/sci/ - Science & Math

>>8482942
Cute fingers.

>>8482967
Thanks!

What are you studying? What are you researching? What are you thinking about?

OP is thinking about starting K-theory to see a connection between rings and topology.

Starting exams soon so I don't have much time to do some of my own stuff but I was reading through a book on Lie groups last night.

Rather interesting for those in undergraduate studies, you can take the exponential of a matrix A in an obvious way, setting:

[math] exp(A) = \sum_{k=0}^\infty \frac{A^k}{k!} [\math]

It's rather useful, especially for solving DEs with matrices.

>>8483096
I'm studying linear algebra and it's kicking my ass. Guess I was a brainlet all along.

>>8483353

Who isn't?

>>8483353
LA is also kicking my ass
>at least I've got stats down

trying to get a handle on clifford algebras and find some applications of lifting modular forms

>>8483096
Reading on motivic integration and kinda getting my ass kicked

>>8483508
something by Hales? might find these useful
https://publicationsthomashales.wordpress.com/motivic-integration/

>>8483524
>https://publicationsthomashales.wordpress.com/motivic-integration/
Ah neat ! I'm reading this at the moment http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521149762 cause it's the only book they had on the subject at my library (that being said, it's really good) but it can't hurt to have more references at hand

In topology to prove that f:(X,T)->(Y,T') is continuous you can prove that for every open O' in T' f^-1(O') is an open of X.
Now Let's say I want to show that R^n\{0} and (R*+) x S^(n-1) are homeomorphe (where S^(n-1) is the sphere of radius 1).
for n=1
f(x,y)=xy from (R*+) x S^(0) to R\{0} is a bijection.
Now how would I show it's continuous ? Id' take the opens of R without the 0 ( ]a,b[ is a basis of all of the opens of R right ?) and then show it's an open of the topology of products where an open is open of (R*+) x open of S^(0) .
Could you show me how to this with the intervals ]a,b[. I'm lost.

>>8483564
In the first line it should be "is an open of T. " Sorry.
Also how would you do the same thing for the general case. (I've got the bijective function but I'm again blocking on how to manpulate intervals).

>>8483564
Consider an interval [math]I = ]a,b[[/math]. What is [math]f^{-1}(I)[/math] ?
Since [math]I \subset \mathbb R^*[/math], you have either [math] b < 0[/math] or [math]0 < a[/math]. In the first case, [math]f^{-1}(I) = ]-b,-a[\times \{-1\}[/math], which is open, and in the second case, [math]f^{-1}(I) = ]a,b[\times \{1\}[/math], which is also open.

>>8483580
That helps a lot thanks.
Just a question:
I know that the "reciproque" of f is :
f^-1(x)=( |x|, x / |x|) right ?
So I got how you were able to take the absolute value of an interval but the second part when it is -1 or 1 (which I know is S^(0) I don't get.

>>8483634
>>8483580
Me again I think I got it by just instead of thinking about the whole interval just taking one element of it and doing the operation and I get either 1 or -1. The interval just makes it for all of it.
And taking intervalls is the right way because they are a basis of opens for the usual topology of R right ? Because you need to show for ALL opens right ?

>>8483641
>I know that the "reciproque" of f is :
Are you french ?
>And taking intervalls is the right way because they are a basis of opens for the usual topology of R right ?
Oui, si tu prends un ouvert U de R* et (u, v) dans [math]f^{-1}(U)[/math], alors par définition il existe [math]\eta > 0[/math] tel que [math]]uv - \eta, uv + \eta[ \subset U[/math]. Alors [math]f^{-1}(]uv-\eta, uv+\eta[)[/math] est un ouvert de [math]]0,\infty[\times \{\pm 1\}[/math] par l'argument vu plus haut, contient [math](u,v)[/math] et est inclus dans [math]f^{-1}(U)[/math].
Du coup, [math]f^{-1}(U)[/math] est voisinage de tous ses points, donc est ouvert.

Just took my third exam for combinatorics, it was on graph theory.

let's be reality here guys, combinatorics > everything else.

>>8483674
Ok merci magl. J'ai enfin compris !

Should I focus on studying analysis or algebra this vacations? I can't decide which will benefit more and I find both interesting af.

>>8483454
Stats was my absolute worst math class so far

>>8483713
Why not study both then?

>>8483720
What level are you studying?
>2nd year undergrad here

What's a good progression to learn analysis to a beginner level? Baby Rudin->Papa Rudin->Rudin Functional Analysis? I'm nearing the end of Baby Rudin. I've had a course on vector spaces but I've heard that Halmos' Finite Dimensional Vector Spaces can help to prepare one for functional analysis.

>>8483720

What was bad about it for you? Taking it next year.

>>8483877
Halmos is just a pleasant writer in general, very concise and easy to understand. I haven't tried to delve into Rudin though, so I can't comment on the difference between the two.

Is ( f'(x2) / f'(x1) ) * ( f(x2) / f(x1) ) solvable if you don't know/care who f is but know its values at x1 and x2?

>>8483723
Sounds like a plan then.

>>8483096
Ok, I think there's actually a way for category theory to be useful for once.My end goal is to completely mathematically characterize topological phase transitions.

I'm currently looking at topological insulators and phase transitions, and to determining if the system has a topological phase is to look at the quantum particle statistics.
In general this can be done in two ways: the braid group (holonomy) formalism or the operator product expansion (principal bundle) formalism. However they each had their own drawbacks: firstly, it is not a priori clear how the braid group formalism can be used to determine particle statistics if the gauge symmetry is a Lie group other than U(1), while the tensor fusion categorical formalization of the OPE approach can characterize Chern-Simons actions (and therefore the particle statistics) with arbitrary semisimple Lie algebras as gauge symmetry. On the other hand, the categorical approach has only been studied on closed compact manifolds, which means that edge effects cannot be characterized in this way, while (I believe) this can be done from the braid group perspective.
Now a recent paper caught my attention (https://arxiv.org/abs/1504.02401)) that tells of a way to establish an equivalence between the holonomy and the principle bundle formalization of gauge theories. What I'm hoping is that this would serve exactly as the bridge that I'm looking for. If the author establishes this equivalence in a constructive manner I may be able to transfer the structure that I need from the OPE/categorical approach in order to capture non-Abelian statistics into the braid group formalism.

If all of this works out (it probably won't) you can expect a publication and maybe a Nobel.

>>8483993
You are right, it won't work out.

I am currently tackling Hilbert spaces. I have an exam soon and we only got a shitty hand out which is not very helpful in explaining the steps

>intermidiate stats
>allowed 1 note sheet for exams
>got 100% on first 5 exams
>forgot calculator and notes on counter at home for 6th exams
>67%
Is this what brainless feel like when they have their notes?

>>8484084
>Taking any stats at all
>having to use a calculator
You're already a brainlet m8.

>>8483993
>unironically appraising your own work as nobel-worthy
the level of delusion is unreal

>>8484162
the ability to do mental arithmetic is no reflection on the ability to understand and apply concepts to real world problems

>>8484183
You didn't even understand. I'm not talking about your ability to do stupid mental calculations, but the need to use a calculator at uni for fucks sakes.
Are you still in high school ?
I've never had to use a calculator once at uni.

>>8484216
good for you
>I'm in university
>still using a calculator
What's your point? I prefer not to do stuff in my head. Greater chance of error

>>8484227
The point is if you have to calculate stuff for your exams you're likely not to do any real maths.
By that I mean actually using concepts and ideas instead of doing stupid calculations.

>>8484243
In stats (and numerical methods) you're very much applying concepts and calculating...

>have you ever seen a stats paper?

>>8484266
This is why I said
>Taking any stats at all
It shows you're a brainlet.

>>8484166
>autist can't detect obvious joke

>>8484269
im out
>this guy
>must be trollin me

>>8484216
>my courses are the exact same as everyone else's
Some courses emphasize computation where it's only reasonable to use a calculator. Fuck off with your stupid attitude.

>>8484291
>>8484285
What's you school m8.
Doubt it's a good one.

>>8484295
It's in the top 20 for math. So yeah, fuck off now pls.

>>8484300
>top 20.
this is the new meme.
Next year it'll be
>top 200

>>8484300
Lol bunch fuckin dorks arguing over who beter at putting numbers together. Here's a helpful hint faggots...when you can sell a ketchup Popsicle to a dumb bitch in white gloves all you'll need to put your numbers together is commas

Basic question. I do not understand some of the assertions here. How is CAB acute? I also do not understand how this proves that 3 and 4 are acute, given that they are congruent with right angle triangles.

I just started working through a calculus textbook despite having dropped maths in yr 10 and not having any formal mathematical education in 3 years. I'm having a lot of fun and I'm excited for gaining new knowledge.

>>8483993
>Ok, I think there's actually a way for category theory to be useful
>for once
nice try m8e

>>8483508
Lou van den Dries has some good notes on motivic integration if you haven't already looked at them.

>yfw geometers have a proof for the Riemann hypothesis for varieties over finite fields
>yfw number theorists still don't have a proof of the Riemann hypothesis for the zeta function

Any geometry overlord here? Can you give me some tips to git gud at it?

>>8485126
Ah I didn't know about these, very nice, thanks !

>>8483720

stats was and never will be math

>>8485624
What kind of geometry?

>>8483096
Catching up on machine learning papers before getting back to topos theory. I'm going to go through the DNC and GGS papers. After that, I'll go through some of the OpenAI papers, then it's back to Kostecki's Intro to Topos Theory.

>>8483473
What books are you using? I found particularly using the one written by Porteous

How do I get better at math when I have no one to ask questions?

>>8486056
Ask questions here

>>8486083
I'm in calc 1 and a retard so I would just waste time and people would shitpost at me

>>8486092
what about other people on your course or whoever is teaching you?

>>8484809
CAB is acute because it's the constructed situation. It is a fact. Note that the figure does not match that (AB should be sloped to intersect BD). Then, the indirect method is used to prove that the assumption that AB||BD leads to a contradiction, and is thus false. Obviously, under the parallel postulate, CAB is acute xor AB is parallel to BD.
My best guess at the hidden parallel postulate is concluding that FE=GH=BA due to parallel lines.
It can also be shown under the assumption that CAB is also a right angle, which is a contradiction.

>>8485771
square area

>>8486056
>>8486092
Post in SQT or here. No one cares if you are dumb since we are all dumb at some level of mathematics.

>>8483353
It's a good way to start.

>>8483508
Getting your ass kicked by math every now and then is a good thing as it forces you to study the things properly.

>>8483993
Let's hope it works. What would be the physical implications if it did, or would it be to reformalize the stuff?

>>8485794
Nice. Is it going well?

>>8485899
learning clifford algebras in the world of quadratic forms, so the book by Lam (intro to quadratic forms over fields)

i'll take a peek in Porteous though, thanks

>>8486168
thankyou my man

>>8483342
by DEs, you mean the encryption?

I have been working through this shit in my free time this semester. https://www.msri.org/summer_schools/419


Currently learning about quotient stacks.

>>8485703
What kind of stat class did you take? Its built up from measure theory, probability theory, analysis, calculus and linear algebra. I dont like it either but it sure as fuck is mathematics.

I love these threads by the way, fellow math nerds.

>>8486679
differential equations

Dunno if I should become a physicist or a pure mathematician, which one brings more flexibility?
I want to finish my bachelor/master and work in whatever I feel like without to much restriction.

>>8486956
What do you like in math? What do you like in physics?

>>8486056
Ask in MSE, seriuosly. Those guys always answer my questions no matter how stupid they are.

>>8485771
>What kind of geometry?
Analytical geometry.

preparing for my second midterm in calc 3

not sure how important this will be to me as a CS major, but i love it

CS or Engineering?
I'm a junior in hs. 4.1
I've taken AP CS at my school
and approx 7 other AP courses.
Taking AP Calculus.

>no question thread in catalog

How do I write the negation of this statement? Do I just negate the red part, or do I have to do something to the blue bit? We were only taught how to negate very simple p, q statements and I honestly have no idea where to start with this.

>>8488007

>>8488055
Are you retarded? Switch the universal quantifier to an existential one and the existential one to a universal one

>>8488064
>Are you retarded?

Quite possibly. ty anon

In highschool atm. Going to Geneva's university in 2 years in the the physics degree

>>8482942
Exploring possible graph theoretic ways to model Sokoban and other "grid-based" games.

Has anyone tried this approach before? Any papers I could check out?

>>8488088
I feel like I have seen something on Sokoban before. I will check.

Another grid game I know of that is solvable using math is "lights out".

>>8488064
>>8488068
And you also have to negate the if,then statement

Currently doing Linear Models in R with the package Swirl() !!!!!!!!

>>8482942

not having a gf

Going to teach myself a course's worth of statistics. So far managed to get A's on exams by cramming through, but taking time series next semester so I should probably actually learn the prerequisite material instead of bullshitting the grade. Statistics is such an interesting field, but also such a fucking slog to actually get through.

>>8486439
>What would be the physical implications if it did, or would it be to reformalize the stuff?
The point is to completely mathematically characterize particle statistics, which can provide a theoretical origin for topological phases, including all quantum Hall (integer and fractional) phenomena.

>>8483723

The historical record disagrees with you. Mathematicians not exclusively doing statistics, astronomy or accounting is a recent trend. Maybe 50 years old. You've been lied to. Even today, *with* the growing trend of linguistic mathematics, most mathematicians still do statistics or statistics related work.

I'm studying the basics of modular arithmetic. I have a lot of work to do.

Haven't touched math/physics in ages and have an exercise to first calculate the total braking distance in meters, given the speed, traction and reaction time and then calculate the speed again, using said distance, traction and reaction time.

Basically given the speed of 100km/h, traction of 0,7 and reaction time of 1 it would be 83.9598760937531m and then given the distance of 83.9598760937531m, traction of 0,7 and reaction time of 1 I need to calculate the speed again, which would be 100km/h in this case.

I'm using v*r-t+v^2/(2tg) to get said distance in meters (converting km/h to m/s before, of course) but I'm having trouble coming up with a way to get the speed again.
I know that normally it would just be the square root of distance*2tg but how do I get the speed if I calculated it with that speed*reaction-time at the beginning?

Any college faculty on here or am I the only one?

>tfw you get cucked out of teaching discrete math in the spring

wtf
https://en.wikipedia.org/wiki/Zeta_function_universality

What's up, folks?

>>8490595

>>8482942
https://en.wikipedia.org/wiki/Knaster%E2%80%93Tarski_theorem

Learning theoretical CS with prof, for use in FOL in finite domains

I made it past all the code monkey shit I think I finally made it FeelsGoodMan

>go to a great school for math
>fuck around and get Cs and Bs
>kinda sorta want to get back into math to eventually teach at community college
fugg

>>8490235
If you're a woman just say its sexism and they'll re-appoint you. That's what happened with some Professor at my college. Worked out great.

My college is the "most diverse campus in America," so they've got to prevent sexism like reassigning a teacher.

>>8491526
>>8490235
url related

https://www.change.org/p/robert-l-barchi-stop-sexism-at-rutgers

How do I make the Laplace transformation of x2y''+xy'+y=e^x ?

Can anyone recommend a book on statistical inference that has a very theoretical approach? The course I'm currently taking is pretty practical and I'd like to know how the methods we use are constructed and their usefulness justified.

>>8483096
I'm studying differential geometry

I'm in my second year of mathematics undergrad and I'm thinking about dropping 100 euros on math books to read and work through in my spare time. Any suggestions?

>>8492385

Just use libgen. Use the money to spend on an ebook/pdf reader the size of a book instead. Or just use it on pens and paper which you will need if you want to be decent at math.

>>8492457
>Or just use it on pens and paper which you will need if you want to be decent at math.
This is truth. At the rate I am going through pens and paper youd think I was eating them.

Is it OK to ask for a reference here?

I'm working with a family of elliptic curves over finite fields and I have a conjecture about the number of points it has. I've tried searching the literature for some hints on how to prove this, and found that the curve is what's called a 'supersingular elliptic curve'.

Now, I'm a math brainlet and the definition of that term is beyond my current abilities, but there are some related theorems that seem to imply that the number of points on such a curve over Z_p is p + 1.

Unfortunately, the device which I read this on has broken down and I haven't written down the name of the book. There's a related question on MO, but they don't provide any sources either: https://mathoverflow.net/q/1269

Does anybody know about some resources, lecture notes, textbooks, where I could find more on this in a comprehensible manner?

>>8492499
>I'm working with a family of elliptic curves over finite fields and I have a conjecture about the number of points it has. I've tried searching the literature for some hints on how to prove this, and found that the curve is what's called a 'supersingular elliptic curve'.
Do you mean every curve in the family is supersingular or just one in particular?

>Now, I'm a math brainlet and the definition of that term is beyond my current abilities
it basically just means there's a (relatively) large amount of maps from the elliptic curve to itself

>Does anybody know about some resources, lecture notes, textbooks, where I could find more on this in a comprehensible manner?
this is an exercise in silverman's 'arithmetic of elliptic curves' and is also proved in husemoller's 'elliptic curves'

>>8492512
>Do you mean every curve in the family is supersingular or just one in particular?
Each and every one.

>this is an exercise in silverman's 'arithmetic of elliptic curves' and is also proved in husemoller's 'elliptic curves'
Thanks, family. I'll take a look at those. I think the former is the one I was reading. I'm not big on automorphism groups etc. so it was a bit over my head.

>>8492523
here's one last reference which goes pretty cleanly (the result you want is corollary 4.32 on p131) is Washington's Elliptic Curves, Number Theory and Cryptography. (you can find this on google/libgen easily)

>>8492523
i meant endomorphisms not necessarily automorphisms

over C most elliptic curves E just have the endomorphisms where you send every point (x,y) to some multiple [N](x,y)=(x,y)+(x,y)+... (N times) , so End(E)=Z

but some like y^2=x^3-x have extra endomorphims like where you send (x,y) to (-x,iy) (and so you say these have 'complex multiplication')

>>8492528
Thanks again. This is precisely what I was looking for.

The theory looks pretty interesting, too. I might dive more into this after the semester's over.

>>8492528
Your comments about complex elliptic curves are mostly wrong. Elliptic curves have tons of endomorphisms and, in fact, automorphisms: clearly translation by a point gives and automorphism and so the group of automorphisms contains the elliptic curve itself as a subgroup. Curves of genus 0 and 1 both have uncountably many automorphisms, it's the higher genus curves that only have finitely many (in fact at most 84*(g-1) many by a theorem of Hurwitz).

>>8492540
you're talking about analytic endomorphisms

in the arithmetic or even algebraic point of view you want to preserve the group structure, especially the distinguished point which serves as the identity on the elliptic curve (such maps are called isogenies), and so translation by a point is not considered an endomorphism

I literally know shit about math, save that it was the only thing I used to enjoy before I droped out of hs, and wasted 5 years being a NEET. am planning to enroll in a math course at my uni. but will I be able to succeed, if I'm motivated enough ofc?

What's the best way to prepare, get the basics down? & can I understand and study the more deeper and complex theorems on my own?

At an impasse m8s.

I am about to finish linear algebra and while my grades are fine, I realized I am no good at writing proofs. I'm good at computations and really enjoy problem solving. Should I study applied maths or probability/statistics?

I was also even considering just dropping maths and going pure chemistry for the problem solving aspect, but I fucking hate labs. What do I do? I want to solve problems.

>>8492548
Ah sure, but then maybe it would've been better if you indeed said "isogenies"...

>>8492558

Which math course? I took my first math class, precalculus, at 24 years old since i was 16. I got an A and a year later, I'm about to finish up Multivariable calculus in a couple weeks (been getting pretty good grades).

It's fun and I really enjoy it. I'm sure you can do it anon. If a brainlet like me can, you can. Work HARD. Read the chapter, go to ALL lectures, do ALL the homework and do extra problems to prepare for exams and you'll be okay. If you don't understand something, don't be afraid to go to office hours and find out.

>>8492568
endomorphism is standard terminology
https://en.wikipedia.org/wiki/Endomorphism_ring
https://en.wikipedia.org/wiki/Complex_multiplication
>In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers

isogeny is just more specific for when you speak of algebraic groups

>>8492570
It's the european system, so it's just "math", you specialize later. So I'm guessing precalc first, but really fast I heard so I want to prepare on my own a bit.

And thanks mate, glad to hear you found your passion. Your story gives me hope. ( I always have this feeling that I'm either too old or stupid to begin at my age) Cheers

>>8482942
Sad that no one ever upload a collection of problems set for a diversity of math course from different universities. For someone that is learning mathematics on my own, this would really help. Now I'm downloading some from some top tier universities.

>>8483096
>OP is thinking about starting K-theory to see a connection between rings and topology.
Start then with cohomology rings m8.

>>8485610
What do you mean by "Riemann hypothesis for varieties over finite fields"?
Mordell conjecture?

>>8492614
Weil conjectures, probably

>>8492614
what this guy said
>>8492624

specifically (3) here
https://en.wikipedia.org/wiki/Weil_conjectures#Statement_of_the_Weil_conjectures

>tfw Weyl != Weil
?? explain?!?!?

>>8492721
Weyl = German physicist
Weil = French mathematician

What kinds of maths do I need to know for math graduate school? My major requires the basic stuff like Real Analysis and Abstract Algebra, but then I have to choose 13 upper division math classes and it can be anything I want. What should I take? What do grad schools care about? What is the most "open" field to do research? I'm a sophmore pure math major, just finished Multi-variable, Linear Algebra and my "Mathematical Reasoning" class. Now I have to start taking upper div math.

>>8490595
neat.

>>8492923
the approximation itself is surprising enough
and then the density of approximations just makes it weirder

>>8492873
if you want a job when you finish the following:
pde
numerical analysis
linear programming
probability
statistics

try to be a good numerical matlab code
over the summers learn algorithms and advanced data structures or take the cs courses

try not to look like these people

I've decided to pursue a math minor and will start upper division math in spring quarter. I haven't had too much experience with proofs, though. Is there any resources I could use to practice proofs over my winter break?

>>8492968
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/index.htm

>>8493001
Thanks!

>>8492457
libgen?

>>8492598
>Sad that no one ever upload a collection of problems set for a diversity of math course from different universities. For someone that is learning mathematics on my own, this would really help

well looks like you answered your own question
>download from some top tier universities

What are you guys's thoughts on proof by contradiction?

I can live with it, but it always leaves me with a slightly dirty feeling because there's no real essence to it by itself. It always seems like "taking the easy way out".

how to get job with applied math MS

>>8493442
http://gen.lib.rus.ec/

>>8493455
Go into banks

>>8493449
It's not "taking the easy way out". It's valid under classical logic. There is additional merit in doing a constructive proof, but it's not like you have failed to actually prove something by using contradiction.

Are there any connections between elliptic curves and matrices?

>>8493443
Well a collection of said set papers in a single place to download is better than searching in every university site.

>>8494770
theres a strong connection between rational elliptic curves and 2x2 integer matrices with determinant 1:
https://en.wikipedia.org/wiki/Modularity_theorem

basically a certain function associated to an elliptic curve, defined using data about how many points the curve has over finite fields, turns out to satisfy a nice modularity relation
[math] f(\frac{az+b}{cz+d})=(cz+d)^2f(z) [/math] whenever [math] \begin{bmatrix} a & b \\ c & d \end{bmatrix} \in SL_2(\mathbb{Z}) [/math]

>>8494847
Thanks, that's interesting. I've known about the proofs of Wiles and the other guys, but didn't know about this connection to linear algebra.

Can some of you niggers explain stochastic processes adapted to the natural filtration to me?

>>8489649
That sounds nice. The best of luck with that!

>>8492612
I know how to get a cohomology ring out of a space, but suppose I could get a ring out of an abelian category using tricks I have (at least independently) developed. I'd like to connect this to homotopy groups, which I believe to be possibly possible, due to the microcosm principle and, in particular, the similarity of homotopy of continuous maps and natural transformations of functors between abelian categories.

Any interesting topics in cryptography? Even just simple combinatorics would be neat.

>>8496255
elliptic curve cryptography, and the supersingular isogeny Diffie–Hellman key exchange which is meant to prevent future quantum computers from making it vulnerable

>>8496259
Anything relatively more obscure? Those things are relatively well heard of.

calc II for college rn (lmao) but when I've got free time next I want to work through Concrete Mathematics, anyone have thoughts on that?

>>8496273
If computer science is your goal, that sounds fine.

Hi, sorry for not having a refined mathematical language, I don't know much of it. I just want indication of what to study to learn something of it.

Suppose I have 100 shirts. Suppose I say to you they are made of half white and half black cloth and with that information you were to imagine how they look like.

Perhaps 50 shirts are pure black and 50 pure white. Perhaps every one of the 100 shirts have a white top and black bottom or vice-versa, or one side and the other 50-50. Or perhaps all white and black thread is mixed before production and so the shirt end up looking grey, but made of 50% white and black thread. Or even, I could have a combo of them, like 10 whites, 10 blacks, 20 grey mixed thread shirts, 30 shirts with bottom white and top black, 30 shirts with left black and right white, etc. Nevertheless, it is "balanced", 50% is black cloth and 50% is white cloth.

What kind of mathematical problem is this? Where can I read more about it?

>>8496323
I don't see the "problem" part of it.

>>8496342
Ok, say your costumers want variety and you want a good outcome for your sales.

If you make 50 whites and 50 blacks, they will see you have only 2 types of cloth and of shirt. If you arrange the individual threads arbitrarily, you'll end up with 100 different shirts, but they will all look most likely greyish, of the same type.

You must work with alternative strategies.

Perhaps it is most efficient if you can split up into pairs: (top white/bottom black) & (top black/bottom white) is one pair. (left w/right b) & (left b/right w) is another pair, etc. Having 50 logical settings, with white and black alternating, creating 100 designs. On more complicated approach, a shirt can have 4 squares, two w, two b, and its pair will be the same but with inverse colors. Then there can be different numbers of stripes. Except if I just use the design of the stripes, the shirts will be too similar. So then, how can I discover more and more possible pairs coming from the simplest problem? I guess my question is: is there a way to calculate, not only how many ways there is to match black and white, but how to vary the way they vary?

>>8496370
> I guess my question is: is there a way to calculate, not only how many ways there is to match black and white, but how to vary the way they vary?
"Combinatorics" is the field of math if you were wondering.

>>8493449
imo there's nothing wrong with it.

>>8493449

The proof method that has no real essence to it by itself is induction.

>>8493449
>>8496870
I agree with this. Contradiction proofs will usually (not always) give you a good feeling about why the theorem has to be true, because they show you what goes wrong if it were false.

Induction is "write out case n and n+1 and then fiddle around with the expressions until they just werk".
It's rare for an inductive proof to help you actually understand the theorem.

Anyone have a suggestion for a reading course?

I'm a 2nd year undergrad and my interests are leaning toward algebra / geometry / topology.

My background is basically all of your standard undergraduate math - group/ring/field theory, real analysis on metric spaces, basic point-set topology (compactness, connectedness, etc.)

What are the best universities in Ontario for an undergrad in Math?

>>8486795
What fun stats are you doing? Maximum likelihood can be defined in terms of measure theory but no stats class i've seen would ever touch that. It mostly seems to be made for brainlets in sciences who need it for research. It mostly seems to be centered around methodologies and formulas instead of proofs, which is why its not math.

>>8492385
Others are suggesting libgen which I agree with if you absolutely need some shitty book for some course otherwise I really recommend buying books. Its a different feeling actually owning the book and being able to flip through it at anytime. Best books I owned in my second year were Probability and Martingales by David Williams and Rudins analysis book. Depends on what your courses you're doing though. If you haven't done abstract algebra and linear algebra yet I highly recommend Algebra & Geometry by Beardon, probably my best book desu.

So im at a shithole school and scored 46% on the subject GRE. Should I kill myself now or wait until the good schools reject me first?

>>8497090
Knot theory, functional analysis, algebraic topology or geometry.

>>8493449
feel the same with induction desu. Theres little acknowledgement of how the formula was chosen in the first place, just that it works.
I don't feel like I'm getting to the essence of the problem.

>>8493449
Theyre better than super tight, terse proofs which dont explain much the direction and necessity of its argument.

>>8492873
Depends on your emphases. I took combinatorics, differential geom., fourier analysis and complex analysis for mine and i feel they were good picks for pure math

>>8492873
>algebra
>analysis
>basic stuff

M8, come on now

>>8492564
Honestly just erite more. I thought i was bad at proofs in linear algebra. Next quarter i took abstract algebra with some old chinese woman who does number theory, and she assigned 5-10 hard proofs per week. It was the hardest class i have ever taken. But i came out a much better proofs-writer as a result.

>>8492558
I dropped out of uni, went homeless for a few years, then got a shittt job and went back. Im in my senior year taking grad classes now.

My answer is it depends. You will be slower than the 20 year olds. But its still very possible tp learn. Youll need alot more discipline than youve ever had before in your life. And you also have to not be a retard.

>>8496152
And it seems what I described has already been done in a slightly different way, the so called Q-construction. Instead of those projective modules I would be using rings to construct a group, and this would most likely lead to a different space eventually. Do you think I should go on with this?

Anyone that uses s or z as a variable should be shot in the head. That shit will look like a 5 or a 2 if you ever have to handwrite it.

>>8489046
>tfw tall white math major
>have asian and white fwb
>both smart but not mathy
>mfw the white girl asks for explanations of basic math shit becausr they think its sexy when i explain math
>tfw the asian girl just likes blowing me

Life is good

>>8497172
Thats why z is always handwritten with a line in the middle.

>>8483353
It's your first exposure, it's supposed to be hard.

>>8497107
Toronto.
Waterloo is a bit of a meme school but also good. Just don't expect to not want to kill yourself.

Ottawa isn't too bad either

>>8497135
How approachable is AT as an undergrad? Any recommended texts?

>>8497264
Very approachable using Rotman's book.

>>8497264
Hatcher, it's sufficiently handwavy to give you a feel for what's going on but it also goes pretty deep into everything. Overall, a good read, though I know some people here don't like it (because of its handwavy quality)

>>8497264
SPANIER
P
A
N
I
E
R

>>8497264
a nice 80 page intro with lots of pictures, examples, exercises and solutions

What jobs can I get if go to grad school for Math?

>>8497600
>wanting to work
>not wanting to play with numbers all day

Savages

Can someone give me some intuiion on why some integrals can't be analytically determined? even simple stuff like e^(x2)...

>>8497825
their hard

>>8497220
>Ottawa
who told you that?

>>8496898
>induction proofs rarely help you understand the theorem
I would have to disagree. Inductive proofs almsot always illustrate the connection between the nth case and the (n-1)th. This is very useful insight, especially for constructive purposes.

>>8497825
Antidifferentiation is a much trickier business than differentiation. The latter has a formal definition to work with, which lets you derive basic derivatives, as well as several theorems that tell you what to do when these basic functions are combined in different ways (e.g. Product Rule, Chain Rule).

The former mostly relies on fitting a function to a specific form, then working backwards using a theorem for derivatives (e.g. Substitution working backwards through the Chain Rule). There are no real equivalents to say the Product Rule for antiderivatives (i.e. no obvious relationship between [math]\int f(x)dx[/math], [math]\int g(x)dx[/math], and [math]\int f(x)g(x)dx[/math]). So any function that doesn't fit one of several specific forms (i.e. [math]e^{x^2}[/math]) cannot be antidifferentiated in a satisfactory way.

Let's say I have a continuous bijection [math]f:X \rightarrow Y[/math] between two topological spaces. Obviously [math]f^{-1}[/math] exists and is bijective, but is it ever not continuous?

Just starting reading about manifolds, and in the definition of charts, the author calls them continuous bijections (onto their corresponding open set) with continuous inverses.

>>8498724
> Obviously f−1 exists and is bijective, but is it ever not continuous?
yes
https://en.wikipedia.org/wiki/Homeomorphism#Notes

>>8498724
Homeomorphisms have continuous inverses by definition. It is possible to have a 1-way continuous map. In fact it's trivial to show.

>>8497551
>EMS book on Algebraic Topology
>Not based Tammo tom Dieck

ishiggydiggy

>>8498967
>In fact it's trivial to show.
kys

>>8499079
>>8499079
no

Writing a thesis on absorption phenomena in quantum walks. The mathematics involved are not too difficult, but the pictures that I've generated are pretty interesting.

https://www.youtube.com/watch?v=XXOCAsIo3Bk
https://www.youtube.com/watch?v=8LgJMeWhJDA
https://www.youtube.com/watch?v=8N9Kumolkks
https://www.youtube.com/watch?v=_Qev2BPnLcQ
https://www.youtube.com/watch?v=2zCTZ-3CUaE

>>8498724
>but is it ever not continuous?

Yes. The typical example is polar coordinates.

>>8499295
cool af desu

>>8499295
Pretty!

>>8499926
>>8500186
seriously there is a lot of low hanging fruit in the field I would recommend it

I am a freshman in nuclear engineering and am thinking about doing a math minor. Is there any point to doing so? At this point the only reason I am thinking about it is that I enjoy math and so far every class I have taken (In calc 3 rn) has been easy.

>>8500358
Do it, knowing math is never a negative thing in life. Though since you can't take actually interesting math courses, stick to applied shit like probability.

>>8497130
Thank you, this was the kind of answer I was looking for. That book about martingales really sounds interesting.

Okay, so I won a prize of 40€ to spend on books and I'm undecided, so tell me what you think of the ones I've found so far (in no particular order):

- Functional Analysis by Rudin Walter
- Theory of Analytic Functions by A. Markushevich
- Modern Geometry, by
B.A. Dubrovin; A.T. Fomenko; S.P. Nokikov
- Numerical Optimization:
Theoretical and Practical Aspects by J. Frederic Bonnans, J. Charles Gilbert, Claude Lemarechal, Claudia A. Sagastizabal

Geometry is my favorite topic, but I've always heard good things about Rudin and Functional Analysis seems cool. Theory of Analytic Functions is a 1140 page behemoth, so it could go either really good or really bad (I liked complex analysis though), and Numerical Methods are the shit.

I have to buy them in one of two stores, so I don't have many options. What do?

Anti-derivatives,
MacLaurian, Big O,

>>8500448
If you're a dunce then Kreyszig is the best functional analysis book of all time.

(I ask this every few months, whenever I visit /sci/)

Who /topos/ here?

>>8496262
Post-quantum cryptography?

https://pqcrypto.org/

gettin' pussy

>>8501755
Top left corner, that guy is cute!

After some reconsiderations and altered definitions, I now have abelian categories that can be essentially embedded in a module category, but need not be small. Sadly, this is not the general case, either, but would generalize Mitchell's work a bit, and maybe allow constructing a local alternative to a category's classifying space.

I have a question for the guys that do lots of Category Theory:

Are you just that fucking pro or is the field basically up for grabs?

>>8502521
I don't consider myself a pro, but I have a firm grasp of (lower) category theory. The trick I use is to simplify stuff. I pretend categories are groups and functors are homomorphisms, and act upon this simplification. This makes things easier to think about, and then the ideas acquired like this are the ones I recheck in a category theoretical sense by adding the forgotten details, what ever they might be.

Similarly, I borrow ideas from homotopy theory while operating with abelian categories. I just say the categories are spaces and functors are continuous maps, which leads to the idea of natural transformations being homotopies. Then, adding the details dropped by my forgetful thought functor, I recheck my stuff to see if it works in a categorical context. So far this has worked.

I can't say if this works for higher category theory, though. I have barely any experience of that. Nevertheless, I'd say you need not be a genius to do category theory.

>>8502521
Quite possibly the dumbest question I've ever heard and I just had my office hours today.

>>8482942
I'm reading "Love and Math" by Edward Frankel. Also studying graph theory on the side for fun.

>>8497264
Learn odes and pdes first

>>8503178

You could at least tell me why it's a stupid question. I'm not denying it, I just want to know.

>>8483096
Just started reading "An Introduction to Modern Astrophysics". Shit's dope.

In a couple of days I present my final of multivariable calculus. Wish me luck anons.

>>8503930
Good luck!

>>8483096
>What are you studying?
Electrical/Network engineering, and it fucking sucks.

>What are you researching?
"Researching" is a big word, but I'm trying to self-learn some analysis (2nd year level here in France). Some concepts I already know, other I discover.

>What are you thinking about?
Engineering school is where all my friends are, is a guaranteed job with a decent salary at the end and my parents are proud of me.

Doing maths, physics, or even applied maths/physics now/after would be almost impossible due to our school system and the only safe job available would be teacher. Even if I do, it would be in the equivalent of a community college when I had the option of trying to get a much better school if I decided myself earlier.

My parents are both teachers and I know it's one of the hardest jobs in the world.

Did I fugged up ?

http://computo.fismat.umich.mx/~fhernandez/Cursos/Calculo2015/spivak.pdf

Is this a good calculus book? I already know a fair bit of calculus but want to learn it more rigorously.

>>8505372
Spivak is /the/ intro to calculus book.

If you're looking to do it more rigorously, I'd say skip it and start doing some real analysis.

>>8505437
What would be a good starting point for real analysis?

>>8505355
>2nd year level
>engineering school in france
fuckin trash
your parents must be disappointed.
But they're subhumans too anyway.

>>8505443
It depends what your background is/what you're looking for.

Abbott's Understanding Analysis is pretty solid all around. Afterwards I'd recommend working your way through baby Rudin for a more serious treatment.

>>8505453
That is not very nice. I'm only in the 3rd year of the school by the way.

I am working on the creation of music based on concepts from mathematics. If you've never listened to noise music or glitch before you probably won't like it, but it might be something new and unique to listen to:

https://ddx-10.bandcamp.com/album/spv-laboratories-vol-2
https://www.youtube.com/watch?v=dqeM0x6AWgg&t=1233s

Trigonometry beginner here, part of a larger exercise I'm doing is simplifying cosx+sqrt(3)sinx. WolframAlpha tell me I can get it to 2sin(x+pi/6) but I can't for my life figure out how.

>What are you guys up to?
Solving exercises.

>>8506303
Ok, going about it the other way around sin(x+y) = sinxcosy+sinycosx and with knowledge that cos(pi/6) = sqrt(3)/2 kinda solved it for me. But it feels really unintuitive to me, does that ever change or am I doomed to be forever stupid?

>>8506303
>>8506308
cos(x)+sqrt(3)sin(x)=2((1/2)cos(x)+(sqrt(3)/2)sin(x))=2(sin(pi/6)cos(x)+sin(x)cos(pi/6))=2sin(x+pi/6)

>>8503517
>>8503930
Good luck with those!

>>8505355
Does it cost you to go to school? If not, then you can just study for fun. If you are going to be in debt after studying, then you must consider the employment. Do you like what you are doing?

>>8506276
This is pretty cool! You aren't the same anon who used hydrogen atoms and their energy states to produce music, are you? I can't remember the name of his project, but it sounded nice.

Do you guys know if anyone has ever made a concept analogous to manifolds but for abelian categories?

>>8506276
What are you using? Matlab? Have you tried SuperCollider? I've tried to make some music inspired by math but I just lack the motivation.

There's also this brazilian composer who makes chamber music based on math concepts. You can listen to it on spotify, Guilherme Carvalho - Topologie Faible.

>>8506349
No I'm not that guy but that sounds pretty interesting

>>8506451
Using MATLAB but I am planning on branching out to other software. I'll check out that composer thanks

>>8506349
>Does it cost you to go to school?
Not much, about 1000USD/year.

>Do you like what you are doing?
Depends, really. Some parts are fun, others are just boring.

>>8499295
What sort of background would one need to look into this type of stuff?

>>8505355
What about getting your engineer degree and then going to "la fac" and getting a masters in pure maths or physics ? Then doing a thesis.
Or you could also directly go into a phd program after you engineer degree.

>>8506928
>Or you could also directly go into a phd program after you engineer degree.
This is what I'm planning to do, but my teacher said that the "gap" between people having done pure math and us is too wide.

I suppose I will have to read some books.

>>8506942
There's no doubt you won't be able to do pure maths with an electrical engineering background. I meant a phd in your field.
Otherwise you have to start again a la fac. Don't know if you'd have to start from une L3 or not though.

>>8483353
Same here man, just can't visualize it like other math

>>8506945
We have a master equivalent.

>>8506956
I'm french I know ^^.
I'm not sure you'd be accepted into a pure maths program though.

>>8506960
A dieu vat, alors.
In the meantime I'm just reading a bit about analysis/algebra. Tons of nice books about it.

>>8506276
>https://ddx-10.bandcamp.com/album/spv-laboratories-vol-2
From what I've heard this is very decent, though way too long for its own good (the first track could probably be 10 minutes, considering it's almost the same sound all the way through).

The YouTube album seems more interesting (though I only heard some segments). But it's too sparse, seems like it has long stretches of near silence.

Anyway I like your work

Little funny problem for you

Calculate 3.3636.. * 0.297297... only using series.

Guys I have a fuck ton of Springer Textbook pdfs. Anyone want one

>>8507126
Can you hand over the ones about graph theory ? Seems interesting.

>>8507126
MEGA FILE ALL OF THEM PLZ

>>8507126
Interestingly enough springer stupidly "gave" away a shit ton of there books for free by way of pdf a while ago accidentally.

Here you go >>8507130


https://expirebox.com/download/b3006fe69288e3f0964d68aeac57e0e6.html

need a min to upload the other one.

>>8507132
My connection is kinda slow with uploads and I don't really want all that progress to be destroied via copyright fuck you's.

Here you go >>8507130

https://expirebox.com/download/204661a71f4074170c85151708e8d6ba.html

>>8507141
>>8507166
Thanks. I think you should just keep them in store and propose them when needed

Care to give the Alen Brown, Carl Pearcy - An Intoduction to A... (suppose it's algebra) ?

Here >>8507169

https://expirebox.com/download/ebd287651f34e9c81ffc9a7db27429d0.html

Also here is a list of all the books:
https://expirebox.com/download/984532c187071912c49909e25531c69e.html

Also I attached a list of books for people to see what they want.

What kind of jobs can I geg with a BSc in Mathematics?

>>8506276
>mfw people think their music is good just because they infused math into it
>mfw Bartok thinks he's some supreme memelord for incorporating the golden ratio in the rhythms of his symphony
>mfw Bach confirms his status as the biggest autist in music by composing the crab canon in AoF on a Mobius strip
Fucking idiot.

Physics student here, doing a course on complex analysis right now. Does anyone have any opinions on how useful complex analysis is when evaluating real integrals arising in physics? We're just getting to the residue theorem after learning about Cauchy's integral formulae. All the exercises we've been doing have been purely mathematical.

>>8506462
It was pretty cool, yes. I hope his work will be refound.

>>8506758
Do you study for money, or could you study for fun? Assuming fun would pay your costs and debts.

>>8507526
>could you study for fun?
My parents could probably pay for me a bit, and there's always a teaching job in the end (about 30 000 USD a year starting), but I guess time will tell.

I think studying maths on the side is enough to be fun. I can do a doctorate without debt.

>>8507536
You won't be able to do the doctorate without studying maths at uni though.
Finish your engineering degree and then start again with maths.
But working on maths while doing your EE course seems stupid. Try to be the best at EE then go onto maths no ?

>>8507462
What do you mean opinions? Complex analysis is used all the time in conformal field theories and quantum mechanics. The theorems developed are nothing but tools for us to abuse. Residues, analytic continuations, etc. are prerequisites knowledge for any semiserious physics.

I'd appreciate it if someone can ask an actually intelligent question for once in these threads.

>>8507536
Go for it then! Studying should be about having fun.

>>8507105
The point of the SPV Laboratories series is that it is a sonic dump of the material I worked on for the previous year. Each track is the maximum track length allowed on bandcamp. For example the first track is actually several tracks I worked on in January spliced together. I was working with repetitions on microscopic scales, so that is why you hear the same sound throughout the first track. SPV Laboratories is a sonic landscape meant to be explored and not necessarily listened to straight through. Thanks for taking the time to look at my work though.

>>8507408
Sometimes there is a significant disparity between concept and execution. When this is the case you just have to try your best to look beyond the music itself and appreciate the process. Not always possible though

>>8507169
Sorry I had to leave for a min. Let me get that for you.

>>8483720
>stats
>math
...

Guys. I'm starting to enjoy math. Did I catch the autism?

GUYS I PASSED REAL ANALYSIS!!!!

What do I do now, though?

>>8507748
No anon, you're just a nerd.
Now hand me your lunch money, dweeb.

>>8507750
take analysis II

>>8507748
Yes, yes you did. Soon you will be one of us!

>be physicist
>find a few typos and errors in a mathematical text I'm reading
>mail the author the errata
>he sends me $10 for it
>mfw

>>8508071
Maybe you were paid for your silence, or maybe to prevent you doing what happens in your pic.

>>8508080
You mathematicians secretly enjoy it though

>>8508093
That is obviously a rape scenario, just like your ordinary "physicists trying to do math" moment.

>>8508071
sauce?

>>8508096
Be grateful that we're putting some actual concreteness into your work, boyo.
>>8508099
Nagi Ichi.

>>8508104
Yes, I am grateful. You finding concreteness for the pure stuff is what makes money flow into math research. You do important but dirty work with your applications. Another important but dirty job would be that of a cleaner, without them we'd be buried in our own filth.

>>8508110
More like we're your cashcows and if it weren't for the actually intelligent people going into physics you wouldn't have dinner to eat tonight. It seems that you're rolling in so much of your own filth and ejaculate (i.e. category theory) to realize that.

>>8508116
You made two mistakes in your post, let me correct them: Category theory diminishes your libido so much you will seriously not roll in your ejaculate, and I only eat lunch.

>>8508130
How sad. It'd honestly be better for your well being if you were adopted by a physicist like me.

>>8508116
>>8508110
>>8508130
>>8508138
What about people doing applied physics ? What are we ?

>>8508138
Satan is tempting, but I see through your lies, you wicked, wicked devil! You want to corrupt my mind so that I would start living in the "real" world. I refute this view with the Smith-Wildberger paradox, "how can the world be real if our numbers aren't real?"

>>8508145
Engineers.

>>8508151
Oh you'll learn to love it soon enough.

>>8508170
Are you implying you'd induce some kind of a Stockholm syndrome while holding me captive?

>>8489073
>Cramming
so, learning it but not really?


you are a joke.

>>8508182
I neither confirm nor deny that statement. Non-constructivists BTFO.

>>8508217
An interesting response. Is it even provable you want me to be your slave?

>>8508231
I want you to be my slave iff you want to be my slave.

>>8508235
Can you really make the choice to become a slave? That is, does the axiom of choice wreck the concept of slavery so that we could report its deniers to some human rights authority, and have them arrested for human trafficking?

>>8508217
>>8508235
do you have any more of these?

>>8508253

>>8508243
You don't need the axiom of choice for that, just the axiom of eternal obedience and loyalty to me.

>>8508261
You want me to be your pet? Cat-egory theory?

>>8506762
A basic understanding of quantum mechanics and not too much knowledge about higher level maths. Here is a list of the key concepts I've used in my thesis:
- method of stationary phase
- constructing generating functions
- hadamard products
- contour integration
- computing high powers of 2x2 matrices
- computing determinant, eigenvalues and eigenvectors of tridiagonal matrices
- estimating roots of recursive polynomials
- how to program in MATLAB or another language
I only knew 3 of these things before I started and the rest I was able to figure out.

I have a Calc 3 test today and havn't started studying. I have a cheat sheet I can bring, gonna load up on examples

>math thread
>half the posts are anime

lol, virgins detected.

>>8508410
>visiting a weeaboo Japanese ripoff website filled with anime to converse about mathematics
topkek, virgin detected.

>>8508390

I'm going to guess you knew these three:
>- constructing generating functions
>- contour integration
>- how to program in MATLAB or another language

Did I do well? If I failed just one, it's probably the last one for
>- computing high powers of 2x2 matrices

Suppose I have a group with just two elements, say, x and y, with relations x^2=e=y^2. So it looks like
< x, y | x^2, y^2 >
Now suppose I have a set of "words" constructed by alternating these elements. For example, the word
xyxyxyxyxy
The question is: how many ways can I delete any number of elements in a given word so that it reduces down completely to the identity.

I'm not really looking for an answer to the question; I want to find out for myself. My question is where can I look to learn more about this?

>>8508702
you mean just two generators right? that group has more than two elements as you noted by constructing larger words

it sounds a bit like
https://en.wikipedia.org/wiki/Word_problem_for_groups

>>8508715
Ahh, yes, you're correct, the group would (probably) be the set of all reduced words, with generators x and y.

I'll check out the link, though, thank you.

I've got a PDA with the language S = A ∪
{(,), [, ]}, where A is all legal maths expressions except the round & square brackets.

I need to design a pushdown automata with a singular state that parses strings formed of symbols & only accepts the strings if & only if the opening & closing brackets match correctly.

I'm totally lost & would really appreciate some help.

what to read to get started on category theory?

Studying quadratic inequalities.

im working on a phd and i am fully funded but i am mega mentally ill. so im having a hard time focusing on anything or even going to class. today i walked around some random woods doing pulls from a fifth while reading about solvable groups instead of going to class. i feel like such a fucked up retard.
anyways, my thesis was on converting sets of binary trees to polytopes and studying them. that was kinda interesting. i was doing some other graph theoretic stuff for fun too. ive just been feeling really messed up lately and can barely function

>>8490595
huh

>>8483342
[math] e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!} [\math]

ftfy

>>8509263
[math[e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}[/math]

>>8509270
[math]e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}[/math]

>>8508950
I wouldn't, category theory is pretty useless.

>>8507748
>>8507751
>>8508071
>>8508080
>>8508093
>>8508096
>>8508104
>>8508110
>>8508116
>>8508130
>>8508138
>>8508151
>>8508170
>>8508182
>>8508217
>>8508231
>>8508235
>>8508243
>>8508253
>>8508256
>>8508261
>>8508272
can you fucking chill your autism with these weeb images?

>>8508950
Awodey or Mac Lane

WEEBS OUT REEEEEEEEEEE

>>8508520
I actually knew nothing about generating functions, but from algebra I know how to do an eigenvalue decomposition to do products of 2x2 matrices.

>>8509445

Damn, that's a shame, from the little they taught us about generator functions they seemed cool as fuck.

Also, what made you choose a PhD on quantum walks? Are you developing them for a concrete algorithm or are you just probing and see what you come up with?

>>8509263
>>8509270

>>8509398
I would recommend not using Awodey. Unless you are not inclined to do mathematics. Then by all means, use Awodey.

>>8509274

well i've learnt a lot of useless math and i've been enjoying them.

(E,d) a metric space. A,B two subsets of E. adherence(A) intersected adherence(B) = null
f : E -> R such that f(x)= d(x,A) / (d(x,A)+d(x,B))
Show that the application f is continuous on E.
The correction I have just shows that d(x,A)+d(x,B) = 0 can never happen.
What's used implicitly here is that lim f(x) when x -> a = f(a). And we see that it works for all a's because there's no such f(a) that doesn't exist (where the bottom part of the fraction would be 0).
Right ?

>>8508950
First off, make sure you aren't falling for the autistic memesters that shit up this thread.

If you really want to study pure category theory, Mac Lane is still THE text. However, reading Mac Lane cover to cover is turbo overkill if you want to do anything else. Your algebra texts will probably teach you the majority of the category theory you need as they go, and you can just flip to the relevant section of Mac Lane at the times they don't.

>>8509457
Well I know about generating functions now. They're incredibly useful for combinatorial problems.

I kind of fell into the topic. Basically my goal in my program was to graduate as fast as possible, so I picked an advisor who seemed comfortable with letting me out in 4 years. He was interested in determining a logical definition of Brownian motion in imaginary time at first, but he understood that research goals can change depending on the interest of the person. So I read through some stochastics literature and then came across quantum walks in a paper by Ambainis et. al. I was really intrigued by the conjecture in his paper and spent some time trying to prove it myself. After I found a paper by Bach and Borisov proving the conjecture, I used their techniques to prove a more general theorem. From there I started working with finite quantum walks in two dimensions and making numerical simulations etc etc. So no I am not developing a concrete algorithm I am instead studying purely mathematical properties of the walk and trying to relate them back to something more physical.

What kind of jobs can I get with a BSc in Mathematics?

>tfw Villani's coming to give a talk at my uni
do i ask him about the spider?

>>8483580

>]a,b[

What the fuck? Why are the fucking brackets reversed?

>>8509688
kill yourself you pretentious brainlet faggot

>>8510234
It's equivalent to using (a,b). I haven't seen an open interval represented like that since High School.

>>8510342
Are you okay?

Awodey is not very good for those actually wanting to do category theory. It's more or so for CS students who have not had much of an exposure to mathematics. He simply isn't a good writer for the audience ([ure mathematics).

>>8510514
>>8510234
It's more of a European thing.