/mg/ - maths general

[Anonymous No.10616540]

Previously >>10595623
Talk maths

[Anonymous No.10616638]

Threadly reminder to work with physicists.

[Anonymous No.10616767]

>>10616638
just noticed that the Einstein poster has a happy face in the '68 physics panel and a sad one in '98. Is that supposed to be Hilbert on the right?

[Anonymous No.10616791]

Fixed point theorems are so fucking based, bros.
What's your favorite fixed point theorem?
For me, it has to be Kleene's Second Recursion Theorem.
Banach Fixed Point is great too since it's so simple to prove and yet is the essential tool for Existence/Uniqueness for ODEs!

[Anonymous No.10616834]

>>10616815
https://www.genealogy.math.ndsu.nodak.edu/
>>10616791
Poincaré Birkhof.

[Anonymous No.10616846]

>>10616791
For me it's Brower

[Anonymous No.10616854]

i was about to ask why is there a new thread when the last one isnt dead but alas, it was at the bump limit. a severe improvement from 2 threads ago which died at 87

[Anonymous No.10616980]

>>10616834
that's cool actually
maybe one day someone can make a six degree of separation game with mathematicians

[Anonymous No.10617121]

Has anyone attempted to do with knotted surfaces in 4-space what Thurston did with knot complements in 3-space?

This is complicated I imagine by the strangeness of smooth structures in 4-manifolds but it's an idea that just popped into my head today.

[Anonymous No.10617279]

Does anyone remember if not uncountable implies countable requires third removed?

[Anonymous No.10617281]

>>10616980
>maybe one day someone can make a six degree of separation game with mathematicians
https://en.wikipedia.org/wiki/Erd%C5%91s_number

[Anonymous No.10617471]

>>10617279
Ordinal and cardinal shit require AC if you go far enough, but where is this "far enough", that I do not remember. AC itself implies LEM.

[Anonymous No.10617495]

Did the Latvian/Lithuanian tranny and the Finnish girl kill themselves or what?

[Anonymous No.10617630]

>>10616791
Lefschetz

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10617780]

Daily Putnam/Olympiad Problem >>10617778

[Anonymous No.10617871]

>>10617279
Yeah it does. Almost everything of the form ((not (not p)) implies p), requires LEM, because proving stuff without LEM requires actually constructing stuff and double negations don't give you much to use in a construction.

[Anonymous No.10617881]

is there a name for this type of geometry, radial areas projected from an origin area

[Anonymous No.10617917]

>>10617471
That's Diaconescu's theorem.
>>10617871
Thanks lad.

[Anonymous No.10617923]

>>10617917
>That's Diaconescu's theorem.
Yep.

[Anonymous No.10618063]

If I'm doing an integral with spherical coordinates where the radius has been named R, should I just integrate with R from 0 to R or should I name one of the R's differently?
It looks pretty dumb to let 0=<R=<R but the answers seems to become correct anyway.

[Anonymous No.10618068]

>>10617881
A foliation induced by a metric or energy function?

[LMC !!6bFXHDKL67m No.10618128]

Daily Brainlet Filter >>10618126

[Anonymous No.10618132]

>>10618063
It's bad practice, but it's mostly irrelevant

[Anonymous No.10618133]

I was thinking of perhaps creating a youtube channel going over a (high-level) math textbook this summer. Is this a good idea or already been done to death?

[Anonymous No.10618137]

>>10618133
for reference, im the >guy that did the commutative algebra thread around october that ultimately failed

[Anonymous No.10618167]

I'm having second thoughts as a physicist and I have an undergrad in mathematics.
My favourite area is abstract algebra.
What are some hot/interesting developments currently in that kind of region?

[Anonymous No.10618170]

Should I just kill myself or try to live all the way till my PhD studies start?

[Anonymous No.10618171]

>>10618167
if you still call it abstract algebra, you're not qualified to understand the developments currently in that region

[Anonymous No.10618176]

>>10618171
yeah I know, obviously, I just wanted a sort of direction, like you tell me, "........ is hot right now", then it's up to me to put in the work to get an understand of ........
Just want to get a taste of what I could have as an alternative. I'm already going through D&F so I still have a long way.

[Anonymous No.10618181]

>>10618167
I'm working on a generalization for Kempe's Univesality Theorem. There's some applications for it in machine learning. But hey, don't steal my idea.

[Anonymous No.10618184]

>>10618176
Inverse Galois problem

Group extension problem

Are all trace 0 matrices commutators?

The Gerstenhaber problem

[Anonymous No.10618185]

>>10618171
what do people in the know call it?

[Anonymous No.10618197]

>>10618185
It's like asking what are open problems in analysis. What analysis?
Real analysis? Complex? Functional? PDEs? Analytical number theory? Analytic combinatorics?

Abstract algebra is the second year undergraduate term for basic algebra. From there it splits into at least group theory, ring theory and field theory. Then you have finite/infinite group theory, noncommutative rings/modules, commutative rings/modules, homological algebra, algebraic K-theory, algebraic geometry, algebraic number theory, etc.

If you ask for 'abstract algebra', it means you don't have the maturity (or knowledge) that is required to see the point of it all.

[Anonymous No.10618214]

>>10618133
I honestly think that's something that's only interesting if we're either working with someone who has extensive knowledge of maths and can relate the constructions used to techniques from other problems and theorems in an interesting way, if it's a von Neumann tier dude, or if you're really funny.
If you fit one of the three, go for it.

[Anonymous No.10618366]

>>10618137
That was a really cool idea, I remember you

[Anonymous No.10618393]

>>10618366
h-hey

[Anonymous No.10618405]

I'm thinking of doing a masters in Germany. Any unis I should look into or avoid?
Areas of interest: low-dim topology (thesis), group theory (most fun class during bachelor), complexity theory (only topic I studied independently).
Already know about Bonn (too big/intimidating for me) and Goettingen (looks comfy).

[Anonymous No.10618424]

>>10618405
I heard there's some apparent discrimination towards non-german speakers

[Anonymous No.10618456]

>>10618424
Yeah that is huge in Germany. I don't care though. It is just one cost that you have to bear.
I'm currently B1.2 in German and working hard to get to C1 by the end of my Masters.
I could go to the Netherlands or the UK.
The Netherlands is nice but I like the Germany employment market (both research and industry) far more.
The UK is too expensive and their unis too crowded.

[Anonymous No.10618509]

>>10618405
Sometime ago I saw a pamphlet for a master program in Berlin, it was in english and it looked ok. However
>Berlin

[Anonymous No.10618646]

Can anybody help with
>>10614871

[Anonymous No.10618658]

>>10618646
Time series analysis is the field of statistics that deals with taking a series of values across time and describing/predicting it.
Analysis of demand resembles your situation quite a bit, so you can probably pick up some tricks specifically from there, but I can't really help you get those.

[Anonymous No.10618680]

Can you faggots switch to fonts that are legible at an ordinary level of zoom, please? Thank you.

[Anonymous No.10618732]

>>10618393
If you make a channel I would watch your videos

[Anonymous No.10618874]

>what are you working on?
Finishing up my linear algebra course and trying to learn more about SVDs also preparing for research this summer
>what are you reading?
Reading, Writing and Proving by Ulrich Daepp and The Game of Cops and Robbers on Graphs by Anthony Bonato
>dumb question you need answered:
What is a good text to read about Singular Value Decompositions? My professor said we won’t have bough time to get to it but it seems like a fairly important topic.

[Anonymous No.10619056]

>>10618658
Thanks!

[Anonymous No.10619127]

Based mathematicians I need your help.

What's the best weighted kappa to use for three raters?

I will have n=≤89 cases which will be graded like so “<10%”, “10-20%”, “2-3%”, “>30%”, &c.

I can't find any statistics package for calculating weighted kappa with three raters so I think im just going to end up converting the percentage categories into nominal values and then use Fleiss's kappa. Presumably this is not going to be as accurate?

[Anonymous No.10619152]

>>10618197
>algebraic geometry
we are geometers you bitch, not algebrists.

[Anonymous No.10619200]

What's the derivative with respect to x of f(x,s(x))?
Is it f'(x)+f'(s)ds/dx?

[Anonymous No.10619298]

>>10619152
the best geometers are also algebraists (see Serre, Grothendieck)

>>10619200
given that you have a function in two variables, f'(x) is already completely wrong since it doesnt even make sense. In the following let [math]x_1,x_2[/math] be the placeholder for the first and second variables.

[math]\frac{\text d}{\text dx}f(x,s(x))=\frac{\partial f(x,s(x))}{\partial x_1}+\frac{\partial f(x,s(x))}{\partial x_2}\frac{\text d s(x)}{\text dx}[/math]

[Anonymous No.10619301]

>>10619152
Geometers study algebraic geometry so that they can do algebra, and algebraists study algebraic geometry so that they can do geometry.

[Anonymous No.10619350]

I'm getting my mind fucked for a second

Let [math]B[/math] a ball around 0 and [math]S^n[/math] the sphere. Why exactly is [math]H^n(\mathbb R^n, \mathbb R^n\setminus B;G)\cong G[/math]? Is [math]\mathbb R^n / (\mathbb R^n\setminus B)\approx S^n[/math]?

[Anonymous No.10619356]

>>10619298
it's only one variable, there's no x2

[Anonymous No.10619357]

>>10619356
The function has two inputs, hence two variables. just because you decide both inputs will depend on x does not mean its not a bivariate function, and that the chain rule doesnt apply

[Anonymous No.10619358]

>>10619298
>[math]x_2[/math]
You mean s.

[Anonymous No.10619369]

>>10619200
>>10619356
>>10619358
yeah i messed up the inputs but should still be legible

[eqn]\frac{\text d}{\text dx}f(x,s(x))=\frac{\partial f(x_1,x_2)}{\partial x_1}(x,s(x))+\frac{\partial f(x_1,x_2)}{\partial x_2}(x,s(x))\cdot\frac{\text d s(x)}{\text dx}[/eqn]

[Anonymous No.10619371]

>>10619350
Yes they are homotopic.

[Anonymous No.10619374]

As someone in my mid twenties, will I ever catch up to people who have been studying university level mathematics since they were 18?...

[Anonymous No.10619394]

>>10619350
What does the / mean again?
>>10619374
>since 18
Jokes aside, it has happened before.

[Anonymous No.10619396]

>>10619394
/ means quotient space, \ means set minus

[Anonymous No.10619413]

>>10619396
Thanks, lad.

[Anonymous No.10619421]

>>10619374
what do you mean catch up? catch up as in reaching the same level of proficiency in mathematics or as in recovering the time lost? the former is up to you but the latter is unlikely unless you're a genius.

[Anonymous No.10619422]

>>10619369
Why do you use two different x? It's the same x f and s are a function of

[Anonymous No.10619428]

>>10619422
irredeemable

[Anonymous No.10619465]

>>10619421
Aren't they the same thing? Recovering the time lost would mean reaching the same level of proficiency.

[Anonymous No.10619490]

>>10619465
I assume anyone trying to get better at math does it because they want to contribute to a subset of mathematics or because they want to use math to invent/discover/make something. and there's only so much you can learn before you get to this level, someone who starts learning at 18 will probably reach that level earlier in life.

[Anonymous No.10619505]

>>10619490
Oh I see.

Well I reckon I'll be OK.

Not trying to compete with Scholze here. Although who wouldn't want be in possession of such a mind.

[Anonymous No.10619512]

>>10619505
>>10619505
Me desu.

[Anonymous No.10619590]

>>10619512
Mochizuki's "proof" of the ABC conjecture is incorrect. Inter-universal Teichmüller theory (abbreviated as IUT) is a failure.

[Anonymous No.10619592]

>>10619590
>Mochizuki's "proof" of the ABC conjecture is incorrect.
How so?

[Anonymous No.10619616]

>>10619512
>>10619590
>>10619592
http://www.unz.com/akarlin/intro-apollos-ascent/

>An extreme example today would be the work 0f Japanese mathematician Shinichi Mochizuki. At least Grigory Perelman's proof of the Poincare Conjecture was eventually confirmed by other mathematicians after a lag of several years. But Mochizuki is so far ahead of everyone else in his particular field of Inter-universal Teichmuller theory that nobody any longer quite knows whether he is a universal genius or a lunatic.

[Anonymous No.10619619]

>>10619616
>Anatoly Karlin is a Russian alt-right, white nationalist, anti-Semitic conspiracy theorist blogger who promotes racialist pseudoscience.
Yeah, no.

[Anonymous No.10619622]

>>10619619
>Anonymous is an anatolian shitposter, cocksucker, AIDS spreader who quotes rational wiki
Yeah, no.

[Anonymous No.10619630]

>>10619590
>>10619616
A proof is not less correct because few people understand it.

[Anonymous No.10619638]

>>10619622
this is /mg/, we're reasonable and well-adjusted people here. maybe you lost your way back to /pol/?

[Anonymous No.10619644]

>>10619622
>>Anonymous is an anatolian shitposter, cocksucker, AIDS spreader who quotes rational wiki
Who are you quoting?

[Anonymous No.10619669]

>>10619422
FFS. f is a bivariate function. f' isn't meaningful. You can't differentiate a function with respect to its argument if it has more than one argument. You have partial derivatives with respect to each argument, e.g. ∂f/∂x1 and ∂f/∂x2; i.e. you have to name those arguments so you can express which argument each partial derivative is with respect to.

d/dx f(x,s(x)) = f[x1](x,s(x)) + f[x2](x,s(x)).s'(x)

where f[x1] is the partial derivative of f w.r.t its first argument and f[x2] is the partial derivative of f w.r.t its second argument.

[Anonymous No.10619740]

>>10619622
>Yeah, no.

[Anonymous No.10619808]

One time I was working on understanding some 1970-ish combinatorial design paper. At one point I got fed up. I put my notebook down and I layed down on my bed and I just started going through the terms and the argument in my head. I took a good 30 minutes of just thinking really hard about the problem and then it made sense.

[Anonymous No.10619946]

>>10616540
>maths
Pretty sure you mean math, OP.

[Anonymous No.10620052]

>>10618133
>Is this a good idea
yes

[Anonymous No.10620365]

>>10619127
Pls respond

[Anonymous No.10620369]

>>10619946
sorry anon, maths requires intelligence, americunts need not apply :^)

[Anonymous No.10620411]

> Did YoU knoW the SuM oF aLl naturAl NumbErs is -1/12. HoW crAzY rIgHt!

[Anonymous No.10620629]

Does anyone know of a review/monograph about the best attempts at the P!=NP problem?

[Anonymous No.10620639]

>>10620629
scott aaronson p=np pdf

[Anonymous No.10620865]

Okay I don’t want to make a thread about this because this board has enough low-effort content as it is, but how smart do you have to be to excel in mathematical research? I’d like the honest truth, whether it be IQ, experience, or any other factor that could tell you whether or not it’s worth pursuing.

[Anonymous No.10620873]

There's a proof in the generic group model about the hardness of the discrete logarithm problem. Are there similar results for integer factorization? I only know of the proof that the RSA problem is as hard as integer factorization in the generic ring model, but neither problem is shown to be hard in the paper.

[Anonymous No.10620874]

>>10620865
>IQ
130 minimum to be a grad student at a mediocre university, 150 to be at a good one, 170+ to actually do good research
>Experience
a lot

[Anonymous No.10620877]

Can someone explain how this example shows that cohomology with compact supports is not a homotopy invariant? I'm not getting it

Which exactly is the space that is homotopy equivalent to R^n that has different cwcs

[Anonymous No.10620880]

>>10620874
I know people with sub-130 IQs at mediocre universities. Maybe 130 is the minimum for a good uni?
I’ve gotten mine tested and it came out to 131, by the way.

[Anonymous No.10620911]

>>10620874
I’ve gotten tested by a local psychologist and it’s around 134, currently no research experience (20) - are you saying I’m fucked? Are you currently doing a PhD program?

[Anonymous No.10620915]

>>10620911
>Are you currently doing a PhD program?
Yes, at a top 10, not even kidding, but I have a feeling I'm doing so badly im gonna get kicked out
> are you saying I’m fucked?
not sure, but i'm fucked, that's for sure

[Anonymous No.10620922]

>>10620911
>no research experience (20) - are you saying I’m fucked?
I'm 26 with no experience and I got in a PhD program. You are not fucked.

[Anonymous No.10620923]

>>10620915
Are you the same Anon? I’d like to talk with someone about this. Do you use discord?

[Anonymous No.10620926]

>>10620922
Do you produce quality research in a pure math field?

[Anonymous No.10620929]

>>10620926
I haven't started yet.

[Anonymous No.10620930]

>>10620923
yes and i dont use discord, also i cant really spare much time, i am REALLY fucked (2 exams next week, I havent gone to class at all for the second one and i havent even touched it yet)

[Anonymous No.10620951]

>>10620930
>can’t really spare much time
>browses /sci/

[Anonymous No.10620953]

>>10620951
h-hey i need a break too

[Anonymous No.10620957]

>>10620877
You can find a homotopy from R^{n+1} to R^n, which clearly doesn't preserve H_c.

[Anonymous No.10620958]

>>10620957
thank you, that fact always escapes me

[Anonymous No.10621056]

>>10620877
friendly reminder that hatcher is absolutely terrible as a first encounter with cohomology

[Anonymous No.10621062]

>>10621056
what's better? Im not having much trouble with it other than the hideous font

[Anonymous No.10621077]

>>10621062
de Rham cohomology of differential forms is the best introduction to the concept of cohomology imo. but good for you if you like what you're reading, to each his own.

[Anonymous No.10621078]

>>10618063
slap a prime on the variable of integration

[Anonymous No.10621080]

>>10621077
>his
their*
>de Rham cohomology of differential forms is the best introduction to the concept of cohomology imo.
what book do you recommend? i tried bott tu but it started with a lot of prereqs i didnt know at the time (eg differential forms)

[Anonymous No.10621111]

>>10621080
The Geometry of Physics by Theodore Frankel covers everything, I believe.
A lot of graduate level physics books start from zero and work their way through the subject.

[Anonymous No.10621120]

>>10621111
i'd rather have one for mathematicians, but thanks

[Anonymous No.10621140]

>they deleted the Étale shiteitte ne thread
How do the jannies just go and do such devillish things?
>>10621120
John Lee's Introduction to Smooth Manifolds works, even if it reads like it's for children. Otherwise, any Differential Topology text.
Also, I'd recommend swapping from Hatcher to Fuchs-Fomenko.

[Anonymous No.10621149]

>>10621120
I purposefully gave you a "physics" text because you are a baby at the subject.
It's already way more rigorous than your level. It's also a mathematical physics text, which is mathematics, not physics.

[Anonymous No.10621181]

>>10621140
what do you think of Tu's intro to manifolds?
i'd guess it probably leads nicely to bott tu's book
>>10621149
fine i'll give it a look, but i am looking for rigour since i already have some familiarity with topological k theory and riemannian geometry

[Anonymous No.10621247]

>>10621181
It seems like a standard text on smooth manifolds. Besides, his book on DiffGeo was good, so that one is probably also nice.

[Anonymous No.10621313]

>>10621181
>what do you think of Tu's intro to manifolds?
the best introduction to smooth manifolds. maybe too easy.

[Anonymous No.10621327]

>>10616638
Wish I knew any physics Bros so we could do some random research. Not like groundbreaking stuff but just some stuff that interests us both and also helps pad the CV. I'd call it Brosearch.

[Anonymous No.10621392]

>>10619369
this is really retarded notation please stop

[Anonymous No.10621440]

>>10621392
>>10621392
i was making a point of clarifying it you idiot

[Anonymous No.10621524]

God tier:
>gives all non review definitions and non-trivial theorems in bold, explains the intuition and relation to other subjects in plain prose, specifies when some greek/fraktur/etc letter will be used to denote something for the rest of the text, will unapologetically skip a hard, important proof after spending five pages on a biography
Good tier:
>gives the great majority of definitions in bold, borrows prose to be faster, keeps formal for definitions, but might be informal for lengthy constructions and proofs
Bad tier
>assumes the reader can recognize that lambda stands for a scalar and similar autistic shit, paradoxically specifies that x in f(x) is a member of some set after having defined f, has no appendix fixing notation, uses theorems from the exercises for proofs, defines scarcely
Ilegible tier
>it's just fucking prose, what the fuck is wrong with you man
>>10621440
>it was clear in my head

[Anonymous No.10621756]

>>10616540
Is there a generalized version of the universal cover and the Galois correspondence to higher homotopy groups?

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10621813]

Daily Putnam Problem >>10621806

[Anonymous No.10621819]

Are there any graphs that can not be represented as planar without at least one curved edge?

[Anonymous No.10622306]

>>10621819
Yeah non-planar graphs for example

[Anonymous No.10622335]

>>10621140
>fuchs fomenko
fucking based

[Anonymous No.10623059]

You have been visited by the enthusiastic category theorist. Coproducts and universal properties will come to you if you respond to this post.

[Anonymous No.10623120]

>>10621440
oh wow two (you)s for one, thanks!

[Anonymous No.10623123]

>>10623059
sauce?

[Anonymous No.10623134]

>>10617881
Overlapping concentrics?

[Anonymous No.10623183]

What do you guys think of my tattoo? Honest answers only

[Anonymous No.10623360]

>>10623183
>not tattooing Perelman's proof of the soul conjecture
Never gonna make it.

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10623617]

Daily Putnam Problem >>10623607

[Anonymous No.10623679]

>>10623059
What's up with the shape of those boards

[Anonymous No.10623690]

>>10623183
The quadratic reciprocity is based, the rest is kinda embarrassing (especially the face portrait)

[Anonymous No.10623918]

post yfw first cup of the day

[Anonymous No.10623984]

>>10623183
embarrassing, no kidding

[Anonymous No.10623994]

>>10623183
nice check this one out

[Anonymous No.10624009]

>>10623994
That's pretty metal

[Anonymous No.10624013]

>>10621524
>uses theorems from the exercises for proofs
What's wrong with that? Dense books couldn't and shouldn't always spoonfeed you with all the stages of a proof

[Anonymous No.10624157]

>>10623918
coffee addicts should go to rehab

[Anonymous No.10624336]

>>10623123
https://www.youtube.com/watch?v=SNbTQw1i_ms&list=PLJkwIz2V3XbgUdM5PbLOlC7kRGOo66upN&index=7

>>10623679
Le quirky design. Everyone hates it.

[Anonymous No.10624476]

have you read this?

[Anonymous No.10624497]

>>10624476
i haven't, no

[Anonymous No.10624609]

>>10623059
Help me /mg/, I've read too many John Baez blog posts and now all I think about are functors

[Anonymous No.10625551]

>>10624476
I have, and I like it very much

I'm actually in an undergrand seminar on discrete math this semester, and I asked to do a lecture on the probabilistic method (using the final chapter in the book)

Hope it'll go well

[Anonymous No.10625760]

>>10621327
based.
I want some brosearchers too

[Anonymous No.10626130]

Daily random question:
What lectures did you/do you dislike at uni? If you liked all, please respond too (by saying you liked all)

[Anonymous No.10626183]

>>10626130
Analysis 1 and 2

[Anonymous No.10626186]

>>10626130
Statistics (sadistics)

[Anonymous No.10626227]

Can someone give me a resource that goes over integrating k-forms over R^n real quick? I tried Hubbard&Hubbard but they have intractable computations using these weird parallelograms and I don't want to peruse 500 pages to understand their last chapter. Assume I'm pretty well versed with the algebraic concepts.

Alternatively, can someone just tell me how to compute, say, if I have a closed 1-form [math]\omega[/math] in R^2 and a smooth homotopy [math]h [/math] between [math]\gamma_0\gamma_1[/math] with same endpoints, that [math]\int_{\gamma_0}\omega=\int_{\gamma_1}\omega[/math] (assuming Gauss/Stokes), while being explicit if possible.

[Anonymous No.10626232]

>>10623918
It accelerates my bowel movements, give me an hour long boner, makes me yawn constantly because it doesn't really helps me wake up. All of that simultaneously.

[Anonymous No.10626245]

>>10626186
brainlet

[Anonymous No.10626252]

>>10626130
I hated: probability/statistics, all my physics lectures (except the mathematical physics ones, those were goat) and so far all algebraic geometry classes I've been in (two times) since the lecturers literally just handwaved through the material and the algebra and I didn't understand what was going on.

[Anonymous No.10626263]

>>10626227
For reference, this a snapshot of the lecture notes from which I'm supposed to learn this subject

[Anonymous No.10626272]

>>10626130
Probability and statistics. Super boring class, not at all what I was expecting.

[Anonymous No.10626278]

>>10626186
Stats done with measure theory:
>nice subject with nice notation
Calc stats:
>incomprehensible garbage
>>10626227
Apply Jordan closed curve, then Stokes.

[Anonymous No.10626279]

>>10626278
Im looking for an explicit calculation

[Anonymous No.10626290]

>>10626279
I invert one of the two paths and concatenate them. By Jordan Closed Curve, there's an area that has this loop as a boundary. By Stokes, the integral along the loop of Omega is equal to the integral along the area of dOmega. Since Omega is closed, dOmega is constant zero, and the integral is zero along the loop.
The integral along a path depending only on the endpoints follows immediately from the integral along any loop being zero.

[Anonymous No.10626293]

>>10626290
where does the homotopy come into play?

[Anonymous No.10626294]

>>10626293
in the jordan curve part i assume, actually.

problem is the lecturer did something using the pullback of the 1-form through the homotopy h

[Anonymous No.10626302]

>>10626293
It doesn't, any two paths with the same starting and endpoints are homotopic in R^n.
If you're working over some other space, you can use the homotopy to show that Jordan works.
>>10626294
Technically.

[Anonymous No.10626322]

>>10626302
To be fair i meant to say the form was over an open subset of R^n, not R^n itself

[Anonymous No.10626335]

>>10626322
That's trickier, but you essentially pretend that the homotopy is the surface you wanted to begin with.

[Anonymous No.10626343]

>>10623183
I wouldn't have done it to be honest, but Euler is a great mathematician so I can at least complement your taste there. Not sure why you have a klein bottle and mobius band. Did Euler contribute to the discovery of non-orientable surfaces? I suppose if it's just your favorite results that's fine, though I might've been a bit more autistic with some of my choices, like getting "Hodge theaters" tattooed on my butt cheeks, one word on each cheek.

[Anonymous No.10626353]

>>10626186
>>10626252
>>10626272
>probability and statistics
what was wrong about it? i'm a freshman and haven't had it yet

[Anonymous No.10626378]

>>10626130
Graph theory. The only maths we used was basic set theory and integer arithmetic, so arguably it wasn't even a maths course.

[Anonymous No.10626423]

>>10626353
Not them, but I hated prob because my teacher was one of those old and boring af dudes.
Statistics was better because the teacher was a qt, a cute!

[Anonymous No.10626445]

Lol they made the autism test into a real thing

Perhaps nobody noticed since it's in the AT section of Munkres

[Anonymous No.10626717]

complex or arithmetic algebraic geometry?

[Anonymous No.10626811]

Fuck me I should have gone to class

[Anonymous No.10626852]

>>10626811
tell them to stop having a stroke when they write this shit

[Anonymous No.10626957]

What's your opinion of knot theory? is it cool enough to study solely

[Anonymous No.10626970]

>>10626811
Tell your boomer professor to fuck off or TeX up his shit.

[Anonymous No.10627011]

i know that it's mostly engineers and physicists that work with differential equations, but can any one of you math anons perhaps help out with my question?

>>10626534

[Anonymous No.10627085]

Why does the theory of continuous nowhere differentiable functions feel so distinctly pointless?

[Anonymous No.10627115]

>>10627085
because they only exist as possible places to find counter examples

[Anonymous No.10627128]

>>10627085
>>10627115
>what are fracral curves.

[Anonymous No.10627135]

>>10627128
begone popsci spook
leave this holy place

[Anonymous No.10627181]

Would I be making a huge mistake if I go into a grad program in Applied Math? I'm thinking of studying Optimization.
I also like some Pure Math but I don't think I like enough topics in Pure Math to make a career out of it.

[Anonymous No.10627229]

I'm on my first year and I can't find motivation to study, should I just be a hero?

[Anonymous No.10627232]

>>10627181
lol

[Anonymous No.10627265]

>>10627181
applied math is based, don't get fooled by anything people here say.
Except you have to be real careful where you enrol, it's easily taught badly

[Anonymous No.10627411]

>>10627135
Its a genuine subject you pseud.

[Anonymous No.10627464]

>>10616540
How can I find the vector between a hyperplane represented by a linear system, and a point.

For example, the vector from point (1/2, 1/2, 1/2) to the line represented by x+y=1, y+z=1

I have found resources that explain how to do it with a hyperplane represented by a single equation, but not by a linear system that can't be represented by a single equation

[Anonymous No.10627473]

>>10627464
Fuck if I know what you mean with between, a line isn't a hyperplane, and every hyperplane can be represented by a single equation.
>>10627229
Nah.

[Anonymous No.10627477]

>>10627473
More specifically, a line isn't a hyperplane in anything that isn't R^2.

[Anonymous No.10627499]

>>10627477
>>10627473
When I say between, I mean with its base at the point (1/2, 1/2, 1/2), and its tip at the point on the hyperplane nearest that original point (1/2, 1/2, 1/2). So in my example, I want to find the vector from (1/2, 1/2, 1/2) to the line in 3-space.

How can I find the vector from a point in n-space to the nearest point on an [n-m]-dimensional hyperplane represented as a linear system? If an [n-m]-dimensional hyperplane can be represented by a single equation in n-space, then how do I find it?

[Anonymous No.10627516]

>>10627499
x+y=1=z+y, thus x=z.
Thus the line is given by (t, 1-t, t), where t runs through the reals. If t=1/2, we have (1/2, 1/2, 1/2) and the line passes through the point you wanted.

[Anonymous No.10627525]

>>10627516
Ah I should have investigated the example before posting. Is there a general method for n dimensions, and in my example pretend I said the point (2, 3, 4)

[Anonymous No.10627625]

Why am I so dumb?

[Anonymous No.10627631]

>>10627625
Your teachers didn't start with trigonometry as operations on the unit circle.

[Anonymous No.10627893]

EE major
I made As in calc 1, 2, 3. And a C in Differential Equations.

Fuck Differential Equations so much. The averages in my class were so high, I'm genuinely convinced 1/4 of the class was cheating, or I happened to sign up for the section with everyone being an autistic savant except me

Fuck this class, glad I never have to take this shit again

[Anonymous No.10627905]

>>10616540
Anons help. I always finish homework first, and finish math guides and my classmates ask me for help.The problem is when we have an exam, the professor adds difficult excercises we never seen before (but related to). My question is: how can i study for math exams correctly? Guides or normal problems are not enough.

[Anonymous No.10627921]

>>10627905
What class? As a general rule, find a grad text on the subject.
If calc, Polya. If combinatorics, Lovasz. If complex, Alfohrs, etc.

[Anonymous No.10627946]

>>10627921
First year of college and we are studying Trigonometry and math progressions.

[Anonymous No.10627973]

converges or diverges?
im getting diverges with AST but my professor said it converges absolutely. what am i doing wrong?

[Anonymous No.10628001]

>>10627973
without the (-1) it diverges by the comparison test
def not absolute convergence

[Anonymous No.10628021]

>>10626957
(k)not theory is autism embodied

[Anonymous No.10628022]

>>10627893
... But diff eq is super important in EE
.t EE

[Anonymous No.10628037]

>>10618874
Please respond

[Anonymous No.10628044]

>>10627085
>so distinctly pointless?
Ito calculus and stochastic integrals in general would like a word with you.

[Anonymous No.10628098]

>>10628037
Unironically just read the wiki article, it does a well enough job. But if you need more, Strang the gigachad has a good video https://www.youtube.com/watch?v=mBcLRGuAFUk
And mit open course ware has some nice notes. Honestly. for undergrad material they've got a pretty good selection of notes to choose from.
http://math.mit.edu/classes/18.095/2016IAP/lec2/SVD_Notes.pdf
https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/positive-definite-matrices-and-applications/singular-value-decomposition/MIT18_06SCF11_Ses3.5sum.pdf

[Anonymous No.10628100]

>>10627973
It cannot converge absolutely. The terms tend to 1 in the modulus. The alternating series test doesn't tell you anything about absolute convergence, only conditional, and that series doesn't tend to 0 so it cannot conditionally converge. Your professor probably missed the square root term

[Anonymous No.10628127]

>>10628100
if positive terms converge to 1 and negative terms converge to -1 then the series diverges or converges conditionally?

[Anonymous No.10628212]

>>10628127
it diverges conditionally
but i can force convergence and get approximately .232249521405

[Anonymous No.10628249]

>>10627499
A (hyper)plane is the set of points x whose dot product with the normal vector n is a constant d: n·x=d. Any point p can be expressed as the sum of a point x on the plane and a scalar multiple of the normal: p=x+kn. Multiplying by n gives n·p=n·x+kn·n = d+kn·n => k=(n·p-d)/(n·n). Thus the vector is ((n·p-d)/(n·n))n. If the normal has unit length, n·n=1 and this simplifies to (n·p-d)n. IOW, it's the distance of the point from the plane multiplied by the unit normal vector.

[Anonymous No.10628267]

>find cool page with continua examples
>missing plenty of info
>hasn't been updated since 2003
>apparently one of the collaborators died in 2006
Well, now I understand why it was left in dust.

[Anonymous No.10628309]

>>10627905
A good exam will never be exactly the same as your worksheets/homework. They are meant to check whether you actually -understand- the subject, not whether you managed to memorize some theorems and apply them mechanically. That's why you're asked to come up with, and write down a solution to a problem you've never seen before (but presumably can be solved quickly by applying the theory you've studied) in 2 hours or less. You need to learn to think creatively, within the context of whatever you're studying, and the only way to do this is to check many sources and solve many different problems. Work out on problems from books (undergraduate level, especially since you're studying simple trig and algebra; follow >>10627921's advice only once you start to find undergraduate books really boring and trivial). YouTube videos and other such media are good too. Revise your notes and try to prove the theorems yourself.

The quote in pic related is by Paul Halmos; read it. The proper study of mathematics is never a purely passive endeavor.

[Anonymous No.10628377]

Can you say that an ideal X object has symmetry between its \ and /, from which X is formed? Like, can we have the axis of symmetry between \ and /?

[Anonymous No.10628394]

>>10628377
I mean, originally I was thinking about a brain asymmetry, and if you think about it it shapes X figure when left hemisphere relative to right side of body etc, so technically you can call it a symmetry?

[Anonymous No.10628418]

>>10627893
DEs is fucking easy and literally the only important type of calculus for DEs. get fucked.

[Anonymous No.10628503]

I wish to know more about discrete conformal mappings so that I can manufacture anal lubricant. Are there similar interesting results in discrete geometry(is that even the right word) I as an engineer should be aware of? I like discrete things.

[Anonymous No.10628912]

>>10627265
What do you mean, "taught badly"? What should I look out for?

[Anonymous No.10628956]

I want to review my first 2 year of analysis during summer, should I go for Rudin? My analysis teacher literally shilled Rudin during one class. I also plan to read Linear Algebre from Hoffman, good idea?

[Anonymous No.10629008]

>>10628956
Try Simon

[Anonymous No.10629027]

>>10628956
>two years of analysis
What analysis and which Rudin?

[Anonymous No.10629049]

>>10629027
My real analysis course covered 75% of the topics of "Principles of Mathematical Analysis" from Rudin.

[Anonymous No.10629056]

>>10629049
>2 years to cover 75% of Baby Rudin
Drop out of uni.
But if reviewing is the idea, Royden's good.

[Anonymous No.10629091]

>>10627905
Go with the mindset that you are going to kill, and it should go well

[Anonymous No.10629225]

Why do unbased physishits have such things as natural units setting [math]\hbar=c=1[/math] yet based mathematicians have to keep dragging, say, factors of [math]2\pi i[/math] or exponentiating over a transcendental base. When do we get our natural units?

[Anonymous No.10629516]

>>10625551
i have the book too and im in a seminar
i did some stuff with latin squares

[LMC !!6bFXHDKL67m No.10629983]

Uploaded if anyone wants it: >>10629902

[LMC !!6bFXHDKL67m No.10629986]

>>10629983
some other gems in there too

[LMC !!6bFXHDKL67m No.10629990]

wait shit I forgot to mention the book title: Fuckin' Concrete Contemporary Abstract Algebra Introduction by First Course Radical Solution Dummies: Dummit, Foote, Hungerford, Shifrin, Gallian, Fraleigh, Beachy, Herstein, Saracino, Artin, Deskins

[Anonymous No.10630936]

In mathematical analysis it's not enough to slap the quotient rule onto this to prove it's differentiable right? You'd have to go through first principles with

lim(z->z0) = (f(z)-f(z0))/(z-z0)

right? I can't get it to simplify down to get anything out of it is all so starting to think it's a fools errand for this equation or something.

[Anonymous No.10630944]

>>10630936
That's not a real valued function

[Anonymous No.10630948]

>>10630944
yea this is complex analysis

[Anonymous No.10630964]

>>10630936
>it's not enough to slap the quotient rule onto this to prove it's differentiable right?
It is desu.

[Anonymous No.10631048]

>>10630936
just remember that complex differentiable = real differentiable (in two variables) + cauchy riemann

So you would just need to show that the real and imaginary parts separately satisfy quotient rule and then add them together to get quotient rule for dz

most of the rules from real analysis pass to complex analogously

[Anonymous No.10631059]

>>10631048
this helped out a lot anon, thanks

[Anonymous No.10631102]

>>10630936
>>10631048
do you know if there's a simpler way of seperating out u(x,y) and v(x,y) from 1/(z^2-1) than rationalizing the denominator btw? Wanna avoid handling the ugly result in the differentiation if I can.

[Anonymous No.10631142]

>>10629983
>>10629990
What is this? Did /mg/ did this? Is it a paper or something more akin to a textbook?

[Anonymous No.10631574]

>>10616540
ok anons i am a bit confused. how does one acquire mathematical 'understanding'. what does it mean to understand a concept? does simply memorizing all the different connections a concept have to other related concepts or intuitions pertain to understanding?

[Anonymous No.10631596]

>>10631142
it's extremely rare, and the digital copy posted is LMC special edition FOR FREE!!!

[Anonymous No.10631613]

>>10631574
for me this involves having some sort of tactile or visual intuition for the concept
sometimes this means being able to prove it in air with minimal words and mostly swiping my hands around, as though i'm following a diagram or approaching a bound for some limit.
i think understanding goes beyond just being able to recall the connections to certain intuitions, i think a huge part of it is just "feeling" like it's right and like the argument is natural, similarly to how you can easily memorize the map of all the places you need to go in a city, but as you spend time walking around and getting to know the place you just have a subconscious feel for where the "right" places to be and the "wrong" places to be are (even if you don't know exactly where you are at any moment)

[Anonymous No.10631760]

>>10631102
What I meant with that is that you can consider d/dz as if it were "real" differentiation, ie: you can just take the normal derivative taking z as a variable and ignoring its complexness. And that you can prove that by using the condition CR+real differentiability to convince yourself of it.

[Anonymous No.10632134]

>>10631574
literally just collecting as many information about it as you can. The more you things you know about it the better you understand it, it's that simple.

[Anonymous No.10632180]

So I've learnt in class that the Riemann surface of the square root function corresponds to the following topological space:

take two disjoint complex planes, and remove the axis [math]x\leq 0[/math], then identify the axis of one with the opposite axis of the other and vice versa.

So i've tried doing this for an nth root. Pick a primitive nth root of unity s, and take n disjoint complex planes and remove the axis as before. Index these planes in terms of a power of the root of unity s, from 0 to n-1. Then glue one of the 0th axis to the opposite axis of the 1st plane, then the other axis of the first to the opposite of the second, etc, and finally the remaining n-1 axis to the remaining 0th axis.

Is this correct or should I just be taking the first non-trivial anticlockwise root of unity

[Anonymous No.10632207]

>>10632180
Also, if instead of n, what would happen if we have an irrational real number? Or a complex one for that matter? Is it still a Riemann surface? I'd think not because the winding number is only an integer quantity.

[Anonymous No.10632300]

Why does it seem like pretty much every single mathematical institute has a research group in algebraic geometry, these days?

[Anonymous No.10632350]

>>10632300
goat institutes goat mathematicians goat subject

[Anonymous No.10632611]

>>10632300
Because it's the biggest field in math right now

[Anonymous No.10632617]

HOW DO I Understand caragories?? What differentiates a topos from a set, and what textbook should I read to understand monoids and catagories etc

[Anonymous No.10632798]

What's a good graduate level rigorous revision book for Differential Topology and Differential Geometry?

[Anonymous No.10632811]

Guys I'm really fucked... differential forms dude here again... I'm tasked with what possibly looks like the easiest exercise.

>
Let [math]R[/math] be a Riemann surface, [math]\sigma:[0,1]\to R[/math] a path from points [math]p[/math] to [math]q[/math]. And [math]f:R\to \mathbb C_\infty[/math] a holomorphic function (ie: [math]f[/math] a meromorphic function on [math]R[/math]). Show that [math]\int_\sigma \mathrm d f =f(q)-f(p)[/math].
>

How do I deal with the fact that the path could pass through infinity? Do Mobius transformations preserve the value of the integral? If so, perhaps I could move the path, but how can I be sure that the path doesn't land again on infinity, perhaps at a different point?

[Anonymous No.10632813]

>>10632798
From what I've heard DT is Milnor's Topology from a differentiable viewpoint and for DG is Tu's book

[Anonymous No.10632839]

>>10628022
>>10628418
Exams were 90% of our grade. We were not allowed calculators. We were not allowed notes. We were only allowed a laplace transform table for one exam, and only one question was it actually useful for.

90% of the problems (and credit) on each exam was from problems that forced you to solve the problem with only one type of method. These problems were simplistic, however, in order to fully solve them, they involved trig identities, lengthy partial fractions, lengthy u-sub integrals, lengthy integration by parts, etc

I can do differential equations with a laplace table and some formulas/notes to remind myself of solving strategies. Literally 50% of my grade in this class was based on my ability to use partial fractions and solve lengthy problems of guessing the form of the solution.

I dont give a fuck what you say. This class, how it was taught to me and how I was graded, is and was pure cancer.

[Anonymous No.10632903]

I can't believe it. Category theory might actually be useful in real world engineering. Like making airplanes and shit. Some computational geometer used category theory to compose mathematical functions together to summon exceptionally complicated geometry from the platonic realm while respecting certain topological properties. Respecting certain topological properties is important in engineering because it lets us make stuff in the real world. This geometry we can now make with this approach, it shouldn't even be possible, but it is anyway.

[Anonymous No.10633394]

What is the space X you get from attaching RP2 with RP2 along RP1's in each?

[Anonymous No.10633399]

>>10632811
The path is at least piecewise differentiable.

[Anonymous No.10633422]

>>10632811
The function is meromorphic, so only has isolated pole singularities. The path crosses the poles only finitely many times and you can calculate the integral on the complement of this measure 0 set. You now have a finite number of open intervals, so you'll want to use Stokes' on these subintervals and try taking a limit.

[Anonymous No.10633494]

>>10632811
That's a basic result in complex analysis, just expand df.

[Anonymous No.10633598]

>>10631574
I'm of the mindset that understanding is just being able to apply something creatively. You can "understand" a hammer by being able to drive in a nail, by seeing a nail and knowing you'll need a hammer, by seeing two pieces of wood and knowing that you can join them by driving in a nail with a hammer, and by designing a birdhouse with the understanding that you'll join all the wood with nails and a hammer. At each level, you have a greater "understanding" by being able to more creatively apply the simple ability to mechanically do something. Swap hammers for, say, derivatives and integrals, and that'll be your "understanding of calculus".

[Anonymous No.10634000]

tfw feels awkward to continue formally addressing profs I've worked with now that my undergrad is done but feels even more awkward to suddenly switch to first names

I'm too autistic for this shit

[Anonymous No.10634111]

>>10634000
lmfao. im in the same boat. i don't know if i should start addressing my advisor by his first name like everyone does. but it's been a year already since i started calling him prof. -. i thought of asking him if i could call him by his first name, but too autistic to do it

[Anonymous No.10634113]

>>10634000
Basically everyone at my uni goes by their first name.

[Anonymous No.10634115]

>>10631574
One prof of mine says that learning mathematics is like learning to read or to speak your mother language: on the first few years you utter some basic phonemes and associate meanings to them, and with every passing year you learn more complex phrases and eventually you'll be able to express yourself on your own words. With mathematics, it's the same thing: first you learn the basics, exercise by proving some basic facts e.g. about one-variable calculus or basic algebra and eventually you'll be able to research, solve problems and write papers on your own.
>>10632903
Have you already read An Invitation to Applied Category Theory? https://arxiv.org/abs/1803.05316

[Anonymous No.10634119]

>>10632839
>wahhh wahhhh i have to do basic algebra
k
sounds like a shit class, but DEs is a great subject

[Anonymous No.10634139]

>>10634000
>tfw working with a cute and smart profesor
>forever oit of reach cause I cant call her by her first name

[Anonymous No.10634333]

>>10634139
>I cant call her by her first name
Why not?

[Anonymous No.10634622]

So an Eisenstein maass form attached to the cusp at infinity (working any level) has Hecke eigenvalue p^(s-1/2)+p^(1/2-s).

But what about the Eisenstein forms attached to other cusps? What does the Hecke operator Tp do to these? How might I calculate this?

[Anonymous No.10634640]

>>10633394
Klein bottle

Note that RP1 is just the circle, so what you're describing is the connected sum. If you dont know what the connected sum is, it's just removing a circle from each space and identifying the wholes. When doing it on graphs it's basically equivalent to identifying two closed loops on your space. Then the rest of the proof is just cutting and gluing

[Anonymous No.10634666]

I'm a 3rd year undergraduate and I'm currently working with a prof in a modelling project and we're most likely going to publish a paper this winter.
I'm planning to go to grad school but in a completely unrelated area (I'm thinking about arithmetic geometry or something related to number theory).
Does the fact that I have a publication with my name in it counts for admissions or it should be related to what I plan to do in grad school?

[Anonymous No.10634691]

>>10634622
I wish Alexander Nevskiy wasn't so bad a film otherwise. Eisenstein knew how to make those battle scenes, oh boy.

[Anonymous No.10634735]

>>10634666
You are never going to publish as a third year undergraduate in arithmetic geometry so I say go for it. Research experience is better than no experience

[Anonymous No.10635162]

>>10634119
>Study pure math at a post grad level
>an undergrad celebrates passing a notoriously difficult undergrad class
>insult the undergrad when their major is not related to pure math and they are being tested on pure math skills (which will never happen in a professional environment or even in their later classes)

Im glad math grad students earn a pittance while I make lods e mone in the aerospace field. Maybe you can put a down payment on a house with all that hubris. Probably not though, kek

[Anonymous No.10635192]

>>10630936
Any composition of meromorphic functions (functions with a discrete set of points on which they are not differentiable) is meromorphic by the chain rule. So yeah it's differentiable everywhere except at its poles at 1 and -1

[Anonymous No.10635262]

Why are wagies so pathetic? How is it so hard to understand that people do math out of passion for the subject? Or how do they not get that there is life apart from making money?

[Anonymous No.10635265]

>>10634640
Thanks so much!

How about X is obtained by attaching a copy of the Mobius band to the boundary of a punctured torus T^2 \ Int D^2 using a
homeomorphism of their boundary circles?

[Anonymous No.10635274]

>>10635265
This is again a long-winded way of asking what's the connected sum of a torus and projective space. In this case it's the connected sum of 3 copies of projective space, but the proof is a bit harder and longer, but it's essentially just cutting and gluing several times.

[Anonymous No.10635350]

>>10635162
you can cope all you want, it doesn't make babby's first ODEs any more difficult to the average intelligent person

[Anonymous No.10635531]

I've heard it said that past babby tier calculus, integration is not about length or volume anymore. But then, what is it?

For example, how could I interpret a path integral in the complex plane? Or integrating a form on a manifold?

[Anonymous No.10635761]

>>10635162
>muh money
The engineer's last refuge. Just get used to sucking corporate cock and chasing those dollar signs. We'll be busy unveiling absolute truths about the nature of reality :^>

[Anonymous No.10635778]

>>10635531
Lots of mathematicians claim there's no intuitive spacial interpretation for complex integrals, although tristan needham's visual complex analysis tries to. In any case, integration is best thought of as an anti-derivative, i.e. if this function or form describes the change in some function over space or time, what is the total amount of change?

[Anonymous No.10635794]

>>10635761
math has nothing to do with reality

[Anonymous No.10635814]

>>10635778
so as a local antiderivative for a function?

[Anonymous No.10635897]

>>10635531
>Integration isn't about length or volume later on
>says the bachelor's senior to the sophomore, after taking extremely advanced courses such as complex variables and differential geometry, which are very recent and weren't alomost entirely developed in the nineteenth century with later additions by Cartan
It's largely contextual, i.e. interpreting it as a volume while working with residues is weird, but most of the time it's still some sort of volume.

[Anonymous No.10635900]

>>10635897
Should have listed PDEs.

[Anonymous No.10635910]

>>10635897
I still think of integrals as being averages and it never creates too much problem.

[Anonymous No.10635920]

why did you follow a career in math /mg/? was it worth it?

[Anonymous No.10635951]

How is pic related for someone looking to get into pure mathematics with only an applied backround? (Up to and including elementary ODEs)

[Anonymous No.10635977]

>>10635951
>How is pic related for someone looking to get into pure mathematics with only an applied backround?
Why don't you try it and find out?

[Anonymous No.10636309]

>>10635794

[Anonymous No.10636327]

>>10635794
engineers, ladies and gentlemen
not good for much but damn are they funny

[Anonymous No.10636350]

>>10627631
^ in public schools most teachers who teach trigonometry have genuinely no understanding of it whatsoever

[Anonymous No.10636476]

wow no one has commented on the >math>s of OP (until me).
new record

[Anonymous No.10636518]

I'm thinking of giving up

[Anonymous No.10636541]

>>10636518
dont

[Anonymous No.10636592]

>>10635262
>Or how do they not get that there is life apart from making money?
My experience interacting with engineers (at least those who stop at a BSc) has led me to believe that they mostly choose that degree with the sole intention of working a 9 to 5 job that pays well, yeah.

[Anonymous No.10636599]

>>10618405
I was at TU München and I don't regret anything. I can recommend anything taught by the algebra group (Liedtke, Kemper, Viehmann). If you're into computational logic, the Isabelle chair (Nipkow) used to offer great classes as well.
One downside is that the campus is quite far from the city center (~30mins by S-Bahn).

The other university in Munich also seems fine, but a bit more theoretically oriented.

[Anonymous No.10636608]

>>10636327
do you mean like mathematical symbols exist as physical objects in space for instance an inscription on a piece of paper with graphite or ink or do you actually think mathematical objects and laws exist? just curious if you’re schizophrenic

[Anonymous No.10636627]

>>10632839
>Exams were 90% of our grade.
Dude. A lot of you cheat on the assignments, why are you surprised that they usually don't (and shouldn't) count for more than 20% maximum?

>We were not allowed calculators. We were not allowed notes.
That's standard and completely reasonable.

>We were only allowed a laplace transform table for one exam
Pretty nice of your professor honestly.

> and only one question was it actually useful for.
The point of the table isn't to be used in every single question, but to save you the effort of having to memorize the Laplace transforms.

>90% of the problems (and credit) on each exam was from problems that forced you to solve the problem with only one type of method.
In a class for non-math students, that's pretty much the standard because math professors have extremely low expectations of undergrads. Also you bitch about this but I'm confident in stating that you would not like the alternative of being given fresh problems that haven't been solved in class.

[Anonymous No.10636643]

>>10636608
neither

[Anonymous No.10636677]

In my undergrad half of my class were retards that couldn't do math and got angry because they couldn't understand the basics (most women lmao) and the other were pretentious "geniuses" who also got mad if someone else could solve a problem they couldn't.
What are the odds a grad programs has "people" like this?

[Anonymous No.10636700]

i really really want to understand category theory. is this a new field, it seems lots of people dont know about it, what is the best text

[Anonymous No.10636720]

>>10636691
Please, help.

[Anonymous No.10636788]

>>10636720
There's openboard.

[Anonymous No.10636966]

>>10636677
>In my undergrad half of my class were retards that couldn't do math and got angry because they couldn't understand the basics (most women lmao)
At least 70% of most of my classes were full of people like this (math ed majors) who just bitched and complained about everything. I hope grad school is better

[Anonymous No.10636983]

>>10636788
Thanks, m8.

[Anonymous No.10637013]

>>10636627
Fuck you. Fuck you you stupid piece of pretentious shit. Just because you know how to masterbate with fucking abstract useless shit doesn't mean you have any clue how to do any of the shit I was forced to learn in that class. It's not even useful for engineering, I've never come across it once and I've done two internships. Fucking stupid that we're force fed that garbage.
Feel free to talk all you want about how "fair" the class and the standards were in your deluded worldview since that's apparently the only thing mathematicians do all day. I'll be over here helping humanity.

[Anonymous No.10637021]

>>10637013
>I'll be over here helping humanity.
By doing what?

[Anonymous No.10637041]

>>10637021
Engineering, you moron.

[Anonymous No.10637060]

>>10632903
Can you give the source, please?

[Anonymous No.10637096]

>>10637041
>engineering
>helping humanity

[Anonymous No.10637106]

Say you have an [math]n[/math]-element set [math]A[/math] and it's powerset [math]P(A)[/math].
How would you go about counting the number of subsets [math]X \subseteq P(A)[/math] such that the elements of [math]X[/math] are pairwise incomparable by inclusion?

[Anonymous No.10637134]

>>10637041
>Engineering, you moron.
What makes you think you'll be helping humanity?

[Anonymous No.10637360]

The book I'm using for complex analysis (Brown-Churchill) states this theorem as a sufficient condition for a function being complex-differentiable. Later on, when holomorphic functions are introduced, it states that a sufficient condition for a function being holomorphic in a domain D is the same one found in this section (and another one which is equivalent but for polar coordinates). My question is, in order for the function to be analytic in the entirety of an open set D, would the only difference be that instead of having the partial derivatives only be continuous at [math]z_{0}[/math], I would need them to be continuous in the whole set? So when the partial derivatives only exist but aren't continuous anywhere but at a single point, then the function is just differentiable at that point, but if they are continuous at the whole set then it is holomorphic? Assuming the Cauchy-Riemann equations hold everywhere, of course.

Also, can I say anything about a function if the Cauchy-Riemann equations hold at a point and the partial derivatives are continuous there, but I don't have any information about any points around it (so the partial derivatives may not exist or C-R equations may not hold outside of that point)? Is it not complex-differentiable anymore, but at least real-differentiable?

The sufficient conditions for holomorphy and complex-differentiability are kinda fucking me up right now, I'm finding information that kinda contradicts each other because some state that a statement is sufficient to show that a function is holomorphic while others say that it is only complex-differentiable.

[Anonymous No.10637371]

>>10637360
holomorphic at z = complex differentiable on an open neighborhood of z.
this is all you need to know to answer your questions for yourself.

[Anonymous No.10637375]

>>10637134
I have the potential to do so, unlike you. Mathematics is worthless given the current numerical methods and their accuracy.

[Anonymous No.10637376]

>>10635951
Never heard of the book, but sounds like it might be too basic for you. If you already have studied up to ODEs you might be better off studying real analysis and a decent book on linear algebra. You presumably have some experience computing integrals and doing some matrix operations so these will serve as intuition for more abstract concepts.

[Anonymous No.10637416]

>>10637371
For the first part, I think it's right because if it's differentiable on an open neighborhood then the conditions must hold for each individual point in said neighborhood, and that would require each individual point to have continuous partial derivatives.
For the second part, I think it's also right, because (unless the author just adds conditions to the theorem that are inconsequetial), then removing the existence of the partial derivatives at the neighborhood would make it impossible to guarantee the complex-differentiablity, but the continuous partial derivatives at the point are still enough to say that the function is differentiable in the real sense.
A confirmation would be nice but still thanks.

[Anonymous No.10637594]

>>10636677
math grad students are usually pretty based, from my experience

[Anonymous No.10637597]

>>10637375
lol
if this reply is not ironic, then i truly laugh at your existence

[Anonymous No.10637601]

>genuinely curious about math but getting shit grades
>just being in it for the money and getting good grades

[Anonymous No.10637603]

>>10637360
Holomorphic = CR + one-time continuously differentiable in R^2

That's all you need to know about holomorphicity. Note that one-time continuously differentiable + CR actually implies infinitely continuously differentiable, so in general, you can forget about differentiability of holomorphic functions.

[Anonymous No.10637608]

new thread
>>10637606
new thread
>>10637606
new thread
>>10637606
new thread
>>10637606
new thread
>>10637606