/sci/ - Science & Math

First for fuck trannies.

>>12139430
>Elliptic Curves

>>12139336
I'm stupid and on mobile, can you tell me in words?
Every time I highlight to try to copy paste what you wrote it overwrites it with some optional math menu thing

>>12139430
found a math basics channel run by a military dude the other day
its neat

>>12139476
Proper etiquette is to post it if you mention it

>>12139450
Based.

>>12139470
[math]\forall n \in \mathbb{Z}^ {+}, n! = \int _{0} ^{\infty} \exp(-t) t^n \ dt[/math]. This is known as the [math]\Pi[/math] function and when you take [math]n = 0[/math], you'll get [math]0! = 1[/math].

https://www.symbolab.com/solver/improper-integral-calculator/%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%7Dx%5E%7B0%7Ddx

>>12139494
he probably means smarter every day (not a math channel, but more sci general. I suppose there won't be math channels by military people)

I need a list of open problems in math, anyone have something comprehensive? Wikipedia isn't that useful for specific stuff. I mostly wanna read up on since this is my final two undergrad semesters before I move up to masters

I still don't know what is it people here have against Nikolaj.

>>12139516
He's living the life in Vienna, eating cakes, studying math and fucking Balkan women who study management or economics.

I am jelly desu but I'm coming to study there next year and beat him up desu

>>12139430
Fuck Bismarck.

>>12139516
Can you please stop saying my name.

>>12139521
Wait, have I been foodposting here or do you blur the lines with some Discord channels.
Btw. there's a talk/discussion of sorts in the Hatcher reading group one in an hour.

>>12139503
I claim... erm..

[math]\sum_{n=0}^{M-1} \dfrac{Z^n}{(n+A)^s} = \dfrac{\int_0^\infty x^{s-1}e^{-A\,x}\cdot \dfrac{1-(Z\,e^{-x})^M}{1-(Z\,e^{-x})}{\mathrm d}x}{\int_0^\infty x^{s-1}e^{-1\, x}\ {\mathrm d}x} [/math]

>>12139503
Ty, I'll do my best to understand

>>12139557
>Can you please stop saying my name.
Your name is Nikolaj, your youtube channel is Nikolaj-K, even your fucking discord is Nikolaj-K, what the fuck am I supposed to call you, screenshot in german?

My degree in Math and CS has the following courses:

Low level courses:
Calculus 1, 2, and 3
Linear Algebra
Discrete Mathematics
Probability
Abstract Algebra
Intro to Computer Science 1 and 2
Computer Systems

High level CS courses:
Analysis of Algorithims
Concepts of Programming Language
Elements of the Theory of Computation
Advanced Algorithims
Complexity Theory

High level Math courses:
Modern Algebra 1 and 2
and two high level math courses of my choice

Does this seem like a good Math and CS degree course load?

>>12139577
>no real analysis
>no complex analysis
>no topology

>>12139588
I know right? If I take Complex and Real analysis, I won't be able to take topology or differential geometry which are classes I really want to take. I might just major in math and minor in computer science.

>>12139588
>>12139596
Also is it weird to take 3 classes of Modern/Abstract Algebra?

>>12139596
...you're literally only allowed to take 2 extra courses? those aren't just the bare minimum?
what the fuck is wrong with your school?>>12139599
yes, there's no reason you should be required more than a year which covers basic group/ring/field/module theory.

today i drank a pepsi, smoked a marlboro, and ate a burger king. for no apparent reason, i suddenly have a craving to study elliptic curves. where do i start?

>>12139613
Start by fixing your addictive lifestyle.

>>12139596
Replace topology with real analysis.

>>12139588
This.

>>12139613
Do you have a good foundation in number theory, algebra, and complex analysis? If not, start there.

>>12139573
Say... Bogolyubov

>>12139470
Here's my shot at motivating the definition:

If you want to count all the functions from the domain A to the codomain B, you got [math] b^a [/math] functions, where a and b denote the size of A and B as set, respectively. E.g.

A={x,y}
B={u,v,w}

1) x u, y u
2) x u, y v
3) x u, y w
4) x v, y u
5) x v, y v
6) x v, y w
7) x w, y u
8) x w, y v
9) x w, y w

those were 9, or 3^2 functions, which happens to be [math] b^a [/math].
You can derive at the formula easily, since for every of the a elements, you got b options.
[math] \prod_{k=1}^a b = b \cdot b \cdot b \cdots b [/math]
[math] = b^a [/math]

If you count the injective functions, i.e. those where no points to the same function, this list gets filtered. Because no value can be assigned twice.
Namely 1, 5 and 9 must be kicked out. We end up with 6 functions. If we want a formula, we can again start the counting game, and be aware that at every multiplication, we removed one option from the next assignment.
Counting gives
[math] \prod_{k=1}^a (b + (-k+1)) = b \cdot (b-1) \cdot (b-2) \cdots (b-a+2)\cdot (b-a+1) [/math]
[math] = \dfrac{b!}{(b-a)!} [/math]
E.g. in our case, [math] \dfrac{3!}{(3-2)!} = 3! = 6 [/math].

If we want the formula be true for A=B, we need (b-b)!=1, which already does the trick.

From another standpoint, we could also argue that the identity function assignment should work for every A, so when A is empty, we still want the identity function to be a valid function, so 0^0 should be 1 too. (At least you need that if you want the class of sets and functions to form a category.)

Maybe from a more arithmetical standpoint, note that we can prove that [math] \sum_{k=0}^n\dfrac{(-1)^k (-k)^n}{k!\,(n - k)!}=1 [/math] for all n, assuming 0!. Which is nice. As a consequence, or realization of this, note the nice pattern:

...

8! = + 0^8 - 8*1^8 + 28*2^8 - 56*3^8 + 70*4^8 - 56*5^8 + 28*6^8 - 8*7^8 + 8^8,
7! = - 0^7 + 7*1^7 - 21*2^7 + 35*3^7 - 35*4^7 + 21*5^7 - 7*6^7 + 7^7,
6! = + 0^6 - 6*1^6 + 15*2^6 - 20*3^6 + 15*4^6 - 6*5^6 + 6^6,
5! = - 0^5 + 5*1^5 - 10*2^5 + 10*3^5 - 5*4^5 + 5^5,
4! = + 0^4 - 4*1^4 + 6*2^4 - 4*3^4 + 4^4,
3! = - 0^3 + 3*1^3 - 3*2^3 + 3^3,
2! = + 0^2 - 2*1^2 + 2^2,
1! = - 0^1 + 1*1^1,
And finally, if you want to,
0! = + 0^0

>>12139609
Well no, it's the bare minimum to graduate, I'm sure I'll be able to take more classes. I plan on minoring in philosophy though. It seems like I should just give it up and take some extra topology and differential geometry classes though. I don't really know why I'm going to have to take 3 algebra classes too, but hey at least I'll get good at Algebra.

>>12139626
yes, albeit rusty

>>12139639
I'm confused: Are you double majoring or double minoring?

>>12139647
Elliptic Curves, Modular Forms, and Their L-functions by Lozano-Robledo is a great introductory text to elliptic curves that is aimed at upper undergraduates. It'll cover some stuff from the areas of math I mentioned, but it expects you to be comfortable with the basics.

>>12139649
Neither it's a single Major called Mathematics and Computer Science, the major is described as a major for Math majors who want to learn more computer science or for Computer Science majors who want to be more mathematically rigorous.

>>12139639
What are the course descriptions / syllabi of the algebra courses?
Also, you may be able to stack on an extra course for 2 of your 8 semesters depending on your university's policies if you really are up against the wall between 3 programs.
IMO if you have the flexibility the best thing you can always do is start taking courses in all 3 areas and if you like all of them a lot, go for it. Chances are one might be not as interesting as you thought and you'll end up with plenty of room in your schedule. This is what happened to me with Math and CS. I still ended up with plenty of CS experience and know-how, I just never took the upper level specific stuff and took more math classes instead.

>>12139661
That would better explain the course load. If you're more interested in math, then I would just major in math and double minor in CS and philosophy if that's allowed. Just note that if you do go that route, it'll be a lot of work.

>>12139664
>What are the course descriptions / syllabi of the algebra courses?
First class
>A first exposure to groups, rings, and fields.
Second class
>Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings
and for the third class
>Vector spaces and modules, Galois theory, linear transformations and matrices, canonical forms, bilinear and quadratic forms
but other then that their doesn't seem to be much info.
Also I'll just give up the philosophy and minor and take the extra math classes instead. Fuck it I can self learn philosophy easily.

>>12139685
>A first exposure to groups, rings, and fields.
>Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings
>Vector spaces and modules
I learned all of this in the first algebra class I took and we briefly covered Galois theory at the end. Not sure why this is being split up over three whole classes.

>>12139696
Maybe we go more in depth into it? I'm not really sure to be honest. It's weird though.

>>12139710
Probably, but it still seems weird. At my uni and all others I've seen, algebra is split up in Algebra I and Algebra II, with the option to take a grad class during your senior year if you meet the requirements.

>>12139696
Are your professors treating teaching like a speedrun or something?

>>12139696
my class was also all these things but it was very fast paced and barely anything was covered in depth. my depth of understanding of algebra and the way people think about algebra suffered from it.
>>12139718
must be

>>12139718
It was a summer class, so we had more time than usual, but it wasn't super in depth especially towards the end.

>>12139696
what institution?
I can understand brief exposure, just a glimpse of what's ahead

>>12139737
Did you lads see stuff like the proof that the sign function real or the explicit presentation of the dihedral groups?

>>12139754
UT

>>12139793
Former, yes; latter, no.

>>12139793
>proof that the sign function real
what? this is not a real sentence
>explicit presentation of dihedral groups
of course, how else do you define them?

>>12139870
>this is not a real sentence
Wrong.

>>12139635
Understood, mister Bogolyubov.
>>12139870
>2020
>he still restricts himself to speaking in sentences
Maken't will.

>>12139509
There are so many open problems in math that your are gonna nee to be a little more specific and narrow it down to a single field. Also there are a lot of "open problems" that never really end up on lists of "open problems" because most open problems are in new areas of math that are under development. Most people would only know about these problems if they work in the same field. Basically there is not really centralized area to read about open problems. Most of them are listed in different textbooks and stuff.

If you are interested in open problems that ypu could start working on or at least understand in the next year or two, then you should look into combinatorics.

>>12139509
not sure how comprehensive this is but: http://www.openproblemgarden.org/
wikipedia also have lists of open problems but they're broken down by topic iirc

>>12139430
>go to shit tier university
>uni has many profs with under 2.0 on ratemyprofs
>calc 3 prof doesn't follow textbook, gives sample problems that are nothing like his exams
for example, anyone see something called the "universal derivative equation" before?

[math]\lim_{h\rightarrow0}{\frac{f\left(x+h\right)-f\left(x\right)-f^\prime\left(x\right)h}{\left|h\right|}}\frac{\left|h\right|}{h}=0[/math]

apparently this form applies to vectors better than the other form? literally zero results when i try to search for this online

>>12139977
[eqn]\lim_{h\rightarrow0}{\frac{f\left(x+h\right)-f\left(x\right)-f^\prime\left(x\right)h}{\left|h\right|}}\frac{\left|h\right|}{h}=0[/eqn]

>>12139977
See pic related.

>>12139981
lmao what the fuck

>>12139888
Can you just tell me what you meant by "the sign function real?"
Do you mean showing that the homomorphism which sends a permutation to its sign is well-defined?

>>12139977
there's nothing spooky about it, see e.g.
https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative

>>12139977
>>12139981
I think maybe your professor is using a different word for a very common idea.
Some people call this the total derivative. Some people call it the differential. Some people just call it "the derivative." Some people call it the Jacobian (which is an abuse of notation). Some people call it the pushforward (for unexplainable reasons to someone in calc 3).
Basically, the idea is the same as the usual derivative. The universal/total derivative is the matrix which satisfies this equation when you send any vector h in the domain to the zero vector. You can think of it in terms of partial derivatives. The total derivative times a unit vector in the x direction tells you the partial derivative in the x direction. The total derivative times any vector tells you the directional derivative in that vector's direction.

>>12139981
>>12140013
Oh yes, of course I forgot that it's also called the Frechet derivative. But I think when you call it the Frechet derivative you're usually looking at infinite dimensional spaces instead of R^n.

One reason that you define it by an equation this way is that it's kind of tough to define a matrix by a limit equation where all the objects are vectors. You could have limits in each variable in the domain and range, and this would give you the entries of the matrix (read: the jacobian matrix is the matrix of partial derivatives). But you shouldn't define it that way for more complicated reasons.

>>12139992
>>12140013
thank you for the explanation

>>12139991
[math]\textrm{sgn} : S_n \rightarrow \{\pm 1\}[/math] given by [math]\textrm{sgn} = \begin{cases}
1 : \sigma \ \textrm{is even} \\ -1 : \sigma \ \textrm{is odd}
\end{cases}[/math]

>>12139981
>>12140025
I think it's abuse of notation to denote if by f'·h and at the same time define it implicitly there. But I assume he demands it to be a linear map acting on h.

>>12139925
kek

>>12139986
Is there a way to make latex stuff work on the archives

>>12140076
The point is
"The derivative of a map f: R^n to R^m at p in R^n is a function f'(p) : R^n to R^m such that the following equality is satisfied
[eqn] \lim_{h\rightarrow 0}{\frac{\left|f\left(p+h\right)-f\left(p\right)-f^\prime\left(p\right)(h)\right|}{\left|h\right|}}=0 [/eqn]
Where the limit is taken over h in R^n."
Then, one proves that f'(p) exists, is unique, and is linear.
There's no abuse of notation.

>>12140082
Have you tried https://chrome.google.com/webstore/detail/tex-all-the-things/cbimabofgmfdkicghcadidpemeenbffn/details ?

>>12139577
hahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha

>>12140127
I don't use chrome, sadly
Thanks tho

In a non-trivial ring, is the set of zero-divisors contained in a proper ideal?

I'm trying to solve this problem: on a Noetherian scheme [math]X[/math], show that the set of points [math]x\in X[/math] such that it's local ring [math]\mathcal O_{X,x}[/math] is an integral domain is open.

The previous problem was to do this in the case [math]\mathcal O_{X,x}[/math] is just reduced - in that case, take any point [math]x[/math] whose local ring is reduced, and consider an affine open neighbourhood [math]\text{Spec }A [/math] around it. Then the nilradical is finitely generated by Noetherianness, say, [math]\text{Nilrad }A=(f_1,...,f_n)[/math], and since [math]A_x[/math] is reduced, then there is an element [math]s\in A-x[/math] that kills every sufficiently large power of the [math]f_i[/math], and thus the basic open set [math]D(s)[/math] only contains points with reduced local rings.

However, in the case of integral domains, there is no "integrality" ideal, so to speak, as there is a "reducedness" ideal.

>>12140177
>In a non-trivial ring, is the set of zero-divisors contained in a proper ideal?
Nah.
Take [math]\mathbb{Z}_2 \times \mathbb{Z}_2[/math].

>>12140135
>Phoneposter

Can someone give me a qrd on projective toric varieties? As in how to I explicitely go on defining on an calculate with it.

>>12140189
>>12140177
I've realised that showing integrality usually has both the algebraic (reduced) aspect, and the topological (irreducibility) aspect, so trying an algebraic argument would be bust.

How about this: By Noetherianness, [math]X[/math] has finitely many irreducible components, and by the above, we can assume [math]X[/math] is also reduced. Now the problem reduces to showing that we can find an open subset in one of these irreducible components that satisfies the given property, since any open subset of an irreducible space is irreducible. So take any affine open subset of the irreducible component. Irreducible components intersect in closed subsets, and by Noetherianness, there are only finitely many intersections, so we can throw away finitely many closed subsets of our chosen open affine and still have an open set. Then this open set has the property.

>>12140288
>Noetherianness
I don't think this is a recognized mathematic

>>12140329
term.

>>12140329
not him but
>submit paper
>gets accepted
>editor """""""corrects""""""" the word "closedness" to "closeness"
>mfw
WHAT THE FUCK AM I SUPPOSED TO CALL THE PROPERTY OF BEING CLOSED IN A NOUN THEN HUH?

>>12139446
BASED FPBP

>>12139494
https://www.youtube.com/user/MathDoctorBob/videos

he's not actually military but that's the vibe I got from his older vids
>>12139508
no but i kinda like him
not /mg/ tho

>>12140338
Shit sucks man. Hopefully it is going to be clear from the context

>>12140089
I'm not sure that the only solutions of this have to be linear ones. Maybe in R^n, but also there I donno.

>>12140508
>geometrically perfect circles
no such thing

>>12140508
Yes, you're right. It does have to be assumed to be linear. Obviously, if it's not assumed to be linear you can just pick f'(p)(h) = f(p + h) - f(h) and the whole thing is trivially 0. My bad.
>>12140089
As pointed out, one in fact needs to assume that f'(p) is a linear map. No clue why I didn't realize that.

>>12139430


https://www.youtube.com/watch?v=VFojALyTYZk&feature=youtu.be

>>12140811
what the fuck

>>12140811
Kino.

>>12140811

Escher was keen on intersecting polyhedra.

>>12141091
Are there any mathematicians who were/are also painters?

>>12139430
And there it is, 4 weeks into the semester and it's happening all over again, I cannot be fixed, if all those years were meant for something, it was for me to realize that I'll never change, yup, failure is an intrinsic characteristic of my very existence, I can't exist without it and just like that I'm failing again. Five subjects, I haven't studied a single one, there's a multivariable calculus test on monday, I barely know anything besides double integrals, then next week there's a physics and a proof-based geometry tests and again, I barely know anything. What do I do all day? I shitpost on this website, I watch useless fucking videos of animals on youtube, I search for netorare hentai that I haven't seen yet, all fucking day and every single day is wasted like that, for how long? I wonder when have failure became such an essential part of myself? No matter what I do I can't get rid of it, that's it for me friends, guess I'm finished now, I had dreams when I started college, now I have nothing.

>>12139446
based
>>12139450
based

>>12141143
Elliptic curves are boring

>>12141116
you can always come back from that with some work. 4 weeks is a lot but not insurmountable (i recovered from a month long bout with bronchial pneumonia mid semester once). just quit hitting this stupid site.

self discipline.

>>12141152
Not really.

What is it called when you're trying to prove something that's not a theorem? Like something along this format but you have to prove if the conjecture is true or false? (basically what word to replace Theorem with)

>>12141216
Lemma
Corollary

I'm trying to figure out how long it takes Mars to travel 1 degree of azimuth across the sky. I've been timing it and I'm getting anywhere from 2:50 to 3:05~3:10. It seems really inaccurate doing it this way.

Is there a way to do this using distance or something? Thanks lads.

>>12138674
>>To add to this, every classical theorem can be faithfully translated into an intuitionistic one, by Godel-Gentzen for example.
>So inasmuch as it makes sense to speak of the "number" of theorems, it would increase if anything.

All the theorems relying on contra position, on having a proof of the existence of an object without even being able to make it explicit, do not hold in intuitionistic logic.

>>12141104

I'm not aware of any mathematicians who had a meaningful artistic career (I bet someone can remind me of one which will make me headslap, no, Kaczynski doesn't count), but there have been plenty of artists who took interest in mathematics, with greater or lesser success. The Renaissance masters are the most obvious example which needs trotting out, and Dali, who took after the old greats, regularly incorporated mathematical themes. His final painting was a very simple abstract concered with the swallowtail castrophe curve, and he had jesus crucified on a three-dimensional projection of a teserract. Here, we have a dodecahedral interior enclosing a Last Supper.

Where Escher is concerned, it's very important to note a conscious shift that he took as a young man. He bummed around Europe, and the town scenes of rural Italy stayed with him for the rest of his life. After a "learning his craft" phase, Escher took a CONSCIOUS decision around the mid 1930s (IIRC) to spend the rest of his life making art involving patterns and structures, objects that he enjoyed contemplating.* He was always very careful in interviews and talks to make clear that he was not a mathematician (and he used his own idiosyncratic private language to describe his techniques), but in the latter half of his life he was aware that his art had a properly mathematical content, and was gratified to interact with mathematicians and explicate his work along mathematical lines, as well as he could. In the definitive Escher book, a simple watercolor from early days seems almost an absurd experiment next to the usual printmaking. That's another thing. Escher was a printmaker, not a painter. He'd do woodcut blocks and complex lithographs and mezzotints for his pictures.

*This was especially influenced by his visit to the Alhambra, with its geometric patterns.

>>12141302
Good and interesting post. I didn't any of that regarding Escher. In fact, the relation between math and art never really crossed my mind before now which was why I asked in the first place.

>>12141318

There are a series of "reddit-tier" associations which are fairly well-known by people familiar with art history. Classic artists often have interest in the platonic solids, as I just indicated with the Dali example (which apes Renaissance ideals).

Sometimes, modern conceptual artists take a process and just autistically carry it all the way through, to see what it actually looks like. The conceptual artist Tom Friedman decided to draw a tree-diagram starting with a line segment, then branching off two in 45 degree angles which were slightly shorter, and so on and so forth until termination. One might find such a piece boring, but it's another example of mathematical art, at any rate.

Primitives have been making visual depictions of knot-patterns forever, which sometimes have rotational symmetry and therefore fascinate. Try actually looking at a page of the Book of Kells. Staring at it, for twenty minutes or longer. Analyzing it. The same thing more-or-less, smaller and smaller, again and again. Fractals. Pic related doesn't do it justice, you can zoom in much closer on a university link (Trinity Dublin collections, can provide link if requested).

https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf

should I cite tai's method for an integral in my paper?

>>12141531
No.

Is there a name for a the topological property where, given a space X, getting rid of any single point will result in a homeomorphic space. I don't mean homeomorphic to X but to each other.
For instance no matter what point you get rid of on the space (0,1) you'll be left with spaces all homeomorphic to each other; but if you do that with the space [0,1] there actually are points that you can take out and end up with a different space.
Basically I'm wondering if there's a word in topology to quantify when all the points in a space are topologically the same

>>12141104
Fomenko.

>>12141544
>Is there a name
No.

>>12141116
>I had dreams when I started college, now I have nothing.
what were your dreams?

>>12141552
What is this absolute kino?

>>12141552
Also a historian

>>12141575
>he hasn't read homotopical topology

>>12141295
Yes, which is why the Godel-Gentzen translation is not the identity mapping, rather it inserts double negations into the theorem statement as needed to preserve intuitionistic provability.
When combined with the observation that intuitionistic logical equivalence is a strict refinement of classical logical equivalence, such translations exhibit that classical logic can be embedded into intuitionistic logic, but not vice versa, and so any structurally-sound method for counting theorems would require at least as many intuitionistic theorems as classical ones.

The "cancellation law for groups" states that for some group (G, *), with 'a', 'b' and 'c' all being members of that group, the following holds true:
a * b = a * c => b = c
b * a = c * a => b = c

The proof is very trivial:
>since each element has one unique inverse, we can compose on left and right by a's inverse ', which must also a member of G
>after that we apply associativity, inverses and identity axioms to get what we want.

How can we just "compose" an inverse on both sides and assume that the equality still holds?
If we can add a^-1 to both sides then we can also remove it because nothing changes, but isn't *that* what must be proven in the first place?

>>12141706
Fuck me I'm retarded, I forgot that you can assume something and then prove it. Jesus...

How do you pronounce `Tschirnhaus'?

>>12141706
You don't use the property your trying to prove.

It's just that if you have a*b = a*c, the equality will remain if you perform the same operation on both sides of the equality.
Just like how you learn to solve basic equations in 8th grade.

>>12141773
cheernhouse

that's a union not an intersection

Hey guys check out this cool painting i made

>>12141295
The point is that for all classically provable statements, there is always intuitionistically provable statment that's classically equivalent to it.

Example: Noncontradiction is intuitionistically provable, i.e.
[math] \neg (A \and \neg A) [/math]
is a constructive theorem
(Proof: given a reason x to believe A and a reason f to believe A leads to absurdum, apply the procedure f to x and thus an absurd conclusion f(x) is obtained)

Now there's a classical rule that
[math] \neg (P \and Q) [/math]
is equivalent to
[math] \neg P \or \neq Q [/math]
and classically we also have the double negation elimination saying
[math] \neg \neg A [/math]
is equivalent to just
[math]A [/math].
So the constructively proven
[math] \neg(A\and\neg A) [/math]
is classically equivalent to
[math]\neg A\or A[/math]

There are several schemes of translations (rewritings) that each map any classically provable statement to one that's constructively provable in this way.
If we view theorems connected via such short rewriting procedures as equivalence class, then dropping LEM does not make any such class empty. No theorem is lost in that sense.

Compare it to me discarding the possibility to use "9+5=14" but still allowing the rules "9+4=13" and "13+1=14". You then have to make syntactical detours, but the theorems you prove remain the same.

More concretely, some existence claims will constructively only survive as non-rejectibility claims. The constructive frameworks however allows for a nicer range of semantics.

* Classical reasoning example (common sense application of LEM):
"After the car accident, I found myself waking up in a hospital room without windows and I knew that either it was day, or it was night!"

* Epistemic logic semantics (out of place use of LEM):
"After the car accident, I found myself waking up in a hospital room without windows and I knew that either I had a reason to believe it was day, or I had a reason to believe it was night!"

Which is just bullshit.

>>12141295 #
The point is that for all classically provable statements, there is always intuitionistically provable statment that's classically equivalent to it.

Example: Noncontradiction is intuitionistically provable, i.e.
¬(A and ¬A)
is a constructive theorem
(Proof: given a reason x to believe A and a reason f to believe A leads to absurdum, apply the procedure f to x and thus an absurd conclusion f(x) is obtained)

Now there's a classical rule that
¬(P and Q)
is equivalent to
¬P or Q
and classically we also have the double negation elimination saying
¬¬A
is equivalent to just
A.
So the constructively proven
¬(A and ¬A)
is classically equivalent to
¬A or A

There are several schemes of translations (rewritings) that each map any classically provable statement to one that's constructively provable in this way.
If we view theorems connected via such short rewriting procedures as equivalence class, then dropping LEM does not make any such class empty. No theorem is lost in that sense.

Compare it to me discarding the possibility to use "9+5=14" but still allowing the rules "9+4=13" and "13+1=14". You then have to make syntactical detours, but the theorems you prove remain the same.

More concretely, some existence claims will constructively only survive as non-rejectibility claims. The constructive frameworks however allows for a nicer range of semantics.

* Classical reasoning example (common sense application of LEM):
"After the car accident, I found myself waking up in a hospital room without windows and I knew that either it was day, or it was night!"

* Epistemic logic semantics (out of place use of LEM):
"After the car accident, I found myself waking up in a hospital room without windows and I knew that either I had a reason to believe it was day, or I had a reason to believe it was night!"

Which is just bullshit.

Could the manga guides to calculus and linear algebra prepare someone for studying analysis and proof based linear algebra unironically?

>>12141216
Proposition

>>12141556
Get a PhD with good grades and then a comfy teaching job in a comfy university, just that, and now I can't even achieve it, I'm pathetic.

>>12142142
Yeah, anything will do as long as you do a lot of exercises. It's proof-based books which need more selectivity.

>>12142140
>#
Phone poster spotted

>>12142142
The manga guides are legitimately good and I will always recommend them to anyone who can obtain one.
>>12142163
The manga guides have very little exercises, actually.
What they do have are good explanations and a lack of running text.

>>12142163
>proof based books
Wdym, pick a good proof based one? Would Velleman, How to Prove it be good?

Today I begin Munkres Topology
Thank you Axler for the very fun book
Now I am done

Also can someone remind me of the proof for the complex spectral theorem cause I gave the book to my hippie friend and told her it was "sacred geometry", so I can't check the proof
Gonna try and prove it myself too though

>>12142208
Yes, I used that one and liked it a lot. I tried Book of Proof and that other one people recommend that has a lot of pages (forgot its name), but I felt Velleman's was better, it talked about somethings that the others didn't cover or covered poorly. Reading "conjecture and proof" on the side is also good.

>tfw no math bf

>>12142343
Here

>>12141216
Proposition is common, you could also use "Claim" or "Fact" to be less formal.

>>12141302
One of the highest quality posts I've ever had the pleasure to read on 4chan.

>>12141579
A pseudohistorian. He's a crackpot who believes millenia of human history are faked.

>>12141116
start helping other people and the universe will help you

>>12139516
Unbelievably based

>>12139557
NIKOLAJ SENPAI!!!!!!!

>>12141116
After deeply analysing your post, I think I see the issue.
Stop jacking off to netorare. Netorare is the porn of losers. Netorare is the porn of a man who's fundamentally conceded that he can't satisfy a woman and needs other men to do it for him. You can't take a hold of your future, and the world passes you by.

>>12142343
Surely you mean \mathbf.

>>12142140
>classically equivalent
yeah and so nobody gives a fuck outside mainstream maths

>>12142477
huh?

>>12141116
Hahahahahahahaha How The Fuck Is This Problem Real Hahahaha Nigga Just Walk Away From The Screen Like Nigga Close Your Eyes Haha


Really though just do something else. Become something different.

I am going to marry every cute math tranny.

>>12142579
trannies ruined /mg/
>>12139446
fuck you trannies and fuck you trannyjanny

>>12142433
Man, I know it's pathetic, but I really enjoy seeing other men fucking the main character's gf in those hentais, pic related sums up my feelings about it
>>12142537
I have an internet addiction, I already accepted it, right now I should be studying for tomorrow's test and look where I am, haha, this is bad I'm totally fucked

>>12142373
Holy based...

>>12142617
Your addiction is taking the place of energy required for change (and human connection, for that matter. Hence NTR). Just stop, do something else, and therefore change into someone else.
As a side note, porn is usually not even an addiction. It's just a habit, like junk food, its comforting mediocrity. Similarly, it's not enough to deny junk food to yourself. That eventually fails. You have to change into someone who doesn't even think about shoving that shit into themselves.

>Stockholm University announces several two-year postdoctoral positions within algebra and geometry (interpreted broadly), including in particular algebraic or arithmetic geometry, topology and representation theory. More information about the positions and how to apply may be found at https://www.su.se/english/about/working-at-su/jobs?rmpage=job&rmjob=13009&rmlang=UK
>The deadline is November 1st. The starting dates are flexible.
>Successful applicants will be funded by Wushi Goldring's or Dan Petersen's Wallenberg Academy Fellowship grant.
Go for it, anon, and get yourself a cute IKEA shark!

>>12139430
Is getting math PhD worth it? I heard the pay is shit

>>12142777
Without a PhD, you're nothing in the world of math.

>>12142776
Is it highly competitive? I don't stand a chance if there's a lot of people also applying for it.

>>12142785
I don't know. I just noticed that in my email. Maybe it is, maybe it isn't. Why not give it a try? Especially if you are not 24 and braindead already.

>>12142777
I guess this would depend on what this "it" is.

>>12142779
What's the point then? Spend so much time and money to study something so hard with lots of competition and bad pay? Seems like a waste of life to me.

>>12142799
>24
Fuck, I am, just turned 24 in august, am I finished

>>12142818
Welcome to the loser club. We have cookies.

>>12142801
The pay is not bad, the problem is how long it takes and how hard it is to get there, but after a PhD you're practically guaranteed a job with decent pay.
>Seems like a waste of life to me.
What is life if not wasting time until death? At least waste your time with something you like.

>>12142826
>What is life if not wasting time until death? At least waste your time with something you like.
You're right. I just don't like how narrow and hyper focused a PhD in math is. I wish I can learn about reality in a more big pictured fashion

>>12142776
I don't speak Swedish.

>>12141554
Ok if there's no name let's call in homogenous

>>12142914
And you most likely don't have to. There's this one postdoc in my department who did his PhD in Stockholm, and he probably doesn't speak it either.

is it possible to even learn math for free? I fucked up in school years ago and have all the time in the world

>>12142996
Libgen all the text books you need

>>12142228
use the assumption that a matrix is normal in conjunction with the fact that it has an upper triangular matrix, and consider an orthonormal basis

>>12142996
Yes.

>>12142908
>narrow and hyper focused
That's what higher education in general has become. It's not exclusive to math, everything is compartmentalized nowadays.

>>12143059
>higher education in general has become
For better or for worse?

Never got an answer but kinda figured it out myself but still not what I'm looking for. Measuring how long it takes for a planet to travel 1 degree of azimuth using it's rise and setting times over the horizon gets me different numbers. For Mars, it varies anywhere from 3 to over 4 minutes. I assume the speed changes? I'm not sure how I would go about measuring or figuring out how it changes though without having to sit there and watch it for like 2 fucking days. If anyone can shed some light on this it would be much appreciated.

>>12143069
Doesn't matter, that's the only way progress can be made in modern academia, it was the only path that we could follow.

Hey, retard here. How do I change the period of this function to span exactly 24,000 while not changing the behavior of the function, like the amplitude, modulation, etc?

1/2 ((1/2 sin(x - π/2) + 0.5) (1/2 sin(x/2) + 1.5)) + 1

>>12143100
scale x

>>12142776
>Wushi Goldring
kek

>>12143059
that should be a cue to do something else
>>12143086
FALSE. if you can't progress within a system then step outside of it. any true /sci/entist knows this

>>12143107
Simply multiplying x by 24000/2 doesn't seem to do the trick as it would for a standard sinusoidal function. What am I missing?

>>12142579
Kys

>>12143114
We are progressing within a system, it's just that this system divided itself into several smaller parts, this is for every area of knowledge.

>>12143249
It didn't used to be like this.

>>12143283
Ok then, what is your suggestion? How can we move foward without hyperspecialization?

>>12141302
Piet Hein comes to mind although I'm not sure how significant his contributions to mathematics were (if he indeed made any). There's also a Soviet mathematician who painted but I can't seem to remember his name.

>>12142965
thank you, my homo genius

>>12142799
>>12142818
>24
stop demoralizing, i know PhDs at good institutions who /started/ their PhD at this age

>>12142965
>>12143433
https://www.youtube.com/watch?v=3EF5h6WJAq4&list=PL03A1BFDC75064F12&index=2

>>12143467

>>12143459
I'm 27 myself. 24 is a meme from the spring.

>>12143468
forever trash tier

>>12143467
>>12143468

i knew it had to be so

Bros... physics chads.... where were u in 92

>>12143518
The void.

>>12143524
Nice!

>>12143518
Inside my father's balls

>>12143518
physics/math chad = played tennis pretty well in high school, confirm?

>>12143588
https://youtu.be/95aCwZOX-Go

>>12143648
i hate hearing these "people" talk. shut the fukc up!!

>>12143459
most people start their PhD between 23-26 years old. it’s a forced meme from tourist retards

>>12143684
This.

>>12143669
Hello based department? Hey bud it’s for you.

https://youtu.be/grkWGeqW99c

>>12143684
>Tourist
The only tourist here is you for not knowing the 24 meme and not knowing who the anime tranny is, bet you don't even know that there's a math genius who spams touhou posts here, you need to lurk more, you just outed yourself as a newfag.

Has ANY work been done on P vs NP. Do you guys think it would be possible to reduce every NP situation to a factoring problem in some type of algebraic structure

>>12143699
Shut up, reddit.

>>12143648
Jesus this is bad.

>>12143705
>Has ANY work been done on P vs NP
No.

Sure just let me have an ivory tower.

>>12143742
Ok.

>>12143742
Hmm, well the max we can do is an Ivory dildo. If that's not enough you're gonna have to do a PHD.

>>12143727
Fucking newfags who doesn't even know the regulars here and think they can post shit without a good six months of lurking beforehand, you're the cancer of /mg/.

>>12143801
Shut the damn up anime poster

>>12143837
Case in point

>>12143891
Nigger no one cares

>>12143900
stop spamming /mg/
if you werent a newfag youd know that you cant get rid of anime posters you fucking moron
shut up and go to /sqt/ or shit up one of the lesser threads

>>12143773
Sign me up for the PhD. I wanna be a winner.

Can someone help me with my group theory homework?

>>12144040
Post it.

>>12144040
Yes

>>12144040
Sure.

>>12144040
You better not be in my class nerd. I’ll bully you on Zoom.

>>12144107
yeah same

Suppose I have and operator [math]T:D(T)\subseteq E\to E[/math] that is invertible and bounded. Then is the unique bounded extensión also at least invertible?

>>12144126
[math]D(T)[/math] dense I forgot

>>12141116
You need to get totally fucking FUCKED up drunk and high like almost kill your self you will realize how much of a loser you are and change

>>12144126
No. Pigeonhole principle, the extension isn't even injective.

>>12144126
>>12144131
>>12144137
Yea I fucked it up invertible when viewed as a function to its image which is also [math]D(T)[/math]

>>12144147
What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What? What?

>>12144152
That the image of the original densly defined operator is also equal to [math]D(T)[/math]

>>12144155
Wait, one second.
I have [math]F \subseteq E[/math] is dense.
I have [math]T: F \rightarrow F[/math] is bounded and invertible.
[math]T[/math] has an extension to [math]E[/math] with image in [math]E[/math], is that what you mean?
Like, this doesn't quite necessarily work unless you assume that [math]E[/math] is Banach or something similar, but if it is indeed Banach, the extension is trivially injective, surjective and bounded, so it has bounded inverse by the bounded inverse thoerem.

>>12144172
Yea E is at least banach, so if you say it's trivial I suppose I'm just worrying for nothing., just wanted some extra confirmation.

How do you specify what branch cut you're on, arithmatically?
When we say [math]e^{i2\pi}=e^{i4\pi}=1[/math], that's clearly false when you start using natural logs and fractional exponents.

Is there a function f(n), where n is an index for what branch you're on?
So:
[math]e^{i0\pi} = 1+f(0)[/math]
[math]e^{i2\pi} = 1+f(1)[/math]
[math]e^{i4\pi} = 1+f(2)[/math]
or similar?

>>12144256
Thinking of the winding number?

>>12144373
yes
why isn't this standard for dealing with euler's identity? why are we satisfied limiting a+ib to a single branch cut?

https://youtu.be/Do92KeSE7jE

fund my math degree peasants

DO NOT DISTURB MY CIRCLES

>>12144378
I blame topologists

>>12144378
Because wtf cares which branch you're on and differentiating between the 2nd and 7th branch?

https://youtu.be/ajztzs8Us48

https://www.scientificamerican.com/article/what-is-pi-and-how-did-it-originate/

CIRCLES

>>12144471

>>12144444
What a waste of quints

>Real Anal
>succ(x)
>group theory
>stable marriage """problem"""
what did mathematicians mean by this?

>>12139430
What do you guys think of https://web.evanchen.cc/napkin.html?

>>12144577
Sounds like a good, albeit ambitious idea. I've always thought that CollegeBoard should offer AP Algebra or Linear Algebra course that would be a good introduction for highschool students to pure math. I know a lot of the top highschools in the US offer courses in them and I'm sure the same is true of Europe.

I have to show that [math]G/Z(G)[/math] is abelian if and only if for [math]x\notin Z(G)[/math] its conjugacy class is a subset of [math]Z(G)x[/math].
I can't do it bros.

>>12144622
What have you tried if anything?

>>12144577
I'm a brainlet in an unrelated field but I liked perusing it, it's intriguing
Also I like the philosophy behind it, how writing this kind of stuff cements the knowledge in your head

>>12144633
Oh you know, just a bit of seething, another bit of coping.

>>12144577
I think it’s a pretty good intro for anybody really. If you know algebra you’re pretty set. It hits the sweet spot of being approachable for the ambitious high schooler and intrigued loser alike.

>>12144535
>NTR set theory
>Futanari conjecture
>>12144577
do you guys think evan will become a great mathematician? or will he quit into finance or CS like most middle class asian strivers?

>>12141116
You need to do some psychological exploration mate what the fuck kind of upbringing did you have? Your answer is in your past. When you feel that you need to get to work, DO IT NOW DO IT NOW DO IT NOW. It's not too late. I was there

>>12144378
>why isn't this standard for dealing with euler's identity? why are we satisfied limiting a+ib to a single branch cut?
wtf do you even mean by this? the function [math]z \mapsto e^{z}[/math] is not injective, that's all. [math]e^{n2\pi i}[/math] equals exactly [math]1[/math] for all [math]n[/math], so your function f(n) is identically zero.

>>12144622
>>12144645

Well maybe just try for real before you give up.
Like, take [math]y,x \in G \setminus Z(G) [/math]

You're curious whether or not they commute, so you check [math]xyx^{-1}y^{-1}[/math]
Well would you look at that? It looks like we just end up multiplying x by something that is in the conjugacy class of its inverse. So what happens if the conjugacy class of [math]x^{-1}[/math] is a subset of [math]Z(G)x^{-1}[/math]?
If you understand that, writing the proof is just an exercise in writing.

You need to investigate more before you give up. There was no weird trick involved or something like that. Just writing down definition and checking the commutator of two elements.

What did he mean by this? To me it seems like a non sequitur

Are there any useful ways to generalize the notion of the dimensionality of a vector space to something more flexible so that operations don't necessarily need to be constrained to being between elements of the same dimension.

>>12145490
this has nothing to do with dimension. you cannot add two elements of distinct vector spaces.

>>12143114
>>12143283
There is a very, very simple reason for this. 200 years ago, people knew less. So people who wanted to study things were able to study most things, and learn a lot of the things before reaching the frontier of what was known. This is why polymaths existed. These people could do research in a ton of areas because it didn't take them 15 years to just get to the modern day knowledge in a very very specific field.
Well now, it takes 15 years just to get to the modern day knowledge in a very very specific field. So you could spend your life learning a bunch of fields very well. Or you could do what most mathematicians and scientists do and spend your life getting a broad understanding of many fields and a very very deep understanding of one particular specific field that you really love. Or maybe 2 or 3 such fields.
This is far more productive than everyone trying to learn everything and most people failing tremendously, when they could have been contributing in particular fields.

>>12143705
Well someone very legitimate recently released a "proof" that RP = NP (RP is "find a solution with a certain chance at false positives in polynomial time") which is practically as good as P = NP. But then some grad student found a counterxample set of inputs to one of the lemmas. I don't think anyone knows yet where exactly the proof goes wrong and whether there's any hope of fixing / using it.

>>12145473
>scientific studies have shown
cool bait. link the studies.
i've figured it out by the way, it's a nice puzzle

>>12145426
What would happen if you excised [math]\pi^{-1}(N)[/math] out of [math]X_p[/math] and similarly the boundary spheres of your balls?

>>12144577
It's fine, but this is the sort of shit that convinces no-shot high schoolers that "omg math is epic and based pilled! i want to be a category theorist when i grow up!"
Chen's obsession with only expositing algebra and number theory in any detail or beauty and then using that as a vehicle to shove people into a categorical mindset could be compared to religious indoctrination. But hey, it's better than the heaping plate of shit that AP calculus or the AMC/AIME/AMO feeds high schoolers.

>>12145525
>But then some grad student found a counterxample
ref to that?

>>12145490
You could look into the notion of graded algebras I guess. I don't know.

>>12145542
Alright, I found it, and it turns out it's Yuval Peres who is apparently very much not some random grad student and is in fact a big name.
You can understand why I'd think it's some rando given that it's a fucking Facebook comment.

>>12145502
I can do whatever I want.

>>12139685
>Second class
>>Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings
If that's the second class, then wtf are you even gonna cover in the first class beyond the definition of a group, ring and field?

>>12145535
I would get isomorphisms
[math]H_n(X_p, X_{p-1}) \simeq H_n(X_p, \pi^{-1}(N)) \simeq H_n(X_p - X_{p-1}, \pi^{-1}(N) - X_{p-1}) [/math]
and
[math]H_n(\coprod D_\alpha^p, U) \simeq H_n(\coprod D_\alpha^p - S_\alpha^{p-1}, U - S_\alpha^{p-1} ) [/math] where U is the preimage of [math]\pi^{-1}(N) [/math] under the map [math]\coprod D^p_\alpha \to X_p [/math]. But I don't see how [math]H_n(\coprod D^p_\alpha, U) \simeq H_n(\coprod D^p_\alpha, S^{p-1}_\alpha) [/math]

>>12145585
I may be wrong, but I believe that U will be homotopy equivalent to the spheres. In this case, by applying the LES of the pair(s) and the five lemma, you would get the isomorphism you don't see how you would get. More precisely, you will then have ... -> iso, iso, something, iso, iso -> ... which means that this something (the map between the homology groups of pairs) is an isomorphism.

Why are all textbooks on functional analysis so fucking shit? I really like the field but fucking hell how has nobody written a good book about this stuff yet.

Does anyone have recommendations for some less well-known textbooks? Or online courses or anything?

>>12145599
>U will be homotopy equivalent to the spheres
If that is the case, then I see how'd follow. But I really don't see why that has to be the case

>>12145473
who's the cute girl

>>12145663
what's wrong with Lax? genuinely asking, haven't tried it yet, but it looks good on the surface

Any recommended topology books? I'm currently reading Engelking's General Topology and would enjoy something similar

>>12139430
>Just finished my multivariable calculus test
>I'll probably score 4~5/10
I'm finished bros

>>12145720
Munkres

>>12145694
Lax more like Laxative

>>12145723
based undergrad failure

>>12145663
Lax is good tho.

>>12145663
Just use kreyszig, then follow up with something on boring shit like pdes if you need more of that

>>12145694
It doesn't has exercises

>>12139557
What’s the discord?

>>12145760
>doing exercises in textbooks
ishygddt

>>12145771
>not doing exercises in textbooks
ishygddt

>doing anything
ishygddt

>>12145760
Are you lying or are you complaining about there being few exercises?

>>12145682
I guess you could try to argue it is the case using the convexity of your balls.

>>12145766
https://discord.gg/ezs9HA

>>12145796
The one ai grabbed from libgen didn't

>>12145822
>reading textbooks on a screen

>>12145833
>Buying from jewpringer in 2020

>>12145782
>not having dedicated problem books
ngmi

>>12145822
It doesn't have end of chapter exercises, yes, the exercises are in the middle of the chapter. Just ctrl+f "Exercise".
Were you really criticising the book based on flipping through it in two minutes? Not gonna lie, that's pretty based and /sci/-pilled of you.

>>12145909
>Not gonna lie, that's pretty based and /sci/-pilled of you.
The chartmaker way

>>12145930
Chartmaking is a cutthroat business controlled by various shilling lobbies that will make sure to piss on your hard work every time they spot it if you fail to include their various financers.

>>12145847
I remember a teacher had his office filled with yellow books. I thought he had bought them but he told me they were replicas made from the ebooks.

>>12145943
That is not only illegal but a waste of paper, just read online for fuck's sake

>>12145909
You had already posted spoiler tags no /sqt/ to no effect

>>12145950
Looking up theorems/propositions isn't the same on digital as on physical.

>>12146048
Yeah it sucks looking stuff up in a paper book because you cant just search.

>>12145995
Yes.

>>12145909
lmao you are right

>>12145942
Post a good chart
We're all friends here

>>12146195
No one has said this one is bad yet. In fact, two people have said that it's good.

>>12146320
It is good, except for Hirsch's, don't know what it's doing there. Lee's topplogical manifolds is better.

>>12146366
Lee's topological manifolds covers stuff like cobordism and smooth approximation of functions?
I am aware that Hirsch is fucking ancient, right, but I couldn't really think of anything else for differential topology.

>>12146366
>Getting filtered by Hirsch

>>12146366
wtf dude, Lee covers something totally different
>>12146382
Guillemin and Pollack is a gentle introduction, Hirsch is the real deal though

While the CR-equations are necessary conditions for complex differentiability, they aren't sufficient, right? For a complex valued function to be differentiable at a certain point, the CR equations must be satisfied at that point as well as the all the partials must exist and be continuous at that point as well. Do I have that right?

>>12146460
Close but no dice.
https://en.wikipedia.org/wiki/Looman%E2%80%93Menchoff_theorem

>>12146460
If the diff equ is fulfilled, I suppose that means the partials necessarily exist. Also, if they exist once, they also exist for higher olers in complex analysis

How do I show that [math]x\mapsto \integral_{-\infty}^x \phi(t)dt[/math] is a bump function if phi is a bumb function? Proving smoothness is easy but I can't prove compactness of support.

>>12146595
That's not true though, its support will be bounded below but not above if the function is positive.

>>12146622
Oh sorry you are right I forgot to write the condition the condition [math]\int_\mathbb{R}\phi=0[/math]

>>12146635
Ok nevermind I think i have a solution, i have psi x = 0 for all x inferior to lower bound of support of phi and I have psi x = integral phi = 0 for all x supperior to upper bound of the support of phi.

>>12146653
That's more or less the proof, well done.

>>12145663
stein and shakarchi moron

>>12146412
Guillemin and Pollack is undergradkino. It was my first experience with the juicy stuff in topology and I fell in love.

>>12146757
same

>>12146757
>kino
>juicy
>fell in love
tell me how I know you're an effeminate faggot

>>12146817
How do you know I'm an effeminate faggot?

>>12146933
No, no, he asked you to tell him, not to ask him.

>>12145560
>Yuval Peres
why do israelis love TCS and discrete math so much
>>12145720
Engelking is a sick name
>>12145847
wonder if there is a kinda chinaman on alibaba who would counterfeit GTMs

>>12145560
lmao imagine having a phd only for nigga to call you a random undergrad student

>>12147116
I have a PhD, nothing special tbqh

QUICK SOMEONE MAKE A NEW THREAD WITH A PICTURE OF A MATHEMATICIAN IN THE OP BEFORE THE USUAL DUDE CAN PUT HIS JOKE OF THE WEEK

>>12147159
I know, it was kinda funny.

>>12147274
Mate you had a picture of a mathematician and time, yet you didn't make the thread

>>12147484
Mate I'm literally range-banned from making threads.

>>12147274
Dr. Fukaya is the man.

>>12147606
>>12147606
>>12147606