay exchange. Fuck off and just talk about how diff geometry is based and redpilled

[Anonymous No.9785125]

>>9785121
>gay
Why the homophobia?

[Anonymous No.9785126]

>>9785121
>gay
Why the homophobia?

[Anonymous No.9785136]

>>9785125
>>9785126
I only feer homos because homology looks like witchcraft bulkshit to me. But yea, faggots are not welcomed.

[Anonymous No.9785139]

>>9785136
>this stupid
>thinks he can dictate who is or isn't welcome in /mg/

[Anonymous No.9785140]

>>9785139
What you gonna do about it bitch? Spam anime unitl you are banned for avaterfagging?

[Anonymous No.9785142]

>>9785140
Here's your (You), little retarded boy.

[Anonymous No.9785146]

>>9785095
Well you have the deRham theorem, which says that deRham cohomology is the same as singular cohomology. So you can interpret cohomology in terms of differential forms.

Moreover on a Riemannian manifold you have the Hodge Theorem, which says every deRham cohomology classes has a unique harmonic representative. So now the space of harmonic n-forms is isomorphic to the nth singular cohomology.

Connections are valued in 1-forms, Curvature is an endomorphism valued 2-form

You have chern-weil theory, which lets you compute chern classes in terms of differential forms.

There are also other topological invariants you can define with differential forms. Like Donaldson polynomial invariants of 4-manifolds, which are defined via the moduli space of yang-mills connections.


Point being, differential forms provide a lot of topological information.

[Anonymous No.9785147]

>>9785142

[Anonymous No.9785148]

>>9783258

I'm literally trying to remember all the high school math right now. don't worry anon

[Anonymous No.9785553]

What’s the best big balls review of trig? I’m considering Chrystal’s Algebra but not sure how the coverage is, and Gelfand seems far too low level. There’s also an “advanced trigonometry” book I’ve forgotten about until now that may ne suitable.

Anyhow, any recs would be great, gg /mg/

[Anonymous No.9785561]

Hello fellow anons. Could you do me a favor and check what I wrote. I took the proof from math overflow and expanded on the parts that I didn't understand very well.
Did I make any mistakes? Does it make sense at all? English is not my first language so suggestions about grammar or vocabulary will also be greatly appreciated.
Thanks in advanced.

[Anonymous No.9785867]

>>9785561
>Spelling-/notationwise
In your definition of C_v the second V(G) should be E(G). Also just use \text{ and } for the word after it or just a comma.
I don't think the notation V(G)/r is standard, you may want to use \setminus \{r\} instead.
Also in the second part \cup A looks weird on its own, try \cup_{i\in I} A_i instead. Also f: A-> \cup A might be technically correct but it is much clearer if the function assigns to an index in I an element in A_i.

>the proof itself
The first argument about the no-cycles is not correct: a vertex v can have two or more incident edges if e.g. v=f(C_w)=f(C_u). There is however a unique edge that connects v to a vertex that is closer to r; use that.
Your argument about the minimum path after that is currently also incorrect, because the minimum path may not be unique in G. If you fix the no-cycle argument you will find a unique one in T though.

The second part is correct, but you could be clearer: just give the cycle you would have if there would be two edges.

[Anonymous No.9785895]

>>9783234
Every proper simply connected domain in the complex plane is conformally equivalent to any other one so I'm going to say yes.

[:^) No.9785914]

>>9785561
The truth table for [math] \implies [/math] says that from false follows everything, so the
>Axiom Of Choice =>
part is trivially true

[Anonymous No.9785922]

>>9785914
:^)

[Anonymous No.9785933]

>>9785914
You're thinking of -> instead of =>.

[Anonymous No.9785975]

>>9783466
link it fagg

[Anonymous No.9786515]

>>9785553
bump

[Anonymous No.9786523]

I completely fucked up my education. Twenty years old, and I could barely compute integral, solve a simple task or write a simple program. I thought about dropping out but could get through by bullshit or cheating.

Is it possible to recover?
>inb4 dumb frogposter

[Anonymous No.9786611]

>>9786523
No
Once you reach the age of 19 your pineal gland stops producing math hormone and it's literally impossible for you to learn any more math. No one older than 20 has ever learned anything.

[Anonymous No.9786811]

>>9785867
Thank you for the help. I will make the corrections you suggested.

[Anonymous No.9786930]

https://www.quantamagazine.org/mathematicians-explore-mirror-link-between-two-geometric-worlds-20180409/

[Anonymous No.9787123]

Which mathematical topics are most employed in modern theoretical physics?

[Anonymous No.9787146]

>>9787123
You'll have better luck asking in more appropriate places like >>>/toy/physics/ and >>>/biz/.

[Anonymous No.9787168]

>>9787123
Bullshiting with abuse of notation. It just werks.

[Anonymous No.9787175]

>>9787168
I'm wondering more about the work of Witten and the like who actually understand math

[Anonymous No.9787180]

>>9787123
Bullshitting in general. It just werks.

[Anonymous No.9787211]

trying to get my head around mathematical induction

[Anonymous No.9787227]

>>9787211
When you're done that learn about transfinite induction.

[Anonymous No.9787230]

>>9787211
First you show the claim holds for some index n, usually n=0 or n=1. Then you show that if it holds for n=k, then it holds for n=k+1. This gives you a chain reaction: you know it holds for n=0, so it holds for n=1 by what you proved. Now it holds for n=2 because it holds for n=1. Thus it holds for n=3 because it holds for n=2. Continuing like that, you actually get that the claim is true for all natural numbers n.

[Anonymous No.9787234]

>>9787230
I know that much you faggot, I'm just trying to do as many exercises as I can to get a grasp of what works and what doesn't.

[Anonymous No.9787239]

>>9787234
He was just trying to help you ungrateful piece of shit

[Anonymous No.9787251]

>>9787234
If you know that much, you really can't be struggling. Either you don't really understand the fundamental idea yet or you are just too stupid to have any mathematical future.

[Anonymous No.9787272]

>>9787180
For sure bullshitting your way to a Field's Medal just works.
Kys your self brainlet.

[Anonymous No.9787300]

>>9786930
HMS > SYZ

[math]{\operatorname{D} ^b}\operatorname{Coh} \left( X \right){ \cong _{{A_\infty }}}{\operatorname{D} ^\pi }\mathcal{F}\left( {{X^ \vee }} \right)[/math]

[Anonymous No.9787302]

Is Tex broken?

[Anonymous No.9787304]

>>9785867
>>9786811
Here is the corrected version.

[Anonymous No.9787325]

Where does Differential Geometry reside within modern mathematics? Is it a based and respectable field like Algebraic Geometry/Topology or is it all "hurr durr physicist do calculus and tensor index gymnastics on manifolds"?

I feel drawn more towards Topology/Geometry than I do towards Analysis or Algebra, and of the choices within the former it is DG that stands out the most to me.

[Anonymous No.9787328]

>>9787272
Beautiful math does not equate to empirical truth. Guys like him do mental masturbation which cannot be falsified in all likelihood. Critics like Penrose and the "not even wrong" guy are onto something with string theory.

It is bullshit in the end. If he had a useful result like proving Navier-Stokes or shit, then that would have been something.

[Anonymous No.9787336]

>>9787328
This is math general, not physics general. If you accuse Witten of mental masturbation then you are accusing everyone here of the same thing.

Likewise to call it bullshit is to call pure mathematics bullshit. The retards above accusing theoretical physicists of bullshiting were referring to their usage of mathematics being pretty loose and imprecise, not to the validity of their theories.

[Anonymous No.9787363]

>>9787336
I like being behind an empiricist behind enemy lines. If your theory is invalid but with pretty math, why even pretend it is physics, as it predicts nothing of the natural world.

[Anonymous No.9787369]

>>9787325
Differential Geometry is as serious a field as Algebraic Geometry.

If you are interested in Complex Geometry, you will almost certainly end up doing both.

[Anonymous No.9787402]

calc 2

[Anonymous No.9787403]

>>9787402
>>>/toy/

[Anonymous No.9787410]

>>9787369
>Complex Geometry
I might check it out one day, but it strikes me as being just a bit too contrived. Just like Complex Analysis where you get all these beautiful results because you are in essence studying functions that are solutions to a very well behaved PDE, but tell me I'm wrong.

[Anonymous No.9787450]

>>9787410
There is nothing really contrived about it.

A complex manifold is just a smooth manifold with R^n replaced by C^n and diffeomorphic replaced by biholomorphic.

You can define Hermitian metrics, which are the complex analog of Riemannian metrics.

A Hermitian metric naturally defines a non-degenerate 2-form. When the form is closed, the manifold is symplectic and we call it Kahler.

There is the Kodaira Embedding Theorem: A compact Kahler manifold such that the cohomology class of the 2-form factors through the integral cohomology, has the structure of a projective variety. (i.e. Identify the class of the 2-form with the first chern class of some ample line bundle, via the exp sequence, and this ample line bundle determines the projective embedding)


More generally we have complex analytic spaces and GAGA.

A complex analytic space is just locally the zero locus of some holomorphic functions. Every scheme finite type over C has a corresponding complex analytic space. In sufficiently nice cases, we have a sort of equivalence between coherent sheaves on the scheme and coherent sheaves on the analytic space.

[Anonymous No.9787474]

Is there any place (like a video lecture) where someone manages to explain some advanced stuff in a way that you can understand pretty early?
For example something you'd usually do in grad school or late undergrad but it's explained in a way that you can understand with just early undergrad or high school knowledge.
I'm trying to figure out if I would enjoy studying mathematics for real, I like it so far but it's just early stuff.

[Anonymous No.9787501]

>>9787474
Assuming you haven't done any "proof-based" courses (ie, the way math is actually done) grab an intro textbook on abstract algebra, number theory or real analysis (Baby Rudin) to see if you like working through proof-based exercises (ie, actual math exercises).
Supplement with materials that teach you the language of set theory and show you how proofs are written.
Whether or not you enjoy proofs and the process of having to demonstrate everything will give you a good of idea of whether you enjoy further study.

[Anonymous No.9787512]

>>9787474
A layman's introduction to higher math topics may pique your interest, but it's the pleasure of solving problems that is at the core of everyone's enjoyment of mathematics.

[Anonymous No.9787567]

>>9787501
Thanks, it sounds like it's worth looking in to.
I have had a few courses where proofs were a large part of it but that was many years ago when I was lazy and didn't know about that I could enjoy it yet.
>>9787512
I have the pleasure of problem solving but any examples I've seen from more advanced stuff was so weird that I couldn't see if the things I enjoyed earlier weren't there anymore and it's appeal was something completely different.

[Anonymous No.9787587]

Formal proofs.

>come at me bros

[Anonymous No.9787588]

>>9781931
Learning Eigenvalues/vectors. Anyone have any tips to help out?

[Anonymous No.9787596]

>>9787588
What are you finding difficult?

[Anonymous No.9787609]

>convince yourself that this theorem is true

[Anonymous No.9787641]

>>9787567
There are a lot of topics to choose from, and much of it is quite weird. There are plenty of applied fields you can study if the really esoteric pure stuff doesn't interest you.

[Anonymous No.9787653]

>>9787588
The 3b1b video is good. Remember that any scalar multiple of an eigenvector is another eigenvector with the same eigenvalue.

[Anonymous No.9787655]

>>9787596
Finding the Eigenspace is giving me trouble, I have a quiz on it tomorrow and remembering the whole process is giving me trouble. Just need to practice it more though.

[Anonymous No.9787662]

Is set theory a spook?

[Anonymous No.9787698]

>>9785553
bumperino to the neutrino

[Anonymous No.9787777]

>>9787641
The weirdness was just because I didn't understand it at all yet. I hope I would enjoy the pure stuff in the same way as simpler things now.

[Anonymous No.9787810]

>>9787777
First courses in Abstract Algebra, Real Analysis, and Topology (point set topology) serve as a good gateway into mathematics, so work your way towards those.

[Anonymous No.9787826]

/mg/ youtubes
https://www.youtube.com/watch?v=9cqRxo1V_OM

[Anonymous No.9787871]

So I chose this text to learn Differential Geometry from. Anyone familiar with it?
Which topics do you guys think are the most interesting?
After getting the fundamentals down what should I tackle next: Differential Forms, Lie Groups, Fiber Bundles?

[Anonymous No.9787908]

>>9787810
Thanks for the tips. Right now I just have to try to get back what I knew in the past though.
Before I dropped out of computer engineering many years ago I had discrete mathematics, linear algebra and started the calculus course but never did that one (also some probability and statistics).
I think I'll start studying mathematics for real since it can be enjoyable and I can probably enjoy the next stuff I'll learn too but I don't know if I'll be able to enjoy the stuff towards the end (or in grad school if I do that) or if it gets different when it gets more serious.

[Anonymous No.9787944]

>>9787662
Yes. Praise (strictly constructive) type theory.

[Anonymous No.9787945]

>>9787655
Isn't it super easy after finding the eigenvectors?

[Anonymous No.9787952]

>>9787655
>evaluate determinant of [math] A - \lambda I [/math]
>set it to zero
>solve for lambda (get fucked by Galois if you're more than 4x4)
>do some change of basis fuckery to find eigenvectors (?)
>eigenspaces are the spaces spanned by eigenvectors with the same eigenvalues

[Anonymous No.9787956]

>determinants
Hahahahaa

[Anonymous No.9788002]

>>9787952
>get fucked by Galois if you're more than 4x4
Suddenly I feel like doing this for 5x5 matrices...

[Anonymous No.9788004]

>>9785975
He won't because he's a larping faggot.

[Anonymous No.9788019]

>>9787328
>>9787363
>physics
Refer to >>>/toy/.

[Anonymous No.9788063]

>>9781931
God dammit 4chan has ruined me

I can't even watch a youtube video without thinking about Amerimutt memes anymore

[Anonymous No.9788067]

>>9787123
Differential geometry, harmonic analysis, differential equations, probability, algebraic geometry, representation theory, operator algebras...

[Anonymous No.9788087]

>>9786611
Well, it's like, fallen behind peers beyond redemption. Having to catch up all material starting from high school literally makes me feel hopeless.

[Anonymous No.9788092]

>>9788087
The best time to plant a tree was 20 years ago. The second best time is now.

[Anonymous No.9788139]

I hate this general.

[Anonymous No.9788142]

>>9787826
Posts like this is why I hate this general so much.

[Anonymous No.9788162]

>>9788139
why

[Anonymous No.9788169]

>>9781931
Did Mochizuki get BTFO yet?

[Anonymous No.9788237]

Have any of you guys ever studied or come across the idea of "tacit knowledge" while studying the philosophy of math? Pic related, Polanyi is the guy.

I know next to nothing when it comes to mathematics but I study something very similar to tacit knowledge in many ways, called hermeneutic phenomenology or hermeneutic ontology, and I've always wondered how it applied to math. I've been meaning to learn math for years just for the sake of satisfying my curiosity, at least up to a college level, but I never fucking do it.

I just read this article by Breger in The Growth of Mathematical Knowledge and it blew my mind - he was basically answering half the questions I've always wanted answer about how tacit knowledge precedes formalisation, abstraction, and normalisation in the historical development of "how math works." But I need to dig deeper - I especially want to understand how certain mathematical developments go from being a hunch or rough-and-ready method in some guys head to being absorbed into "math as a whole" as a non-contradictory, mutually supportive part of the whole structure of mathematical knowledge.

I'm gonna have to learn math obviously, and buff up on my history/philosophy of math, but if any of you guys were forced to read some big book on math & tacit knowledge that I could at least start cracking on right away, I'd appreciate the recommendation.

[Anonymous No.9788254]

>>9787871
I enjoyed this book, the 3 by John Lee are also great. Differential forms are kind of part of the fundamentals, so do that first, lie groups/algebras will require vector bundles, so study fiber bundles first then move on.

[Anonymous No.9788264]

>>9788237
>>>/lit/

[Anonymous No.9788284]

>>9788169
>Did Mochizuki get BTFO yet?
No, and he never will.

[Anonymous No.9788303]

>>9788237
>I know next to nothing when it comes to mathematics
Yes, we can see that from your post.

[Anonymous No.9788315]

>>9788264
Yeah I thought of asking /lit/ too, but I want to see if math people who live and breathe this stuff have ever considered it.

Not just because that perspective would have more insight into the formation ("phenomenological constitution") of mathematical knowledge, but because being against such "meta" considerations in the first place would also be interesting and potentially informative.

[Anonymous No.9788354]

>>9788284
>wasting time on /sci/ instead of finishing your proof
y u do dis Mochizuki?

[Anonymous No.9788358]

>>9788315
>phenomenological constit
Take your word salad someplace else faggot.
/lit/ is probably as good a place as any.

[Anonymous No.9788364]

>>9788358
Plz, I didn't want to talk to undergrad LARPers.

[Anonymous No.9788379]

>>9788358
>faggot
Why the homophobia?

[Anonymous No.9788400]

>>9788364
You don't want to talk to me either.
And the feeling is mutual.

[Anonymous No.9788694]

>>9788063
Thanks for reminding me of him. I used to watch his vids as a first year student and kept laughing at how deformed he was. Now, years later, I finally understand why. He's cool, though, so thanks to Mutt Doctor Bob for his videos on abstract algebra.

[Anonymous No.9788855]

Any textbook suggestions for a first course in Algebraic Topology? Is Hatcher still the gold standard?

[Anonymous No.9788889]

>>9788855
>Hatcher
>gold standard

[Anonymous No.9788910]

>>9788889
Fucking anime posters

[Anonymous No.9788938]

>>9788910
>>>/r/eddit/

[Anonymous No.9789204]

>>9788855
R O T M A N
O
T
M
A
N

[Anonymous No.9789209]

>>9788855
>Any textbook suggestions for a first course in Algebraic Topology?
Matveev

[Anonymous No.9789226]

>>9788855
>>9788889
I totally see what Hatcher was trying to do and I admire his effort. But let's be honest, his book is NOT a good introduction to algebraic topology.

[Anonymous No.9789266]

>2018
>not studying pineapple theory

https://www.math.wisc.edu/~miller/old/m773-07/pineapp.pdf

[Anonymous No.9789305]

>>9782147
No don't. My prof made us do that and it is not fun. Some terminology in classical texts is no longer in use or means something else now. Prescheme is now scheme, scheme is now seperable scheme. It's a nightmare to update your definitions.

[Anonymous No.9789313]

>>9789266
"sweet pineapple" doesn't seem to be defined in that paper. Is a pineapple function the same as a function?

[Anonymous No.9789320]

>>9789204
Might give Rotman a shot; he's pretty based. Learning Galois Theory from his text atm. May he rest in peace.
I was also looking at Massey but no Homology.
>>9789226
I've read some of it but I dunno, I feel like I need to supplement it with something else. I really liked reading his introductory section on Homology where he gives an overview of the whole idea. It's nice to get a little preview like that to give me the motivation to actually learn Homological Algebra.

[Anonymous No.9789322]

>>9789305
Did you mean to reply to this?>>9782744

[Anonymous No.9789324]

I chose this as my first foray into Algebraic Geometry. Is it a worthwhile? I don't want to start with Hartshorne.

[Anonymous No.9789329]

>>9789320
Massey's pink book on homology and cohomology is nice, but I don't know if it's good for an intro intro, but more like for someone who already knows something. Then it can be used for learning the theory from the perspective of the Alexander-Spanier (co)homology. A word of warning, though, the version on Libgen comes with the typewriter font, so that could be the case for all the versions. You could try that one after reading Rotman, as his book covers singular, simplicial and cellular homologies and singular cohomology.

[Anonymous No.9789334]

>>9789324
>Is it a worthwhile?
Why don't you read it and find out?

[Anonymous No.9789340]

>>9789209
This is what I'd recommend for anyone trying to introduce themself to algebraic topology as well.
It's really a great little book for those who just want a quick cherry-popping without a gigantic time investment

[Anonymous No.9789352]

>>9789313
>pineapple
computable
>sweet
Turing

[Anonymous No.9789377]

>>9789334
For sure, let me just read the whole textbook so I can decide whether or not I want to read it.

[Anonymous No.9789379]

>>9789340
>just want a quick cherry-popping without a gigantic time investment

I ain't that kind of girl, sweetie ;)

[Anonymous No.9789382]

>>9789377
Check the ToC, read the introductory chapter, see if you like the author's style of exposition by reading the first proper chapter. Proceed or drop after that.

[Anonymous No.9789545]

>>9788237
Don't expect to get a good response from this general. We're all cunts here.

Can you define tacit knowledge?

[Anonymous No.9789858]

>>9789204
Thanks for the rec. I like how he introduces category theory early. Seems like a great text.

[Anonymous No.9789882]

>>9785068
>>9785080
>>9785101
>>9785120
no wonder everyone dislikes you on you know where

[Anonymous No.9790056]

>>9788855
If you can read (simple) french I would say Topologie algebrique by Felix and Tarne.
Tammo tom Dieck's book is nice, but maybe too advanced for a first course.
You can select some chapters from Shastri's Basic algebraic geometry.
Also, read Homology and cohomology theory by Massey.

[Anonymous No.9790066]

>>9789324
No it is not. Here is a post from the last /mg/:

>The first chapter of Hartshorne is too much concise. Try mixing it with Hulek (chapters 0-3) and Shafarevich (chapters 1-2). *After* you learn the theory try to work out the examples from Harris's book. There are also video lectures on youtube, search 'algebraic geometry nptelhrd'.
>I'm currently waiting the publishing (5 July 2018) of Introduction to Algebraic Geometry by Cutkosky, from the toc it seems nice.
>If you want to learn commutative algebra intended for algebraic geometry (w/o schemes) try 'Undergraduate commutative algebra' by Reid.
>Also stacks project's chapters 'fields' and 'topology' are helpful.

[Anonymous No.9790090]

We are living in a projective space.

[Anonymous No.9790241]

New to mathematics here, trying to tech myself using Simmon's precalculus mathematics in a nutshell but I can't work out what I'm doing wrong with this integral exponent problem and it's driving me mad. Can anyone point out to me where I'm going wrong? Sorry for the bad notation, I don't know how to use LATEX yet.

[Anonymous No.9790703]

>tfw going to try to study Zorich Mathematical Analysis 1 during the summer
Wish me luck lads, going to try and be less of an idiot

[Anonymous No.9790712]

>>9790703
use Pugh instead

[Anonymous No.9790720]

>>9790241
What is the first line supposed to be? Is the first term a^(n-4)*b^4 or (a^n) - 4b^4? Is the second term ab^(n-1) or (ab^n) - 1?

[Anonymous No.9790736]

>>9790712
Why

[Anonymous No.9790743]

Not sure if this is where I should ask, but how can I write this in Matlab?
xn=x(n-1)*2+5000
a=xn-x(n-1)-5000

With x(n=0) having a predetermined value.

[Anonymous No.9790749]

>>9789324
Just do Ch.2&3 of Hartshorne and get it over with.

Then you can freely do actual geometry.

[Anonymous No.9790756]

This summer id like to study for an actuarial exam, the highest level of college math I’ve done is vector calc II, linear algebra, and discrete math. Am I ready for the tests? Which one should I start with? Thanks

[Anonymous No.9790766]

>>9790756
Assuming you're american FM is considered the easier of FM and P, however I personally found P to be easier since, even if you don't recall certain results, you can derive most on the spot. Study hard, though, don't do that!

[Anonymous No.9790770]

>>9790756
most people start with probability, but you could also write financial mathematics first if you wanted.
You're not "ready" for the tests in the sense that you would almost certainly fail if you wrote one right now. The actual mathematical content is laughably easy (you might need to integrate by parts occasionally but the rest is high-school tier), but the style of problem you get on actuarial exams takes some practice to get used to. You need to be very consistent and fairly fast at them.

[Anonymous No.9790816]

>>9790720
a^(n-4)*b^4 and ab^(n-1), sorry for the ambiguity.

[Anonymous No.9790820]

Is every compact manifold Jordan measurable?

[Anonymous No.9790825]

>>9790820
Yes.

[Anonymous No.9790830]

>>9790816
Then you're correct/the solution guide is wrong, but you did it in a terrible way by turning exponents negative for some reason, just do
(a^(n-4) b^4)(ab^(n-1)) =
a^(n-4) * b^4 * a * b^(n-1) =
a^(n-4) * a * b^4 * b^(n-1) =
a^(n-4 + 1) * b^(4+n-1) =
a^(n-3) * b^(n+3)

[Anonymous No.9790843]

>>9790825
Can you give a proof strategy?

[Anonymous No.9790855]

What's the most interesting paper published this year so far?

[Anonymous No.9790956]

>>9790090
Are you implying that the universe is projective or that it can be embedded in a projective space? This is confusing.

>>9790703
*Cries for you*. Almost 600 pages of real analysis. Why don't you find a <200 pages set of notes with the same (or even more) content? This book is selfharm, especially for self learning.

[Anonymous No.9790970]

>>9790843
Smooth sailing.

[Anonymous No.9791007]

>>9790970
I dont get it

[Anonymous No.9791008]

>>9790956
Not everyone are geniuses

[Anonymous No.9791029]

>>9790830
thank fucking god, this problem had been driving me mad all day but you're the second person to tell me I was correct and the guide was wrong. thanks anon.

[Anonymous No.9791055]

>>9791008
Neither are we.

[Anonymous No.9791159]

Clifford algebras sure are nice.

[Anonymous No.9791178]

Test.

[math]f(x)\mbox{d}x[/math]

[Anonymous No.9791200]

>>9790090
Projective space is a dream.

[Anonymous No.9791242]

>>9790090
Find an exact mirror copy of me and I'll believe you.

[Anonymous No.9791244]

>>9790720
What is the first line supposed to be? Is the first term [math] a^{n-4} * b^{4} [/math] or [math] a^{n} - 4b^{4} [/math]? Is the second term [math] ab^{n-1} [/math] or [math] ab^{n} - 1 [/math]?

>>9790816
[math]a^{n-4} * b^{4}[/math] and [math]ab^{n-1}[/math] , sorry for the ambiguity.

>>9790830
Then you're correct/the solution guide is wrong, but you did it in a terrible way by turning exponents negative for some reason, just do
[math](a^{n-4} b^4)(ab^{n-1}) =[/math]
[math]a^{n-4} * n^{4} * a * b^{n-1} =[/math]
[math]a^{n-4} * a * b^{4} * b^{n-1}[/math]
[math]a^{n-4+1} * b^{4+n-1}[/math]
[math]a^{n-3} * b^{n+3}[/math]

pls use/learn laytecks. https://sites.google.com/site/scienceandmathguide/other/-sci-infographics/joseflatex.png?attredirects=0

[Anonymous No.9791252]

>>9791244
>pls use/learn laytecks
"No!"

[Anonymous No.9791255]

>>9781931

[Anonymous No.9791260]

>>9787871
From the thumbnail I thought it was Algebra: Chapter 0 and was confused for a second

Why do all math books look the same bros? Can't they have some creativity

[Anonymous No.9791262]

>>9790090
Over which ring? This is important.

[Anonymous No.9791267]

>>9791242
You don't exist.

[Anonymous No.9791279]

>>9791252
[math] \rotatebox{180}{oh okay} [/math]
> [math] \rotatebox {180}{does a 360 and walks away} [/math]

[Anonymous No.9791289]

>>9791252
[/math]\textcolor{RubineRed}{\mathcal{okay}}[/math]

[Anonymous No.9791291]

[math]\textcolor{RubineRed}{\mathcal{okay}}[/math]

[Anonymous No.9791292]

>>9791267
Yeah that's what I thought, idiot.

[Anonymous No.9791296]

>>9791252
[math] \mathbb{oh, okay} [/math]

[Anonymous No.9791301]

anyone know what [math]2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2 [/math] is?

[Anonymous No.9791311]

>>9791301
All I can tell you is that it's not prime

[Anonymous No.9791316]

>>9781931
central simple algebras

[Anonymous No.9791416]

>>9791316
those are the worst algebras

[Anonymous No.9791426]

>>9791301
42

[Anonymous No.9791429]

>>9791426

[Anonymous No.9791432]

>>9791301
2↑257

[Anonymous No.9791433]

>>9787474
Topology by munkres doesn't assume anything at all but you gotta be pretty smart to follow with no background

There is a series of video lectures by Frederick Schuller called the geometry and anatomy of theoretical physics or something like that on YouTube which starts with basic logic and by the 10 lecture is doing some pretty advanced differential geometry stuff, going over topology and some other stuff that I really recommend

[Anonymous No.9791440]

>>9791432
dude did you just?

[Anonymous No.9791445]

>>9785068
literally what you do, hank. for goodness sakes

[Anonymous No.9791452]

>>9787871
Try using Tu's book instead. Either Lee books are too big and too broad to get into the field quickly.

[Anonymous No.9791453]

The group is the most beautiful mathematical invention of all times.

[Anonymous No.9791457]

>>9791453
What beautiful is there in a group?

[Anonymous No.9791460]

>>9791453
>mathematical invention
No such thing, there are only mathematical discoveries.

[Anonymous No.9791476]

>>9791460
How so?

[Anonymous No.9791480]

>>9791476
We created a list of axioms and we simply discover their implications, we don't invent new math.

[Anonymous No.9791481]

>>9791453
Lol no.

[Anonymous No.9791482]

>>9791453
Yeah, I like the unique group a lot too.

[Anonymous No.9791489]

>>9791480
>We created a list of axioms
What do you mean?

[Anonymous No.9791493]

>>9791489
>What do you mean?
Proof itself, of any sort, is impossible, without an axiom (as Godel proved). Thus faith in God is a prerequisite for all proof.

[Anonymous No.9791495]

>>9782744
https://math.stackexchange.com/questions/59773/can-i-go-through-hartshorne-without-knowing-much-analysis

All primary English books in AG begin translates/transcriptions of Grothendieck works EGA or SGA,Grothendieck rebuild AG.

Miles Reid, Igor Shafarevich,David Mumford,David Eisenbud,William Fulton publisher books as introduction or different view AG,get good bases in commutative algebra and go for it.

http://math.stanford.edu/~vakil/216blog/FOAGdec3014public.pdf

http://math.mit.edu/classes/18.721/index.html

[Anonymous No.9791502]

>>9791495
>All primary English books in AG begin translates/transcriptions of Grothendieck works EGA or SGA,Grothendieck rebuild AG.
>Miles Reid, Igor Shafarevich,David Mumford,David Eisenbud,William Fulton publisher books as introduction or different view AG,get good bases in commutative algebra and go for it.
What are you trying to say?

[Anonymous No.9791535]

>>9781931
CSfag learning my way through babby's first Abstract Algebra textbook. Shit's cool. I'll review Linear Algebra after I'm done to consolidate both by association.

[Anonymous No.9791604]

>>9791460
This.

[Anonymous No.9791607]

>>9791493
This is the cringiest shit I've read all day.

[Anonymous No.9791672]

>>9791255
>probability theory
>implying Bayesians weren't btfo long ago by neural nets
>implying anyone has any formal understanding of cutting edge ML other than "it just werks"

[Anonymous No.9791675]

>>9791607
It's a Jordan Peterson tweet

[Anonymous No.9791832]

>>9781931
What I hate about math is how much is hidden behind needlessly complicated symbolism and language. A common theme in many fields. Established people trying to make it as hard as possible for newcomers, making very simple concepts as complicated as possible.

[Anonymous No.9791841]

>>9791832
>needlessly complicated symbolism and language
If this was true someone would write a textbook with simplifications that would sell very well, but this isn't the case

[Anonymous No.9791847]

>>9791841
If someone would write such a textbook, who would buy it? Education establishment decides which books are popular.

[Anonymous No.9791850]

>>9791847
>Education establishment
This is a spook

[Anonymous No.9791853]

>>9791850
>This is a spook
>spook

you mean CIA?

[Anonymous No.9791861]

>>9791850
All they care about is proper notation and rigor. They clearly don't give a fuck about simplification and expression of ideas.

You don't explain a mathematical concept to someone with a formula and a mathematical deduction. You explain the concept in simple terms and then build a structure on that.

[Anonymous No.9791873]

>>9791832
Have you ever considered that you just might be too stupid for it?

[Anonymous No.9791895]

>>9791873
Loaded question.

[Anonymous No.9791959]

>>9791607
A UofT professor wrote that

[Anonymous No.9791987]

>calculus exam in 6 hours
>boiling diarrhea kicks in in the middle of the night not letting me sleep
AAAAAAAAAAAAAAAAAAAA

[Anonymous No.9792011]

>>9791987
AND NOW I JUST FUCKING VOMITED MY GUTS OUT WHAT THE FUCK GUYS WHY IS MY BODY FAILING

[Anonymous No.9792012]

>>9792011
That's just stupidity leaving the body
You'll ace it

[Anonymous No.9792061]

>>9791832
Give a single example of notation or language you consider needlessly complicated.

[Anonymous No.9792083]

>>9791861
GTFO brainlet.

[Anonymous No.9792089]

>>9781931

Studying Calc 2. Just started this week, actually. I was trying to use my cursory understanding of calculus to crack open Griffith's Introduction to QM. Got my ass kicked before I even made it out of the first chapter on Schrodinger's Equation (I don't know how to integrate Gaussian distributions).

>inb4 mathlet

I know. I'm trying to get better.

[Anonymous No.9792108]

>>9788087
>>9788087
I'm in the same situation. Relearning maths over the summer. Got discord? It's nice to do together

[Anonymous No.9792116]

>>9792108
Advanced mathematics is a good server for that.

[Anonymous No.9792122]

>>9792116
>>9792116
>>9792116
link?

[Anonymous No.9792124]

>>9792122
https://discord.me/math

[Anonymous No.9792127]

>>9792124
>https://discord.me/math
>You must claim and verify your account before you can send messages to this server.
Oh well...

[Anonymous No.9792158]

I was originally going to study computer science and go into software engineering because I enjoy programming. However, I feel that being a programmer for a company may not align with my personal morals. For example, I would refuse to make a product that I thought was immoral. I see most companies that most programmers want to work for (Apple, Facebook, Microsoft, Google, financial companies, gaming companies, etc.) as evil.

Because of my issue concerning morality, I have thought about focusing on pure mathematics and becoming a mathematician instead. The only problem is I am quite the brainlet, and feel that I would never achieve anything that would earn me an Abel Prize or Fields Medal.

I'm lost. :(

[Anonymous No.9792163]

>>9792158
Refer to >>>/adv/ and >>>/g/.

[Anonymous No.9792175]

>>9792158
>a programming job is somehow equivalent to winning a Fields Medal
Your head's not screwed on right.

[Anonymous No.9792305]

>>9792127
Just do it or be without a server. That's the only active one with quality.

[Anonymous No.9792451]

>>9792012
>That's just stupidity leaving the body
>You'll ace it
I vomited the whole fucking night and today I was diagnosed with virose. I can barely eat or my stomach will propel up all of it the moment it touches the acid. I wanted to do that exam so bad, now I'll have to wait until the end of the semester to do it.

[Anonymous No.9792507]

>>9791672
>implying Bayesians weren't btfo long ago by neural nets
fuck off brainlet

[Anonymous No.9792605]

Any mathemagicians here that can tell me what is going on here?
>t.Someone revisiting high school maths

[Anonymous No.9792714]

>>9792605
Doing stuff suitable for convergent series to a divergent one.

[Anonymous No.9792752]

Do amerimutts really just have one hour long lectures?
>tfw 4*45 minutes masterrace

[Anonymous No.9792760]

>>9792714
Brief explanation....Why can't I do what I just did?

[Anonymous No.9792763]

>>9792158
Learn math and become actuary

[Anonymous No.9792792]

>>9792760
What you did is somewhat analogous to doing this: [math]\infty = \infty + 1 \Rightarrow 0 = 1[/math].

[Anonymous No.9792799]

>>9792760
What is the notion of convergence did you use to assume that 1+11+111+...=n? Under the standard definition of convergence, the limit of the sequence of partial sums, that diverges.

[Anonymous No.9792800]

>>9792792
Fucking Latex.

[Anonymous No.9792820]

>>9792792
>>9792799
>>9792800
Kek. Thanks for the explanation. I can't stop laughing at my stupidity.

[Anonymous No.9792825]

I want to understand how physicists use abstract algebra, like in field theory. Where should I start if I don't know shit, especially about physics?

[Anonymous No.9792888]

>>9792825
Here's a random snippet from a text on Differential Geometry I just started reading.

>The notion of a connection on a fiber bundle and the notion of a gauge field are essentially
identical concepts discovered independently by mathematicians and physicists.

It has something to do with Lie Groups, so you need to learn about Smooth Manifolds and Group Theory as a starter.

[Anonymous No.9792988]

>>9789882
where is you know where?

[Anonymous No.9792994]

>>9792988
>where is you know where?
reddit

[Anonymous No.9793030]

Why doesn't Latex work?

[Anonymous No.9793193]

How the fuck do you align things in latex? I'm showing that a bunch of statements are equivalent, so I have a bunch of things like (i)[math]\implies[/math](ii):. I want the [math]\implies[/math] aligned.

[Anonymous No.9793201]

>>9793193
Pic related is:
\begin{equation*}
\begin{split}(h_{j'}\circ h_j)\circ\lambda_i & =h_{j'}\circ(h_j\circ \lambda_i) \\
& =h_{j'}\circ(\lambda_j\circ\varphi^j_i) \\
& =(h_{j'}\circ\lambda_j)\circ\varphi^j_i \\
& =(\lambda_{j'}\circ\varphi^{j'}_j)\circ\varphi^j_i \\
& =\lambda_{j'}\circ(\varphi^{j'}_j\circ\varphi^j_i) \\
& = \lambda_{j'}\circ\varphi^{j'}_i \\
& =h_{j'}\circ\lambda_i,
\end{split}
\end{equation*}
and removing the * gives you a numbered equation.

[Anonymous No.9793205]

>>9792752
Lectures are pretty garbage but the flip side is it gives your profs more time to go one-on-one with students.

[Anonymous No.9793207]

>>9793201
Thank you anon, I tried a bunch of stuff from stack exchange that didn't work at all, this works perfectly.

[Anonymous No.9793211]

>>9793207
No problem. You do the obvious thing and replace = by \Leftrightarrow in that thingy, and it still works.

[Anonymous No.9793213]

>>9793211
Or actually does it? I hope it does.

[Anonymous No.9793873]

>>9793030
[math] \latex [/math]

[Anonymous No.9793874]

>>9792752
Standard was 3 hours here. I think it's 2 now.

[Anonymous No.9793887]

Heya, I'm new to maths in general, and I have often heard the term 'mathematical maturity' thrown around. Example being that "The only prerequisite to Baby Rudin is mathematical maturity". How do I gain this? Also I don't want to read those logic or proof books.

[Anonymous No.9793916]

Hypothesis testing and significance testing for my statistical inference class. I know I'm a scrub

[Anonymous No.9793921]

>>9793887
>How do I gain this?
Do more math. Maturity is just a different word for experience.

[Anonymous No.9793925]

I bought myself an A level math revision textbook to embark on a journey, I did ok at GCSE math years ago but a lot/ nearly everything isn't making sense from the A level book.

Aside from an heroing, what do? I was thinking youtube tutorials for each subject bt I was hoping for everything to make more sense from the book alone. I think the maing problem is that not all answers are explained at the back of the book and it is only a revision book, although the best one I could find on Amazon. I also got a physics one, but that's pretty hard too. The subjects are very interesting though. I got a biology book as well and that is pretty easy and intuitive.

[Anonymous No.9793937]

Guys, I have finally got my article on functional analysis accepted in a prestigious math journal.

It makes HELL lot of difference to talk IUTT on 4chan and ACTUALLY publish something

[Anonymous No.9793951]

>>9793921
I figured, but what math should I do? What topic in pure math would be most accessible to somone that knows almost nothing about pure math?

[Anonymous No.9793968]

>>9793951
It's most important that you study something you either want or need to learn rather than what you think you _should_ study. It's not like math is just one railroad that everybody follows in the exact same order.
That said, you will need to learn linear algebra and analysis fairly fast if you want to do anything worthwhile.

And Rudin is not a topic, Rudin is a book. It requires mathematical maturity because it's a shitty book that doesn't explain what it's doing. If you use better resources (and there are plenty available for free) real analysis is perfectly accessible.

[Anonymous No.9793985]

>>9793968
When I referred to Rudin I meant to refer to it as a book.
But if Rudin is shit, then would Abbot or Tao be better?

[Anonymous No.9793992]

>>9793985
Tao is a meme

[Anonymous No.9794001]

>>9793937
Doxxed

[Anonymous No.9794008]

>>9793937
No shit. Thanks for this incredibly clever insight.

[Anonymous No.9794073]

>>9793937
Karsten?

[Anonymous No.9794098]

>>9793937
Congrats. I'm not into functional analysis, but do you mind giving a brief explanation on what the paper is about?

[Anonymous No.9794107]

>>9793887
If you're completely new to maths you can start with Spivak's Calculus which is a more accessible intro to rigour.

[Anonymous No.9794176]

>>9793968
Rudin is a terrible introduction but a great text to go through AFTER you've taken your first analysis course.

[Anonymous No.9794592]

Hey guys, I am a computer engineering major with a mathematics minor entering my second year of school in the fall. I didn't take any major classes this first year, I just got all of the required classes like english, history, art history, etc out of the way. I took calc 1 and 2 in high school and got a 99 and 97 respectively. I am enrolled for calc 3 in the fall. If I don't remember much of calc 2 should I really stress over reviewing before calc 3? Also, I bought a linear algebra textbook and a general logic/discrete math textbook and I really want to read them but would it be a waste of time as I am not taking those classes until spring? Can I really teach myself math?

[Anonymous No.9794604]

>>9794592
>If I don't remember much of calc 2 should I really stress over reviewing before calc 3?
Knowledge of results such as the "chain rule" and "quotient rule" should be enough. But knowing deeper results such as "integration is the converse of differentiation" is still highly recommended.
>would it be a waste of time as I am not taking those classes until spring?
Definitely. Studies have shown that learning things before you take classes in them is generally not a good thing to do as your brain simply won't retain the data.

[Anonymous No.9795364]

>>9794604
stfu

[Anonymous No.9795366]

>tfw to dumb to understand the tensor product
I mean in the universal property sense

[Anonymous No.9795582]

>>9781931
I’m studying how to get my mustang to 600 horse power. Only 150 horses left to go. Fuck your impractical science mumbo-jumbo. My field actually gets me laid.

[Anonymous No.9795595]

>>9795366
I find the universal property of tensor products more clear than that of direct products.
What is so hard about it? Multilinear maps are special linear maps, and it is possible to see them as linear maps from an appropriate space.

[Anonymous No.9795668]

>Prove [math] A \implies B [/math] in lectures
>Exam question: does [math]B \implies A[/math]?

[Anonymous No.9795713]

>>9795366
Every multilinear map factors through a unique linear map.

[Anonymous No.9795718]

>>9795595
>>9795713
Yeah but what the fuck does that actually mean concretely? It's obvious that the Cartesian product is a (category theory) product, it's far less obvious to me that the kronecker product is a tensor product for instance.

[Anonymous No.9795812]

2nd year fag here who just finished Linear Algebra and will declare a math major. What were some topics that you thought you would like that you knew nothing about and ended up not really caring for? What topics disappointed or surprised you?

[Anonymous No.9795946]

>>9785066
What are the pros and cons of learning integrals before differentials? I... I don't know calculus.

[Anonymous No.9796273]

>>9795668
And this is wrong because?

[Anonymous No.9796304]

Guys Can anyone recommend me a legit Decision Theory book with exercise examples that is aimed at Mathematician and Statistician and not the Social scientists and Philosophy?
Class notes and lectures are fine too

[Anonymous No.9796316]

>>9795718
We knew 4chan was full of strange individuals, but this is beyond that.

[Anonymous No.9796322]

>>9796304
The Prince by Macchiavelli.

[Anonymous No.9796341]

>tfw don't know whether to continue coasting along easily in computer science with perfect GPA or do dual degree in computer science/ applied&computational math
I just want to actually grasp math concepts in depth instead of remember them so I can do complex things with computers ;_;

[Anonymous No.9796359]

>>9796341
Theoretical CS provides plenty of mathematical challenge. Not the same type as ACM, but some of the most challenging proofs I've had to do have been reductions, approximation algorithm correctness, etc.

[Anonymous No.9796375]

>>9791987
Fuck this happened to me years ago. Night before calculus exam. Gastro hits. Up all night shitting myself.
Go to exam. Run out the door multiple times during exam to vomit. Finish exam, rush home to shit my life away. Sleep for 1 hour. Rush back to university for molecular bio exam...vomit again several times during exam.
Go home to celebrate finishing another year of university with an insane fever all night.

Fuck that was a shit day.

[Anonymous No.9796392]

>>9796359
In Australia, the CS major is more part of an IT degree. It's more about being a software developer. Maths is entwined in most subjects but there's no dedicated math subjects except discrete structures for my CS major. For computational/simulation science you get a second major which is focused more on... Computational and simulation science.

But I want to focus on security which means I can't do the computational science second major BUT I still want to learn enough math to help my hobbies involved in simulations and my career plan in security.

[Anonymous No.9796454]

>>9791987
>real analysis exam at 11:00
>wake up at seven
>a bit tired, I'll have some coffee and it'll be fine though
>go to take daily multivitamin
>take sleeping medicine instead
oh no oh no oh no oh no

Happened a few years ago, still swung an A somehow.

[Anonymous No.9796547]

>>9795718
>Yeah but what the fuck does that actually mean concretely?
That is precisely what it means. I don't understand what you mean by "concretely".

[Anonymous No.9796565]

>>9796341
>>9796359
>>9796392
Refer to >>>/g/ or >>>/adv/.

[Anonymous No.9796605]

>>9796565
Shut the fuck up, nerd.

[Anonymous No.9796606]

>>9796547
>That is precisely what it means.
What do you mean by "precisely"?

[Anonymous No.9797001]

>>9793925
Khan academy

[Anonymous No.9797016]

>>9793887
"Introduction to Mathematical thinking"

[Anonymous No.9797074]

>>9781950

>brilliant
>fearless warrior

people say you can't have it both ways

[Anonymous No.9797076]

>>9795668
If you don't reflexively ask yourself this every time you see a one-directional implication you're a failure as a mathematics student

[Anonymous No.9797091]

>>9791426
>>9791429
I, too, got that reference

[Anonymous No.9797103]

>>9797076
>>9797076
this is very true

[Anonymous No.9797116]

>>9797076
You don't have to reflexively ask yourself, because if it was an equivalence, your proof would have written an equivalence and not an implication (unless it is an open problem, but you won't see any of those on your exams). So the answer is obviously no
But this >>9795668 post reeks of brainletism. Would you have preferred to get the same question that was already proved in the lecture?

[Anonymous No.9797119]

>>9797116
*prof not proof

[Anonymous No.9797165]

>>9797116
>Would you have preferred to get the same question that was already proved in the lecture?
Obviously he would have wanted it to be the same, so he wouldn't have to learn anything. You are too smart to see it via the lens of an idiot, and thus you asked a stupid question.

[Anonymous No.9797206]

>>9797116
>You don't have to reflexively ask yourself
Even if the converse is obviously false you should have a better idea why than just
>my prof would have told me if it was true
you absolute brainlet

[Anonymous No.9797513]

>>9797206
This. You should understand WHY the converse is false. Luckily this is usually pretty easy to do through counterexample.

[Anonymous No.9797884]

>>9792158

>morality

Stop falling for this ruse, people who care about morality and ethics are those who will be thrown to the lions like the Christians

[Anonymous No.9798227]

How do I prepare for an Integration Bee?