/mg/ - maths general

[Anonymous No.11183694]

Avila aged really fast edition, previously >>11176582
Talk maths.

[Anonymous No.11183991]

Threadly reminder to work with physicists.

[Anonymous No.11184138]

>>11183920
What are CP?
this course has around 31 ECTS/semester average with
the 5th semester (36) and the 6th (20) being the outliers

[Anonymous No.11184247]

>>11183694
I never did calculus or A level math (UK) but I was looking through some maths books and I think I've got alot of holes in my math knowledge.
Should I just work through from pre algebra to fill them and then progress to calculus?

[Anonymous No.11184328]

>>11183694
Why do mathematicians hate abstraction? I never would've believed this was possible, but somehow all of the professors in my department have a strong distaste for constructions in math that aren't "real."

[Anonymous No.11184469]

>>11184328
That sounds very subjective. I mean they use the reals, which aren't real.

[Anonymous No.11184555]

>>11184328
So what math professors hate complex numbers now?

That sounds really wrong and stupid.

[Anonymous No.11184559]

I'm trying to figure out what's the best way to approach learning Calc 3 efficiently and comprehensibly. I learn much better from lectures then books so i'm thinking that using Khan's series on Calc 3 is ideal since 3blue1brown is the one who made those videos. However Khan has jack shit in terms of problems to solve so I need a good source of problem sets.

Is Brilliant sufficient or should I just use it as a supplement? What's the best source for problem sets?

[Anonymous No.11184592]

>>11184328
>but somehow all of the professors in my department have a strong distaste for constructions in math that aren't "real."
What do you mean by this?

[Anonymous No.11184640]

>>11184559
take any standard calc textbook, it should have a plethora of problems for you to practice with

[Anonymous No.11184678]

Broke guy. I'm finishing my first semester of Math Bacc (Canada).
I'm good at maths, 95% average in my classes.
How do I get a tutor or math corrector job (at my uni), is it even possible given I have no title? I guess I'm competing against graduates.
Any insights are appreciated.

[Anonymous No.11184687]

>>11183991
I've seen this comic before but I don't get it? Is there a joke I'm missing?

[Anonymous No.11184693]

>>11184678
Which uni?

[Anonymous No.11184707]

>>11184693
Uqam, maybe switching to UdeM.

[Anonymous No.11184748]

i've been studying boolean math the last 72 hours and i have only slept 4 hours. how tf do i understand this shit faster?

[Anonymous No.11184782]

>>11184678
I have tutored and corrected through my Uni (St. Boniface), but we're tiny. You won't be able to do it until at least next year, and forget about being a corrector for a while. The secret is to be on good terms with some profs, particularly with the ones running the programs/needing a corrector. They have to trust you enough to do a good job and like you enough to give you the job instead of someone else. Bon succès!

[Anonymous No.11184784]

>>11183694
Explain this 2 me: http://files.eshkolot.ru/C1_Nick_Land.pdf

[Anonymous No.11184791]

>>11184784
>.ru
I ain't clicking that shit senpai

[Anonymous No.11184806]

>>11184687
Oh it's no joke sweetie. It's reality.

[Anonymous No.11184900]

>>11184687
There is no joke. But see the calendar on the wall, they solved each other's problem 30 years in advance.

[Anonymous No.11184973]

>>11184247
i dunno what "pre algebra" means, but you should have good ability to do algebraic manipulations before you do calculus. you could still understand the basic concepts of calculus but you would have a very difficult time trying to solve problems if you don't have a decent amount of practice with algebra

[Anonymous No.11184984]

>>11184592
I have no idea, that's what I was hoping to understand. I had a conversation with one where he insisted on thinking about exact couples in terms of homology groups instead of modules because only the former were "real" things. Another had a similar complaint about simplicial sets.

[Anonymous No.11185003]

Can someone please help me out here, no clue what I should do. If possible, explain it to me as you would explain it to a beginner (although I know what cardinality and bijection means but thats it really).

[Anonymous No.11185088]

I saw this problem in a question somewhere. The answer,
according to the response, was to enter a value for x, see if it
works, then go down or up, and try again... Say you have the equation:

[eqn]x^x = 5[/eqn]

You input 2 for x, and get

[eqn]2^2 = 4[/eqn]

So then you try 3, and get

[eqn]3^3 = 27[/eqn]

This is useless. The answer is irrational, and it will take a long
time to solve it. Using natural logs, you get this:

[eqn]x^x = 5\\
x ln(x) = ln(5)\\
x = ln(5)/ln(x)[/eqn]

This doesn't help. Here is what I did to solve it. Multiplication is
just a form of addition, in that x + x = 2x. Exponentiation is then
just a form of multiplication, in that x * x = x^2. So, to solve x^x,
you would need to make a new operation - one above exponentiation,
like multiplication is above addition. So let x^x = x@2, where "@" is
the symbol for this new operation, whatever it may be called. We get
this:

[eqn]x^x = 5\\
x@2 = 5[/eqn]

To solve, all we have to do is find the inverse of @2. I will use the
symbol & to signify the inverse operation of @. So we get this:

[eqn]x@2 = 5\\
(x@2)&2 = 5&2[/eqn]

And 5&2 is the answer. This is not the square root of 5. It would be
something "above" square roots, like x^x = 5. Is this the only way to
solve it? Calculators aren't programmed with operations above
exponentiation, and I'm not sure any exist... Are there other ways to
solve x^x = 5, or x^x = .5, whether x is real or imaginary or complex?

[Anonymous No.11185095]

I saw this problem in a question somewhere. The answer,
according to the response, was to enter a value for x, see if it
works, then go down or up, and try again... Say you have the equation:
[eqn]x^x = 5[/eqn]

You input 2 for x, and get
[eqn]2^2 = 4[/eqn]

So then you try 3, and get
[eqn]3^3 = 27[/eqn]

This is useless. The answer is irrational, and it will take a long
time to solve it. Using natural logs, you get this:
[eqn]x^x = 5\\
x \log_x = \log_5\\
x = \log_5/\log_x[/eqn]

This doesn't help. Here is what I did to solve it. Multiplication is
just a form of addition, in that x + x = 2x. Exponentiation is then
just a form of multiplication, in that x * x = x^2. So, to solve x^x,
you would need to make a new operation - one above exponentiation,
like multiplication is above addition. So let x^x = x@2, where "@" is
the symbol for this new operation, whatever it may be called. We get
this:
[eqn]x^x = 5[/eqn]
x@2 = 5

To solve, all we have to do is find the inverse of @2. I will use the
symbol & to signify the inverse operation of @. So we get this:
x@2 = 5
(x@2)&2 = 5&2

And 5&2 is the answer. This is not the square root of 5. It would be
something "above" square roots, like x^x = 5. Is this the only way to
solve it? Calculators aren't programmed with operations above
exponentiation, and I'm not sure any exist... Are there other ways to
solve x^x = 5, or x^x = .5, whether x is real or imaginary or complex?

[Anonymous No.11185121]

>>11185095
Another thing - why is addition commutative, multiplication
commutative, but not exponentiation? 2^3 is not equal to 3^2, and this
causes problems. Try to solve:
[eqn]2^x = 8[/eqn]
The answer is log(8)/log(2), I know. But log(x) is just 10^y = x,
where log(x) is y. This also seems stupid. You need a calculator with
built-in log functions to solve this. All you do is complicate the
equation 2^x = 8 with log functions. If exponents were commutative,
you would solve it like this:
[eqn]2^x = 8[/eqn] (so...)
[eqn]x^2 = 8\\
x = sqrt(8)[/eqn]

But this is not the case. Why?

[Anonymous No.11185198]

>>11184328
what in the world? people i've met are usually the opposite.

[Anonymous No.11185206]

>>11184328
One of the most important tools in mathematics is the capacity to abstract many concepts. If you want to prove shit for general shit you need to be capable of abstracting your concrete examples into general hypothesis.

[Anonymous No.11185209]

>>11185003
well, you've got the right map F. now you need to show it's a bijection. remember bijection means surjection + injection (onto + one-to-one).
take an arbitrary function g in C. what should you put into F in order to get g out of F? this is how you prove F is surjective.
now, just follow the definition of injectivity to find that F is injective - in other words, if F(a1, a2) = F(b1, b2), show that a1 = b1 and that a2 = b2.
carefully write down why!
then you'll have shown F is a bijection, and you'll be done.
alternatively, you could write down an inverse for F. this is not hard to do in this case. then you just need to show it's an inverse by showing G(F(a1, a2)) = (a1, a2) and F(G(f)) = f where G is your inverse to F.

[Anonymous No.11185216]

>>11185121
why should exponentiation be commutative? what makes you think such an operation would be commutative?
i wouldn't imagine many algebraic structures with commutative exponentiation are very interesting, indeed, then 1 = 1^0 (definition) = 0^1 (commutativity) = 0 (definition) so you're dealing with a trivial ring.
commutativity isn't always a good thing, it is a mighty restriction which kills all sorts of interesting and nuanced math and helps to make other interesting math possible.
associativity on the other hand, THAT'S the kicker. nonassociativity of exponentiation is fucking criminal.
>>11185095
there's no nice form for your answer, provably it is not able to be respresented by "elementary" functions.
what is elementary, you ask? polynomials and roots, logs, exponents, trig functions, etc.

[Anonymous No.11185256]

>>11184328
Mathematicians come in all shapes and forms, but I think most share a dislike for pedantry.
Making a statement more abstract than it needs to be does not make you sound smart. It makes you sound like a crackpot.
Now about the specific context you were referring to ( >>11184984 ) I think maybe what people mean by "real" things are things that are more or less tangible, eg. discrete groups, finitely generated abelian groups, vector spaces, manifolds, complex numbers, number fields, etc.
Basically things that are somewhat "finite-dimensional" over Q or R and computable to some extent.

[Anonymous No.11185274]

>>11184328
are you talking about analysis department ?

[Anonymous No.11185278]

>>11185256
>We dislike for pedantry
>but we want rigor as well!
Mathematicans once again go out of their way to describe the empty set

[Anonymous No.11185301]

>>11185095
>>11185121

[Anonymous No.11185584]

Post more of these. There was at least one more with fractions that I didn't save. Does anyone have it?

[Anonymous No.11185641]

can someone tell me, a brainlet, how this works? how does the 0.400 end up only in the denominator once?

[Anonymous No.11185664]

Some OC

[Anonymous No.11185723]

>>11185664
I'm sorry mate, maybe next time.

[Anonymous No.11185818]

>>11184328
they dont hate abstraction, they hate unnecessary abstraction and generality

[Anonymous No.11185828]

>>11185818
but isn't that the bread and butter of advanced math?

[Anonymous No.11185829]

>>11185828
no, thats the bread and butter of the undergrad category theorist

[Anonymous No.11185842]

>>11185818
They hate the undergrad category theorist.

[Anonymous No.11185864]

Right, a bit of basic probability for you all
Say I flipped a fair coin 10 times. How would you find the probability that neither heads nor tails ever comes up 3 times in a row?

[Anonymous No.11185872]

Right, a bit of basic probability for you all
Say I tossed a fair coin 12 times. How would you find the probability that neither heads nor tails ever comes up 4 times in a row?

[Anonymous No.11185890]

>>11185872
>Say I tossed a fair coin 12 times. How would you find the probability that neither heads nor tails ever comes up 4 times in a row?
is it 1854/2^12?

[Anonymous No.11185898]

>>11185664
The meme makes you look like you don't actually know what commutative algebra is about.

[Anonymous No.11185899]

>>11185890
I dont actually know the answer, the numbers in the question are totally arbitrary, I'm more interested in what different methods people would go about solving it which is why I said "how would you find" not "what is"

[Anonymous No.11185902]

>>11185872
for brainlets like me, just count explicitly the interesting cases out of all the cases

[Anonymous No.11185904]

>>11185899
I would find the probability that it has A = heads 4 times in a row, B= tails 4 times in a row, and C= heads and tails 4 times in a row. Then the answer is 1-(P(A) + P(B) - P(C))

[Anonymous No.11185911]

>>11185872
You can compute recurrent relation
[math]f(n, i, k) = f(n - 1, i, k - 1)[/math] for [math]i \gt 1[/math] and [math]f(n, i, 1) = \sum_{k=1}^{K}f(n-1, i - 1, k)[/math]. Where K is up to 3.

[Anonymous No.11185914]

>>11185911
for k > 1, I mean

[Anonymous No.11185996]

Inf(A + B) = inf(A) + inf(B), can the same be said about countable sum of sets: inf(Sum[n = 1, infty] An) = Sum[n=1,infty] inf(An) ?

[Anonymous No.11186005]

>>11185996
>inf(Sum[n = 1, infty] An)
How do you define Sum[n = 1, infty] An?

[Anonymous No.11186008]

forall a in R a in Sum[n = 1, infty] An iff
exists a1,...an,... in R a1 in A1,... an in An,... such that a = Sum[1,infty] ai

[Anonymous No.11186011]

>>11186005
>>11186008
actually R should be replaced R*, I think

[Anonymous No.11186015]

>>11186011
by R_{>=0} cup {+infty}, to be precise

[Anonymous No.11186023]

>>11185996
well since for any sum a_i, each a_i >= inf(A_i), we have inf(Sum A_n) >= sum inf(A_n).
Pick e>0, and take b_n < inf(A_n) + e/n^2. sum b_n <= sum inf(A_n) + eC for some constant C. Since e is arbitrary, inf(Sum A_n) <= sum inf(A_n), and you're done.

[Anonymous No.11186025]

>>11186023
forgot to mention that b_n lies in A_n

[Anonymous No.11186046]

Another question (sorry for trouble)
for any at most countable A,B we know that
Sum [i in A cup B] ai <= Sum[i in A] ai + Sum[i in B] ai
now given at most coutable familie of at most countable sets Ai is it true that
Sum[j in bigcup[i = 1,infty] Ai] aj <= Sum[i = 1, infty] Sum[j in Ai] aj?
I know that I basically already used implicitly the axiom of choice to well-define this question (so that I know that bigcup[i = 1,infty] Ai] is at most countable)
If this also turns out as yes I will accept the axiom of choice in my list of usable axioms

[Anonymous No.11186096]

I have a request for you /mg/

Can one of you jack off onto a piece of paper with math scribblings over it? I need a picture of this but can't find anywhere and I'm in no position to obtain such thing right now.

[Anonymous No.11186098]

>>11185641
please help a brainlet out...why doesn't the bottom one cancel out when you multiply all of the terms by 0.400?

[Anonymous No.11186133]

>>11184247

I got you covered nigga https://files.catbox.moe/pnp45u.pdf

[Anonymous No.11186149]

>>11186098

> multiply all of the terms by .4

The numerator of the left hand side is [math]\frac{(0.005+x)*x}{(0.400)^2}[/math].

When you multiply by [math]\frac{0.400}{0.400}=1[/math], the denominator becomes [math]0.150-x[/math] and the numerator becomes [math]\frac{(0.005+x)*x}{(0.400)}[/math].

[Anonymous No.11186151]

>>11186149

*the numerator becomes [math] \frac{ (0.005+x)*x }{ (0.400) }[/math].

[Anonymous No.11186160]

>>11186149
>>11186151
but why doesn't cancellation work? I would think that the 0.4 would stay in one of the numerators instead of it ending up in the denominator since there's two of them in the numerator and only one in the denominator

[Anonymous No.11186162]

>>11186096
That's degenerate. What the fuck is your problem?

[Anonymous No.11186170]

>>11186096
>can one of you
We can't.
Ask in /r/.

[Anonymous No.11186172]

>>11186160

I don't know how to answer that question chieftain. Just write it out.

Use the fact that a fraction [math]\frac{A}{B}[/math] can be written as a product [math]A*B^{-1}[/math].

[Anonymous No.11186179]

>>11186172
>Use the fact that a fraction ABAB\frac{A}{B} can be written as a product A∗B−1A∗B−1A*B^{-1}.
I know about that property, but I've never encountered it when the B is also a fraction...

do I flip that shit ?

[Anonymous No.11186189]

>>11186179

Assuming that B is a product, you "flip" every factor in the product.

This works because when you multiply B by B^{-1}, you're supposed to get 1. If you flipped every factor of B, then you can group the factors with their inverses and they will all cancel out.

[Anonymous No.11186195]

>>11186189
holy mother, it worked (assuming I did this correctly without breaking any rules)

[Anonymous No.11186313]

>>11185898
But then, what is commutative algebra.

[Anonymous No.11186540]

funny to think about how countries literally in flames like brazil and france can have world class institutes of mathematics lmao

[Anonymous No.11186551]

>>11186540
What does a problem with fires have to do with the quality of math institutions??

[Anonymous No.11186552]

can som1 pls explain why there is no algebraic relationship between area and volume?

[Anonymous No.11186556]

>>11186552
>can som1 pls explain why there is no algebraic relationship between area and volume?
Area = volume/depth

[Anonymous No.11186559]

What are some good books for physicsfags who need can't into PDEs for their quantum mechanics classes?

[Anonymous No.11186568]

>>11186540
>literally in flames like brazil and france
>look down at my arms
>look around the rest of my body
>look at the rest of my house
>look outside the window
>look back at my computer
>literally in flames
Huh, never noticed.

[Anonymous No.11186584]

>>11186552
Of a general object?
Eg. for a sphere there is one.

[Anonymous No.11186586]

>>11186552
there exist surfaces with infinite surface area but finite volume.

there exists surfaces of equal surface area and diffrerent volume, and vice versa.

That should tell you everything

[Anonymous No.11186591]

>>11186552
There are, but they're inequalities.

[Anonymous No.11186593]

>>11186586
>there exist surfaces with infinite surface area but finite volume.
doesn't there also exists surface area with infinite surface area and zero volume

[Anonymous No.11186594]

>>11186593
prolly

[Anonymous No.11186597]

>>11186540
>France
>in flames
Nigga turn off your tv

[Anonymous No.11186601]

>>11186594
i mean, an infinitely long straight line ticks the box

[Anonymous No.11186603]

>>11186601
sure, but i dont think a 1-dimensional example is particularly revealing

[Anonymous No.11186610]

>>11186594
A smooth closed surface? No, there isn't. Just project it onto (x, y, 0), select a small enough circle around (0, 0, 0) for the covering to be given by a finite amount of circles and do a basic volume inequality.
A shitty piece of shit fractal with barely measurable surface area? Maybe.

[Anonymous No.11186612]

>>11186593
Well yes.. Actually any infinite smooth surface will do. A plane for example

[Anonymous No.11186696]

If I have a complex inner product space V, is it OK to call the group of isometries SU(V)? I don't want to say SU(n) since I'm not making any reference to the dimension of V.

[Anonymous No.11186698]

>>11186696
Sure. You see GL(V) all the time, don't you?

[Anonymous No.11186701]

>>11186698
OK, makes sense. Thanks.

[Anonymous No.11186706]

>>11184707
Will you be attending SUMM?

[Anonymous No.11186707]

>>11185095
tetration

[Anonymous No.11186868]

Who else is taking the Putnam next week? How are you preparing?

[Anonymous No.11186876]

I found a stack answer that for any 2-form in the punctured plane [math]\omega(x,y) = g(x,y) dx \wedge dy[/math] we can construct an explicit potential function [math]h(x,y) = \int_1^{\sqrt{x^2+y^2}} t\, g\left(\frac{tx}{\sqrt{x^2+y^2}}, \frac{ty}{\sqrt{x^2+y^2}}\right) \,dt[/math] showing that it is also exact. Maybe I'm doing a really stupid calculus error but using Leibniz rule (for integrals) and computing the exterior derivative explicitly, I only seem to get [math](g(x,x)+\frac{1}{x2+y2}\int_1^{\sqrt{x^2+y^2}} t\, \left(x\frac{\partial g}{\partial x}+y\frac{\partial g}{\partial y}\right)dt)dx \wedge dy[/math]. And I don't know how to get rid of this extra term.

[Anonymous No.11186890]

>>11186876
>potential function
>for a two-form
I'm extremely confused, can you link to the stack thread?

[Anonymous No.11186894]

>>11186890
https://math.stackexchange.com/questions/612837/how-to-compute-the-de-rham-cohomology-of-the-punctured-plane-just-by-calculus/613088 The computation of the second homology group. I forgot to put that the one form is [math]h(x,y) d\theta[/math] with [math]d\theta = \frac{-ydx + xdy}{x^2 + y^2}[/math]

[Anonymous No.11186898]

>>11186868
A reminder that if you don't make at least a 10, you'll never make it

[Anonymous No.11186918]

>>11186898
>You got a 1 last year
oof, guess I'll just die.

[Anonymous No.11187041]

I've got 2 differentials equations that models the motion of a spring-mass-damper system.
[eqn] m_2\ddot{x}_2+c_2\dot{x}_2+k_2x_2-c_2\dot{x}_1+k_2x_1=f(t)\\m_1\ddot{x}_1+(c_1+c_2)\dot{x}_1+(k_1+k_2)x_1-c_2\dot{x}_2-k_2x_2=0 [/eqn]
where all the Cs and Ks and Ms are constants and f(t) is an arbitrary forcing function of time.

Q: is there any good way to simplify this system other than writing down the transfer function?

[Anonymous No.11187044]

>>11187041
oops, the last k2x1 term in the first line is supposed to have a subtraction sign in front of it, not an addition sign

[Anonymous No.11187104]

>>11186898
>10/120 is your benchmark for success
dont set the bar too high there bud

[Anonymous No.11187115]

>>11185584
>giving the universal coefficient theorem as a hint
[math] H^*( ; ) \cong [x]/(x^{n+1}) [/math] with [math] |x| = 1 [/math].

[Anonymous No.11187132]

>>11186313

it is highly related to geometry. in fact, most of it is about algebraic geometry

[Anonymous No.11187236]

>>11186559
Brezis.
>>11186696
Isometries are unitaries, not just special unitaries.
>>11186876
The coordinate function in the second term is symmetric under [math]x\leftrightarrow y[/math].
>>11187041
Sure. Just linearize around hyperbolic fixed points.

[Anonymous No.11187278]

>>11187236
>nearize around hyperbolic fixed points
they are already linear, no? where can I read about this?

[Anonymous No.11187481]

What is a good abstract algebra textbook at intermediate level between undergraduate and graduate? Is "Algebra: chapter 0" or "Abstract algebra" from dummit and foot good? Any recommendations?

[Anonymous No.11187619]

>>11187481
Just go for a graduate algebra text.
It won't bite, I promise.

[Anonymous No.11187628]

>>11185664
this is unironically worst "meme" I have ever seen. also seconding >>11185898

[Anonymous No.11187666]

>>11187619
Which one then?

[Anonymous No.11187668]

>>11187666
dummit dummy

[Anonymous No.11187678]

>>11187666
Any of them works. Lang, Alluffi, Grillet, Rotman, the Encyclopedia of Mathematical Sciences's Algebra sequence, etc.

[Anonymous No.11187681]

>>11187481
>What is a good abstract algebra textbook at intermediate level between undergraduate and graduate? Is "Algebra: chapter 0" or "Abstract algebra" from dummit and foot good? Any recommendations?
catch-all algebra books are a literal waste of ink, get a proper book on group theory, a proper book on homological algebra, etc.

[Anonymous No.11187684]

>>11187681
wot bout the coommutative algebraist?

[Anonymous No.11188058]

If I have a bitstring of length 10 with 6 1s and 4 0s, how can I work out the number of arrangements where neither 1 nor 0 ever appears 3 times in a row?

[Anonymous No.11188101]

>>11183694
How much calculus should I know to understand probability / statistics? I've forgotten the majority of what I learned in college and want to relearn the essentials for what I'll need for my MS program.

[Anonymous No.11188110]

>>11187041
>PDE’s
Take you and your applied faggotry to >>>/lgbt/

[Anonymous No.11188117]

>>11185301
ah, the W function

[Anonymous No.11188124]

>>11188101
>probability in a masters
The entirety of classical real analysis, all the way from multivariable calculus to measure theory.
However, they might teach you measure theory again in the beginning, depending on the program.

[Anonymous No.11188149]

>>11188110
No ;3

[Anonymous No.11188218]

Where do some definitions come from? Like for a countably infinite set? If it has one-to-one correspondence with the natural number set, then it is countably infinite. Why is that the definition? Could a different set have been chosen for the definition? Or is the set of natural numbers the most basic so choosing a different set would not be the simplest definition?

[Anonymous No.11188235]

>>11188218
God made the natural numbers; all else is the work of man.

[Anonymous No.11188239]

>>11188218
Definitions come from experts in the field deciding that a certain definition is more useful than another. You could potentially rewrite the definition of countably infinite to mean there exists a one to one correspondence with the set of rational numbers, or the set of even integers, or the set of multiples of 117, but using the natural numbers is just the most obvious and intuitive choice.

[Anonymous No.11188240]

>>11188218
The natural numbers were the first set the human mind was familiar with, and anything conceivable as a discrete entity must be mapped to a natural number. You cant have "half a thought".

To answer the question more generally:

Welcome to foundation of mathematics, Its literally all just intuitive notions and concepts. Literally everything is just made up and if its consistent with everything else, its okay.

[Anonymous No.11188247]

>>11188218
>Where do some definitions come from?
From mathematicians. Usually at some point some mathematician publishes something and over time his definitions get accepted by other mathematicians and become part of standard mathematical literature.

>Could a different set have been chosen for the definition
Yes, for example the natural numbers divisible by two, that is an equivalent definition. But if you have multiple equivalent definitions the simplest and most intuitive one usually should be chosen.

[Anonymous No.11188249]

>>11188110
>PDE’s
It seems to be an ODE?
Can you not tell the difference, Mr. Undergrad?

[Anonymous No.11188264]

>>11187041
>good way to simplify this system
Pretty sure that if you just sum the two equations a bunch of shit cancels out.

[Anonymous No.11188267]

>>11188110
>NO! YOU CAN'T TALK ABOUT "THAT" MATH HERE!! ONLY MY SPECIAL AUTISM SANCTIONED MATH!!!

[Anonymous No.11188278]

>>11188249
Sorry i dont dabble in appliedshit mr engineer poojeet

[Anonymous No.11188282]

>>11188267
Go make your own thread you dumb physishit. Nobody gives a flying fuck about your engineer tier homework problems you fucking faggot

[Anonymous No.11188285]

>>11188282
then call the thread "pure math" general next time you fucking retarded incel. imagine getting so wound up over something so minuscule. ego issues much?

[Anonymous No.11188302]

Ok so I started Abstract Algebra from Dummit and Foote based on your recommendations, it's comfy.

[Anonymous No.11188321]

>>11187681
what's a good "proper" book on group theory?

[Anonymous No.11188348]

>Ok so im a retarded faggot who deserves to be liquidated and im comfy being a blight on this earth :P

[Anonymous No.11188351]

>>11188110
>PDE’s
brainlet

[Anonymous No.11188355]

>>11188351
alas, that is one's mind on category theory. many such cases. sad!

[Anonymous No.11188357]

>>11188278
>appliedshit
What is "applied" about PDEs?
It certainly is less applied than things like number theory.

[Anonymous No.11188391]

>choose a PhD advisor
>already having doubts if it was a good choice
fuk

[Anonymous No.11188402]

>>11188218
>>11188239
>>11188240
>>11188247
All answers are retarded or could it be the same poster posted his thing thrice?
A set B is countably infinite iff there exists its proper subset A and a bijection f from A to B.
Prove that this definition is equivalent to the one with natural numbers.
Also there is a definition of a finite set that is expressed only in terms of set itself and does not refer to natural numbers. (Think of a one)

[Anonymous No.11188421]

>>11188402
>A set B is countably infinite iff there exists its proper subset A and a bijection f from A to B.
>every Dedekind infinite set is now countable

[Anonymous No.11188427]

>>11188402
Neither do you answer his question, not do you make a meaningful comment.
It's probably you who is retarded.

[Anonymous No.11188431]

>>11188402

[Anonymous No.11188454]

>>11188391
Just hope that he has to fuck off and you have to pick a new PhD advisor!

[Anonymous No.11188461]

>>11188402
I bet your parents used to call you blockhead.

[Anonymous No.11188575]

>>11187236
>The coordinate function is symmetric under [math]x \leftrightarrow y[/math]

Don't really understand what to do with that. I suppose you mean an arugment that uses the antisymmetry of the wedge product, but symmetric coordinate functions are perfectly valid.

[Anonymous No.11188631]

>>11188357
>number theory
>more applied than PDE
please tell me you're not being serious

[Anonymous No.11188739]

>>11188575
don't listen to that autist.

[Anonymous No.11189004]

>>11185584
Found it.

[Anonymous No.11189060]

>>11187481
Richard Elman UCLA lecture notes has to be the way to go

[Anonymous No.11189104]

>>11188058
N= All arrangements - the ones with strings of 3 of 1 or 0 or both

[Anonymous No.11189162]

>*cracks open a beer*
>*turns on blackpenredpen 7 hour integral video*
ahhhh....saturday night well spent

[Anonymous No.11189335]

>>11188631
freshman, you do not know how mathematicians study pde.
it's pathetic reading your posts and knowing it's you coping on /mg/ about how when you got to college there were smarter people than you everywhere.

[Anonymous No.11189342]

>>11188302
Aluffi is a modern and much better approach. It's often called the new D&F.

[Anonymous No.11189371]

Could anons that intuitively understand diff geometry and forms comment/explain these two passages?
1)
>Since differential forms exist on an open set, not just
at a single point, there is a notion of differentiation for differential forms
I don't see why they are not defined just at a point (like vectors/derivations). By definition it's a linear functional on vectors so if vectors are defined pointwise, shouldn't the forms be as well?
And does this mean that, unlike vectors, I can add forms in a small neighborhood?
2) The top answer to this question
https://math.stackexchange.com/questions/2721933/can-you-really-integrate-functions
Could anyone illustrate this using a constant function on an interval? The proof seems logical but if it's so simple, why I haven't encountered it in any of the dozen or so books on differential geometry?

[Anonymous No.11189392]

Does anybody here have a physical copy of Pugh's Real Mathematical Analysis? Can you tell me about the quality of the printing? A lot of people are complaining on Amazon about the physical book having a trash quality, poor printing etc etc, but a lot are also praising it.

[Anonymous No.11189398]

>>11189392
What if based Pugh is a conman snake like all Californians?

[Anonymous No.11189402]

>>11189398
I think that's more of a problem with the jews at Springer than Pugh himself. Those motherfuckers charge $60 for a book and they make it the cheapest way possible literally, just read some of the comments on amazon about Pugh's book, Springer really drops the ball when it comes to physical books.

[Anonymous No.11189508]

>>11189392
I printed a .pdf like a true big cock brainchad. Springer can go fuck themselves.

[Anonymous No.11189565]

>>11183694
"This implies an equivalence relation on the set of topological spaces."
If X and Y are the topological spaces, how would this sentence be written in set builder notation or using logical operators or something that would make it more clear?

Would it be like this?
For all x in X and y in Y, x ~ y

[Anonymous No.11189570]

>>11189565
This is the full paragraph for context:

"Suppose f : X Y is a bijective (one-to-one and onto) function between
topological spaces X and Y . Since f is bijective, the inverse f −1 exists. If both
f and f −1 are continuous, then f is called a homeomorphism. Two topological
spaces X and Y are said to be homeomorphic, denoted by X ∼
= Y , if there exists a
homeomorphism between them. This implies an equivalence relation on the set of
topological spaces (verify that the reflexive, symmetric, and transitive properties
are implied by the homeomorphism)."

[Anonymous No.11189576]

>>11189570
The paragraph comes from here
http://planning.cs.uiuc.edu/node130.html

[Anonymous No.11189591]

>>11189565
>>11189570
>For all x in X and y in Y, x ~ y
No. The equivalence relation ~ is on the set of topological spaces (i.e. x and y should be topological spaces and not elements of topological spaces) and the relation x ~ y means that x and y are homeomorphic.

Try to write the sentence with set builder notation now.

[Anonymous No.11189595]

>>11189570
>>11189565
The class of topological spaces is not a set as every set can be made into a topological space and the class of all sets is not a set.

[Anonymous No.11189606]

>>11188218
>Could a different set have been chosen for the definition?
Yes. You could use the integers, for example.
>Or is the set of natural numbers the most basic so choosing a different set would not be the simplest definition?
That's pretty much the reason why.

[Anonymous No.11189621]

>>11189591
For all elements in the set of topological spaces, element ~ element
maybe?

[Anonymous No.11189623]

>>11189595
What the hell are you saying?
>the class of topological spaces is not a set
A class is a set. Why wouldn't it be a set?
>every set cam be made into a topological space
True. This has nothing to do with the class of topological spaces being a set though, so I don't understand what the fuck you're saying. Maybe you're interpreting what he wrote as having stated that the class of topological spaces is a topology, or maybe you're confusing a topology with a topological space. If you are, it is true also that the class of topological spaces is not a topology.

[Anonymous No.11189626]

>>11189621
Yes.

[Anonymous No.11189645]

>>11189626
thanks

[Anonymous No.11189647]

>>11189623
https://math.stackexchange.com/questions/1641036/is-the-set-of-all-topological-spaces-bigger-than-the-set-of-all-metric-space This is really basic shit.

[Anonymous No.11189652]

>>11189623
>>11189623
such a stupid post. equip the set of all topological spaces with the discrete topology. does it contain itself?

[Anonymous No.11189655]

>>11189595
Are you saying the author of my textbook is wrong or that my other post is wrong?

[Anonymous No.11189660]

>>11189655
Maybe the author is only talking about the set of X and Y and not the set of all topological spaces, I'm not sure.

[Anonymous No.11189663]

>>11188631
>please tell me you're not being serious
Number theory is wildly used in CS, if you ever saw a PDE course you wouldn't be so retarded.
Spoiler, a PDE course isn't "let's solve this basic PDE".

[Anonymous No.11189664]

>>11189655
If your textbook uses the term "the set of all topological spaces" without clarification, then it's pretty much wrong. Proving that the identity is a homeomorphism("reflexivity)", the inverse of a homeomorphism is a homeomorphism ("symmetry"), and that the composition of homeomorphisms is a homeomorphism ("transitivity") is fine.

[Anonymous No.11189666]

>>11189663
PDEs are the basic object used all the fucking time in physics and engineering and whole fields of study are dedicated to a particular pde or a class of similar ones.

[Anonymous No.11189670]

>>11189652
Ah, my bad. The most set theory I've ever encountered was in a topology class, so I never heard of a proper class before.

[Anonymous No.11189682]

>>11189664
>If your textbook uses the term "the set of all topological spaces" without clarification, then it's pretty much wrong.
It doesn't, it just says "Two topological
spaces X and Y are said to be homeomorphic if there exists a homeomorphism between them. This implies an equivalence relation on the set of topological spaces." I don't know if that's talking about the set of all topological spaces or just X and Y.

[Anonymous No.11189692]

>>11189682
>I don't know if that's talking about the set of all topological spaces or just X and Y.
It's definitely talking about the set of all topological spaces. According to the other poster, this is not really a set, but for the purposes of topology it's fine to regard it as one. The problem with describing it as a set isn't very relevant to what the author of your book is trying to say.

[Anonymous No.11189750]

>>11189666
sure thing, but mathematicians who study pde do not study applied math. they study functional analysis, dynamical systems, and geometry. it's very very pure.
you almost never do anything of use to a physicist or an engineer as someone working in PDE.

[Anonymous No.11189755]

>>11189692
I think I get it now; the author is saying that homeomorphisms themselves are reflexive, symmetric, and transitive, and that this will be the case for any homeomorphic topological spaces.

[Anonymous No.11189777]

>>11189663
>if you ever saw a PDE course you wouldn't be so retarded.
>Spoiler, a PDE course isn't "let's solve this basic PDE".
and how is this relevant ? we're talking about applicability of the field as a whole, not about content in some course (which differes greatly by the target audience)
I'm not disputing that number theory is applicable, of course it is. but PDE is literally as applied as it gets, and I'm not even gonna write why, you have to be brain dead to not see that, lmao.
>spoiler, ""heat"" equation is not named by coincidence

[Anonymous No.11189784]

>>11189750
I could say the exact same thing but replace "someone working in PDE" by "someone working in number theory"

[Anonymous No.11189838]

>>11183694
Would anyone be able to tell me why these graphs don't map into homeomorphic subsets of R2?

[Anonymous No.11189859]

>>11189838
Let A and B be homeomorphic. If I delete a point x of A, I can delete a point y of B such that A\{x} is homeomorphic to B\{y}.
Corollary: Let A and B be homeomorphic. If I delete a point x of A, I can delete a point y of B such that A\{x} and B\{y} have the same number of connected components.

Example of application of corollary: Delete a point on the unit circle. The result is homeomorphic to the open unit interval and connected. Deleting any point on the line makes it stop being connected, so the line and the circle aren't homeomorphic.

[Anonymous No.11189876]

>>11189859
>Deleting any point on the line makes it stop being connected, so the line and the circle aren't homeomorphic.
Could you clarify which one of the graphs you are talking about (if you're talking about one of the graphs in the picture)?

[Anonymous No.11189878]

>>11189876
The first two, though rather than a line, it's the closed unit interval.
I've also messed up because you can delete the edges, but the general technique works for most of those.

[Anonymous No.11189887]

>>11189878
Sorry, which edges can you delete?

[Anonymous No.11189889]

>>11189887
These.

[Anonymous No.11189893]

>>11189889
Aren't those vertices/nodes?

[Anonymous No.11189982]

>>11189893
there exist a point in the closed interval such that if you delete the point, the space will become disconnected with two components. there is no point with this property on a circle. therefore closed interval and circle are not homeomorphic.
use similar reasoning to show that no two graphs from the figure are homeomorphic.

[Anonymous No.11190132]

>>11189777
>and I'm not even gonna write why,
Of course not. Else everybody would realize that you are an idiot.

>we're talking about applicability of the field as a whole
Number theory is used in CS, just like PDEs are used in engineering.
Where is the difference?

[Anonymous No.11190172]

>>11190132
>Where is the difference?
if we didn't know number theory, we would probably still have computers, albeit much slower and not secure etc. if we didn't know PDEs, we wouldn't have any technology whatsoever with computers being only the tip of the iceberg.

[Anonymous No.11190281]

are these terms equal? I solved it the first way by using the fact that 3sqrt(3x) = 3x^1/3, then took the integral of that, but my book says the answer is the second one

[Anonymous No.11190295]

>>11190281
On the left, you need to put the 3x in parentheses.

I.e. (3x)^1/3

[Anonymous No.11190297]

>>11190172
So you are measuring "appliedness" in terms of impact in other areas?
That's idiotic, but okay.

[Anonymous No.11190309]

>>11190295
thanks, I guess I've gotten accustomed to problems being sqrt(x), with x being on its own, so there's no need for the parenthesis when you change it to powers

[Anonymous No.11190797]

This isn't really a question about mathematics, but I'm about to graduate with my BS in math. My favorite professor whose research I am already invested in wants me to go to grad school, but looking 4 years down the line, what do you do postdoc if not teach or be a corporate research slave?

[Anonymous No.11191115]

>>11189982
Is it because of a violation of surjectivity, injectivity, or continuity?

[Anonymous No.11191188]

>>11190797
Live the Kaczynskian dream

[Anonymous No.11191453]

>>11191115
what do you think ?

[Anonymous No.11191476]

>>11187041
So does nobody besides yukarianon know? I love you yukari baby, but your explanation makes no sense to me.
>>11188264
No, that doesn't work.

[Anonymous No.11191548]

>>11191476
>your explanation makes no sense to me.
https://en.wikipedia.org/wiki/Hyperbolic_equilibrium_point

[Anonymous No.11191549]

Can the totient function be used for results in number theory that don't involve primes?

[Anonymous No.11191560]

>>11191549
The degree of the m'th cyclotomic field over Q has size phi(m)

[Anonymous No.11191562]

>>11191548
I'm humble enough to admit I pretty much only understand half of that. In what kinda textbook can I learn more?

[Anonymous No.11191581]

>>11189784
you’d still be a buffoon for your original post

[Anonymous No.11191585]

>>11191549
>results in number theory that don't involve primes
What did he mean by this?

[Anonymous No.11191595]

UH OH feeling sexy... Yaaaas,, time to do category theory yayaya. Tsksksksksk.

[Anonymous No.11191599]

>>11191595
mmmmmmmmpfffff
updoots?
I am only an undergrad btw. I hope I don't come across as too advanced or intimidating yayayayaya tsksksksksk

[Anonymous No.11191606]

>>11191581
which one

[Anonymous No.11191609]

man, you really are a sad excuse of a poster you know that? why are you so obsessed about trannies?

[Anonymous No.11191611]

>>11191609
who's obsessed?

[Anonymous No.11191624]

>who's obsessed?

[Anonymous No.11191630]

>>11191562
Stable manifolds, hyperbolic fixed points, Hartman-Grobman and the like?
An ergodic theory/dynamical systems textbook, i.e. Yves Coudène's.

[Anonymous No.11191640]

[Anonymous No.11191646]

>>11191630
ty <3

[Anonymous No.11191657]

>>11191599
>>11191595
I want to stab this tranny so bad.

[Anonymous No.11192030]

>>11191453
Maybe continuity because if you delete a point, then the circle would be an open set but the line wouldn't

[Anonymous No.11192080]

>>11190797
Don't do it. With a math background you can get any kind of job that pays better and has less bullshit than in academia.

[Anonymous No.11192104]

>>11191657
the only thing unattractive about her is her shit taste in what is interesting to study

[Anonymous No.11192163]

>>11192104
>her

[Anonymous No.11192229]

These questions are from a math competition I participated in a week ago and I still can't find an answer for them. Anyone have any idea how to approach these?

Evaluate the following limit:

[eqn]\lim_{n \to \infty} n^{-2} \sum_{i=1}^{\infty} \sum_{j=1}^{n^2} \frac{1}{\sqrt{n^2+ni+j}}[/eqn]

Eliminate [math]\theta[/math] from the equations:

[eqn]\cos^3(\theta) + a\cos(\theta) = b [/eqn][eqn]\sin^3(\theta) + a\sin(\theta) = c [/eqn]

[Anonymous No.11192246]

>>11183991
>physicists
>picture of penises on the wall
>closeup of a gaping anus on the computer screen
physicshomos. not even once.

[Anonymous No.11192261]

>>11184687
It's a famous comic drawn by Dijkgraaf (the D in WDVV). It appeared in the cover of some IAS notes on quantum field theory course for mathematicians.

[Anonymous No.11192262]

>>11185842
>>11185829
>be brainlet and very gay analyst
>no longer creative, just memes about undergrad category theorists 95% of the time
rent free

[Anonymous No.11192265]

>>11192229
>Anyone have any idea how to approach these?
What have you tried?

[Anonymous No.11192269]

[Anonymous No.11192278]

>>11192229
First one is obviously 0
Simply prove the series converges using whatever criterion so as n tends to infinite you dont end up with a 0•∞ indetermination.


Second one id use complex numbers (sin and cos definition using complex exponent)

[Anonymous No.11192305]

>>11192265
I suspect the trig question will come down to some obscure version of the Pythagorean identities or maybe the half angle, double angle, etc formulas, but I haven't found anything useful.

>>11192278
>Simply prove the series converges using whatever criterion
And which series test would you use to prove that?

[Anonymous No.11192581]

>>11192080
Where are those dreamy jobs? I want one too.

[Anonymous No.11192855]

>>11192581
>dreamy
Ordinary ones, are you retarded? For you anything not in academia is dreamy? Are you an undergrad?

[Anonymous No.11192892]

Now that the dust has settled, [math] \mathbb R [/math] or [math] \bf R [/math] ?

[Anonymous No.11192907]

Can one of ya'll help me out?? How do I show that [math] \{a + b\omega : a,b \in \mathbb{Z}[/math] for [math] \omega = e^{2\pi i/3}[/math] is closed under multiplication?? I can't getit for the life of me damnit

[Anonymous No.11192911]

>>11192907
note that w^2 = - w - 1

[Anonymous No.11192912]

>>11192911
FUCK

[Anonymous No.11192950]

What is the group [math]\{1, -1 , \pm\frac{1}{2} + i \frac{\sqrt{3}}{2}, \pm\frac{1}{2} - \frac{\sqrt{3}}{2}\}[/math] isomorphic to??

[Anonymous No.11192958]

>>11192950
w^3 = 1
and -1
That's C6 ( for odd m, mth cyclotomic field isomorphic to 2m)

[Anonymous No.11192961]

>>11192892
>that book
Who are you? Let's be friends.

[Anonymous No.11192962]

>>11192950
nvm lamo

[Anonymous No.11192993]

>>11192229
the sums in your first problem don't converge

[Anonymous No.11193002]

>>11192907
>>11192950
how is your homework going my friend, finished already???

[Anonymous No.11193028]

>>11193002
Yes. The second problem was quite easy after remembering exponential form for complex numbers. The anxiety of it being due in 53 minutes usually translates to me covering my bases on /sci/. I made an error on that problem and didn't notice it until around 6 AM this morning. It was a four part problem and the error was on the first part, so it delegitimized my entire proof. I'm done now, thankfully, so thanks mates. Got an email from a prof. interested in my work a few days ago, and there's a strong chance that I'm going to do a PhD in the biomedical sciences, even though my BS is in math... not sure why I'm saying this, weird story. Gonna grab a coffee and then to class. Have a good Monday gamers

[Anonymous No.11193057]

>>11192961
https://youtu.be/tkS_6xY132g

[Anonymous No.11193661]

Let [math]M[/math] be an oriented Riemannian manifold. On one hand we have [math]TM[/math] and the Riemann tensor considered as a section of some bundle of endomorphisms: for each pair [math]X_p,Y_p \in T_pM[/math] we have [math]R(X_p,Y_p) \in \mathfrak{so}(T_pM)[/math]. On the other hand we have the principal [math]SO(n)[/math]-bundle [math]FTM[/math] of frames on [math]TM[/math] and the [math]\mathfrak{so}(n)[/math]-valued curvature 2-form [math]\Omega[/math]. Can you please explain the relationship between [math]R[/math] and [math]\Omega[/math], preferably without the reference to an explicit choice of frame?

[Anonymous No.11193703]

>>11193661
Does this help?
https://mathoverflow.net/questions/121792/scalar-curvature-notion-for-cartan-connections

[Anonymous No.11193748]

Does this mean that the derivative is never zero or that it's not always zero?

[Anonymous No.11193754]

>>11193748
Never zero.
You can make just about any curve smooth if you let the derivative zero.

[Anonymous No.11193758]

>>11193754
So the path traced by y=x^2 isn't smooth?

[Anonymous No.11193762]

>>11193758
Are you pretending to be retarded?

[Anonymous No.11193765]

>>11193748
Good catch, actually - to say "the derivative of the path" is non-zero is formally not what they mean, they should say that that function is non-zero at each point t.

>>11193758
The curve is in C and the only interpretation of the one you wrong down is [math] \gamma(t) := (t, t^2) [/math]. The derivative of that is [math] \gamma(t) := (1, 2t) [/math] and this is never zero.

[Anonymous No.11193766]

>>11193748
It isn't the zero function, the derivative can be zero on parts (which would correspond to the path "stopping" for a time before resuming).

[Anonymous No.11193768]

>>11193748
>>11193754
in all differential geometry a smooth curve means that the derivative exists everywhere. it can be zero somewhere, it can be zero everywhere, not important. if you add the requirement that the derivative is always non-zero, then it's usually called a regular curve.
I don't know if there's a different terminology used in complex analysis.

[Anonymous No.11193771]

>>11193765
Ohhhh gotcha, should they have said zero vector?

>>11193762
No, I'm just looking at my complex analysis textbook for next semester, I'm new to this

[Anonymous No.11193774]

typo: the second function (the derivative of gamma) should get a prime, [math] \gamma' [/math].

Again, note that the parameter is real and the image value is complex.

[Anonymous No.11193777]

>>11193771
>should they have said zero vector
Well then you'd have to call every complex number a vector..

[Anonymous No.11193789]

>>11193768

[Anonymous No.11193797]

>>11193789
are you color blind by chance?
>>11193748
stupid question

[Anonymous No.11193799]

>>11193789
I approve of your use of yellow on white

[Anonymous No.11193806]

>>11193789
what's your point ?

[Anonymous No.11193816]

I thought about it some more, if the derivative is zero, the function really isn't pointing anywhere. That may be a stupid analogy but I get the idea.

[Anonymous No.11193822]

>>11193816
I literally just drew the issue for you, it can just do a fucking L-turn if you let the derivative zero.

[Anonymous No.11193825]

>>11193816
in particular it prevents the curve from turing around and flowing back

[Anonymous No.11193827]

>>11193822
Your drawing helped, I was just putting it into words

[Anonymous No.11193828]

>>11193799
go back

[Anonymous No.11193849]

Speaking of which, I have pic related for Complex Analysis, anyone have any other recommendations or input?

[Anonymous No.11193856]

>>11193849
Kodaira is best.

[Anonymous No.11193858]

>>11193789
it's not "intuitively smooth" only if you identify the curve with its trajectory. it's perfectly smooth as a motion, which is what a curve represents in the first place.

[Anonymous No.11193868]

>>11193856
>100$+ on amazon
Is the second edition by Stewart and Tall any good? Or is there a PDF of either floating out there?

[Anonymous No.11193877]

>>11193868
>pdf around
Obviously, good old libgen.

[Anonymous No.11193994]

I'm interested in geometric art. I came up with this method of computing a quantized/digital circle's point coordinates using the real numbers. Anything cool I can go with in this direction? Any theorems I should know?

[Anonymous No.11194025]

How do I improve my writing on a blackboard? Whenever I do a talk/lecture on a blackboard, not using a beamer, I feel that it kind of sucks because stuff gets less and less readable as time moves on, and I either write to many or too few details down.

[Anonymous No.11194036]

>>11193994
I think you're just computing the floow of [math] r^2-x^2 [/math] for all [math]x<r[/math], but yeah this sort of setup has a rich history*
See also diophantine geometry and quadratic forms.

*see
https://en.wikipedia.org/wiki/Gauss_circle_problem

[Anonymous No.11194083]

there ya go


y[r_, x_] := Sqrt@Floor[r^2 - x^2]

getRekt[r_, x_, s_] := Rectangle[{x, s y[r, x]}, {x + 1, s y[r, x] + 1}]

pic = Table[
Graphics[
Table[{Thick, Red, getRekt[r, x, s]}, {x, -r, r}], {s, -1, 1, 2}]]
, {r, 0, 20}];

Export["circleJerk.gif", pic];

[Anonymous No.11194091]

>>11194083
I should have done Sqrt@Floor instead of Floor@Sqrt but whatever

[Anonymous No.11194097]

there ya go


y[r_, x_] := Sqrt@Floor[r^2 - x^2]

getRekt[r_, x_, s_] := Rectangle[{x, s y[r, x]}, {x + 1, s y[r, x] + 1}]

pic = Table[
Graphics[
Table[{Thick, Red, getRekt[r, x, s]}, {x, -r, r}], {s, -1, 1, 2}]]
, {r, 0, 20}];

Export["circleJerk.gif", pic];

[Anonymous No.11194101]

with Ceiling and up to r=40

[Anonymous No.11194102]

>>11194083
>>11194091
>>11194097
Thanks for the stroke, retards. Now go back to >>>/trash/

[Anonymous No.11194106]

>>11194102
reee

PS I switched around Floor@Sqrt in the text snipped but failed to edit it in the text, reee2

[Anonymous No.11194119]

>>11194025
these tips are mostly obvious but many people still fuck those simple things up
- don't write too small letters
- make sure your lines of writing are horizontal. a lot of people write lower and lower when they go from left to right on the blackboard
- often one is writing a sentence or symbols and you've reached the right side of the blackboard but also you have just already finished the sentence. do not try to squeeze it in, continue writing FROM THE LEFT SIDE OF NEW LINE
- wipe the fucking blackboard properly i am triggered when traces of previous writing are left
as for the amount of detail, I think giving not enough detail is a more common problem than giving too much detail.

>>11193994
your question is very general
drawing curves with pixels is basic computer graphics, google bresenham's line algorithm

[Anonymous No.11194138]

>>11194119
>bresenham's line algorithm
going down your route I found
https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

[Anonymous No.11194169]

>>11194119
>blackboard stuff
Thanks for the advice! I think that one of the problems with being too detailed is that you lose too much time as some people in the audience always think that it's necessary to ask more detail questions the more you try to give them in the first place.
Probably dropping cursive writing would also be a good idea, at leas on a blackboard.

[Anonymous No.11194198]

Are these two articles redundant? See "sum of positive divisors function" under Definition in the Divisor function article
https://en.wikipedia.org/wiki/Divisor_function
https://en.wikipedia.org/wiki/Divisor_summatory_function
Asking to see if I should request a merge

[Anonymous No.11194233]

Does the maths general know of any good mathematical podcasts?

[Anonymous No.11194258]

>>11194198
the second sums over all naturals smaller than the argument, the first only over the dividing ones

>>11194233
I'd be interested in that too - although I'd think it's hard to find an audience. I'd do podcasts if people were interested. Needs people who're reed a lot (or work really a lot) and willing to rant about that periodically - do you know any such folks?

[Anonymous No.11194273]

>>11194198
I think the first only over the dividing ones (to some power), while the second (for k>1) takes into account how to further divide that divisor.
quote
> More generally, one defines (...) where dk(n) counts the number of ways that n can be written as a product of k numbers

>>11194233
I'd be interested in that too - although I'd think it's hard to find an audience. I'd do podcasts if people were interested. Needs people who're reed a lot (or work really a lot) and willing to rant about that periodically - do you know any such folks?

[Anonymous No.11194327]

How do you get into mathematics while being a retard at physics? I like number theory because I can understand the results - I rarely understand the proofs. But I also find it depressing because it's not clear to me how, for example, algebraic number theory, is applicable to the natural world.

[Anonymous No.11194355]

>>11194327
Sounds like engineering is more your speed

[Anonymous No.11194441]

>>11194327
A little bit in cryptography

[Anonymous No.11194445]

>>11194327
Just do it? If you like a topic in math, e.g. number theory, and you understand the results than that's a good sign. Proofs are in general difficult at the beginning of your studies, and by beginning I mean at least 1.5 years. So don't worry too much, in particular not about physics.

[Anonymous No.11194454]

>>11194273
I'm curious about a podcast, but it might be a better idea to start a blog for math. Listening to rambling about mathematics makes me incontrollably angry, and I know for a fact that this is in some intensity true for at least 80% of mathematicians.

[Anonymous No.11195103]

>>11194327
>it's not clear to me how, for example, algebraic number theory, is applicable to the natural world.
I hope we will get an answer from this anon >>11188357

[Anonymous No.11195479]

Pozdrawiam davida bowie

[Anonymous No.11195513]

>>11188357
PDEs and cryptography are both applied in that they don't exist without number theory.
PDEs are used in Optimization and Physics with some LA to find roots of systems of non-linear equations.

[Anonymous No.11195516]

How do I learn how to graph functions? I'm taking calc1 and the rest of the stuff seems fairly straight forward but I can't wrap my head around actually graphing a function when it gets complicated.
I have things like
>|x-1|-sgnx
>cos(arcsin x)

When they give me polynomial forms I can sort of find the points but when it comes to these I'm just lost.
Also I see cases in my textbook when the Asymptote is x=y but I can't seem to figure out why. Can someone help me please?

[Anonymous No.11195582]

>>11195516
just plot it by points lmao

[Anonymous No.11195589]

>>11195516
use wolfram alpha, anon

[Anonymous No.11195645]

>>11195516
>>|x-1|-sgnx
for x<0 you have |x-1| = 1-x and sgn(x) = -1. therefore the function there is -(1-x) = x-1. can you draw x-1?
for 0<x<1 you have |x-1| = 1-x and sgn(x) = 1. therefore the function there is 1-x. can you draw 1-x?
for x>1 you have |x-1| = x-1 and sgn(x) = 1. therefore the function there is x-1. can you draw x-1?

[Anonymous No.11195777]

https://link.springer.com/book/10.1007/978-3-030-33143-6
Ya boy Shelly Axley just revolutionized mathematical pedagogy again.
Now [math]Open ~ Access^{TM}[/math].

[Anonymous No.11195845]

>>11195777
now this is based

[Mathematical models of human m(...) No.11195861]

https://www.youtube.com/watch?v=cYuepljq5vA

[Anonymous No.11195895]

>>11195861
Pitch me that video.

[Anonymous No.11195918]

>>11195895
Human memory is a multi-staged phenomenon of extreme complexity, which results in highly unpredictable behavior in real-life situations. Psychologists developed classical paradigms for studying memory in the lab, which produce easily quantifiable measures of performance at the cost of using artificial content, such as lists of randomly assembled words. I will introduce a set of simple mathematical models describing how information is maintained and recalled in these experiments. Surprisingly, they provide a very good description of experimental data obtained with internet-based memory experiments on large number of human subjects. Moreover, more detailed mathematical analysis of the models leads to some interesting ideas for future experiments with potentially very surprising results.

[Anonymous No.11195941]

Should I take Graph Theory or Cryptography next semester?

[Anonymous No.11195970]

>>11195941
Whatever interests you more. I don't think either is too bad. Cryptography sounds a little more interesting to me, since it's more mathematical afaik.

[Anonymous No.11195982]

>>11195513
>PDEs dont exist without number theory
never post here again disgusting freak

[Anonymous No.11196203]

>>11195941
There isn't really a standard curriculum for those subjects so it depends greatly on your uni and your lecturer

[Anonymous No.11196232]

Why is it that math fags always think they are smarter than phys bros when math fags cant even understand basic classical mechanics most of the time

[Anonymous No.11196252]

>>11195982
Concrete thinker detected.

[Anonymous No.11196253]

What's he writing?

[Anonymous No.11196257]

>>11196232
I don't know man. I was like this in undergrad, but I've gradually realized how embarassing this perspective actually is.
>t. doing phd in math but taking a theoretical mechanics course right know and 1) it's fun and cool as fuck 2) you're right that most of my math bros would get totally fucked in the ass by this

[Anonymous No.11196266]

>>11196253
"consider this cat of locally ringed..."

[Anonymous No.11196285]

>>11196232
it's not that physics itself is that much simpler - it's mostly the fact that engineering degrees are... well... for engineers.
also muh abstraction and all that.

[Anonymous No.11196311]

>>11196285
No ones talking about engineers. Its just that its a known fact that phys bros have way bigger cocks than math fags. Anyone can be a mathematician, but only gods can be theoretical physicists

[Anonymous No.11196408]

>>11195777

how can a single jewish man kill the entire industry of textbooks like this

[Anonymous No.11196481]

>>11184748
sleep more
take more walks

[Anonymous No.11196483]

I'm supposed to find the root that has x on the first power. I know about the binomial theorem, so in this case 2x^(17-k)+x^(-1/3)^k where I'm supposed to find the k value.

In most cases I can express both value as x on some power, I equate it with what I'm supposed to find. So I could do this if it was like x^2+x^(-1/3) because then the first number will be on the power of (n-k), the second is on (k) and it will equal to 1.

But I have a problem with this one, because I don't know how to express 2x as a power of x.
Or is there any other way I could do this? I might lack basic skills in algebra so please be patient I'm dumb

[Anonymous No.11196487]

>>11184748
>how tf do i understand this shit faster?
stop studying for a while. 100% serious.

[Anonymous No.11196504]

>>11185664
fucking saved. just dab on the haters, they're just busy coommuting

[Anonymous No.11196515]

>>11196232
math people are good at math, not at computing boring integrals.

[Anonymous No.11196576]

>>11193748
which [math]\LaTeX[/math] font is that?

[Anonymous No.11196781]

>>11196408
Control the yellow cover, control the maths.

[Anonymous No.11196799]

>>11185664
this is fucking stupid but props for making OC, we need more people like you

[Anonymous No.11196877]

>>11196483
bump, someone please help me im dumb

[Anonymous No.11196963]

>>11196483
>>11196877
you're not supposed to express 2x as a power of x
i guess the problem is probably to find the **coefficient** next to the x to the first power.
to do this, you need to find the correct term in the binomial theorem, I mean for some k you will have a term
(17 choose k) * (2x)^(17-k) * x^(-1/3 * k)
for some k this is (some number)*x and you're asked to find this (some number)

[Anonymous No.11197103]

>>11196963
Yeah I know this, but what I've done in other cases is I expressed both terms as a power of x and this way I could just remove x completely and left with the equation of (power of first number)^n-k + (power of second number)^k = 1

I understand what I'm supposed to do, I just don't know how to find the k

[Anonymous No.11197515]

Wtf is a cs poojeet doing in my algebra class. I wanna break his kneecaps

[Anonymous No.11197741]

>>11183694

Calculus I - Derivatives and Limits
Calculus II - Integration and Infinite Series
Calculus III - Multivariable Calculus
What would Calculus IV be?
i.e what does more advanced levels of calculus entail or does it peak with vectors and polar graphs?

>inb4 look at college syllabi

[Anonymous No.11197851]

>>11197741
Remember all that cool shit you did in Cal 1 through 3 but were never asked to prove?

Well now you get to prove it.

[Anonymous No.11197960]

>>11184328
Kek