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/sci/ - Science & Math


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10973904 No.10973904 [Reply] [Original]

talk maths, formerly >>10960172

>> No.10973931

>>10973904
mathematically speaking why is OP a fgt

>> No.10973933

>>10973931
Why the homophobic language?

>> No.10973939

>>10973933
sory it was vareables. OP = fgt.

>> No.10973949

>>10973904
Daily reminder that pure math today is just a series of disconnected autism tunnels

>> No.10973956

>>10973949
Nah.

>> No.10973961
File: 49 KB, 678x452, 1F6B2A87-1B71-4323-81AE-8A63795115B7.jpg [View same] [iqdb] [saucenao] [google]
10973961

This is the peak performance

>> No.10973978

>>10973904
How do I enjoy math?

>> No.10974012

>>10973956
Really? So how exactly is pure math research today pragmatic in any way whatsoever?

>> No.10974847

>>10973949
>autism
yes
>disconnected
no

>> No.10974889

>>10974856

>> No.10974894

>>10973961
Are the people around Scholze smart too?

>> No.10974896

>>10973949
Not everything in life has to have 'value'. Plus, parts of pure math are starting to have real life applications now. Algebraic topology in machine learning for example.

>> No.10974897

What is the best book to self learn advanced algebra (or beyond)?
I already have some basis in field thanks to my computer science bachelor but I want to study advanced mathematic further.

>> No.10974907

I don't think a scientific community which doesn't value its "middle class" and only counts on the superstars by sharply separating itself into two castas -- staff and professors -- is not viable in the long run. Talking not only about math, but STEM in general.

Especially here, in Germany, it is a disaster. People are leaving academia one by one. Soon, the German STEM will become shit tier.

>> No.10974909

>>10974897
There are no books on "advanced algebra" because it's too big as a field, there are books on specific fields of advanced algebra (lie theory, arithmetic, algebraic geometry etc etc.). For a book on basic algebra which you seem to be looking for, try the two volumes of Jacobson (Basic Algebra I&II), which has good exercises, or Artin's book Algebra.

>> No.10974915

>>10974907
Midwits are getting filtered. Who cares? It's not like they were going to contribute anything significant anyway.

>> No.10974916

>>10974909
>basic algebra

Guess I know far less that I thought but thanks.

>> No.10974917

>>10974897
Lol. Just go work for FAANG. Leave the math for us mathematicians.

>> No.10974918

>>10974915
So what's your h-index, my little social Darwinist?

>> No.10974927

prove without using Lebesgue measure, that if a function f is integrable on [a,b] then it also must be integrable on any [c,d] subinterval of [a,b]

>> No.10974929

>>10974918
I'm an undergrad.

>> No.10974940

>>10974929
No wonder

>> No.10974941

>>10974927
what have you tried ?

>> No.10975063

>>10974907
What even is the problem?
Why shouldn't people be separated based on merit and people who aren't as competent be treated worse?

>Especially here, in Germany, it is a disaster.
Is it?

>People are leaving academia one by one.
Firstly, evidence? Secondly, why is this the reason?
I would guess that it is due to having a university culture with an extremely relaxed attitude to students, where you can take half a decade for your bachelor, slowly work yourself through your Masters and then decide to do a PhD for good measure and in the end you have an unmotivated staff member who only sits in the department because he drifted along and eventually just leaves into a less competitive environment.

>> No.10975066

>>10974927
>prove without using Lebesgue measure
I don't know what this means.

The result is obvious using the Hölder inequality, but you obviously have to use the definition of "integrable" which involves the Lebesgue measure.

>> No.10975068

>>10975063
Because social Darwinism is flawed.

>> No.10975084

>>10975068
Competition is a necessary component of science.
People have to scrutinize each other and work hard to create something relevant, nobody gains by having unmotivated idiots slurping coffee on the cost of the taxpayers and shit out some rehashed paper on a beyond irrelevant topic.
Also it isn't like people are forced to partake in this, if you want a comfy office job you can surely get one.
Yes, academia is rough, but why shouldn't it be.

I am in Germany and I have to say that a good percentage of students should have been kicked out long ago, just for their own good and again, I suspect it is these students who move into academia then struggle and leave and good riddance.

>> No.10975095

>>10975066
I think he wants to show it for Riemann integrable functions.

>> No.10975122

>>10974894
What's the probability of the answer being 'no'?

>>10975063
>Why shouldn't people be separated based on merit and people who aren't as competent be treated worse?
Are you seriously implying there's effective rational behind jobs in academia that could be separated from social politics?
Unless you could that into what makes for "competent", in the sense that some bully personalities are more fit than others.

>> No.10975151

>>10975122
>What's the probability of the answer being 'no'?
50:50, he either is or isn't.

>> No.10975172

>>10975122
>Are you seriously implying there's effective rational behind jobs in academia
I have no clue, but intuitively yes.

>that could be separated from social politics?
I see absolutely no relation to social politics or why it would be "effective" at anything.
In fact in my entire life I have not seen or heard of a single instance in which "politics" (especially the Democratic form) was effective at doing anything.

>Unless you could that into what makes for "competent", in the sense that some bully personalities are more fit than others.
There are multiple grammar mistakes in there, I can not decipher the meaning.
Up to now you have vaguely described "what" you think is wrong, namely that underperforming members of academia get treated worse, you have failed to describe "why" this is an issue and "how to change it" and most importantly "why should this thread care".

I personally do not care very much for the answers, as you yourself are completely unable to express yourself, but I am a firm believer in meritocracy and that the entirety of academia should be harsh. So that the conditions we face in Germany right now can be avoided.
Out of interest, how many semesters did your bachelor/master take compared to the "Regelstudienzeit".

>> No.10975176

introduction to quantum theory or fundamentals of probability theory?

>> No.10975321

>>10975172
Disclaimer, I don't understand what they're saying either, but I'll jump in to complain. Like, meritocracy is fine in principle, but when it becomes too strict about who is "competent" and who isn't, your community of "competent" mathematicians starts to get weird. To work as a mathematician in today's economy you've got so spend a lot of time at it, and sacrifice a lot. You must often seclude yourself from family and friends to write. You certainly can't waste much time on other facets of life. IMHO you've got to sacrifice some nontrivial chunks of your humanity to make it as a mathematician. And some people are fine with that, but they're pretty weird anti-social people, and since they do nothing but research, aren't good members of the community. Many otherwise good mathematicians are being excluded from the community of "competent" mathematicians because they can't compete with these folks who are willing to sacrifice chunks of their humanity to work.

But I suppose that none of this is a flaw in the meritocracy, but is instead the result of a ratio for supply/demand for mathematicians that is way too high ...

>> No.10975346

>>10975122
No from a woman 1-30 percent. No from a man 50 percent.

>> No.10975463
File: 33 KB, 339x521, file.png [View same] [iqdb] [saucenao] [google]
10975463

I tried doing this algebraically and maybe it's because its 6am and I never went to bed or I'm just a brainlet, but this is as far as I got:
[math]69000(x) = 102000(x - 4) - 80000[/math]

x = 14.8, which is the number of years worked with a bachelors. How would I get it to the 18.8, which would be the actual desired starting point (including tuition), without just adding 4 to x?

>> No.10975717

Point set topology is a waste of my time, I could study number theory or combinatorics but no, I have to study this hyper autistic shit
>set can be both open and closed
>a whole fucking book on counterexamples

>> No.10975749

>>10975717
Do you think anyone does point set topology unironically after undergrad?

>> No.10975841

Sorry for the stupid question, but I don't know how to expand the left side to get to the right side, can somebody help me please ?

[eqn]

\frac{sin \theta + tan \theta}{1+sec\theta}=sin\theta

[/eqn]

>> No.10975889

>>10975841
Here's a hint.
Express your tangent and secant in terms of sine and cosine. Then you should be able to do the division.

>> No.10975898

>>10975717
Nobody does point-set topology after undergrad. There's a quote which goes like this: "Point set topology is to mathematics as oregano is to Greek food. There aren't any great oregano dishes, but there is a dash present in most Greek dishes."

>> No.10975902

>>10975749
Niche fields are comfy as the low competition makes you automatically popular if you publish anything.

>> No.10975903

>>10975889
Thank you I finally got it. :-)

>> No.10975906

>>10975898
>>10975749
>t. Only read munkres for topology fundamentals
Fuck off.

>> No.10975920

>>10975084
>shit out some rehashed paper on a beyond irrelevant topic.
Except that that is precisely what is happening (in areas the community deems relevant) because people need to churn out papers to fill up their research cv.
There is little time to step back and do deep work within the duration of most phd or postdoc fundings for most people outside of a handful of ascended beings, who certainly deserve a job, but who certainly do not comprise the majority of mathematicians, even among those who do become professors.

>why shouldn't it be
Because people do not produce their best work if they are moving from deadline to deadline and country to country for shitty pay in their late twenties, no matter how good they are. Mathematicians are human beings, with human needs.
I cannot see how anyone in their right mind could rationalize our current state of affairs. There is no incentive for anyone in the community to support this.
Elitism sounds good because it flatters your ego, but it is an illusion.
There are many things beyond the raw mathematical ability that factor into someone being recruited in a specific department or not, including lab culture, politics among the various teams of a lab («oh dear, this year 60% of all jobs were allocated to the stats team»), politics within the team («oops, this young professor wants us to recruit their spouse and you happen to be competing for the same position»), your relationship with the team, how well-connected you are in your field, dumb luck (eg. one professor in a niche field retires and you happen to be the only person working in that field who applied that year), and any number of other things.

>> No.10975930

>>10975906
What's the issue with this? Do I have to read 2 or 3 general topology textbooks to get a grasp on the subject? Get fucked buddy

>> No.10975951

>>10975930
No, but obviously it will not be enough if you want to understand general/point-set topology fully and jump to modern research.

>> No.10975991

>>10975951
I'm sorry, do you do research?
>and jump to modern research.
We told you that general topology is not an active field. Also, a course with its own accompanying lecture notes is sufficient to give a student an understanding of the subject. Reading or even owning two textbooks on the same subject is superfluous unless there's content in both which are not contained in the other.

>> No.10976015

Any recommendations on how to teach myself trigonometry? I'm trying to spare myself a wasted semester and jump to precalculus.

>> No.10976016

Does anyone here use Coq?

>> No.10976027

>>10975991
And what Im trying to get through your thick skull is that obviously you have no idea of the active research in point set topology if your exposition of it is minimal or oriented towards other fields (alg top diff top etc) which is what many popular books do. It's not a popular field, I grant you that, but one of the most famouns mathenaticians from my uni does research on it.

>> No.10976044

>>10976015
Khan Academy, but I would recommend :

https://www.amazon.com/Precalculus-Mathematics-Nutshell-Geometry-Trigonometry/dp/1592441300/

I own and I like it very much (you can find it on LibGen too)

>> No.10976090

>>10976016
Only beta cucks need an external tool to write their proofs. Chads know that what they wrote is correct by construction.

>> No.10976095

>>10976016
urmom used my coq last night (in her vagina)

>> No.10976251

What is the comfiest field of mathematics for casual self study?

>> No.10976289

>>10976016
use agda

>> No.10976292

>>10976251
Just pick something that interests you and which is appropriate to your level.

>> No.10976303
File: 1013 KB, 1000x1000, lola-haengematte-california-green-tuch-family-stand-set-1l.jpg [View same] [iqdb] [saucenao] [google]
10976303

Trying to give some hands on motivations for what the offending set specification in Cantor's theorem looks like

https://youtu.be/0Sl0bcXyTAo

>>10976251
Depends on your level, but I think many like low dimensional Riemannian geometry.

>> No.10976305

>>10976251
tiling theory, polytopes, knot theory,graph theory or combinatorics.

>> No.10976351

>>10976303
>Riemannian Geometry
>casual self study
Jesus Christ.
Do you just mean classical differential geometry on surfaces?

>> No.10976381

>>10976289
OCaml > Haskell

>> No.10976385

>>10976381
oh no you don't bitch

>> No.10976404
File: 950 KB, 1024x435, Torus-Knot_nebeneinander_animated.gif [View same] [iqdb] [saucenao] [google]
10976404

>>10976351
Yeah pretty much, Frenet–Serret formulas etc.
Reminds me thing that Bézier curves are also fun to play with.

>> No.10976417

>>10973949
But what about people like Tao whose whole bread and butter is connecting those tunnels?

>> No.10976420

Can someone recommend me a modern introductory text on combinatorics?

>> No.10976437

>>10974897
My favourite book by far is Aluffi's Algebra Chapter 0. Then depending on what flavour of algebra you like, you can choose to follow one of many different paths.

>> No.10976444

>>10974927
What type of integrable is it?

If Riemann-integrable, then a function is integrable on a compact interval iff it is almost everywhere continuous. Then it follows trivially

>> No.10976446

>>10976420
Enumerative combinatorics by Stanley

>> No.10976536
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10976536

Why did no one tell me that linear algebra is just euclidian geometry with a scaling operation

>> No.10976610

>>10976536
No one gave you the geometric definition of a vector?

>> No.10976640

>>10976536
Because it isn't

>> No.10976684

>>10976536
linear algebra is just linear sets and linear transformations geometry is useful but is not linear algebra. There are euclidean spaces but they are generalization of R3, they can be complex and they can be of dimension n.

>> No.10976780
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10976780

Lads I need some advice. I'm a freshman in college. I've read a transition to advanced mathematics and am currently reading "The Joy of Sets: Fundamentals of Contemporary Set" Theory by Devlin. I am also enrolled in mutli variable calc. What else should I read as a freshman?

>> No.10976789
File: 1.37 MB, 1140x4777, official mg curriculum.png [View same] [iqdb] [saucenao] [google]
10976789

>>10976780
>What else should I read as a freshman?

>> No.10976794

>>10976780
Geometry by David A. Brannan

>> No.10976867

>>10976684
>Linear sets
>A Euclidean space can be complex
Confirmed for never having taken linear algebra

>> No.10976869

>>10976251
Number theory is comfy

>> No.10976887

>>10976794
lol are you serious with this recommendation?

>> No.10976890

>>10976869
>number theory

Not math.

>> No.10976909
File: 124 KB, 496x1070, 1567261222995.jpg [View same] [iqdb] [saucenao] [google]
10976909

So, I've achieved a result that someone had previously written a really long series of proofs for, which implies that P=NP. Is it safe to assume that their proof was wrong and P!=NP? What do I do now?

>> No.10976978

>>10976420
>>10976446
I wouldn't self-study Stanley unless you hate yourself and want to waste a whole bunch of your time for some reason. Stanley's purpose as a textbook is to bludgeon future combinatorialist grad students over the head. Probably dangerous to go alone, especially if you don't have a fairly solid undergrad combinatorics course.

If you understand basic counting techniques, maybe you saw them in high school or an algebra course or something, I think Peter Cameron's book is the best general-purpose introduction to what real combinatorics is beyond balls-in-bins problems.
If you don't know the raw basics of how to put your balls in your bins there's a very nice book called Principles and Techniques in Combinatorics by some Asian guys which was used to teach baby combinatorics to the Singaporean IMO team. Does a better job than anything else I've read of getting your fundamental problem-solving skills up.

>> No.10977027

>>10973904
Question:
Let [math] z,w \in \mathbb{C} [/math]
If I were to prove that:
[eqn] ||z|| \leq || z - w || + ||w|| [/eqn]
I only need to prove that the triangle inequality holds for complex numbers right? If not, what do I need to do?

>> No.10977030

>>10977027
Well what have you tried?

>> No.10977048

>>10977030
Proving from the inequality but its been unfruitful so far.
It's pretty clear to me from the vector diagram it should be from it.
Im really rusty with my algebra :/
Any hints??

>> No.10977064

>>10977027
> I only need to prove that the triangle inequality holds for complex numbers right?
Right. Without multiplication, there's no difference between C and R^2.

>> No.10977122

I used to be a member of one of the math discords servers created by some of you. Due to the platforms lack of any privacy respecting ethics I was wondering if there was an IRC or Matrix channel I could join. The loneliness is at times crippling.

>> No.10977179

>>10977122
>Due to the platforms lack of any privacy respecting ethics
What?

>> No.10977209

>>10977122
>ethics
>>>/x/

>> No.10977216

>>10977122
talk with people at your university

>> No.10977264

>>10974927
you have to prove a few lemmas about riemann sums, like the lower sum doesn't decrease if you make your division of the interval finer, and analogously for the upper sums, then you can take a division of the interval, add c and d to it, and you're basically done

>> No.10977279

>>10977122
Would you like to be my friend? I still use discord tho so thats what I can offer.

>> No.10977313

>>10977122
discord is disgusting.
>>10977179
discord is unethical
>>10977209
discord is unethical
>>10977216
they probably use discord
>>10977279
you sound like a shit friend. why don't you go play with tooker, yukariturd, and discordshit in your little server. we'll continue discussing mathematics here.

>> No.10977322
File: 72 KB, 360x480, 1567324240146.jpg [View same] [iqdb] [saucenao] [google]
10977322

>>10977313
I guess this thread is the best bet. Thank you.

>> No.10977325

>>10977313
Dilate.

>> No.10977452

>>10976978
Thanks anon

>> No.10977453

>>10977279
kys

>> No.10977479
File: 26 KB, 800x650, 1566068322806.png [View same] [iqdb] [saucenao] [google]
10977479

Is the rate of learning inversely proportional to the level of the learning materials?

>> No.10977490

>>10976251
çat theory

>> No.10977517

>>10977490
Schrodinger’s cat?

>> No.10977535

>>10973933
It's fun you faggot, try it sometime

>> No.10977569

>>10977313
>>>/g/
fuck off stallman

>> No.10977576

>>10974889
>>10974856
https://boards.420chan.org/math/thread/15040#i15040
read this fren

>> No.10977589
File: 1.86 MB, 228x170, 1557612554848.gif [View same] [iqdb] [saucenao] [google]
10977589

>>10976909
Wait, fug, I just realized that I can apply the same technique to TSP problems. G-guys...

>> No.10977613

>>10975920
The entire post is entirely meaningless, since I give a different reason for why things are not going too well and you do not defend why your reasons are any more valid then mine.
Why did you bother writing this, saying things are bad 20 times in a row is not an argument for anything.

The entire discussion in the last two posts boils down to:
Me: "X is bad because Y"
You: "X is bad, X is bad, X is bad, don't you see X is bad!"

You offer no proposal for a solution, or even a reason why this is happening.
Your post is completely worthless.

>> No.10977629

>>10977576
Thanks

>> No.10977632
File: 163 KB, 1377x547, anon_advice.png [View same] [iqdb] [saucenao] [google]
10977632

>>10977576
From >>10974856

>> No.10977640

>>10976444
But that's Lebesgue measure 0

>> No.10977738

>>10977122
I'm not a freetard but I dislike discord too and the servers are too big. ##math on freenode is good but it's totally impersonal, get in, ask your question and get an answer, that's it; not a lot of casual chatting. I'm in a similar situation to yours, I go to a crappy university and none of my classmates actually enjoy math, they're only in it for the degree. So far I haven't found a nice comfy place, for now it'll be more lonely afternoons at the library

>> No.10977816
File: 14 KB, 284x400, riemann.jpg [View same] [iqdb] [saucenao] [google]
10977816

If dubs I will one day prove the Riemann Hypothesis.

>> No.10977826

>>10977816
Why would anyone give a flying fuck about the Rainman hypothesis? Woohoo bing bing complex numbers yahoo!

>> No.10978052

Someone link me a series of lectures on vector geometry
I hate my teachers' lectures so much

>> No.10978128

>>10978052
Find one yourself, retard

>> No.10978133

>>10978052
what's a "teacher"

>> No.10978140

>>10976909
Not sure what you mean. Does your result imply P=NP ? Then it's probably wrong. If some crank proves your result as a lemma to prove P=NP, then it is likely either wrong, trivial, or folklore.

None of this resolves P vs. NP, just that you haven't found a proof of it.

>> No.10978145

>>10976909
Publish it as proof that the other guy goofed.

>> No.10978196
File: 283 KB, 1200x800, Kurt-Cobain.jpg [View same] [iqdb] [saucenao] [google]
10978196

Looking at
[math] (x\cdot y)^T = y^T \cdot x^T [/math]
[math] (x\cdot y)^{-1} = y^{-1} \cdot x^{-1} [/math]
over a generally non-commutative operation.

Do maps with
[math] f(x\cdot y) = f(y) \cdot f(x) [/math]
have a name, and what would be other examples

>> No.10978201

>>10978196
Okay, found the name but no good exmaples other than the one mentioned
https://en.wikipedia.org/wiki/Antihomomorphism

There are some examples related to involutions, but they always speak of commutative products...

>> No.10978210

>>10978196
that's just distribution

>> No.10978245

I don't know why but I can't find any decent problem sheets for calc3 (especially surface integrals, line integrals, greens theorem, etc.) Can someone help me, please?

>> No.10978311

>>10978196
>>10978201
Look up opposite ring (or opposite monoid, opposite category, etc. if you want to be more general). Antihomomorphisms as you call them are just homomorphisms to this "new" object.

>> No.10978322

>>10978311
Okay - is there an example going beyond this "free construction"? This kind of gives me nothing to get a feel for how such maps behave beyond its very definition.

>> No.10978325

>>10978245
Find the (n(n-1)/2)-volume of O(n) as a subspace of R^(n^2).

>> No.10978330

>>10975172
The current system is a meritocracy in name only. Merit is always weighted according to some criteria, in too many cases the criteria are something like number of publications and impact factor, and yes the local politics of the hiring lab matter a lot. This has produced a retarded state of affairs where top physicists spend two day doing physics on a good week, the rest of the time being paperwork, while their underpaid student slave away for a decade doing their job for them. How can you look at the current state of the publication culture anywhere except perhaps some parts of pure maths and physics and tell the meritocracy is effective? It's meriocratic in name only, and "harshness" is a retarded way of designing things. Chopping people's head for minor mistakes is also harsh, but at best it will leave you only with a couple uninspired autist that can make perfect copy but have not original idea of their own.

>> No.10978350

>>10978322
>This kind of gives me nothing to get a feel for how such maps behave beyond its very definition.
It's literally just a special kind of homomorphism. I'm not sure what more you want.

>> No.10978371

>>10973904

I've always been terrible at maths and it might be because I've moved abroad when I was a kid and because I skipped a year ahead, but I did manage to get a pitiful C in highschool. Now I wanna see if with a fully developed adult brain maybe I'm a little smarter and can understand stuff I struggled with as a kid. Could you please recommend me some basic beginner stuff for someone with no knowledge of maths whatsoever?

My arithmetic is garbage btw, the other day my friend asked me what 20 x 10 was and I said 500 or something retarded like that. I might have dyscalculia.

>> No.10978379

>>10978325
thanks anon

>> No.10978624

>>10978371
You could start with Khan Academy if you want to learn/review some basics, I also recommend Simmons' "Precalculus in a Nutshell", it covers all the stuff you see in high school in one short book.

>> No.10978646

>>10978624

thank you friend

>> No.10978667

>>10978646
No problem pal, I'm doing pretty much the same thing as you right now, maybe we could study together if you want ?

>> No.10978678

>>10978667

My dad had a stroke so i had to fly over to go take care of him full time so I'm busy atm but drop me a discord or email or something and when my life stabilizes I could hit you up

>> No.10978684

>>10978371
basic mathematics
by lang

>> No.10978702

>>10978678
Sure, you can reach me at : monster888@live.fr

>> No.10978722

EPXLAIN RIGGED HILBERT SPACE PLZ
WHAT THE FUCK IS THIS SHIT

>> No.10978735

>>10978684
Lang is a _____

>> No.10978955
File: 3 KB, 125x125, berns.jpg [View same] [iqdb] [saucenao] [google]
10978955

What's the fucking matter with the Classical modular curve X0(n)?!!
I find it ugly - prove me wrong. It's not important. Or is it?

>> No.10979309
File: 92 KB, 1280x720, scholze.jpg [View same] [iqdb] [saucenao] [google]
10979309

https://arxiv.org/pdf/1909.07222.pdf
>The work of Peter Scholze
>Michael Rapoport
>(Submitted on 13 Sep 2019)

>This is my laudation for Scholze's Fields medal 2018.

>> No.10979321
File: 50 KB, 618x412, MichaelRapoport.jpg [View same] [iqdb] [saucenao] [google]
10979321

>>10979309
Huh, who knew

>> No.10979344
File: 445 KB, 746x676, yukari_smile.png [View same] [iqdb] [saucenao] [google]
10979344

>>10974927
The key is to show that a partition on an interval gives a partition on a subinterval (quite easy). Once that's done then you just need to invoke some standard results mentioned by >>10977264.
>>10978722
Any subspace [math]\mathcal{H}_0 \subset\mathcal{H}[/math] of a Hilbert space can be rigged if the inclusion [math]\iota:\mathcal{H}_0\hookrightarrow \mathcal{H}[/math] is continuous. As, generally speaking, subspaces of self-dual Hilbert spaces [math]\mathcal{H}^* \cong\mathcal{H}[/math] (via Riesz, for instance) have a much larger dual [math]\mathcal{H}_0^* \supset \mathcal{H}[/math], rigging [math]\mathcal{H}[/math] allows us to use the topology and geometry of [math]\mathcal{H}[/math] to study the much larger space [math]\mathcal{H}^*_0[/math]. For instance, if [math]\mathcal{H} = L^2[/math] is equipped with the usual [math]L^2[/math]-norm topology, we can take [math]\mathcal{H}_0 = \mathcal{S}[/math] the subspace of rapidly decreasing test functions (with the subspace topology) and rig it to study the tempered distributions [math]\mathcal{S}'[/math] with the dual topology [math]\sigma(\mathcal{S}',\mathcal{S})[/math] inherited from that of [math]\mathcal{S}\subset L^2[/math].

>> No.10979817

>>10978201
Involutions actually are very important examples in two respects.
Finite dimensional algebras with (anti-)involutions are currently being investigated in relation to the algebraic theory of hermitian forms. The idea is that, given a non-degenerate sesquilinear form [math]\langle \cdot, \cdot \rangle[/math] on a finite-dimensional vector space V, then the adjunction with respect to that form defines an involutive anti-automorphism of the algebra [math]End(V)[/math].
This involution in turn pretty much characterizes the form.
People are therefore trying to find analogues of statements in the theory of quadratic forms to the theory of algebras with involutions.

Secondly, Banach algebras over C with anti-involutions extending complex conjugation have been widely studied in relation to quantum mechanics and noncommutative geometry as well as geometric group theory. The most basic example is that of bounded linear operators on a Hilbert space, with the involution given by the adjunction wrt the inner product (this is the natural framework for quantum mechanics afaik, observable quantities are defined as self-adjoint operators).
Another example is the group algebra associated to a Lie group.

In this context, you should think of the involution as an analogue of complex conjugation in your algebra, or adjunction on complex matrices. A good chunk of the theory consists of finding analogues for the theory of hermitian matrices (representations, spectral theorem etc.) for arbitrary algebras with involutions.

>> No.10979952

How can I decide what to go into for PhD?

I suppose in some sense it's what's available, but beyond that would reading the relevant articles on different areas in the Princeton Companion to Mathematics be a good idea?

>> No.10980002

>>10979309

In all seriousness, she just needs to come out and openly start the transition process, so that she can better devote her mental energy to mathematics. Petra Scholze, the only living female Fields Medalist, here signals that she is asexual (a common trait among mathematicians). May she have a long and fruitful career, and not be immolated, as was Hypatia.

>> No.10980025

Is there a Stats book that coveres everything? Every method used in stats?

>> No.10980110

>tfw forgot all I knew about maths during the summer
oh boy

>> No.10980116

do you fellows know any good astronomy/cryptography postgrad in europe?

>> No.10980119

>>10978140
But what if I have a working algorithm for solving NP-complete problems?

>> No.10980509

>>10979309
>linking to the pdf instead of the arxiv page

>> No.10980669

>>10976437
Aluffi is absolute kino. Good recommendation anon.

>>10974897
I like Ash as an review of undergrad algebra. It's a bit briskly, but you get used to it fast. Hungerford is also pretty comfy.
Lang is Lang, either you will love him or you'll hate him.
But that's just for basic/undergrad stuff at a somewhat more advanced level.

>> No.10980678

>>10975991
There are people who publish on general topology, and there are open problems.
It's just that most stuff that remains is so hard that there's little point in researching it.
There was a reunion of Canadian point set theorists (or was it Americans, I don't remember it that well) that resulted in a pretty neat list of open problems a few years ago, iirc
But it's mostly dead, yes

>> No.10980684

>>10976978
>Principles and Techniques in Combinatorics
I like 'proofs that really count', a book that seems to have roughly the same level as Principles
Knuth's Concrete Math is also neat

>> No.10980701

>>10980110
you knew nothing at all then

>> No.10980921

>>10980119
just implement it ;)

>> No.10980929
File: 1.94 MB, 2592x1944, IMG_20190910_201613_01_01.jpg [View same] [iqdb] [saucenao] [google]
10980929

Guys how do I do this shit? 2. a and b

>> No.10980931

>>10980929
Don't give me the answer just tell me the steps I need to take or give hints

>> No.10980944

>>10980929
csc(x) is just 1/sin(x)
rexepress that 3/2sqrt(3)
sin(x) = y

x = asin(y) + 2nPI
or
x = PI - asin(y) + 2nPI
where [math]n \in \mathbb{N}[/math]

too lazy to tex it all

>> No.10980966

>>10980944
Thanks anon

>> No.10981011

>>10977826
based

>> No.10981051

[math] {\mathbb B} {\mathbb A} {\mathbb S} {\mathbb E} {\mathbb D} [/math]

>> No.10981061

>tfw haven't even opened a maths book since I graduated
it wasn't meant to be like this

>> No.10981080

>>10979952
>signing away 5+ years of your life off of a nontechnical survey article you can read in 10 minutes
What could possibly go wrong

In all seriousness, one of the main purposes of the first year of an American PhD is for you to find the area you want to work in. Apply to places that have a minimum of 3 people whose research summaries you think look neat, and then spend as much time as possible when you get there attending seminars/reading groups, talking to other grad students, and talking to professors (have them supervise you reading something in their field if you can, almost all profs are happy to do this). This last one is EXTREMELY important; absolutely do not pick a supervisor you haven't scoped out in person just because you like their research. It doesn't matter how cool geometric group theory is, if the geometric group theorist at your uni is a gigantic twat you're gonna wreck the next 5 years of your life. finding an advisor you like working for is honestly substantially more important than finding the perfect field. Lots of math is pretty cool, you'll be fine working on lots of different things.

>> No.10981086

What are the general requirements for professors to write a letter of recommendation? Is it likely professors will refuse to write one if I never attend classes and only show up to exams?

>> No.10981111

>>10981086
>Is it likely professors will refuse to write one if I never attend classes and only show up to exams?
Possibly, but even if they do agree it's not going to be a good letter. It may even be harmful.

My somewhat blunt opinion is that if you somehow managed to sneak through an entire math degree so detached from the department that there aren't 3 profs who recognize you at all, you probably will not do well in academia. Talking to other people is a vital part of academic life.

>> No.10981224

>>10981111
It's a huge waste of time to go to uni. Profs are so-so, students are terrible, some of them complain that professors ask for too much proofs on exams, in a maths school. The building is fivefold older than I. The roof is leaking when it rains. I have to go up 4 flights of stairs because there's no way I'm using that lift. Why should I waste 2 hours a day to visit such a place, when I can learn everything from reading a text at home? The worst thing is, this is the best maths university in the country. But I guess when you're living in eastern Europe that doesn't amount to much.

>> No.10981230
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10981230

Can someone give me a quick rundown on how to interpret a divisor, or what it means? I've read the definition and some stuff concerning them several times but I just don't get what they're good for.

Like for example, in pic related I'm meant to interpret [math]Z[/math] to be a divisor on a bitangent [math]L[/math], which in this case should be a point on the line. But what should I think of [math]z_1+z_2 = Z[/math]? They are a formal sum of points; are these points precisely the tangent points? Should I interpret the [math]2[/math] in [math]2Z=V(f)\cap L[/math] as counting the line twice (so as to satisfy the 'tangent' condition, which would tie in well with the last part), or should I interpret it as having two points (so as to satisfy the 'bi' condition in bitangent)?

>> No.10981308

https://ncatlab.org/nlab/show/smooth+manifold#faithful_embedding_into_

Why is the functor from smooth manifolds to real commutative algebras fully faithful? It sends a smooth map F:M-->N to the morphism f |--> f ∘ F.

>> No.10981351

Why are younger math profs so fucking arrogant? I always notice younger profs think their shit doesn't stink but older profs are way more humble. Why is this?

>> No.10981359

>>10981230
>They are a formal sum of points; are these points precisely the tangent points?
Yes, the [math]V(f) \cap L = 2Z[/math] means that L is tangent to V(f) at both [math]z_1[/math] and [math]z_2[/math] (hence bi-tangent)

>> No.10981390

>>10979344
THANKS UR DA BEST

>> No.10981463

>>10978245
are you already into curvilinear coordinates?

>> No.10981469

Given two modules A, B with f:A->B surjective, is it necessarily true that A is the direct sum of Ker(f) and A/Ker(f)?

>> No.10981478

>>10978245
Susan Colley's Vector Calculus has some nice exercises. Grab a pdf on your favourite pirate site and enjoy

>> No.10981479

>>10981469
No

>> No.10981488

>>10981469
>>10981479
eg: [math]\mathbb Z\to \mathbb Z/2\mathbb Z[/math]

>> No.10981499
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10981499

I'm interested in algebraic groups of matrices, namely those over finite or countable degree transcendental extensions over Q.
I can make that less stringent by saying I'm interested in algebraic groups like GL(n), but not over R or C or a finite field.

My issue is that most books are either super general or, similarly, full of algebraic geometry that I think I don't need too much for my case. Does anybody have a reference, and at best an introductory one?
Humpreys or Hochschield don't seem to fit well for the above reasons.

>>10981308
If I had to guess, I'd say something along the lines that the algebra can represent all points (as ideals of functions that are zero at those points)

>> No.10981500

>>10981479
>>10981488
Thanks

>> No.10981505

>>10981500
>>10981469
btw, the splitting lemma (search wiki) gives a characterisation of when it happens

>> No.10981512

>>10981499
>algebraic groups
>full of algebraic geometry
Hmmmm.
I sure wonder what's going on.

>> No.10981584
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10981584

>>10980921
I have. So far I have solved minimum matrix bandwidth, TSP, and maximum clique. Still working on extending it to others. Honestly this is all pretty surreal.

>> No.10981619
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10981619

>>10981512
I can stomach it to an extent, but given my field is specific enough, I'd like to see an algebraic number field approach, seeing where the new elements of the field extension end up in some explicit matrix calculations - if that's rich enough and studied

>> No.10981629

>>10981619
What book is that?

>> No.10981635

>>10981619
Anon, you need to gargle the cum of categories, homosexual algebra and sheaves to drink the dog piss of algebraic geometry, and you need to drink the dog piss to get into actually good things later on.
That's life.

>> No.10981646
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10981646

>>10981629
Forgot. Probably it was some standard-ish springer book. I turned it into a gif, tho.

>>10981635
I'm fine with categories, it's just that the topology stuff is always about proving things I'm not sure I care for.

>> No.10981666

When solving the linear system Ax=b, would log(A)^-1 * log(b) = log(x)? Or would it be something else because of linear algebra weirdness? And by log(A) I mean the matrix logarithm (not scalar).

>> No.10981744

>>10981666
Start with inverting A.
x = A^(-1) b
Linear algebra weirdness.

>> No.10981759

>>10981744
Yes, that is how you solve a linear system, but now what about solving it in log space? How does the algebra work when I take the logarithm of both sides of the equals sign? I need to set up the problem so that the linear solver outputs log(x), not x.

>> No.10981771

Do you guys have a good practical guide to learn Calculus I asap?

>> No.10981776

>>10981771
Ask me anything about calculus I will answer.

>> No.10981778

>>10981776
I have an ideia about limits, but don't know how to use it as a mathematical tool. I know the derivative is supposed to a limit (the tangent line to a point in a graphic, I guess), but also don't know how to use it. I really am fucked, have a test thursday.

>> No.10981783

>>10981778
the derivative is the limit of the slop of a tangent line at a point. That is, it's the limit of f(x) - f(x0) / (x - x0) as x0 tends to x. You can calculate it by actually plugging it into that equations and evaluating the limit but that's retarded so we have general rules instead (the sum rule, the power rule, etc).

What have you been taught in your class so far? We can't tell you what to learn otherwise.

>> No.10981802
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10981802

Is there a shortcut to making this equivalent? Instead of combining the denominator fractions together and then multiplying by reciprocal, and then dividing top and bottom by x? Is there a rule when all the denominators are the same?

>> No.10981812

>>10981802
Multiply above and bellow by x and simplify. You don't need to combine the denominators. Just distribute x over the sum

>> No.10981814

>>10981802
Thats like 3 steps of basic algebra, a shortcut isn't really needed

>> No.10981817

>>10981783
I couldn't learn anything from the classes, really. My teacher recommended James Stewart's books to help with the classes, but I wanted something that was more compact and yet informative. Something that could help me teach myself the basics of calculus enough today to be able to make exercises.
I have everything from high school covered tho, I'm beginning college now and I focused more on Analytical Geometry than Calculus.

>> No.10981819

>>10981817
Pick Courant, Moise or Apostol

>> No.10981828

>>10981778
I can't help you on your test. But I can help you conceptually.

Consider this: in real life whenever you're doing measurements, you will never be exactly right. There's always going to be some margin of error.

Let's take an example of 1/x
As you know, you can't divide by zero. But we can take the limit is x --> 0. That means we slide closer and closer to zero, until we get very close to it, and see what is happening to our function.

You can slide from the left, or slide from the right. Sometimes you will get different answers.
As you can see, as x gets closer and closer to zero, 1/x gets very large. In fact it goes to infinity.

Thus we can't say that 1/0 = infinity, but we can say that [math]\lim_{h\to 0} \frac{1}{h} --> \infty[/math]
Is that making sense?
You can do this at any point along a function, but you see how this can be useful at discontinuities.

Now consider a ratio like this:
[math]\lim_{h\to 0} \frac{6h + 7}{5h + 3}[/math]
As you march closer and closer to zero, the top will go to 7, and the bottom will go to 3. Thus when you get arbitrarily close to 0, the function should equal 7/3. Does that make sense?

Why is this thing with limits important?
Because sometimes you can have "dueling zeroes". So as you approach the limit, the top is going to zero, and the bottom is also going to zero. However, their ratio approaches a constant. So for example [math]\lim_{h\to 0} \frac{sin(h)}{h} --> 1[/math]
We can also have "dueling infinities", where the top is trying to go to infinity, and the bottom is as well.

That's basically what you need to know about limits.

>> No.10981834

>>10981817
You can buy an e-copy of Early Transcendentals on ebay for like $3 and then put it on your phone just so you have it. It's a lot easier when you can just ctrl+f to search for something. I prefer to read an actual book though.

>> No.10981851

>>10981828
Thanks!

>> No.10981878

>>10981851
Ok, but I haven't told you about derivatives yet.

So envision a function, take any two points on the funciton. Let's say one where x=a, and one where x=b.
The slope between them is rise over run. So the slope "m" will be:
[math]m = \frac{f(b) - f(a)}{b-a}[/math]

Ok, but we want to find the slope as "b" gets very close to "a".
To do this, we express "b" as "a+h", where "h" is the difference between "a" and "b", and then take the limit as h-->0.

[math]m = \lim_{h \to 0} \frac{f(a+h) - f(a)}{a+h-a}[/math]

as you can see on the bottom the "a" cancels out, so it's just "h" down there

So consider an example, f(x) = x^2

[math]m = \lim_{h \to 0} \frac{(a+h)^2 - a^2}{h}[/math]

(a+h)^2 = a^2 + 2ah + h^2

the front term gets subtracted off, as you can see, so it looks like this:

[math]m = \lim_{h \to 0} \frac{(2ah + h^2}{h}[/math]

And remember, since we are just sliding close to "0", and aren't actually AT "0", there is no problem with h being zero on the bottom. So we can in fact divide by this "h", which we do, leaving us with this:

[math]m = \lim_{h \to 0} 2a + h[/math]

And since "h" is getting arbitrarily close to zero, it's so small that we don't care about it. We simply assume that it's zero, leaving us with m = 2a.
Since "a" can be any arbitrary point, we just say the derivative of x^2 is 2x.

That's just one example, but that's the general method you follow.

>> No.10981896
File: 761 KB, 1200x1486, yukari_lure.png [View same] [iqdb] [saucenao] [google]
10981896

>>10981230
Here's how an analytic geometer might interpret divisors. They are "bad points" in the sense that they form the zero loci of some section [math]s\in \mathcal{O}[/math] in the sheaf of holomorphic germs on a Riemann surface [math]M[/math]. In neighborhoods away from these points, the Deligne exact sequence [math]1\rightarrow \mathbb{Z}(1)\rightarrow \underline{\mathbb{C}} \xrightarrow[]{\exp}\underline{\mathbb{C}}^*\rightarrow 0[/math] splits and [math]\ln s[/math] is locally well-defined. This interpretation also relates to Riemann-Roch I believe.
In the context of CFT whose partition function [math]Z[/math] is a holomorphic section of a V-bundle on the moduli space of Riemann surfaces [math]\mathcal{M}[/math], Riemann surfaces with nodes (i.e. those obtained from [math]M\in\mathcal{M}[/math] via some "singular" shrinking/pinching operation) form the compactification divisor. You can open the nodes by unpinching the surfaces with a nome [math]q[/math], and sections [math]Z\in\Gamma(\overline{\mathcal{M}},V)[/math] around these compactification divisors achieve singularities when you close the node at [math]q = 0[/math]. So my general understanding is that divisors form no-no points we wish to stay away from but also encodes much topological/geometric data. I can see why (bi)tangent points would fit this interpretation, since non-transversal intersections usually leads to some bifurcation (Morse/Cerf theory).
>>10981351
Complete opposite to my experience.

>> No.10981922

>>10981646
>>10981629
>>10981619
Görtz/wedhorn AG I

>> No.10981948
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10981948

>20 July
anyone else worried?

>> No.10982020
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10982020

>>10981828
I watched that guy on youtube with the big arms talking about secant line and tangent line and how they are basically the same. But in reality if you could zoom in as far as was needed, you would always have 2 separate points right? The line would always strictly be defined as a secant line, it's just that the points are so close you can basically just considerate a tangent line, hence the limit?

>> No.10982033

>>10982020
yeah, it's so immeasurably close that we just say it's the tangent line.

Remember when we just assumed that h = 0 at the end? That's basically what we were doing right there

>> No.10982072

>>10982033
I have ti-86 and am in graph y(x)= mode
y1=((sqrt(x^2+9)-3)/x^2

it doesn't draw anything and there are no values in the table, usually if you mess up the function it will return an error.

>> No.10982115

i'm an older college student in the lowest level math you can get at university. this shit is kicking my ass. i did not like math in high school, and am only starting to learn to find some joy in it now. how the hell do i start understanding more concepts so i can breeze through? am i supposed to be a C student, even in math 96? fuck, why'd they start putting letters with it

>> No.10982120

>guy makes breakthrough in number theory
>gets downvoted to hell in the comment section
the absolute state of reddit
https://www.reddit.com/r/math/comments/d56bd3/my_phd/

>> No.10982126

>>10982120
oh and yes, he is autistic.

>> No.10982130

>>10982115
Work through Euler's Algebra diligently and also consider something like Kiselev or Hadamard's geometry (or just take Euclid if you must). Then try some intro to number theory like Leceque's Elementary Number Theory.
That should help you get more familiar with the basics and give help get a feel for proofs and help develop se mathematical maturity

>> No.10982137

>>10982120
you have to go back

>> No.10982192

>>10982120
Is this actually a breakthrough? It's a 116 page pdf, has anyone here done more than skim?

>> No.10982210

>>10981776
do functions always have at least a 1-sided limit?

>> No.10982212

>>10982130
>Work through Euler's Algebra diligently
Why the fuck should he do this?

>> No.10982268
File: 2 KB, 117x125, steyn NOT impressed.jpg [View same] [iqdb] [saucenao] [google]
10982268

>>10982212
>being on /mg/ and wondering why a math autist would recommend 18th century text over khan academy

>> No.10982350
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10982350

When inputting this function into the graph feature, I entered (sin3x) / (tan2x) and it returns a straight line. When I do it on desmos, it works properly.

>> No.10982385

>>10982210
take the Dirichlet function for a counterexample

>> No.10982424

>>10981080

I'm British, not American.
In general, we apply directly for projects with a given supervisor.
I have a rough idea of what I enjoy, but I wonder about stuff like harmonic analysis where I've never done it before.

>>10981086
You say you're in eastern Europe, and so it's probably going to be difficult for people on this board to advise without knowing about your country's academic culture.
For my masters application, professors from my old university were happy to write references and I never really talked to them.
I get the impression that the US norm is to constantly bother professors and go to office hours for the sake of it.

Anyway - you should just try asking them.
What other options do you have?

>> No.10982439

>>10981224
again, anyone who isn't willing to endure minor inconveniences to be around math people and part of a math community is not going to have a good time in academia. i'm literally just reiterating what the other guy just said to you.
research is not about sitting in your room and learning from books. it's about talking to people, collaborating with them to come to new ideas, being stumped by their conjectures and coming up with a few neat ideas of your own to surprise them. that's what doing math is about. it is rarely, VERY rarely, a solitary process.

>> No.10982445

>>10982120
>>10982126
that's what i figured, just looking at his post and the responses being like "the writing style is... nontraditional..." i get the sense that it's complete crackpottery and makes absolutely no sense. i hope he actually manages to humiliate himself in front of tao.
cannot believe so many r*dditors are encouraging this moronic garbage.

>> No.10982449

>>10973904
Best way to get started with math as an anon that needs to restart learning basic baaaasic algebra but wants to get into trig, stats and whatever other autism thats useful?

>> No.10982452

>>10982449
lang's basic mathematics
gelfand's algebra (super cheap online)
there are also probably pdfs everywhere of both
khan academy if the first two are too hard

>> No.10982478

why does my calculator return -6.8... when I press tan(2pi)? It says 0 when I do tan(pi), shouldn't tan(0) or tan(pi*n) always be 0?

>> No.10982491

What's with all the calculus talk, there's stupid question thread for those
/sqt/

>> No.10982525

Whats better to get ready for first semester of math?

https://www.ombplus.de (you can change language to english)

or

serge lang basic mathematics?

>> No.10982576

>>10982212
Because Euler starts from literal zero, explain things mich better than most books that try to tackle the same level of math and isn't actually aimed at retards and children (he dictated the book to his scribe to teach the scribe e basic math. Euler was already blind by them).
The version you can find in English is the one with commentary by Lagrange, what makes it even more of a treat.
It was the standard textbook for basic math in most of Europe for over fifty years after it's publication and thus was translated in pretty much all languages that matter for this site's users.

>> No.10982622

>>10982350
y=3/2 is a straight line

>> No.10982624

>>10982212
Euler's Algebra is the first book recommended for elementary algebra on : https://4chan-science.fandom.com/wiki/Mathematics

>> No.10982745

>>10982525
>Sie wollen sich auf ein Ingenieur-, Wirtschafts-, Naturwissenschafts- oder Informatikstudium vorbereiten?
You do not want to do that, you don't care for engineering math.

>serge lang basic mathematics?
I assume you are German, so read a book in German.
The two classics are Forster Analysis and Fisher Lineare Algebra.

If you do not feel comfortable with your current math skills start reading these two and make sure to attend the "Vorkurs" which surely will be happening.

Also, which Uni?

>> No.10983028

>>10982120
The MADMAN uses pronouns in his paper... he's either a retard or a genius.

>> No.10983108

>>10982745
Münster
I missed the vorkurs because i had a different date in mind, now its 3/4 done
So im just refreshing my highschool math until the Vorlesungen are starting.

>> No.10983172

>>10982745
>you do Not want that
Literally says that its for naturwissenschaften & Informatik too no?
Im mainly looking to refresh highschool skills. Forster analysis & Fisher lineare Algebra seems to be beyond that, so i dont know if its a good idea to start with These books despite my highschool skills being rusty.

>> No.10983469

Hi, does anybody know of an accesible math book for babys first proofs? I keep hearing how the proof books are the wrong way to go and it's advised to dive in. I'm thinking about jecht or halmos set theory. Sorry if this question is too elementary for mg

>> No.10983481

>>10983469
Edwin Moise's Calculus book

>> No.10983513

>>10983481
Kind of reminds me of spivak after looking through the first chapter. Why this over spivak though?

>> No.10983530

>>10983513
Spivak is much harder. Moise starts slower, explaining things in a more friendly way and has easier exercises. He also often explain hard things twice, one in a less formal way, and then later (after having used the thing a bit to show how/why it is how it is) he comes back to it again more rigorously.
If you can tackle Spivak, sure go ahead.
Moise is Spivak-lite with some Fourier Series in volume 2.
But yeah, it's Calculus by the way of baby Analysis, but I think it can work as a intro to proofs.

>> No.10983542

>>10983530
Ok, thanks. I actually tried Spivak and, it was really difficult for me, which is why I'm looking at a way to ease into proofs. I'll try Moise

>> No.10983600

>>10983469
http://www.math.cmu.edu/~jmackey/151_128/welcome.html
First book here

>> No.10983616
File: 357 KB, 640x480, 1443623784257.png [View same] [iqdb] [saucenao] [google]
10983616

When do you use <-> instead of <=> or vice versa?

>> No.10983624

>>10983616
Logic.

>> No.10983625

>>10983616
><=>
Double implication or iff or if and only if
><->
Double implication when doing actual propositional calculus/symbolic logic
>vice versa
I don't think it's very common outside of explanations, commentary, etc

>> No.10983644

>>10983616
><->
I don't think that's used much

>> No.10983712

>>10983616
just use [math]iff[/math] lmao

>> No.10983751

What does the notation [math]\mathbb{R}^\times[/math] mean? Asking specifically for its use here http://mathonline.wikidot.com/gln-r-sl-n-r-is-isomorphic-to-r-x

>> No.10983767

>>10983751
it's R (without zero) viewed as a group with respect to multiplication

>> No.10983780

>>10983616
You never use either because math is written in sentences

>> No.10984310

>>10982525
>serge lang basic mathematics?
Lang is a meme.

>> No.10984330

Spivak, Larson or Apostol?
book on calculus

>> No.10984331
File: 3.56 MB, 5247x3836, TIMESAND___8n4cnerdvvgf24f8g7tcrnfff3f33vrdvvgf24f8g5n6iun375693n679670001.jpg [View same] [iqdb] [saucenao] [google]
10984331

>>10984310
I started reading Lang's algebra and I have to agree that Lang is totally a meme. The first chapter was about group and I quickly became confused about what the fuck a group was. After some modest researching, I found out that Lang forgot to say that groups are closed under their operations... which is basically the main thing about groups. Therefore, Lang is a meme.

>> No.10984372
File: 41 KB, 350x268, TURN ON CNN.jpg [View same] [iqdb] [saucenao] [google]
10984372

https://arxiv.org/pdf/1909.07975.pdf
>A Proof of the Twin Prime Conjecture
>Berndt Gensel
>(Submitted on 17 Sep 2019)

>The twin prime conjecture 'There are infinitely many twin primes' is a very old unsolved mathematical problem. This paper develops a sieve to extract all twin primes on the level of their generators up to any limit. The sieve uses only elementary methodes. With this sieve the twin prime conjecture finally can be proved indirectly.

>> No.10984401

>>10984331
Lang's definition is fine. You're just a brainlet who doesn't realize what an operation is.

>> No.10984631

>>10984372
>oh it's just a tr-
>Berndt Gensel
>not a chink name
What.

>> No.10984909

>>10984372
> The sieve uses only elementary methodes

How to tell instantly that its nonsense.

>> No.10984911
File: 76 KB, 492x216, yukari_scratch_ass.png [View same] [iqdb] [saucenao] [google]
10984911

>>10984372
>math.GM

>> No.10985083

>>10975063
>half a decade for your bachelor
you mean one extra year? Imagine being this arrogant.
I am a semester away from my BS, in my third year of uni, but I meet 28 year old sophmores that are more passionate than myself. Fuck, I know a damn history professor who is extremely passionate and prolific in his field who took 10 years to get his bachelors, by just taking 2 classes or so each long semester and working full time, saving money.

>> No.10985387

>>10983172
>Literally says that its for naturwissenschaften & Informatik too no?
But if you are doing math this isn't really for you, the mathematics Vorlesungen for engineers and mathematicians are very different.
Engineering math really is a continuation from Highschool "real math" will basically develop all the ideas from scratch pretty rapidly.

>Im mainly looking to refresh highschool skills. Forster analysis & Fisher lineare Algebra seems to be beyond that
The idea is that they pick you up where Highschool left of, that usually includes some repetition too.

There is nothing wrong with doing the ombplus thing, but it will not really give you the preparation you really need. Because I expect you will be dropped into the contents of these books and having already a certain familiarity will make the whole thing easier.
If you can easily get a hand on a copy (eg. libgen) I would suggest you read the first couple pages and see what exactly it is you do not understand and then look at the specific topic.

>now its 3/4 done
You can still turn up if you want.

>> No.10985394

>>10985387
>If you can easily get a hand on a copy (eg. libgen) I would suggest you read the first couple pages and see what exactly it is you do not understand and then look at the specific topic.

Ty thats what ill do. Im 50% done with the online Course so ill have like 11 full days of using the book to have a better start.

>> No.10985511

[math]569936821221962380720^{3} + -569936821113563493509^{3} + -472715493453327032^{3}[/math] = 3

>> No.10985980
File: 28 KB, 315x475, 1568811604300.jpg [View same] [iqdb] [saucenao] [google]
10985980

Does anyone have a pdf of this book? Libgen doesn't have it

>> No.10986110

>>10982478
lmfao

tan2 = -2.18
tan2 * pi = -6.8

learn to use parentheses retard

>> No.10986123

>>10976789
If you want to do something besides whatever flavour of geometry that is setting you up for, any other math book

>> No.10986150

As someone getting into graph theory, does anyone have recommendations for software that can generate graphs given certain parameters like planarity and number of regions or vertices?

>> No.10986162

>>10986150
Knuth had a graph theory library on his website that could be useful. I'm pretty sure Mathematica has modules for that (if you're rich), Julia's lightgraphs is pretty decent of you know Julia. I'm sure seome somewhere has written a c++ library that can be used for that (or you can just download a bunch of graph theory stuff and make your own random graph maker pretty easily)

>> No.10986166
File: 1.10 MB, 1000x1100, yukari10.png [View same] [iqdb] [saucenao] [google]
10986166

>>10986150
Mathematica & graph theory package.

>> No.10986390

>>10985083
>I am a semester away from my BS, in my third year of uni, but I meet 28 year old sophmores that are more passionate than myself.
Yikes.
Drop out

>> No.10986405

>>10986166
>Non-free software
What is wrong with you?

>> No.10986426
File: 2 KB, 362x52, pyöristäminen.png [View same] [iqdb] [saucenao] [google]
10986426

Posting here so I don't get slid.

So what do you think of my rounding function? it takes values X and C and compares them to one another, and then sums them up to C+1. It returns 0 if X<C and 1 if X>C.

I have a problem with getting _.5 right as it gives a zero divisor, but otherwise it works. Could you give me a hand on it?

>> No.10986440

>>10986426
[math]
round(x) = \lfloor x + 0.5 \rfloor
[/math]

>> No.10986450

>>10986440
ah yeah, thought this was quite similar to flooring, perhaps a little janky. I came from the standpoint that there wouldn't be no need for > and < etc., just summing a function.

>> No.10986467

>>10984330
Abbott, Rudin and Lebl

>> No.10986468

>>10986450
You used the absolute value function, tho.

>> No.10986477

>>10986440
[math] \text{round} (x) = x+0.5 [/math]

Optimized.

>> No.10986481

>>10986477
idk about that bro

>> No.10986488

>>10986481
a shit the latex failed

>> No.10986498

>>10986488
try again mate I believe in you

>> No.10986500

>>10986440
A difference with my function with flooring and ceiling I noted is that the former two use interval notation, whilst mine works fine in the spite of this. I guess you could work my function into non-interval notations for flooring and ceiling as well.

>> No.10986504

>>10986498
nah I've embarrassed myself enough already

>> No.10986511

>>10986500
>abs doesn't use intervals

>> No.10986512

college text books often have the best footnotes because you can really see how people slowly become delirious after spending hundreds of hours going through them and writing it

>> No.10986521

>>10986468
OH NONONONOOO

Before you shit on my precious absolute value function and put it in the pile of wannabe-true-functions, I'll let you know how much simpler absolute value is to compared to stuff like Logarithms and sums

ahem

|x|=sqrt(x^2)

>> No.10986523

I'm interested in type theory but I don't have the necessary prerequisites or mathematical maturity to effectively study it. So I've been wondering, what's the worst thing that could happen if I try to read an introductory text. Certainly I would learn something, if only 10% of the material. Which is more than I would just sitting on my arse all day. I'm probably going to do this regardless, but do you anons think this is feasible? Isn't this more or less how people read papers?

>> No.10986526

>>10986511
>>10986521

>> No.10986531

>>10984911
might as well be a vixra preprint lmao
>>10982115
Depends on what joy do you find in college mathematics. Is it the abstractions? The big theories? The feel of solving a complicated problem? The mindless computations? Broadly speaking, mathematics has different things to offer for everyone, and even among mathematicians there's "theorists", "problem solvers", people who loathe long calculations and people who love them as well.

I find that America's system of placing students in "preliminary courses such as college algebra is often really unmotivating, but if you somehow enjoy taking things so slowly then >>10982130's might be a good suggestion. Another thing you can try is Richard Hammack's Book of Proof to get a glimpse of how mathematicians think.

>> No.10986540
File: 983 KB, 384x288, tech.gif [View same] [iqdb] [saucenao] [google]
10986540

>>10986523
https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ttfp.pdf
https://discord.gg/UqgjEN

>> No.10986550

>>10986540
I am aware of both of those. I was going to go with either that book or TAPL. But that one seems simpler so I'll give it a shot.

>> No.10986551

>>10986521
If you're going to be autistic, at least be good at maths as well.

>> No.10986555

>>10986523
>So I've been wondering, what's the worst thing that could happen if I try to read an introductory text.
Realize that you really need to learn yourself quite a bit of Algebra.
Well, at least that was my experience as more of an Analytard.

>>10986540
Is this fun?

>> No.10986562

>>10986551
Yeah, I'm pretty amateurish, but I just don't really like interval notations because I feel like that's cheating and wonky.

But nonetheless I think I can work that function out to do it's job right, and if it happens wouldn't it be a pretty neat function?

>> No.10986563

>>10986523
The worst that could happen is not understanding anything, then looking at tbe stuff you need to learn before tackling that. And then looking at the prerequisites of the prerequisites. And the prerequisites of the prerequisites of the prerequisites ad nauseum.
Cue existencial dread.

>> No.10986585

Can someone recommends me a book to quickly learn the basics of graph theory (definitions, vocabulary, fundamental theorems and some proofs). I need a quick view on the theory for a group project (I want to be able to choose an open problem).

>> No.10986605

>>10986585
I liked Graph theory by Gould

>> No.10986741

>>10986555
yes

>> No.10986777

Why is mathematics before research level 95% based on memory? Every problem is solved by remembering a previous theorem or using an old trick. How can this be fun?

>> No.10986797

>>10986777
Based trips, but you're wrong.
If you aren't your undergrad analysis/group theory/etc you're doing it wrong.
You have to understand how a few key proprieties and theorem relate to one another, and how a few classic arguments are structurated, what isn't the same as memorizing. You can get by by memorizing everything, but you're supposed to understand, generalize and apply.

>> No.10986821

>>10976417
It's already all connected ... and Tao is not the best example of a generalist mathematician.

>> No.10986868

>>10986797
You misunderstood his post.
Probably because "memorise" triggered you, as it does fairly often to mathematicians.

>> No.10986896

>>10976437
While it's good I wouldn't recommend the categorical approach to a beginner and also it lacks a section on galois theory.
On the other side it's homological algebra section absolutely slaps .
Read along Artin's algebra or dummit and foote to complement

>> No.10986905
File: 81 KB, 500x686, mods-are-asleep-post-confused-looking-anime-girls-with-question-2668527.png [View same] [iqdb] [saucenao] [google]
10986905

>>10986896
>it lacks a section on galois theory

>> No.10986917
File: 240 KB, 500x646, confused.png [View same] [iqdb] [saucenao] [google]
10986917

>>10986905

>> No.10986940

>>10986777
>Every problem is solved by remembering a previous theorem or using an old trick
As opposed to what?

>> No.10986954 [DELETED] 

Sorry for the brainlet question, but I have been stuck on this problem:
[math]\mathrm{If}~f'(5)=\lim_{x\to5}\frac {4^{x/5}-4}{x-5},~\mathrm{find}~f(10).[/math]
If I use L'Hôpital's rule, [math]f'(5)=\frac{8ln{(2)}}{5}[/math]
I don't know where to go from there, and we haven't learned L'Hôpital's rule, antiderivatives, or even the derivative of [math]a^{x}[/math] in my calc class yet.
Can anyone help?

>> No.10986965 [DELETED] 

Sorry for the brainlet question, but I have been stuck on this problem:
[math]\mathrm{If}~f'(5)=\lim_{x\to5}\frac {4^{x/5}-4}{x-5},~\mathrm{find}~f(10).[/math]
If I use L'Hôpital's rule, [math]f'(5)=\frac{8ln{(2)}}{5}[/math]
I don't know where to go from there, and we haven't learned L'Hôpital's rule, antiderivatives, or even the derivative of [math]a^{x}[/math] in my calculus class yet.
Can anyone help?

>> No.10987037

Sorry for the brainlet question, but I have been stuck on this problem:
[math]\mathrm{If}~f'(5)=\lim_{x\to5}\frac {4^{x/5}-4}{x-5},~\mathrm{find}~f(10).[/math]
If I use L'Hôpital's rule, [math]f'(5)=\frac{8ln(2)}{5}[/math]
I don't know where to go from there, and we haven't learned L'Hôpital's rule, antiderivatives, or even the derivative of [math]a^{x}[/math] in my calculus class yet.
Can anyone help?

>> No.10987040

>>10987037
huh. you have your answer.

>> No.10987047

>>10987040
How do I find f(10) from there?

>> No.10987051

>>10987047
take the integral and plug in 10 ?

>> No.10987064

>>10987037
This question is impossible, it doesn't make any sense. They must say some conditions on f, otherwise you can't even begin. There are uncountably many functions with that derivative at 5, you can't possibly extrapolate to how it will behave at 10

>> No.10987065

>>10987051
Is there another way? Because my class has not gone over integrals, antiderivatives, etc. We have not even discussed the derivative of a^x. I don't know how my teacher expects me to do this problem without that knowledge. If not, thank you for helping anyway.

>> No.10987076

hm okay. so the derivative is the limit.
get rid of the limit
plug in 10
f(10) = (4^(10/5) - 4)/5 = 12/5
sorry for not using latex.

>> No.10987078

>>10987037
From the context I infer that f is meant to be 4^x.
Note that f(10) = f(5+5) = f(5)f(5) and apply the chain rule

>> No.10987084

>>10987078
Ah, you want f(10), not f'(10).
So just get rid of (x-5) and the 4 and put 4^(10/5) as the answer

>> No.10987090

>>10987084
this anon is probably right, I haven't seen limit notation of the derivative in some time.

>> No.10987094

>>10987078
>chain rule
Fuck, meant the product rule.

>>10987090
You can have [math]f'(5) = \lim_{x\to 5} \frac{f(x)-f(5)}{x-5} = \lim_{x\to 0}\frac{f(5+x)-f(5)}{x}[/math]
It's just a change of variables of difference

>> No.10987096

>>10987084
>So just get rid of (x-5) and the 4 and put 4^(10/5) as the answer
I'm sorry but I don't understand how you came to this conclusion. Can you explain?

>> No.10987098

How do I interpret [math]K/(K^*)^2[/math] for [math]K[/math] a field?

Is it precisely: Those elements which are not squares other than 0?

>> No.10987101

>>10987096
Look at the formula in >>10987078
f(x) in >>10987037 case seems to be 4^(x/5) (notice that f(5) = 4, so it fits)

>> No.10987104

>>10987098
The book I used for field theory used X/Y to say X is a field extension of Y, dunno of it helps

>> No.10987107

>>10987101
The formula in >>10987094

>> No.10987111

>>10987101
>>10987107
Ah, I get it now. Thank you. That problem had been bugging me for the entire day.

>> No.10987114

>>10987104
It doesn't, since I'm not speaking about field extensions but rather a quotient of fields.

In fact, I already knew the answer before I posted, but not before I started writing it down. I tried writing down how this is stupid since it would be 0 for example for [math]K=\mathbb R[/math], then I realized it was because every element of it is obviously a square and this doesnt hold universally for all fields.

>> No.10987117

>>10987114
(strictly speaking a quotient of groups, since the units arent a field)

>> No.10987457

>>10976015
Soh Cah Toa nigga.

>> No.10987465

>>10977279
You probably already know me. I miss you guys. >>10977738
Had the same experience at ##math. We will figure something out anon.

>> No.10987842
File: 2 KB, 462x47, r.png [View same] [iqdb] [saucenao] [google]
10987842

OK, now it's a bit better defined. Also negative numbers work now.

I think this is the simplest form of rounding without using interval notation or cosines/sines.

>> No.10988599

>>10987842
[math] \color{olivedrab}{>> c\in\mathbb{Z}_+, x\in\mathbb{N}_0} [/math]
>> simplest form