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Board
/sci/ - Science & Math

File: Capture.jpg (128 KB, 994x685)
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talk maths, formerly >>10259038

F
https://en.wikipedia.org/wiki/Jean_Bourgain

F
https://en.wikipedia.org/wiki/Peter_Swinnerton-Dyer

F
https://en.wikipedia.org/wiki/Michael_Atiyah
>>
If S is a subset family, what do you call the structure you get by taking the transpose of the incidence matrix of S?

I've seen it called the dual family but I don't think that is a common term
>>
>>10289246
How do I tie my hands in knots like this?
>>
watch this get a million fucking replies
>>
I want to start a pythagorean commune
>>
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He's wrong but I like it
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Which one of the derivatives is incorrect? I am doing some hw problems and I can't quite eliminate terms
>>
Books on Markov's chain and its applications?
>>
>>10289246
wtf is this sorcery
>>
>>10289852
Now you're thinking with topology!
>>
>>10289246

>pic in OP

That's why mathematicians are retarded.
>>
>>10289246
Cool pic but are steps 2-3 really equivalent/logical? - The ball goes from having two arms coming out of it to having four... Similarly steps 6-7
>>
>>10289864
It's just stretching out the holes
>>
>>10289864
Think of it as bad alchemy. You can take away to make bigger holes but for completely bullshit reasons you can't add to remove holes or start a hole.
>>
I can't find an error in my proof that all Automorphisms on thw field F_n are the identity function.
let a in f_n, f be an Automorphism
a = 1 + ... + 1 a times because the additive group of F_n is generated by 1.
f(a) = f(1 + ... + 1) = f(1) + ... + f(1) = 1 + ... + 1 = a.
>>
>>10289852
It's a form of endless sorcery/witchcraft.
>>10289896
Alchemy and almost all forms of known magic are subsumed by topology (in a general sense). You can decide to study alchemy merely by using a stricter notion of isomorphism (in a general sense).
>for completely bullshit reasons
Completely bullshit reasons like not changing the entire nature of the thoughtform you are working with?
>>
>>10290127
'S correct.
>>10289896
The hole isn't a part of the object and isn't part of the domain of manipulation.
>>
>>10290127
>he additive group of F_n is generated by 1
Not true for all finite fields. In fact it's only true when n is prime
>>
>>10290137
but it doesnt match up with what is expected from an exercise and on google I find examples of functions in Aut(F_n) such as x -> x^p.
https://math.stackexchange.com/questions/616128/automorphisms-of-a-finite-field
>>
>>10290164
o fuck you're right I forgot F_p^2 = F_p x F_p and not Z/Z_p^2
>>
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>>10289246
Operation Complex 6-sphere was a success. Proceed to stage 2.
>>
>>10289620
Based erdos, being part hungarian jew is the best!
>>
Do you think Atiyah will forever have the peace of thinking he solved the Riemann hypothesis, or that he'll look into The Book and see that his proof was wrong?
I wonder what proof he will see inside.
>>
>>10290468
Some people few months before die just lose mind.
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>>10289632
Why do you think he's wrong?
>>
>>10290177
You're both right and wrong F_p^2 can be written as F_p x F_p, but it does NOT have the usual canonical multiplication from cartesian product, so it is very misleading for yourself.

A high power method to prove your result is that the Galois group of a finite field extension is generated by the Frobenius automorphism, and by Fermat's little theorem, this automorphism is the identity.
>>
>>10290468
Erdös will not let him peak into it
>>
how come we use percentages when talking about time instead of per 60
>>
>>10290464
Masterrace Hungarian/German Jew mathematician reporting in.
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>>10290951
historical convention
>>
>>10290468
I figure even if Atiyah got a chance to look at "The book" he would instead take his newfound eternal time in crafting a proof he finds satisfactory for the general Riemann hypothesis. A true mathematician would not look at the solution until they themselves have found it first.
>>
>>10290198
That's foul.
>>
>>10291254
Of course not.
If there is an afterlife, I hope it can just be a big comfy institute where we can all work on math forever and never get too frustrated. Just enough to keep it fun.
>>
I'm going to exhume Atiyah and steal his brain, I'm done with this ADHD riddled brainlet shit I carry in my skuill
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>>10291355
You're swapping ADHD for Alzheimer's and senility? Isn't it basically the same but worse?
>>
>>10291358

I already have a goldfish memory so it's a win win
>>
>>10291254
>yfw his mental faculties in his afterlife stay over from where he left off
remember boys, you have to off yourself if you want a sharp mind up there
>>
>>10290842
>Fermat's little theorem, this automorphism is the identity.
Not true either. The thing she is trying to prove is wrong as she states it.
>>
I have one doubt.
In this picture how is first equation conceived?
Vec(n) is more like rcose(theta)n^
why did he write Vec(n) that way?
Some pages on interset says Vec(n) is scaling of n^ by (n^.l^). This statement is not mathematical. How did he come to comclusion that it is scaled by (n^.l^)??
Here n^ (n cap) means unit vector
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>>10291933
You can view the dot product as related to the projection operator.
https://en.wikipedia.org/wiki/Dot_product#Scalar_projection_and_first_properties
Since n is a unit vector, the dot product gives a number that, when used to scale n via scalar multiplication, gives the projection of L onto n, thus n'
>>
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somebody pls help me understand the highlighted part

it's supposed to utilize the chain rule but I just don't se e it
>>
What do I need to read to get an introduction to this kind of thing

I keep seeing people talk about "charachter tables" and modules and what not and I just don't get it. Should I read this picture?
>>
How does $KL/L$ separable follow from $K/F$ separable? Yes, every polynomial over $F$ must be separable when considered over $L$, but what about polynomials in $L[x]$? It doesn't seem like a valid proof.
>>
>>10292895
sure
>>
>>10293073
You seem to have the impression that a field being Galois over another field means that it's the splitting field over every single polynomial there. Reread the definitions.
>>
>>10293729
I don't. The condition I am disputing is separability, not normality. Reread my question.
>>
"This Remark may be described as a breath-takingly (melo?)dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level."
Do undergrads in your uni know what the theory of heights is?
>>
>>10293985
>Do undergrads in your uni know what the theory of heights is?
There were some undergrads in the elliptic curves course we took, so at least some do.
>>
why is probability such a faggy field
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>>10293985
I learned about heights when I took Algebra II
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>>10294069
I'm sure you learned the hard truth about heights long before that manlet.
>>
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https://arxiv.org/pdf/1901.03436.pdf
>Elliptic Curves over Totally Real Cubic Fields are Modular
>Maarten Derickx, Filip Najman, Samir Siksek
>(Submitted on 11 Jan 2019)

>We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to Thorne and to Kalyanswamy.
>>
>>10294385
I unironically know one of the guys and his work and this is anything but a meme
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>>10294436
>I unironically know one of the guys and his work and this is anything but a meme
I've seen Samir give a talk for the real quadratic case
>>
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>>10289246
>math history seminar
>assigned textbook is old, out of print, based, and redpilled
The author gave "the collection of women on college football teams" as an example of the empty set and assumed his audience was white. He also referred to egyptian and babylonian mathematicians as "oriental." I wonder if my professor will acknowledge any of this in class tomorrow--I know a few humanities professors that would be outraged if they found out about this. I don't plan to snitch for what it's worth.
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>>10294385
is this a big deal or something?
>>
>>10294537
What is the book?
>>
>>10294608
https://en.wikipedia.org/wiki/Modularity_theorem
kinda
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>>10294608
>is this a big deal or something?
Modularity results have been generalized pretty heavily since Wiles. Modularity of elliptic curves over fields other than the rationals, modularity of higher dimensional Calabi Yau manifolds, etc.
>>
>>10294445
George?
>>
Ahem. I have an announcement.
Fuck coordinates, fuck bases and fuck charts.
Thanks for the attention.
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>>10295525
Ok.
>>
Is going full freetard and using Linux a bad move for a math undergrad?
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>>10295635
No. As for what distro, I suggest archlinux (or better artixlinux = arch without systemd), and for tools
. window manager = i3 / dwm,
. editor = vim / sublime text,
. browser = qutebrowser,
Read their documentation on their project page or archwiki. If it is your first time ask for help, this stuff is not straightforward, but it will be rewarding. Just to say (and not to brag), I'm currently a master student in math, I use linux since high school and the above is personal taste developed during the years, but I can do everything I need as a student.
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>>10295666
Thanks, anon. I'll go full freetard, then.
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>>10295666
How is qutebrowser different to/better than chrome/firefox with an extension for extra keyboard functionality?
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>>10295726
I won't say, but I will say it works fine.
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>>10295127
>George?
No
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>>10295666
fuck off satan
>>
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http://www.kurims.kyoto-u.ac.jp/~motizuki/2019-01-15-iu-teich-revisions.txt
Inter-universal Teichmuller Theory III
--------------------------------------
・Slightly modified Figs. I.8, 3.8 ("log-vol." ---> "hol. hull, log-vol.")

・Updated the Acknowledgements

・Slightly modified Definition 3.8, (i), and Remark 3.8.1 so as to take into account the general notion of a "pilot object"

・Corrected a misprint at the beginning of Theorem 3.11, (i), (a)

・Rewrote Remark 3.11.1 and added a references to Remark 3.11.1 in Remarks 3.12.1, (ii), and 3.12.2, (ii)

・Modified the first paragraph of the proof of Corollary 3.12

・Rewrote Step (xi) of the proof of Corollary 3.12

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf
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>>10295666
>qutebrowser
I can't post on 4chan from it. Is that the joke?
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>>10296001
I am doing this right now, so what is the joke?
>>
What are some cheap GTM's?
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>>10295635
No. If anything it's an advantage.

>>10295666
>arch
>i3
>vim
Are you me?
>>
>>10296001

running proprietary javascript is like drinking demon piss
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>>10296453
>Are you me?
Happy to know we are not alone.
>>10296215
Are there cheap GTMs? They all seem to be >45\$.
Once I tried to compute how much would it cost to make a book; printing 400p (=100 sheets) on common paper can go low as 2.5€, using a better paper should not make it much worse, then building a cover should also be cheap modulo tools (large sum) and bookbinding experience (it seems easy to make a perfect binding, but it is harder to open those kind of books, so we want hardcovers).
Then again, we have libgen, screens and libraries so it is not worth.
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>>10296535
I have literally every GTM in my computer, including UTM and many others, but I prefer 100 times having the physical copy, and I have enough money on me. I just don't feel like spending £50-90+ on relatively thin books. I bought Hartshorne hardcover for £40 which I thought was worth it, and Eisenbud's commutative algebra softcover for £15 which was a great deal imo
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>>10296544
Doesn't pages fall out from Eisenbud? (very thick + softcover, it is a genuine question)
That aside, it seems that the version on libgen is not good, someone should make a good scan if its softcover price is so low (unfortunately for the book that would mean ungluing it). Love for the hero, assuming that there is not already a good scan.
As for what book you should buy, if they are on the same price range then go for what you like. Don't know if there are cheep ones, sorry for the dull reply.
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>>10296535
I might as well give the advice I have.
The absolute best font for well formatted texts for printing is gutenberg.org. What you'll want to do is:
>open it up on libgen
>adjust the font sizes, spacing, paragraphs, etc
>as in, the files come up with reddit spacing instead of paragraphs, which is one thing on a pdf, and something completely different on an actual book
>export it as .pdf
>have a look at it
>take it to be printed
Printing an A4 and A5 cost the literal same here, so I usually went for A4 anyway.
Depending on how you plan on keeping it together, you might want to properly split up the chapters into different files.
If the only thing available is an .epub or .djvu from libgen, the procedure becomes:
>open it up on calibre
>clean it up there
>convert to .pdf
>look it over
>print
If the only file available is a .pdf, give up. If you insist on it, find out a way to remove quite a bit of the border before doing anything. Splitting it up is always convenient, but you might end up having to pay for multiple spirals or whatever.
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>>10296573
I'm browsing gutenberg, dooes
http://www.gutenberg.org/wiki/Mathematics_(Bookshelf)
contain all the books on mathematics? Thanks for the tips!
>>
Can someone tell me where the pic in the OP is from?
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>>10296627
Yeah, but remember that gutenberg.org contains only texts that are free domain. You wanna read the classics? It works. Otherwise, libgen is king.
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>>10296572
I haven't really used it that much to be honest. I've given Atiyah-Macdonald much more use since I know it so well (can't count the amount of times I've been reading something else and thought, hey that's a theorem/exercise in AM). But from what I see the binding is actually very good.

Also doesn't have to be GTM, can be anything else. Interests are algebra/geometry.
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>>10296639
>Can someone tell me where the pic in the OP is from?
"Algorithmic and Computer Methods for Three-Manifolds"

I found it through:
https://mathoverflow.net/questions/2949/great-mathematical-figures-and-or-diagrams
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>>10295925
>Corollary 3.12 re-written
Scholze BTFO again?
>>
>>10296848
Thank you!
>>
Because of real life, i haven't done math in like a year. I took vector calc, and am currently taking diffy q, how much past courses should I review or would it even be worth it to review?
>>
>>10297038
if you're confident enough with your calculus then differential equations should be ez
>>
Any college or university mathematics instructors here? If so, how do you select textbooks or other materials?
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>>10297170
HERE COMES THEY MONEYYY
HERE COMES THE MONEY
MONEY MONEY MONEY MONEY MONEY MONEY MONEY MONEY MONEY
CHING CHING DOLLA DOLLA
>>
For real numbers x, a and b, how do you prove (x^a)^b = x^(a*b) if and only if x is greater than or equal to 0?
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>>10298279
We set up the differential equation Df(x)=f(x) and f(0)=1, denoting the solution as exp(x).
ln(x) is defined the Riemann integral of 1/x along x from 1 to x.
Proof that ln(x) is exp(x)'s inverse is left to the reader.
We define a^b=exp(b ln a).
(x^a)^b=exp(b ln exp(a ln x))=x^(ab)

Tl;dr depends on how you define things. The statement is technically wrong.
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>>10298397
>The statement is technically wrong.
what statement?
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>>10298419
>(x^a)^b = x^(a*b) if and only if x is greater than or equal to 0?
>>
Then why is it technically wrong?
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>>10298279
x=-1, a=b=1.
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>>10298424
(x^a)^b = x^(a*b) whenever the LHS is defined.

The LHS is a subfunction of the RHS. If the LHS is defined, the RHS is defined and equal to the LHS. But the RHS may be defined even if the LHS isn't.

x^k is undefined if x is negative and k is irrational, or if x is negative and k is rational with an even denominator.

x^k is defined if x is positive or k is an integer or k is a rational with an odd denominator. For odd n, (-x)^n=-(x^n) => (-x)^(1/n)=-(x^(1/n)).

If x^a is undefined then (x^a)^b is undefined for even if x^(a*b) is defined. E.g. if x is negative, a is irrational and b=n/a for some integer n, (x^a)^b is undefined (because x^a is) but x^(a*b)=x^n is defined.
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>>10298710
For x=-1, a=1/2, b=3 it is defined
>>
>>
>>10298741
Fuck man, is anime good for mathematicians? I don't want to accept it if it's cancerous shit like Haruhi.
>>
>>10298810
>anime
>cancerous
back to the toyfactory cable guy
>>
>>10298810
Playing Touhou is good for you.
I need to get into the habit of doing it daily but booting Windows sucks.
>>
>>10298812
>Haruhi
>not absolute cancer
>>
>>10289850
Stochastic processes by Lawler.

Haven't visited this place in 8 years. Mathematician wanting to understand ergodic theory, any books people recommend? Honestly probably need to review analysis, I wasn't strong in it and just kinda suffered from going through the motions without great intuitive understanding, same with linear algebra. So if anyone here has material they recommend let me know.

t. Unemployed doomer
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>>10298810
haruhi, code gayass, gay-on, gayann fagann, and bakamonofaggotry all ruined anime. anime is shit now because of htem
>>
>>10298817
>1
shmpus suck they're literallya ll the same game
>>
I'm trying to come up with easy to state problems that are absolute pains to prove.
Best I've got is "Show that you can fit a smaller copy of a polygon inside the original."
Number theory is cheating.
>>
>>10299425
>Show that you can fit a smaller copy of a polygon inside the original.
isnt this trivial
you can shrink a polygon to an arbitrarily small size
so it just turns into proving that any polygon has an open circle of a non-zero size in it
>>
>>10299461
My bad, I goofed the phrasing.
Any smaller copy.
>>
Is HoTT a meme?
>>
>>10296853
They're (they = all the American mathematicians shitting on Mochizuki for no good reason) all experts in fields fairly distant from IUTeich. Read this:
About certain aspects of the study and dissemination of Shinichi Mochizuki's IUT theory, October 2018

Remarks on aspects of modern pioneering mathematical research, October 2018

on https://www.maths.nottingham.ac.uk/plp/pmzibf/nov.html .
>>
>>10299471
shit, yeah that is hard to prove
>>
>>10299507
I actually also forgot that it has to be star-shaped, otherwise you can make a G.
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>>10299538
Unofrtunately, that ruins the whole thing, except we can now add an "only if", which is substantially worse than the original problem.
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>>10299425
What do you mean by "fit"?
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>>10299425

Let P be an n-gon centered at (0,0).

Claim: the set Q = $\{0.5v: v \in P \}$ is smaller, a copy and inside P.

-"Smaller": perimeter/area is smaller.
-"A copy": I don't know how a "copy" can be "smaller" so we'll take the fact that Q is similar to P to be trivial.
- "inside": $P\ \cap Q = \{\emptyset\}$, so it's either inside P or outside P. But any line through any point in Q intersects P (easily verified) so it must be inside of P.
>>
>>10298722
> For x=-1, a=1/2, b=3 it is defined
Wot?

Neither (x^a)^b nor x^(a*b) are defined (over the reals) for those values (over the complex numbers, the result is -i).

A concrete example of what >>10298710 is saying is x=-1, a=1/2, b=4. Here, (x^a)^b is undefined (as x^a is undefined), but x^(a*b)=(-1)^2=1.
>>
why do i feel compelled to learn about quasigroup representation theory
>>
If I'm trying to find out how balanced my RPG rules/mechanics are should I have it roll a D100 100 times, or make it run through 1-100 in sequence to get a good idea on what needs to be buffed/nerfed?
>>
>>10300018

You're using a modern computer. It costs nothing to make your test run 5 million times.
>>
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>>10300010
Quasigroups are based.
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>>10299691
I don't see why not.
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>>10289246
No, please. Don’t do this to me. Who will carry the torch now that the old man is gone?
>>
>>10300072
Why not you?
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>>10300033
Ya but which is better to run that million times? I guess 1-100 only requires a single run through
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>>10300081
Are you insane?
>>
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>number theory seminar
>sit next to international student everyday
>international student corrects the prof over every little thing
>not just mistakes on the board, but spoken mistakes that most of the class already recognized and shrugged off 5 seconds ago
>damn annoying
>start packing my notes up at end of today's lecture
>international student chimes in, "oh, and by the way anon, you wrote the incorrect symbol for the natural numbers in your notes."
>can't believe he's doing something like this
>figure he saw me write "positive $\mathbb{Z}$" but missed the "positive" part.
>open my notes again to snub his bullshit
>while I'm flipping to the page where I wrote "positive $\mathbb{Z}$" he points to a regular old "$\mathbb{N}$"
>"this one, you wrote this one incorrectly. the double stock belongs on the first bar."
>insists that a blackboard-bold N may be written as ||\| and not |\\|.
>textbook doesn't use blackboard-bold, so i can't prove him wrong
>google it when I get home
>sure as shit, he was wrong
Should I show him next class period? Might do him good to learn that he's not right about every little thing.
>>
>>10289246
I really want to re learn math, are there any courses only that can help?
>>
>>10300200
http://4chan-science.wikia.com/wiki/Mathematics
Look under Pre-calculus. Get free books from libgen.io. George Chrystal Elementary Algebra is pretty good. Or just learn it from Khan Academy.
>>
>>10300200
depends on what kind of math you mean, khan academy might be what you want
>>
>>10300081
Not her, but I will.
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>>10300197
He seems to have some sort of social disability ,you should explain to him that people don't like to be corrected over every single little mistake , especially when it's trivial...
Be nice to him he seems sad
>>
>>10300197
Everyone I've seen writes it as ||\|.
>>
>>10300010
autism
>>
>>10300060
Jonathan Smith is pretty cool. This is the first time I've seen anyone mention his work here.
>>
>>10300072
What torch? The "doing math" torch?
>>10300780
>someone posts an anime girl
>>her
You've got the 'tism innit?
>>
>>10289246
Has any of you people used Khan Academy from the ground up?
What order of courses did you do? e.g. Math or math by grade.
>>
>>10299425
Show that a continuous non-intersecting closed curve in the plane divides the plane into two connected pieces.
>>
>>10299425
Show that any subgroup of a free group is free
>>
>>10299425
Show that the group operation of the group structure on a cubic curve is associative.
>>
>>10298710
but what about a = 2 and b = 1/2 and x is some negative number
then (x^a)^b = -x (because the square root maps to positive numbers), but x^(a*b) = x
>>
>>10300197
As someone who switched from |\\| to ||\|, you just have shit taste.
>>
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>>10301253
Better an infidel than a tratior. Never respond to my posts again.
>>
>>10301253
|\\| looks better and is more consistent with the bb for Z.
>>
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>>10300966
>anime girl
>>
redpill me on functional analysis in hilbert spaces
i took a course about this, and it felt comfy but i'm not sure if it's serious math
is this a dead subject or is there some research going on, are there big open problems?
>>
Sup /mg/. Since I've accepted that I'm going to be a wageslave after graduation I've been thinking about what kind of jobs to look for. I think I'll just go for software dev because while it sucks I also find it very easy and I have some past experience working in. I was wondering if there were any subfields in particular I should look at that are more mathematically involved, machine learning is obvious but are there others? Especially ones using more discrete stuff than analysis.

thanks
>>
>>10300197
the absolute state of mathematics undergraduate students
>>
>>10301407

>>
>>10301407
lmao, you'll never make it
>>
>>10298823
Walters ergodic theory is nice.
>>
>>10301458
This sounds interesting, thanks.

>>10301467
I mean I can do analysis I just prefer my comfy discrete math
>>
"two irreducible unitary representations of the same group can not be equivalent."

This book defined equivalence of representations to mean "a ~ b <=> there exists T s.t. Ta=bT."

Under this definition of equivalence, isn't that statement false?
>>
>>10301646
Why would it be?
>>
>>10301354
>he fell for the oldest bait in the book
>>
>>10301467
>Implying discrete math isn't just analysis with atomic measures
>>
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>>10301665
OY VEY SHUT IT DOWN THE GOYIM KNOW
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>>10301652

because a and b are representations of the same group, there is clearly some kind of isomorphism between them.
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>>10301681
Yeah, but it's an isomorphism as groups, not as matrices.
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>>10301685

What's the difference?

It would send matrix a_g to matrix b_g
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>>10301691
Taking the inverse and composing gives you an isomorphism of matrices as groups under the multiplicative operation. It is not an additive isomorphism as well.
>>
>Have no idea what the first packet is talking about
Is this one of those topics where it's not supposed to make sense yet or did I miss something big in my previous courses
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>>10301809
You did have a course of analysis, right?
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>>10301809
what did you talk about ? what is this course supposed to cover ?
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>>10301665
EXTREMELY based post
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>>10299425
jordan curve theorem
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>>10301809
what is the first packet? early topology is pretty abstract, yeah, but you should be able to see most things if you think about it in terms of different objects (usually R or R^2)
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>>10299425
Show that the hexagonal packing is the ideal packing of the 1-sphere
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[eqn]\left(2a-b-3\right)^2+\left(3a+b-7\right)^2=0[/eqn]
Putting the above equation into WolframAlpha gives me the integer solutions 2 and 1.
How does it find these solutions?
Is there a method I'm not aware of to solve a single equation with 2 unknowns?
Or is WolframAlpha somehow brute forcing the solution?
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>>10301947
Yes, there is an algorithm to solve diophantine equations of this particular form.
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>>10301163
This is easy if you use topology to prove it.
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>>10301976
a group is free if and only if its cayley graph is a tree. is there anything else to it ?
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>>10301947
Read A course in arithmetic by Serre
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>>10302195
Serre is a meme.
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>>10301845
No?
>>10301851
Didn't lecture, TA just handed out the packet as homework instead.
>>10301887
Topological Spaces, topology on set X, comparable topologies.
It feels like I recognize the words and stuff from linear algebra, but sounds like nonsense when I read it.
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>>10302297
Technically speaking, undergrad real analysis is not a requirment for topology. It is, however, usual, and teachers will probably assume you know what Cauchy sequences, open sets, etc are.
Either way, topology books are usually self-contained, so you should be able to handle yourself through guts and dedication.
You only really need linear algebra for examples and specific exercises, and it's usually the bare minimum.
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>>10301947
Squares are never negative. The only solution to x^2+y^2=0 is when x=y=0. So now it has two linear equations (the two terms which are squared = 0) in a and b.
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>>10302297
do you know some theory of metric spaces ?
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>>10302372
I think we did some if that in vector calc.
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>>10302297
I don't really understand what you mean.
A topology is just a bunch of subsets of a set X.
This collection has some nice properties.
I don't really see why anyone would bother to take topology before real analysis, since you have absolutely no motivation or understanding for what "open sets" are supposed to be. To be honest, I'd recommend looking up what "open sets" and "closed sets" are in R and in R^2 (ie, what the standard topology is), and then pass through your material keeping in mind how things work in R. But topology is a rather abstract topic, so to some degree you'll need to develop a less concrete intuition for the concepts on your own.
Are you required to take topology before taking analysis?
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>>10302380
What the fuck?
What fucked up curriculum is this?
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can someone check this computation?
i.e. sequence is not cauchy
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>>10302297
Just imagine topologies on sets to be regular Hausdorff and paracompact. Everything that is true on general spaces is true for those, but at least you can picture the topologies.
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>>10302398
?
you haven't shown it's not cauchy. In fact, I don't know what you've shown
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>>10302380
Topology is a generalization of metric spaces. You should be familiar with open and closed sets, continuity, compactness etc. And by "familiar" I mean you should really have a feel for these things, not just remembering definitons. Topological spaces are surprisingly general and unintuitive, and metric spaces are like a crutch to help you build some intuition. Good deal of beginner's topology is about figuring out what properties of metric spaces hold also for topological spaces and which don't. Technically you don't need to know metric spaces to learn topology, because the theory itself is self-contained. But even if you learn theorems, understand proofs and shit, you will probably have zero idea what's actually going on and you will think that topology is just some "weird set theory".
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>>10302161
Any free group on a set S is the fundamental group of a wedge sum of circles indexed by S. Then just apply the Galois correspondence to covering spaces.
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>>10302406
set m=n^4, then as m, n-> inf you have ~ 2/3 n^(1/4) which goes to inf.
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>>10302386
>>10302390
There's no clear path here, didn't even start taking "math" courses until end of second year. So probably won't rely too much on any analysis unless she'll cover it in class.
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>>10302423
nigger, you wrote $m\leq n$, how u gonna get m=n^4 there
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A bit unfamiliar with math, can somebody advise? Does anyone know given exactly what conditions it's possible to compute a closed-form expression for sums of the form $\sum_{n=0}^{\infty}a_n \prod_{k=1}^{n} b_k$ where both the $a_n$ and $b_n$ are strictly between 0 and 1?
Or at least, what are this form of sum called? Where can I read more of the theory. Thanks
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>>10302430
> kill himself
thank you
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>>10302431
Nigga this question is harder than the riemann hypothesis
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>>10302398
>x^-4=n^1/4 iff x=1/n
No. Take ^4 on both sides. x^-16=n.
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>>10302438
I'll just show myself out.
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>>10302440
that was a PRINTING mistake, it should be x^(-1/4), nice spotting
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>>10302451
Right, my bad, it was actually correct on the definition.
Should be correct.
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>>10302243
Ignore this, Course in Arithmetic is a great book and "____ is a meme" is a meme
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>>10302569
Except Linear Algebra done Right, that one is a meme.
Recommending Lang's Algebra to undergrads is also a meme, but isn't done as often due to "Lang is a meme". I actually imagine that's the origin, but I wasn't here then.
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>>10302569
>>10302582
someone lang's algebra'd me with serre when i was a freshman at uni who wanted to learn a little more about basic modular arithmetic shit
serre is just as much a meme as lang is to me
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>>10302625
>want to learn about modular arithmetic
>person recommends a book on modular forms
Just because your friend was an idiot doesn't mean Serre is a meme
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>>10302625
Serre has this notation hell going on, but it still isn't hard if you know essential algebra and have access to google.
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>>10302644
well to be fair the very first section was about modular arithmetic
the way i put it was "what can i do with this stuff that's more interesting"
i should probably pick it up again now that i have some actual background, modular forms could be fun now
i'm assuming some complex analysis and group theory is good enough to get it
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>>10302646
i didn't know what a group was (or at least think i knew) at the time for fucks sake
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>>10302662
Just flipped through the first 30 pages.
You'll need:
-essential algebra
-point-set topology
-basic category theory
-some number theory
New requirements might come up later, but it's probably more algebra and some complex analysis at worst.
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>>10302688
i have those things besides (though really not much number theory at all)
except i'm flipping through it now and i'm remembering why i fucking hate algebra
i might just skip to the analytic part with the theorem i cared about at the time anyway, with primes in arithmetic progressions
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>>10302662
You should check out the chapter on modular forms in Serre and see how much you understand. It is a super interesting subject combining complex analysis, group theory and number theory.
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>>10302744
Not any of the previous guys,
I studied that chapter and I have to say it is good but a bit coincise, you need to spell out things and sometime provide a rigorous proof yourself. Not a problem tho.
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>IUT3, Corollary 3.12: Spaces, Pilot Objects, Indeterminacies, Mochizuki Measures
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>>10289378
A branch network.
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>>10289627
So long as it is about sexuality and intellectualism, I'm all for it.
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>>10303184
First cum first serve.
>>
hit or miss
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>>10302855
I agree. That's Serre for you. The best way to work through this chapter and this book is to make your own notes and fill in the gaps that the author has left (which helps you learn a lot, because there aren't any explicit exercises).
>>
why is the Banach fixed point theorem so fucking cool
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>>10303594
Because it allows you to collapse the space to a single point.
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>>10303594
It allows you to find unique solutions to many problems. First example is Cauchy-Lipschitz, but there are many. It is also very simple, hence cool, cooler, coolest.
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>>10303627
>>10303653
but can it help me woo a female?
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>>10303683
No, but that is not the theorem's fault. It's because you are ugly and creepy.
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Can anyone explain me what he meant? How can i know which icon is pressed from a global system. If i click on (x1,x2) then i get using the mentioned formula (u1,u2) which are local coordinates. But don’t all icon have same local coordinates?

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