/mg/ maths general: module edition

[Anonymous No.10143747]

talk maths, formerly >>10129486

[Anonymous No.10143762]

>>10143747
who here can teach me the virasoro algebra in a nutshell

[Anonymous No.10143815]

I like module

[Anonymous No.10143871]

>>10143747

why is modern math so pozzed? why is combinatorics considered such a backwater? why do topology faggots have to be so faggy and loud?

[Anonymous No.10143875]

>>10143871
>faggots
Why the homophobia?

[Anonymous No.10143897]

>>10143747
hmm... i recognize this image. Reid?

[Anonymous No.10143925]

>>10143762
Virasoro algebra is the algebra of conformal generators. Let us work over the Riemann sphere [math]\mathbb{A}^1_\mathbb{C}[/math] for simplicity, such that a local coordinate neighborhood [math]\eta[/math] exists such that [math]\eta(z) = z[/math].
Let [math]\mathfrak{w}[/math] denote the Witt affine Lie algebra on [math]\mathbb{A}^1_\mathbb{C}[/math] generated by the dilation operators [math]l_n = z^n \partial, l_{-n} = z^{-z}\overline{\partial}[/math], then the Virasoro algebra is the unique central extension [math]\hat{\mathfrak{w}}[/math] that fits into the short exact sequence [math]0\rightarrow c\mathbb{C}[[z]] \rightarrow \hat{\mathfrak{w}} \rightarrow \mathfrak{w}\rightarrow 0[/math], where [math]c\mathbb{C}[[z]][/math] is the algebra of convergent Laurent series on [math]\mathbb{A}^1_\mathbb{C}[/math] and central charge [math]c[/math].

[Anonymous No.10143927]

>>10143875
Combining usually dry mathematics with edgy language is funny

[Anonymous No.10143935]

>>10143925
damn bro you made a tex typo somewhere

please repost (or delete and repost)

[Anonymous No.10143940]

opinions on calc 2.

should i take it or nah?

calc 1 student here.

[Anonymous No.10143941]

>>10143935
or maybe if it looks OK to you just post a screenshot because it looks poorly-rendered to me

[Anonymous No.10143946]

>>10143935
The only typo I made is [math]l_{-n} = z^{-n}\overline{\partial}[/math]. Try refreshing your page.

[Anonymous No.10144084]

>>10143940
brainlet

[Anonymous No.10144141]

>>10143940
did you learn integrals or infinite series in calc 1?

[Anonymous No.10144157]

>>10143940
What are you in school for?

[Anonymous No.10144162]

>>10143815
modules are /comfy/

[Anonymous No.10144164]

>>10144162
Free* modules are comfy

[Anonymous No.10144166]

>>10143946
i tried.

again, it's that whatever MathJaX crap 4chan uses, it doesn't play nice with firefox. still only supported in chrome, pic related

[Anonymous No.10144173]

>>10144164
Correct. I've only been working with skew fields for the past four months so I forgot uggo rings existed

[Anonymous No.10144217]

>>10144164
Finitely generated modules over PID* are comfy

[Anonymous No.10144269]

rational trigonometry
https://www.youtube.com/watch?v=9wd0i44vK04

[Anonymous No.10144414]

Redpill me on VOAs

[Anonymous No.10144667]

>>10143940
Calc 1- children tier integration and derivation.
Calc 2-the same but longer and also sequences

[Anonymous No.10144704]

In what part of math do I get to fuck around with functions and graphs?

[Anonymous No.10144709]

>>10144704
"insert anything here" Analysis.

[Anonymous No.10144773]

finally learned what a banach space is lads. ready for my PhD now.

[Anonymous No.10145056]

>>10144738
You'd have to split up the integral if you're going to be integrating over more than 2pi

[Anonymous No.10145117]

>>10144773
Only 1 year left till they teach you about sigma algebras!

[Anonymous No.10145124]

>>10145117
You learned functional analysis before measure theory?

[Anonymous No.10145297]

>tfw have to memorize a bunch of formulae for my meme applied math class exam
>tfw could be studying something useful instead right now

[Anonymous No.10145575]

you ever fail a course, /mg/?

[Anonymous No.10145591]

>>10145575
no, but i did once get a B

[Anonymous No.10145632]

>>10144084
This is what sci isnt. Fuck off back to your containment board.

[Anonymous No.10145675]

>>10145575
I failed a bunch of courses freshman year due to mental problems
never due to brainletism though
>tfw 3.5 undergrad GPA even though it was 4.0 over the last 2 years

[Anonymous No.10145683]

>>10145632
this isnt sci, this is mg, and he is talking about engineering

[Anonymous No.10145754]

>>10145675
I by all rights should have failed my combinatorics course but I think the professor realized I was on the verge of killing myself and gave me a B. My GPA was garbage that year and it's still not great. But grad schools care more about research experience and letters, ri...right?

[Anonymous No.10145827]

>>10145575
It happens. Doesnt make you less intelligent, you just need to try harder. Good luck anon

[Anonymous No.10146043]

>>10145575
Yeah. Bio 101, chem 100 intro calc 2 .
Calc 2 was a mandatory fail due to attendance (>40%). I still dont show up all the time to classes but at least I put in the thought at home.

[Anonymous No.10146094]

If anyone knows about homotopy type theory I'd appreciate a hint here >>10145758

[what goes in all fields? No.10146207]

>>10145827
>Doesn't make you less intelligent.

[Anonymous No.10146245]

>>10146207
He's not wrong, failing a class has no effect on your intelligence. It might change your perception of it though.

[Anonymous No.10146250]

>>10146043
>he took a class w/mandatory attendance
lol use ratemy professor next time man. your presence isn’t necessary for any mathematics class that isn’t proof based

[Anonymous No.10146260]

>>10146250
yeah it's geared towards engineers though so the entire Calc 1 - 3 was mandatory as well as diff eq. it was annoying, the upper level classes dont even have mandatory attendance

[Anonymous No.10146263]

This Runge guy was smart I tell you what

[Anonymous No.10146349]

>>10143871
>muh sets

[Anonymous No.10146386]

I happened to find an old bookshop that sells a lot of math/physics books including: Springer and grad texts books, which are usually very pricey. The man that works there is very old and it’s very easy to steal books. Would you do it? I’m thinking about it

[Anonymous No.10146407]

>>10146260
>geared towards engineers
You people

[Anonymous No.10146416]

>>10146407
Nothing you can do about it. I would have preferred diving into analysis first rather than doing a bunch of mindless work for 3 semesters before you can go into real maths

[Anonymous No.10146435]

>>10145575
Yeah, failed representation theory spectacularly in grad school, but I only had to pass in two subjects and I was attending lectures in four subjects, so I was not really worried. I passed the two I needed.

[Anonymous No.10146439]

>>10143925
Are your posts actually coherent or do you just make up obscure words to confuse people?

[Anonymous No.10146466]

>>10146439
They're usually technically correct, but they're not as impressive as they're designed to appear to brainlets. Most of the time they read like he just opened one of his textbooks to a vaguely related section and copypasted a paragraph.

[Anonymous No.10146819]

>>10145575
Yeah, I failed all my courses in middle school. Top student in my grad school dept. currently.

[Anonymous No.10146863]

>>10144217
>Finitely generated
Coward.

[Anonymous No.10146981]

any good books on integration specifically? not just a calc 2 textbook, but one that focuses entirely on integration

[Anonymous No.10146984]

>>10146981
Mathematical handbook on integral formulas

[Anonymous No.10147001]

>>10146984
thanks

[Anonymous No.10147117]

>>10146981
Inside Interesting Integrals is a classic

[Anonymous No.10147150]

How do I calculate closed forms of function given it's series expansion?

[Anonymous No.10147356]

Any properties/patterns on the addition of any three integers?
Like 6+8+381

An example would be
>the sum of all three integers is always divisible by 3.
>The biggest two numbers are always half the value.
These statements are false ofcourse, but just trying to give an example of the type of patterns I'm looking for.

[Anonymous No.10147415]

Any help on understanding modular forms from a representation theory perspective?

I am trying to understand Bumps book but don't understand at all how we're going to suddenly get from this group representation stuff to modular forms.

[Anonymous No.10147592]

Question on polynomial time.

Given any value n, find 2^n, how is that found in polynomial time?

Is it because we can write it as 2x2x2x.....so big O would be O(n), because to solve this question you have to do 2x2 n# of times?

[Anonymous No.10147595]

>>10147592
yep. You find 2^n by doing n-1 operations.

[Anonymous No.10147601]

>>10144773
you know that can easily be learned using proofwiki.org, I did that "experiment" once, my intention was to do a silly joke about going all the way from the foundations to a concept that can be described as parsimoniously as it happens with banach spaces (by typing it all out to some Omegler stranger). In order to describe all these concepts I had to go through around ten thousand lines of math text, and it took me around a week, I even expanded on it, and learned about the universal property of free groups (to describe the rational numbers, quotient groups, and the like), etc. It was a pretty important experience in my life

[Anonymous No.10147609]

>>10147592
>>10147595
actually couldnt you do:
2x2 = 4
4x4 = 16
and so on
to actually only do log(n) operations

[Anonymous No.10147664]

Another example:

Given any value n and any polynomial equation F find all the zeros of the polynomial, F^n

I know that worse case is that the # zeros = the highest power of the polynomial. So would big O just be O(n*k), where k is the highest power of polynomial F?


This isn't homework or anything I'm just trying to learn how to estimate amount of operations based off what I'm trying to solve.

[Anonymous No.10147680]

>>10147664
You should've learned that a polynomial can be written as [math]p(x)=a(x-x_1)(x-x_2)...(x-x_i)[/math].
Taking powers, [math]p(x)=a^n(x-x_1)^n(x-x_2)^n...(x-x_i)^n[/math].
So that all the roots of a power of a polynomial are the roots of the original polynomial, as long as n>0.
Finding roots of a polynomial is a huge pain and can only be easily done if they have degree less than five. Google the formulas.

[Anonymous No.10147766]

>>10147680
I know how to find roots, I'm trying to find the big O notation of finding F^n as n approaches infinity.

[Anonymous No.10147915]

Math are to do research on?
I do not have an area of mathematics that I like the most, I love all of them. Which field has the most diverse tools so that it requires you to know "everything"?
Differential geometry, algebraic geometry and number theory seem like good candidates.

[Anonymous No.10147936]

>>10147766
I don't see how the roots are different in F and F^n

[Anonymous No.10147958]

>>10147915
all of them

[Anonymous No.10147991]

@10147958
Unhelpful.

[Anonymous No.10147993]

>>10147915
Geometric topology

[Anonymous No.10147995]

>>10147993
You mean algebraic topology sir?

[Anonymous No.10147996]

>>10147995
No.

[Anonymous No.10147997]

>>10147995
No.
https://en.wikipedia.org/wiki/Geometric_topology

[Anonymous No.10148003]

>>10147996
Sauce?

[Anonymous No.10148008]

>>10147997
nice

[Anonymous No.10148024]

>>10148003
My diary

[Anonymous No.10148028]

>>10148024
This is actually a /lit/ meme but we say "my diary desu".

[Anonymous No.10148036]

>>10147415
Seconding this

[Anonymous No.10148045]

>>10148024
Thanks bub, actually found it from the cover.

[Anonymous No.10148128]

any of you have interest in linguistics?

[Anonymous No.10148138]

>>10145124
You can do plenty with banach and Hilbert spaces without measure. Arzela ascoli

[Anonymous No.10148146]

>>10148128
Yes but I don't know much about it.

[Anonymous No.10148154]

>>10148146
http://www.helsinki.fi/esslli/courses/readers/K54.pdf

[Anonymous No.10148155]

>>10148154
Thanks. Do you want to be my gf?

[Anonymous No.10148164]

>>10148155
for a price

[Anonymous No.10148768]

show me the cutest book in your collection

[Anonymous No.10148771]

>>10146981

[Anonymous No.10148775]

>>10147915
Number theory requires you to know everything, specifically algebraic number theory

[Anonymous No.10149284]

>>10146981
Cohn - Measure Theory

>>10148771
trash

[Anonymous No.10149450]

>>10147609
This is how integer exponentiation is normally done. Also, if you want the result modulo m, you'd do that at each step: (a*b)%c=(a%c)*(b%c).

When dealing with a non-integer exponent, you'd use log(x^y)=y*log(x) => x^y=exp(y*log(x)). Note that this can't handle negative x. A negative value raised to a non-integer power is almost surely complex (the reciprocal of an odd number is an exception, but such values aren't exactly representable in floating-point).

[Anonymous No.10149580]

Real analysis exam next week, what’s the best strategy for studying for this type of course? I really fucked up on the first exam so I need a good rebound, I just struggle memorizing the exact wording of theorems, and I fall into the trap of thinking that the problems are super easy because like, I did all of this stuff much less rigorously in elementary calc courses.

I feel like it’s not like a calc course in that you can pretty much figure it out by doing a shit load of problems until you get it. My teacher roasted my ass for making “calculus arguments,” which is completely understandable given that it’s a rigorous course, but that type of thinking is so natural to me by now.

[Anonymous No.10149585]

>>10149580
Know your definitions. Study some of the bigger proofs and really understand them. Review your assignments.

[Anonymous No.10149771]

>>10147356
Let a,b,c be three non-negative integral positive numbers on the real line such that a•b•c =\= 0. Then their sum a + b + c cannot be equal to 2.

The proof is left as an exercise to the reader.

[Anonymous No.10149897]

>>10149450
Cool, thanks for that.

[Anonymous No.10149945]

>>10149580
KNOW all the tutorial problems and homework problems. Do a lot of past exams. You will easily get the hang of what you are expected to know.

[Anonymous No.10150649]

Sup /mg/. Please help a brainlet. I need to give a formal proof to this:

If p is a prime and p|a1*a2*...*an, then p|ai for some i.

How do I do it?

[Anonymous No.10150661]

>>10150649
that's the definition of prime.

[Anonymous No.10150662]

>>10150649
>>10150649
By induction. You can prove that
[math]p|a_1a_2[/math] implies that either [math]p|a_1[/math] or [math]p|a_2[/math], right?
Just say that [math]b=a_1a_2....a_{n-1}[/math], thus [math]p|ba_n[/math] implies either [math]p|b[/math] or [math]p|a_n[/math], and so on.

[Anonymous No.10150696]

>>10150649
Suppose p is prime and p|a1*a2*...*an. Then p|ai for some i. QED

[Anonymous No.10150703]

Okey, so If [math]\{a_{n}\}[/math] is a non decreasing sequence of real numbers such that [math]\sum_{n=1}^{\infty}\frac{1}{|a_{n}|^2}[/math] converges (so [math]lim_{n\to\infty}a_{n}=\infty[/math]) And I want to prove that if [math]y,x\in\mathbb{R}[/math] are such that the sum [math]\sum_{n=1}^{\infty}\frac{1}{a_{n}((x-a_{n})^2+y^2)}=0[/math] it then means that [math]y=0[/math]

[Anonymous No.10150708]

>>10150703
typo it should be [math]\sum_{n=1}^{\infty}\frac{y}{a_{n}((x-a_{n})^2+y^2)}=0[/math]

[Anonymous No.10150726]

>>10150703
If [math]a_n[/math] is non decreasing and convergent then [math]|a_n|>1[/math] whenever n>N, for some N.
Trivial from here.

[Anonymous No.10150729]

>>10150726
Miswrote, since [math]1/a^2[/math] is convergent.

[Anonymous No.10150732]

>>10150729
Ugh, I must be the biggest idiot on the planet.
[math]1/a^2_n[/math]

[Anonymous No.10150775]

>>10150726
>>10150729
>>10150732
I don't see how that work. If I could bound it from below somehow then it would be easy but the problem is that it could be that a finite numbers of terms are negative and could repeat.

[Anonymous No.10150796]

Is there any point in me learning Latex now if I haven't even taken a real proofs course yet? (Although I am self studying a book)

[Anonymous No.10150884]

>>10150796
[math]\displaystyle \LaTeX[/math] is neat, you should learn it. It's easy as fuck too.

[Anonymous No.10150929]

tell me something cool about [math]L^p[/math] spaces.

[Anonymous No.10150945]

>>10150775
>non-decreasing

[Anonymous No.10150954]

>>10150775
You cannot bound it from below because -a, -a, -a, etc satisfies all criteria for any a>1.
Literally just apply |a|>=1, seriously.

[Anonymous No.10150956]

>>10150929
[math]p=2[/math] is nice.

[Anonymous No.10150957]

>>10150796
It's probably a good idea for you to learn it now. If your career goals involve graduate school and/or academic math you will 100% need to know it to a reasonable level. Even most decent undergrad programs will require you to write something in it before you graduate.
You could put off learning it until later like most people, but in late undergrad/early grad school you will be very, very, very busy and probably not appreciate having to wrestle with your computer trying to get something to work before the deadline. Smarter to learn it now while you have free time and energy to learn things.

[Anonymous No.10150979]

>>10143747
What am I missing here? (other than a brain). I know the answer's going to be 0 (or a number so finite it might as well be 0. How would I go about proving it? Or can this integral be solved with normal methods and I'm just overlooking something?

[Anonymous No.10150983]

>>10150979
replace 1000 and 1002 with smaller numbers differing by 2 and see if you can find a pattern

[Anonymous No.10150984]

>>10150945
It's just a word to put it clear that the terms in the sequence could repeat my friend.
>>10150954
Sorry if I'm being really dumb, but I don't see exactly how that solves my problem. Yes, there is some [math]N\in\mathbb{N}[/math] such that for all [math]n\geq N, \frac{1}{a_{n}}<1[/math] But then what? Maybe I'm not seeing another perspective but my idea is that if you asume that [math]y\neq 0[/math] then I could find a way to show that the sum is strictly positive, but for that I need to bound it from below and your condition says that for sufficiently large N I can bound the sum from above with [math]\sum_{n=1}^{\infty}\frac{|y|}{((x-a_{n})^2+y^2)}[/math] but This isn't really anything new since The sum converges to 0.

[Anonymous No.10150988]

>>10150979
>a number so finite it might as well be 0

[Anonymous No.10150992]

>>10150979
>I know the answer's going to be 0 (or a number so finite it might as well be 0

[Anonymous No.10150997]

>>10150983
I did exactly that. The answers as you increase the powers of the num & dom get smaller at an exponential rate so that's why I'm assuming the answer to this meme integral is just 0. Glad to see other people are starting out with the same methods though. Lets me know I'm on the right track. Thank you anon

[Anonymous No.10151003]

>>10150979
*breathes in very very deeply*
y=x-1. Integrate from 0 to 2.

[Anonymous No.10151004]

>>10150984
im a number theorist, all numbers are either [math][0,1]\cap \mathbb Q[/math] or [math]\mathbb N[/math], you can't expect me to think negatives exist

[Anonymous No.10151009]

>>10151004
You can think in terms of equivalence classes and additive inverses though :) plz help

[Anonymous No.10151019]

>>10150979
multiply top and bottom by (x-1)^1000, or by (x+1)^1000, thank me later

[Anonymous No.10151030]

How much of PDE's can I learn in 3 weeks given I've only taken a single course in ODE's? Any good books for this?

[Anonymous No.10151141]

>>10151030
Depends on your goals. If it's for a final and you know jack shit, It's very probable that you are fucked, but it also depends on the course. O'neill is good to learn quickly on the basics and use any pde for scientists and enegineers for the formulas. Weinberger for things that have to do with separation of variables and Salsa for discussion into certain models. PDEs are one if not the biggest field in mathematics so you can get lost in any particular subject (or equation for that matter).

[Anonymous No.10151142]

>tfw left all my work until Sunday night again
>tfw never going to accomplish anything of note at this rate
Anyone else /squandering themselves/?

[Anonymous No.10151157]

Do you guys have any weird habits you just can't break?
Whenever I do an integral substitution with a definite integral I keep the original bounds and substitute back to the original variable before evaluating. My high school calc teacher did it like that for some reason and it's engrained into my mind.

[Anonymous No.10151160]

>>10151141
I would like to know enough to cover my ass for most of classical physics and then perhaps some modern application.

[Anonymous No.10151162]

>>10151157
I write matrices starting at the top left and going down the first column then down the second column and so on as it's what my high school teacher did.

[Anonymous No.10151166]

>>10151157
can't add numbers without the use of my fingers

[Anonymous No.10151177]

>>10151166
The other day I used a calculator to check that 1.5 * 2 really was 3

[Anonymous No.10151178]

>>10151157
This is fine, just make sure you dont keep the original bounds after doing the substitution, before substituting back

[Anonymous No.10151188]

>>10151157
I have a pathological aversion to proofs by contradiction. It costs me time sometimes because I always look for any way possible to not phrase arguments in the "assume x -> prove silly thing" framework, and sometimes that's the only way it works.

I had a prof who wrote everything it was remotely possible to by contradiction even when it was completely unnecessary and it triggered me so hard I've never been the same.

[Anonymous No.10151195]

>>10151157
>>10151166
I can't multiply matrices without using my fingers to match up the numbers

[Anonymous No.10151198]

>>10151195
s-same

[Anonymous No.10151202]

>>10151188
I think this is a common phenomenon. I was enculturated to always try a direct proof (or proof by contrapositive) before attempting a proof by contradiction. It's just cleaner that way, to not use contradiction unless you really need to.

[Anonymous No.10151203]

>>10151195
>>10151198
I do this too
except I use the pencil instead of one of my fingers

[Anonymous No.10151217]

>>10151160
Lol if its intro you will need 0 theory. All books and courses are self contained. Learn fourier análisis.

[Anonymous No.10151242]

Is it feasible to learn some algebraic geometry as an undergrad? If so where to start?

[Anonymous No.10151248]

>>10151242
Cox.
Not a pun btw

[Anonymous No.10151276]

>>10151242
I read Atiyah and Macdonald and enjoyed it.

[Anonymous No.10151353]

Any ideas on how to calculate the intersection between a line and a spline? I'm following this video to use a PID to control a car's steering. Finding the intersection between two lines like in the video is easy. But when the path to follow is a spline I have no idea how to calculate e.

https://www.youtube.com/watch?v=4Y7zG48uHRo&t=69

[Anonymous No.10151385]

>>10151353
Take the difference of the two and find its roots

[Anonymous No.10151391]

>advisor asks me to generalize proof
>can't figure it out
>don't know if it actually can't be done or if I'm just a brainlet
I'm not cut out for this

[Anonymous No.10151466]

>>10151276
>read
you're meant to work through it. You can read it thoroughly in 2 days otherwise

[Anonymous No.10151484]

>>10151391
>working thorugh it
Not the previous guy, but I noticed at some point that if I learn something and give it a while I somehow acquire a better grasp of the subjet. But maybe I'm just growing smarter.
Also, sometimes you think "Ah, I'll go through the book" and you look at the problems and they all are five paragraphs long, so you look for the smallest one, solve it, and go to the next chapter. I for example instantly go out of my way to avoid anything with quotients of cartesian products because fuck those proofs nigga. Or maybe that's just me.

[Anonymous No.10151517]

>>10150703
>>10150708
help bros

[Anonymous No.10151561]

what's the intuition behind quotient groups

[Anonymous No.10151564]

>>10151561
You're pretending a bunch of elements are zero

[Anonymous No.10151565]

>>10151561
It's similar to quotient spaces. Let [math]A\subset X[/math] and the quotient space [math]X/A[/math] is defined by "squashing" [math]A[/math] to a point. Similarly for groups [math]H\subset G[/math], the quotient [math]G/H[/math] is basically "squashing" [math]H[/math] to a point.

[Anonymous No.10151568]

>>10151564
Basically this.

[Anonymous No.10151600]

>>10145575
it can happen for a number of reasons - but the question now is do you have the will to make up for it, anon

[Anonymous No.10151620]

>have to write a proof of the intermediate value theorem by the end of the week
>I'm shitposting on here instead

[Anonymous No.10151623]

>>10151620
Is this the undergrad version of the "I have a 200 word essay due tomorrow"?

[Anonymous No.10151641]

>>10145575
No but once I got a B in a linguistics course because I wrote my linguistic analysis assignments in terms of formal language theory.

[Anonymous No.10151668]

>look at assignment
>have no idea how to do any problems

[Anonymous No.10151688]

>show that the analytic extension of the convex hull of the quotient group of the dual space of a frechet space is isomorphic to the set of elliptic curves going through zero under the operations of convolution and revolution
>looks up the list of definitions again
>looks up the theorems
>it actually takes two seconds

[Anonymous No.10151693]

actual brainlet dropping by

I'm trying to plug the function 200e^0.014(7) into pic related but it won't keep 7 as part of the exponent and ends up giving me the wrong answer

[Anonymous No.10151695]

>>10151693
0.014(7)=
200e^ANS or equivalent button to ANS.
>>>/sci/sqt/

[Anonymous No.10151716]

>>10151641
why

[Anonymous No.10151719]

>>10151620
even if this is your first analysis class it shouldn't take more than a couple hours

>>10151688
I swear I spend half my time just getting twenty definitions into my head then writing down "it follows directly lol".

[Anonymous No.10151721]

>>10151716
The TA didn't understand any of it

[Anonymous No.10151731]

https://mathoverflow.net/a/315226

[Anonymous No.10151736]

>>10151731
fucking geometry

[Anonymous No.10151755]

Very happy I fell for the home whiteboard meme, I feel like I think a lot better standing looking at a board than sitting at a desk.

[Anonymous No.10151767]

What's the addon to read tex?

[Anonymous No.10151772]

How does this action work, it doesn't seem to respect the multiplicative structure of SL2. Eg, we have Y^2 = 0 but applying Y twice to a basis element doesn't result in the zero vector.

[Anonymous No.10151774]

>>10151767
>What's the addon to read tex?
disable adblock

[Anonymous No.10151775]

>>10151774
Don't spoonfed you fag.

[Anonymous No.10151776]

>>10151775
>fag
Why the homophobia?

[Anonymous No.10151777]

>>10151776
Why not?

[Anonymous No.10151779]

>>10151777
>Why not?
There's nothing mathematical about homophobia.

[Anonymous No.10151782]

>>10151779
Nor is there any in your posts.

[Anonymous No.10151786]

>>10151782
>Nor is there any in your posts.
Nor is there any what in my posts?

[Anonymous No.10151787]

>>10151779
Yes there is, it seems a lot of faggots are pretty good mathematicians and that scares the shit out of me cause I'm a decent one.

[Anonymous No.10151790]

>>10151786
COCKS

[Anonymous No.10151791]

>>10151786
mathematical content, idiot.

[Anonymous No.10151793]

>>10151772
These [math]W_m[/math] are Verma modules. Note that we're trying to represent the [math]affine[/math] Lie algebra of [math]\mathfrak{sl}(2)[/math], not [math]\mathfrak{sl}(2)[/math] itself.

[Anonymous No.10151801]

>>10151791
>mathematical content, idiot.
How does this justify your non-mathematical homophobia?

[Anonymous No.10151805]

>>10151801
How does this justify your meta-posting?

[Anonymous No.10151811]

>>10151793
None of that has been mentioned and I don't know what it means, is it implicit or is there a simpler explanation?

[Anonymous No.10151812]

>>10151801
>>10151805

You faggots wasting more effort arguing about homophobia than answering my fucking question.

[Anonymous No.10151813]

>>10151812
don't call me a faggot you fucking faggot homo

[Anonymous No.10151814]

>>10151811
That'll be addressed soon I think. If not then that's a legitimate concern.

[Anonymous No.10151816]

>>10151805
>How does this justify your meta-posting?
define "meta-posting"

[Anonymous No.10151817]

>define "meta-posting"

[Anonymous No.10151857]

is algebraic geometry the most alpha field of study?

[Anonymous No.10151864]

>>10151857
That’s a weird way to spell ‘Probability Theory’

[Anonymous No.10151869]

>>10151864
okay, this is epic.

[Anonymous No.10151914]

>>10151857
No, too many women involved. Most alpha field is probably russian style PDE stuff, like in the book of Gromov "Partial Differential Relations" that noone really understands.

[Anonymous No.10152151]

>>10151914
And also Hormander’s 4 volumes masterwork about the Analysis of Linear Partial Differential Operators

[Anonymous No.10152165]

>>10151620
Like a topological proof?

[Anonymous No.10152166]

>>10151857
definifely not

[Anonymous No.10152182]

lets say i've taken graduate algebra but i'm really bad at remembering the taxonomy of everything, so bad in fact that i went over to applied math, where can i continue learning algebra that isn't heavy in jargon? serious pls

[Anonymous No.10152202]

>>10151816
define define

[Anonymous No.10152208]

>>10152202
to make something very like you can touch it and work with it you know

[Anonymous No.10152214]

>>10151620
do it predicatively or do not do it at all

[Anonymous No.10152246]

>>10151466
.... yeah.... most people use the word "read" as shorthand for "read in the appropriate way."

[Anonymous No.10152388]

>>10152182
>algebra
>not heavily laden with unnecessary jargon
pick one and only one.

[Anonymous No.10152477]

Is there any math paradox where you have a chain or a tree of strict inclusions but then you realise the smallest one contains the biggest one and you ruin math?

[Anonymous No.10152479]

>>10152477
>strict inclusions
I sure hope not

[Anonymous No.10152485]

>>10147664
Any polynomial of degree n is "big o" of x^n. Big Os have nothing to do with roots: you can see that x, x-1, x+2, x-6, ecc all are O(x). Same for larger degrees.

[Anonymous No.10152492]

>>10147664
Also, as anon already told you:
1) there's no formula and thus no standard algorithm for polinomial equations of degree >4, so no predictable amount of operiations
2) If you already know that G(x) is the nth power of some F(x), then G(x)=0 has the same complexity of F(x)=0 despite having higher degree. If you somehow know that G(x) is some nth power but not what is "nth root" F(x) is, then there's probably no better way to compute F than solving G(x)=0 first and then decompose G as product of degree 1 polynomials.

[Anonymous No.10152494]

>>10152479
C'mon i don't wanna fuck up math, you can tell me

[Anonymous No.10152498]

>>10151864
>Probability theory
>math

[Anonymous No.10152500]

>>10150988
>>10150992
My phys-for-mathematicians teacher used often that train of thought when you see a function that is constant and say "might as well be zero huh". I bet he did that because he hates mathematicians or life or both.

[Anonymous No.10152509]

I remember hearing a joke where a mathematician is woken up by a fire alarm, looks out of the window and sees a safe way out, and then gets back to sleep all satisfied because "a solution to the problem exists".

Probably joke had an introductory part about a computer scientist trying to reboot the palace by closing and reopening the window, and a physicist or engineer doing something equally silly—but I forgot.

[Anonymous No.10152513]

>>10151857
No, I've said it before and I'll say it again. I'm a number theorist (in a top uni) but I'm close with the AG department. There are literally 0 women in the NT department, yet somehow about 20% of the AG department are women. Hence NT is the most alpha field of study.

The same argument does not work for engineering and CS because they're glorified plumbing/codemonkeying and they smell bad.

[Anonymous No.10152514]

>>10152477
Yes, it's called proof by contradiction, and it's pretty useful

[Anonymous No.10152517]

>>10152513
Nah it does work, all math is for women and weak incels.

Real men do difficult fields where they actually solve real world problems like engineering.

[Anonymous No.10152595]

>>10152517
>real world problems

[Anonymous No.10152601]

>>10152514
If AcB and BcA you usually conclude that A=B, so no.

[Anonymous No.10152624]

thinking about double majoring into math as an electrical engineer
talk me out of it

[Anonymous No.10152630]

Has anyone here written the GRE test before?

Should I buy the ETS official powerprep package or is there a better alternative?

I know it's easy as shit, but the schools I want have 168 quant score average so I need to beat into the top 99%.

[Anonymous No.10152651]

You can usually mask any proof as a proof by contradiction, but is the converse equally true?—that you can always rephrase a proof by contradiction without using contradiction?

[Anonymous No.10152655]

>>10152601
>strict inclusions
retard

[Anonymous No.10152657]

>>10152630
most important part is the math GRE, not the general one, unless you're not doing math, in which case go fuck yourself

[Anonymous No.10152668]

>>10152657
I'm doing [spoiler]applied[/applied] math, but the school doesn't require math at all.

It doesn't GREs for EU degrees at all, just American ones.

In any case I have good publications in two high quality journals so I really only want to do this because adcom requires, but the average at the school is high so I don't want to look like a retard.

It's not contributing to my application at all other than having a "not retarded" stamp.

I'm not giving those Jews money for a subject test too.

[Anonymous No.10152676]

>>10152655
The symbol of subset inclusion is almost never used to denote strict inclusion and the \subseteq one is often considered redundant. That's why you sometimes see an inclusion sign with a barred line below to denote strict inclusion.

Anyway, assuming that A and B are not equal and reaching the contradictory conclusion that each is strictly included in the other is just a more convoluted alternative to double inclusion.

[Anonymous No.10152683]

>>10152668
There's absolutely no point in purchasing prep materials for the general GRE. The entire syllabus is high school material. Scoring high is entirely a matter of being very careful not to make any errors. I got 170/169 and my prep consisted of reading the exam rulebook the night before.

The math GRE is a different matter and you should probably purchase some sort of study guide for that, because you're unlikely to get above 75th percentile without significant practice. Nothing on the test is particularly high-level (it's usually roughly 50% calculus, 25% linear algebra, and 25% very basic combinatorics/topology/abstract algebra) but you have 3 hours to do 66 questions. You need to have every calculus trick under the sun memorized because there's not enough time to sit and think about the problems for more than 10 seconds each.

And if you intend to apply to American PhDs you probably are giving the jews money for the math exam because almost every decent American PhD program requires it, especially for international students.

[Anonymous No.10152686]

>>10152683
I have a very specific school in mind, but you are right I should probably do the math subject GRE for backup programmes.

Yeah I get that it's easy precalc, but my question was essentially if you need to practice to get >(=)99 in the limited time which I think you have answered already (thanks).

[Anonymous No.10152688]

Can anyone give me some advice on writing SOPs for graduate school apps?

I've looked around online but all the sample ones are fucking autistic
>verily my penchant for the abstract beauty of number theory indeed makes the university of shitsville loom large in my considerations
style bullshit that isn't really helpful.

Is one single-spaced page too short? I've talked about my goals, interests and reasons for choosing the particular university but that only takes up one paragraph each, and I have nothing else to say.

[Anonymous No.10152690]

>>10152651
No. Constructivists rage about it to this day.

[Anonymous No.10152692]

>>10152688
Well my adviser (Masters at third world, but he did his PhD at top 5) told me to write about my actual research interests and achievements, but I don't know most adcoms are saps for the mushy mushy "I'm oh so fucking enlightened by my own passion" shit.

[Anonymous No.10152696]

>>10152688
Also I had 2 pages, but afterwards I was told to limit go 1 page, the SOPs getting into top 10 schools I saw were all vague, mushy 1/2 pagers that essentially said nothing in an unimpressive vocabulary.

[Anonymous No.10152697]

>>10152651
Not always, at least not without fundamentally changing the structure of the proof.
For example the classical proof that [math]\sqrt{2}[/math] is irrational cannot be done without becoming proof by contradiction at some point. You can replace the proof by some other proof that is not by contradiction (e.g. you can use continued fractions, or the rational root theorem, or...) but there is no way to simply rephrase the proof.

[Anonymous No.10152699]

>>10151242
The rising sea by Vakil was a great start for me in undergrad

[Anonymous No.10152705]

>>10152630
>top 99%

[Anonymous No.10152712]

>>10152705
I left out percentile because it should be obvious from the context and I'm sneak phone typing while invigilating.

[Anonymous No.10152721]

>>10152712
I see now that I've read your posts. Sorry.

[Anonymous No.10152749]

>>10152697
For positive integers a and b, if a^2=2 b^2 then a and b have a common divisor greater than 1: in fact, the equality implies that 2 divides a^2, and thus that 2 divides a, and thus that 4 divides a^2, and thus that 2 divides b^2, and thus that 2 divides b, meaning that 2 is a common divisor. We can conclude that if a fraction squared equals 2 then it is not a simplified fraction, and thus that a simplified fraction cannot be equal to sqrt(2), and thus that no fraction can be equal sqrt(2). And thus that the end.
Is this good senpai?

[Anonymous No.10152798]

>>10152676
>>10152601
before you can do math, you must learn how to read
>>10152477
>Is there any math paradox where you have a chain or a tree of strict inclusions but then you realise the smallest one contains the biggest one and you ruin math?
>chain or a tree of strict inclusions
>strict inclusions
>strict

[Anonymous No.10152822]

>>10152697
>for coprime integers a,b a^2/b^2 cannot equal any prime number by the definition of a prime number
>thus sqrt(2) is irrational by the definition of a rational number
there's no assuming the absurd in this proof

[Anonymous No.10152828]

>>10152749
>positive integers a and b
>a^2=2
Contradiction there. If you're retarded, let's do this another way:
>2 divided a^2
>thus 2 divide a
>thus 4 divide a^2
Of that could be true, then 4 divides a, 16 divide a^2, 16 divides a, which goes forever.

[Anonymous No.10152834]

>>10152798
Indeed. I knew already that a circular chain of strict inclusions leads to a contradiction, and thus to the inclusion not being strict. The post asked about specific instances and you just went oh I know how this thing is called. And proofs by contradiction do not necessarily involve inclusions.

[Anonymous No.10152842]

>>10152834
brainlet

[Anonymous No.10152869]

>>10152828
>a^2=2
I've actually said a^2=2b^2. There's a "two times b squared" in there. Of course that is impossible for integers, and that's what is being proved. Which probably means proof is actually just a proof by contradiction without the word "contradiction". Too bad.

>Of that could be true, then 4 divides a, 16 divide a^2, 16 divides a, which goes forever.
No. The implication
>2 divides a^2 thus 2 divides a
is true precisely because 2 is a prime number, which 4 and 16 are not.

[Anonymous No.10152871]

>>10152842
No you.

[Anonymous No.10152874]

>>10152749
>>10152822
>thinking you can give proof that something doesn't exist by literally any means other than contradiction
Honestly, fellas.

[Anonymous No.10152879]

So I'm in my third year of undergrad math, and enjoy it, but I'm having trouble planning for the future. In America, so have those core classes I'm humanities that bring my goal down, so I'm not sure I'll get into a grad program. The professors here aren't very helpful, I'm getting floaty answers and basically told to fend for myself.
Does that seem right? Where should I be looking for more specific math-related future plans?

[Anonymous No.10152883]

>>10143747
I dropped out of highschool.
Any pre-calc or basic math pdfs or a point in the right direction? I'm 22 and I want to go back to school. Please help.

[Anonymous No.10152892]

>>10152883
It depends when you dropped out of high school and how much math you took when you were there.
I'd suggest you try going through volume 1 of the Art of Problem Solving (this is on libgen, I believe). It starts from fractions and goes through all aspects of high school math at a reasonable pace.
It is intended for competition training, but that shouldn't scare you. It's the same material, the problems just make you think about what you learned instead of mindlessly banging out equations. If you need practice with mindless symbol-pushing, then this is easy to find online.

[Anonymous No.10152893]

>>10151814
based

[Anonymous No.10152895]

>>10152879
So what do your undergrad classes look like? Have you done the core ones? Do you have any recommendation letters lined up? You do go to office hours, right?

[Anonymous No.10152899]

>>10152879
>In America, so have those core classes I'm humanities that bring my goal down

[Anonymous No.10152905]

>>10152895
>my uni's curriculum is about half as strong as this
Thankfully I'm not studying maths.

[Anonymous No.10152916]

When I heard the learn’d astronomer;
When the proofs, the figures, were ranged in columns before me;
When I was shown the charts and the diagrams, to add, divide, and measure them;
When I, sitting, heard the astronomer, where he lectured with much applause in the lecture-room,
How soon, unaccountable, I became tired and sick;
Till rising and gliding out, I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.

[Anonymous No.10152919]

>>10152916

[Anonymous No.10152923]

>>10152874
You're right that unless working in a very finite set there's no other way of proving a thing doesn't exist other than asking what if it existed—or is there?
Still, proofs that could be done without
contradiction and are done by contradiction are very upsetting. Imagine that instead of computing a given expression and showing it's—say—five, you prove by contradiction that it cannot be any other number than five.

[Anonymous No.10152926]

>>10152919
I thought it was more of a lyric kind of poem desu.

[Anonymous No.10152932]

u can prove that a 3dimensional vector space has no vector with 4 components without need of assuming there is one, since it follows by definition

[Anonymous No.10152937]

>>10152932
>you can prove that the definition follows from the definition
>>10152923
If there is, I've never seen it. Unless, as anon already exemplified, the definition claims something doesn't exist, and you show that the required object fits under something.
I like proofs by contradiction because they're short. Constructive proofs are usually really long.

[Anonymous No.10152938]

>>10152688
Specialize your essays for each school you're applying too. Each school has strengths and weaknesses and you should be clear as to why you want to go to THAT specific school as opposed to any other. Is there someone you want to work with, do you certain research labs or programs, why do you want to go there? Also you should try distinguishing yourself, talk about your personal interests and what not. They should have a clear image of you. Don't be generic.

[Anonymous No.10152941]

>>10152932
>consider the subspace [math]V[/math] of [math]\mathbb R^4[/math] consisting of all vectors of the form [math](a,0,b,c)[/math]
>every vector of [math]V[/math] has 4 components yet is 3 dimensional

[Anonymous No.10152951]

>>10152937
>>you can prove that the definition follows from the definition
It still counts as a proof though. The same way x=0 is an equation and a line is a curve.

>Constructive proofs
I like those because they show there is something outside the framework you've been working in. The crooked roads of genius etc etc.

[Anonymous No.10152955]

>>10152941
Pedantic. Which I guess is good in mathematics. Let's say there's no set of four independent vectors in a 3d space—happy?

[Anonymous No.10152956]

why are algebraists so fucking cruel when marking papers. one tiny detail slightly wrong and no grade awarded. have done pretty much every other field of math at undergrad level and no one else is as fucking autistic as these cunts.

[Anonymous No.10152962]

>>10152955
obviously. a vector space is n dimensional if and only if its basis has n elements, which implies any set of n+1 elements is linearly dependent

>>10152956
because it probably wasn't a tiny detail in the grand scheme of things, and while analysis gives you some "leeway" in your arguments, everything in algebra is very axiomatic, so something that is wrong is usually completely wrong

[Anonymous No.10152967]

>>10152895
I took an intro to proofs course last semester with induction and sets, currently finishing up linear algebra and mulitvarible calc. I'd say 20 people a class.
I try to go to office hours once a week, usually Monday. Usually we just talk about any issues she noticed on recent quizzes or homeworks, but when I try to push about getting into helping some if the senior projects, I get told to go to the career center, which is a different issue but not really the point here.
Two said they'd write a recommendation for me when I need it, neither of which I'm currently taking classes with.

[Anonymous No.10152976]

>>10152962
u hev to prove that in vector spaces basis exist and all have the same number of vectors tho

[Anonymous No.10152979]

>>10152962
>very axiomatic
yeah, I suppose so. but it sucks getting a 0/10 on a question where you got the rest of the argument correct.

[Anonymous No.10152981]

>>10152938
Thanks for the response. This is reassuring to read because this is basically what I've been trying to write. All my statement drafts have a paragraph dedicated to explaining what specific group/faculty I want to work with at that particular school.
Besides that I have a paragraph describing my background and mathematical interests, and an intro paragraph describing my (admittedly somewhat generic, but how can they not be) career goals and motivations for getting a PhD.
All this checks out to about 375 words, around 2/3 of a page. I'm hoping to be able to pad it out to 500 without becoming too much of a blowhard.

[Anonymous No.10152982]

>>10152979
well, what was you proof then?

[Anonymous No.10152989]

>>10152956
One thing I dislike about mathematics is that every word must have a definite and precise meaning. There's no room for ambiguity. Of course that is what math is for, and applied math teachers giving leeway because they don't want to get lost into details are usually wrong and not very professional. Still, I find this train of definition-lemma-theorem-lemma-lemma-definition-main-proof-corollary-definition-corollary-etc exhausting and mindnumbing.

[Anonymous No.10152991]

>>10152892
Thanks anon, fractions are actually around where I stopped I don't know the rules for multiplying or dividing them etc etc.

[Anonymous No.10152992]

>>10152979
>I spilled the coffee but I still drank it

[Anonymous No.10152998]

>>10152979
I can't accuse you of doing this because I don't know what you actually wrote, but I've graded abstract algebra exams and every time I get at least a few students who complain that I gave them minimal marks for an argument with a fundamental flaw in it.
If you write a proof that has an error, and the error breaks the proof in a way that cannot be fixed, then it doesn't matter if the other 95% is correct because that one wrong step means your entire solution makes no progress at all on the question you were asked.
Part marks are supposed to indicate that you made partial progress towards a solution. If you made no progress, you cannot reasonably get any marks.

[Anonymous No.10153000]

>>10152992
>>10152982
>>10152962
>>10152979
inb4 it's something like prove [math]x+y[/math] divides [math]x^p+y^p[/math] (in characteristic 0)
Proof: [math]x^p+y^p=(x+y)^p[/math], hence clear

[Anonymous No.10153015]

>>10152998
I guess analysis has just spoiled me in its leniency.

[Anonymous No.10153032]

>>10153000
>x^p + y^p=(x+y)^p
>in characteristic 0

[Anonymous No.10153034]

>>10153032

[Anonymous No.10153037]

>>10152388
lol I know. I find it very frustrating. I guess this semen slurping subject isn't for me.

[Anonymous No.10153038]

>>10153000
That's a neat and effective proof once you understand why intermediate binomial coefficients in (x+y)^p are all multiples of p.

[Anonymous No.10153040]

>>10153037
Way to cope with your frustration big boy!

[Anonymous No.10153041]

I swear half of the people here are literally illiterate or brainlet, most likely in their intersection.

[Anonymous No.10153042]

>>10153041
cool story bro

[Anonymous No.10153047]

>>10153042
>t. one of the illiterate+brainlet posters in the last 20 minutes

[Anonymous No.10153052]

>>10153047
cool story bro

[Anonymous No.10153056]

>>10153015
>leniency
>Proves df/dx =(df/dy)*(dy/dx) by saying the dx's cancel out
>i is square root of -1
>you can just cancel out small o's
>works with differentials as if they were really small quantities
Yep. That's leniency.

[Anonymous No.10153057]

>>10153052
>can't read what it says but previous poster wrote it and elicited a response therefore i will post it in an attempt to garner the same consequence. also i suck cocks (translated from npc speak)
you succeeded i guess

[Anonymous No.10153060]

>>10153056
you do know I said analysis, not calculus, right?

[Anonymous No.10153062]

current discussion thoughts

[Anonymous No.10153063]

>>10153057
cool story bro

[Anonymous No.10153066]

>>10153041
>Wheee whee they say im wrong but it's them wrong
>Brainlet illiterate faggots poopoocaca
>Please tell me im right. I use mathematical metaphor because i fit in

[Anonymous No.10153070]

>>10153062

[Anonymous No.10153079]

>>10153060
In my country calculus is commonly called mathematical analysis or just analysis, because the word for calculus is synonyms with computation so any math course could be called that

[Anonymous No.10153086]

>>10153070
This means both arguers since stomping your foot on the ground because "im right tho" is equally foolish whether you're right or wrong when the discussion has no relevance whatsoever

[Anonymous No.10153089]

>>10153079
>Only three men
Sexist

[Anonymous No.10153096]

>>10153089
>assuming

[Anonymous No.10153115]

this proof can't be solved using contradiction
proof:
assume it could
we've reached a contradiction

[Anonymous No.10153123]

>>10153096
If a penis wielder sees himself as a woman then she's a woman all right

[Anonymous No.10153293]

>>10149771
>Proof. Let a,b,c be three non-negative numbers. Suppose abc\neq0 and a+b+c=2. Begin with a=b=c=1. Then 1+1+1=3 which is not 2. However if either a, b, or c, were 0 then our supposition would hold. Contradiction. Hence their sum cannot be equal to 2
Rip this apart

[Anonymous No.10153300]

>>10153115
delete this

[Anonymous No.10153383]

>>10153115
but can you state that within ZFC?

[Anonymous No.10153409]

Is category theory the most autistic field of study ever invented?

[Anonymous No.10153411]

>>10153409
>Is category theory the most autistic field of study ever invented?
Combinatorics

[Anonymous No.10153418]

>>10153411
combinatorics is pretty normie tier math though.

[Anonymous No.10153422]

>>10153411
you best watch your step there motherfucker

[Anonymous No.10153459]

redpill me on stacks

[Anonymous No.10153463]

>>10153459
last in first out

[Anonymous No.10153484]

>>10153409
No, that award goes to universal algebra.

[Anonymous No.10153510]

>>10153411
We're talking mathematics. Autistic means good

[Anonymous No.10153516]

>>10153459
Sheaf of groupoids

[Anonymous No.10153536]

>>10153459
those who work with stacks would have been flagellants in a previous age

[Anonymous No.10153616]

>>10152967
>currently finishing up linear algebra and mulitvarible calc
>>10152879
>So I'm in my third year of undergrad math

What? You should have done those last year at the latest.

[Anonymous No.10153726]

>>10152981
Do you have any research, outreach, or presentation experience? You may want to emphasize those points.
>>10153411
>>10153409
Cardinal arithmetic

[Anonymous No.10154208]

>>10153459
scheme were not enough.

[Anonymous No.10154404]

>>10153459
everything is a sheaf. you are a sheaf.

[Anonymous No.10155060]

ded thred ded general ded board

[Anonymous No.10155066]

Posting to kill this thread

[Anonymous No.10155067]

New thread now that we've reached the bump limit
>>10153853
>>10153853
>>10153853

[Anonymous No.10155568]

>>10151623
* 1st semester freshman version

[Anonymous No.10155582]

>>10152624
I was in your shoes and I just switched to math altogether because I was disappointed in the lack of math in EE and I wanted to go into academia.

[Anonymous No.10155601]

>>10152899