/sci/ - Science & Math

>>9258236
How does studying useless stuff makes you feel?

>>9258238
Nothing is useless, even studying white noise can give you meaningful insights about the structure of the universe, because, suprise, even useless stuff is part of this universe...

>>9258240
How can you persuade a girl to have sex with you using that knowledge?

What does /mg/ think about "Undergraduate/Graduate Texts in Mathematics"?

>>9258236
Is this loss?

Math is Fake

>>9258277
Why that's your metric of usefulness?

Threadly reminder to work with physicists.

>>9258277
get back to /b/ normie

I need a new Calculator... my TI-30X IIS is fucking garbage and i`m tired of making small mistakes due to its weird input...

Any recommendations?

>>9258359
>blaming the tool
yeah okay

get a ti 84 if you must

>>9258236
all 2D are 3D with redundant verticies, so is your waifu

>>9258359
this puppy

>>9258359
FX 115es plus or FX 991ex

>>9258359
Patrician here.

hp50g or hp15c is what you want. Look into swissmicros if you want to waste even more money.

>>9258344
I'm an undergrad physicist taking GR this semester and I love this shit. Everything's about finding paths through crazy spacetime geometries.
I may want to eventually do my grad school studies on GR, and I think I should learn a lot more about geometry from the mathematical side first. Where do I start with this if my curriculum for math didn't ever go beyond ODEs?

>>9259498
any takers?

>Exam week
>caught a terrible influenza, literally dying
>still went to exams with severe sleep deprivation and feeling terribly sick
>Needless to say I really fucked up said exams, awful mistakes to easy problems, etc.
>tfw my perfect grade record is now fucked

Should I just end it?

>>9258359
Get the TI 36x pro engineering calculator.

>>9259076

My man, anything other than this is literally cheating and should be banned.

>>9259530
Okay, let [math]L[/math] be the limit of this sequence, and let [math]\varepsilon = \frac{L}{2}[/math]. By definition, we now have some threshold [math]K[/math] such that [math]n>K \Rightarrow |L-x_n|<\varepsilon[/math], and since the limit is positive, all the entries beyond the threshold index are necessarily positive too.

>>9258236
So how do you define set, /mg/?

>>9259567
you don't
you have to start from something
you can't define was "being" is

I want a linear algebra text

pic related good?

>>9259700
what level are u? shilov isn't good for introductory, but good after for a more advanced treatment

>>9259700
>linear algebra
>good

I would genuinely appreciate some help with this problem.

Let L(V)=L (V,V) be all linear maps from V to themselves.

i)dim (L)=?

choose dim (V)=n->dim (L)=n^2

ii)define L(L (V)) in words. Prove it is a vector space

L (L (V))=L (L (V,V),L (V,V)) so it is all linear maps which map all linear maps from V to V...not sure doesn't seem clear

How to prove it is a vector space? There are the 8 requirements i.e. x+y=y+x and so on. How would I even go about doing this? Since I don't even really know what L (L (V)) looks like. Not even sure how I would prove it for L (V)

iii)dim (L (L (V))=?

dim (L(V))=n^2->dim (L (L (V))=n^4

iv)give an example basis of L (L (V))

I'm thinking all n^4×n^4 matrices where i,j=1 all else 0

Okay, thanks.

Looking for a intro Classical Mechanics text, from my research it seems it will be one of the following:
>Fundamentals of Phyiscs, Halliday & Resnick
>University Physics with Modern Physics, Young & Freedman
>An intro to Mechanics, Kleppner & Kolenhow

From what i understand, Kleppner's is most mathematically inclined and 'rigorous', so I think I'll go with that. When does one learn Langrarian Mechanics?

>>9259763
Also, /sci/ guide recommends Kleppner as 'honours' high school physics, but list these:

Taylor - Classical Mechanics (Great for self study and contains a nice chapter on SR)
Gregory - Classical Mechanics (More to the point than Taylor)
Woodhouse - Introduction to Analytical Dynamics (Mathematical oriented complement to the above)
as university level, I can't help but feel Kleppner is more advanced than these, no?

>>9259763
I was taught out of "Classical Mechanics" by Taylor but our professor strayed from the book quite a lot. I thought it was fine.

Generally, people learn Lagrangian Mechanics in Sophomore year.

>>9259755
fuck off

>>9259718
if ur so good at lin alg, pls help with this problem>>9259755

>>9259770
What year were you when learning from Taylor? I hear it's "too advanced" for someone in my shoes.

>>9259798
I was 2nd semester freshman but out of 150 ppl taking it I was one of <10 freshmen. Probably equal split of sophomores and juniors (mostly engineers)

>>9259806
ok, so you think it'd be solid for a self studier who's completed calc and has had a taste of linear algebra? I know already know basic "khan academy" mecanics, fwiw

>>9259813
Probably. Not sure what khans mechanics are like, but if they cover what all of AP physics did you should be good.

>>9259755
You got the right idea. You can view linear maps on linear maps as n^2 x n^2 matrixes chained with a function that maps n x n matrices to n^2 dimensional vectors

>>9259819
cool,thx

>>9259822
Ah okay. I understood that. So L (L (V)) is all n^2xn^2 matrices and since all M (nxn) is a vector space so is L (L (V)) thanks.

>>9259543
Are you incapable of emailing your professor and telling him that you were going to be sick for the exams? Talk to him and inform him of your situation.

>>9259778
t. dumbass

>>9258294
good if you're undergraduate??
>>9259127
assuming "didnt ever go beyond ODEs" means you just did the standard US math curriculum, ie calc 1-3+ODEs, then a lot:
>Analysis - Tao followed by Royden optionally
>Topology - Munkres
>Differential geometry of curves and surfaces - Do Carmo
>Riemannian Geometry - Do Carmo, alternatively Introduction to Smooth manifolds, Lee
Probably squeeze some abstract algebra to better understand differential forms, Topics in Algebra by Herstein should do, or Artin

>>9259530
Not gonna type it up, but the intuition here:
You don't need contradiction btw
By definition of a limit, for any epsilon bigger than 0, there is some N such that the distance from the limit L to the sequence is less than epsilon.

Now if the limit is positive, by definition of a limit, you can let epsilon be L, and since the distance from any point in the sequence that is less than L from the limit is necessarily positive, then such an N exists.

>>9259700
Axler

>>9258236
Just started complex analysis, and I already don't understand branch cuts, and I'm also retarded at calculating residues

>>9259895

Yes, my professor has more important things to do. Me getting sick isn't his problem.

>>9260015

Residues are awful, just keep practising.

>>9259766
>as university level, I can't help but feel Kleppner is more advanced than these, no?

K&K just requires single variable calculus. Taylor requires at least vector calculus and uses it throughout.

>>9259543
>do horrible on exam for the subject that is the entire reason I go to uni
>screw up on problems so easy I almost lose it in class when seeing how bad I fucked up the problem
>problems were SO easy and SO straightforward that the professor even left little notes of his confusion
>don't have excuse of sickness for my horrible fuckup
>don't have excuse to repair my already damaged self-confidence
>don't have excuse to still continue with my dream subject despite fucking up so bad
how do I end this nightmare lads, it's fucking awful

>>9260743
just wake up anon

>>9258236
why is wheel theory such a neglected field in math? i discovered it an year or so ago and it's shame that there's so few literature

Suppose a 2-sphere with radius R. You are at latitude [math]\theta[\math] and follow a meridian northwise to latitude [math]\theta + d \theta[/math], where [math]d \theta [\math] is very small or whatever. Why is the distance you travel equal to [math]R * d \theta[/math]? Or is it not?

>>9261026
>that formatting
Oh shit what did I do wrong.....

>>9261027
it's /math not \math

>>9261029
Thanks.
>>9261026
>>9261027
Retry:
Suppose a 2-sphere with radius R. You are at latitude [math] \theta [/math] and follow a meridian northwise to latitude [math]\theta +d \theta [/math], where [math] d \theta [/math] is very small or whatever. Why is the distance you travel equal to [math] R ∗ d \theta [/math]? Or is it not?

>>9259498
The limit of the convergent sequence x sub n is a real number > 0 , let this r in R > 0 be k .

For the limit to exist, the following condition must hold:

For any real number epsilon > 0 , there exists a natural number N such that for every natural number n >= N , we have | x sub n - x | < epsilon.

k is a real number > 0 , so there must exist a natural number N such that for every natural number n>=N , we have | x sub n - x | < k .

If | x sub n - x| < k , then all x sub n > N must lie within the interval ( k - k , k + k) .

k - k = 0 , so all x sub n > N must lie within the interval ( 0 , k + k ) .

If k is a positive real number, k + k is a positive real number. (trivial)

Therefor, for all x sub n > N lie within the interval ( 0 , +r ) .

Therefor, there exists a natural number N such that x sub n > 0 for all n > N .


Kind of tired and the proof isn't very formal depending on your level of expertise, but this should give you the idea to resolve the problem with more or less rigor if required.

>>9261031
because a circle is "flat" locally

>>9261069
Thanks !

>>9261081
np
To be more precise, consider the parametrization of the circle [math] \gamma (\theta) = ( r \cos(\theta), r\sin(\theta) ) , t \in [0,\2\pi] [/math] .
The arclength between [math] \theta [/math] and [math] \theta + \varepsilon [/math] is [math] f(\varepsilon):= \int_{\theta}^{\theta+\varepsilon} \lVert \gamma '(\theta) \rVert d\theta = \int_{\theta}^{\theta+\varepsilon} r d\theta = r \int_{\theta}^{\theta+\varepsilon} d\theta = r (\theta+\varepsilon - \theta) = r \varepsilon [/math] .

Who's at the Math GRE right now?

How do I work out the standard deviation for a set of samples I've generated?

I was asked to work out the probability of landing on a certain square within a grid when a counter hits 0, I've done that and have all my numbers, but am not sure how to work out the standard dev for the probability.

e.g.
State: 1 Score: 242
State: 2 Score: 174
State: 3 Score: 82
State: 4 Score: 209
Total samples 707

P(State 1) = 242/707
etc.

need to be able to write the probability +_ the sd for the error, but not sure what the fuck I'm doing, last time I worked out the SD for anything was by putting it all into tables doing f(x) f(x^2) etc.

I've been slowly working on khanacademy World of maths. I treat it as a game or puzzle, because most of the time, I have no idea where the math is actually used IRL.
Is there a resource out there which explains where ad when the math is used?

>>9261165
>consider the parametrization of the circle γ(θ)=(rcos(θ),rsin(θ)),t∈[0,2π].
triggered

>>9261222
Probabilities don't have standard deviations, random variables do. If the states can be added or subtracted, you can treat the states as random variables and calculate the mean and standard deviation. But if the states are just labeled and do not represent numeric data, you can only consider the entropy of the distribution.

>>9261222
The statistically correct thing to do is to produce a confidence interval on the probability -- an interval computed from the sample data, with a known probability of containing the desired probability. I forget the details of the technique, and don't have the time at the moment to re-derive it.

One thing you can do, is notice that your estimate is a binomial random variable, parameterized by the sample size and the desired probability. The standard deviation of a binomial random variable can easily calculated, if you know the desired probability. If you plug in your estimate instead, you should be pretty close.

I'm thinking about getting a major/minor in actuarial sciences, is it that difficult from a mathematical standpoint?

I believe I only need to complete required mathematics and upper level probability to finish it.

>>9261397
Hell, you can go full autist and apply Dirichlet-categorical Bayesian inference, and then derive the confidence intervals from the posterior Dirichlet distribution on the probabilities. But here, the binomial or multinomial variables are the scores obtained, not the probabilities, so the standard deviation would just be the standard deviation of the scores. The probabilities are parameters of the distribution, and they can be fit to a Dirichlet distribution.
https://en.wikipedia.org/wiki/Categorical_distribution#Bayesian_inference_using_conjugate_prior

How the fuck is /mg/ at page 9?
Wake up faggots.

>>9262706
>faggots
Why the homophobia?

>>9262707
so that you ask and bump the thread again, faggot

>>9262707
>all this pearl-clutching
your kind belong in the fields - if that

>>9261309
An answer for this?

>>9261368
>you will never confuse the meanings of the word rational ("reasonable and logical" rather than "expressible as a ratio")
>you will never waste the rest of your life because of this simple misunderstanding

why even live bros?

I'm currently trying to refresh my multivariable calculus knowledge from these 3Blue1Brown videos: https://www.youtube.com/watch?v=JQSC0lCPG24

He gave some nice intuition on the Laplacian and he said that if it is 0 at a point, then if you take the average of the function Around that point, it is going to be roughly equal to the the function At that point.
I know that analytic functions have harmonic (0 Laplacian) real and imaginary parts.
And I know that If you average(integrate) an analytic function Around a point, then you'll get value equal to the value of the function At that point (Cauchy's formula). This agrees with the intuition 3B1B gave.

My question is:
Can we prove that a function f is harmonic at a point (a,b) just by showing that [math] \lim_{r \to 0} \oint_{\text{circle centered at } (a,b) \text{ with radius } r} f ds = 0 [/math] ?

I'm currently trying to refresh my multivariable calculus knowledge from these 3Blue1Brown videos: https://www.youtube.com/watch?v=JQSC0lCPG24

He gave some nice intuition on the Laplacian and he said that if it is 0 at a point, then if you take the average of the function Around that point, it is going to be roughly equal to the the function At that point.
I know that analytic functions have harmonic (0 Laplacian) real and imaginary parts.
And I know that If you average(integrate) an analytic function Around a point, then you'll get value equal to the value of the function At that point (Cauchy's formula). This agrees with the intuition 3B1B gave.

My question is:
Can we prove that a function f is harmonic at a point (a,b) just by showing that [/math] \lim_{r \to 0} \oint_{\text{circle centered at } (a,b) \text{ with radius } r} f ds = f(a,b) [/math] ?

I'm currently trying to refresh my multivariable calculus knowledge from these 3Blue1Brown videos: https://www.youtube.com/watch?v=JQSC0lCPG24

He gave some nice intuition on the Laplacian and he said that if it is 0 at a point, then if you take the average of the function Around that point, it is going to be roughly equal to the the function At that point.
I know that analytic functions have harmonic (0 Laplacian) real and imaginary parts.
And I know that If you average(integrate) an analytic function Around a point, then you'll get value equal to the value of the function At that point (Cauchy's formula). This agrees with the intuition 3B1B gave.

My question is:
Can we prove that a function f is harmonic at a point (a,b) just by showing that [math] \lim_{r \to 0} \oint_{\text{circle centered at } (a,b) \text{ with radius } r} f ds = f(a,b) [/math] ?

Going to do a grad course in Representation theory next semester. I own Artin and Pinter from undergrad. Algebra is not my field of study but want a food grad algebra book for reference for this class and the future. Can anybody with experience with Aluffi and Lang compare and contrast the two?

>>9263003
god dammit, good*

Has anyone here studied Differential Algebra? Any book suggestions?

Why do you lot like maths, it's fucking stressful.

>>9263008
I have some familiarity with Galois Theory and ODEs, if that helps.

>>9260015
How the fuck are you in so far as calculating residues when you just started fucking branch cuts lmao, are you doing an engineering course? if so you're not going to fully understand anything

um...guys?

>>9263059
>x = 2/(3-x)
>2nd degree equation
>has two solutions
Yes, it does. So what?

>>9263059
>some number equation thing in the picture
>math_broke.png
There are no numbers in mathematics, other than NNOs in certain categories.

>>9262974
Take any [math]1[/math]-form [math]\omega[/math] on [math]\mathbb{R}^n[/math] and Hodge decompose it into [math]\omega = d\alpha +
\delta \beta + \gamma[/math] where [math]\alpha[/math] is a [math]0[/math]-form,
[math]\beta[/math] is a [math]2[/math]-form, and [math]\gamma[/math] is a harmonic [math]1[/math]-form where [math]\nabla \gamma = 0[/math]. Let [math]C \in H_1(\mathbb{R}^n)[/math] be a [math]1[/math]-cycle, then
[eqn]
\langle \omega , C\rangle = \int_C \omega = \int_C (d\alpha + \delta \beta + \gamma)
[/eqn]
The first term vanishes by Stokes's theorem. Suppose [math]\langle C, \omega\rangle =
\omega|_0[/math], it then suffices to show that [math]\langle C, \omega\rangle[/math] does not depend on [math]\beta[/math]. To do this note that [math]\ast: C^1(\mathbb{R}^n) \tilde{\rightarrow} C^{n-1}(\mathbb{R}^n)[/math] is a vector space isomorphism, and by Poincare duality [math]H^k(\mathbb{R}^n) \cong H_{n-k}(\mathbb{R}^n) \cong (H_{n-k}(\mathbb{R}^n))^*[/math], there exists [math]\tilde{C} \in H^1(\mathbb{R}^n)[/math] and [math]\tilde\beta \in (\operatorname{Im}\ast)^*[/math] such that [math]\langle C, \delta \beta \rangle = \langle \tilde \beta, d \ast \tilde{C}\rangle = \langle \partial \tilde\beta , \ast \tilde{C} \rangle = 0[/math], thus [math]\langle C,\omega \rangle
= \langle C, \gamma \rangle[/math], and since [math]C\in H_1(\mathbb{R}^n)[/math] is arbitrary [math]\langle C, \omega \rangle =
\gamma|_0[/math].
This assumes the smoothness of [math]\omega[/math] and [math]C \in \operatorname{Ker}\partial / \operatorname{Im}\partial[/math].

>>9261309
Well, where it is used will depend on the maths. I suppose people use maths in stock trading, and a lot of maths is of course used in construction and engineering.

If you mean academic use, then maths is probably mostly used by physicists (save for mathematicians, of course).

>>9263008
Tenenbaum's ODE?

anyone here has experience studying math while struggling with depression? i can't find the energy to push through,i can't concentrate for shit either

>>9259700
Shilov's great but might be difficult to start with.

>>9263309
It's good for escapism. You may feel like shooting yourself, but you can also embed yourself in the mathematical universe and hide there for a while. This, of course, assuming you can get started, which itself is quite a feat sometimes. Basically you should do math for the sake of math itself instead of some other purpose like grad school, so you can take away all the scary parts like grades and focus on the contents themselves. As a side product, if you can get started, you will learn whatever you need to know and not feel as horrible at the same time.

>>9263327
i'm struggling with depression for years. i graduated highschool with bad grades and now i'm trying to unfuck my life so i am getting started. i'm doing a math course and it's too intense for me i struggling to keep up with the pace

>>9263301
Alright, I'll add physics to it then.

>>9263327
If she shoots herself at that angle, she will suffer a long time before she bleeds out, and even then she might survive. At that angle you can count on luck that the shock will make you pass out and the caliber is high enough to make hole big enough to die

>>9263329
How strict is the schedule? Can you do it at your own pace? I know it's hard, but sometimes you just get into the flow and can escape your worldly troubles.

>>9263356
Well, SHE is killing HERSELF, so it is only natural to assume it's not gonna be the optimal way to do it.

>>9263266
Thanks a lot for your response! But, I don't really understand differential forms. Haven't studied them. Where do I start?

>>9263327
true

How do I get my interest in math back? I had a honeymoon phase where everything about math seemed really fucking cool. I liked my calculus courses and reading about abstract algebra and shit blew my mind. But after I started digging in I got bored and disillusioned. Has anyone else experienced this? Am I just a filthy pseud?

>>9259543
>Revolving your entire life around your perfect grades
Jesus dude, take it easy.

My university is putting on a competition like the Putnam competition, i'd like to apply for it but I only have 1 week before the deadline and 3 weeks before the actual exam and I can barely do any problems on PMC papers. They've kept the details of the competition really vague only saying "They'll be similar to IMC and PMC questions". Where do I start? Will I be able to get to a reasonable level in 3 weeks? Should I just give up?

>>9263420
Any differential topology book. Lee should be fine.

The book for my course isnt on libgen so
does anyone know of a mathematical logic book that covers these topics?

• Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals. Equivalent formulations of the axiom of choice and its applications in analysis and algebra.

• Structures and models: Isomorphisms and embeddings, complete theories, elementary equivalence and elementary embedding, Löwenheim-Skolem’s theorems, categoricality, applications on algebraic theories and non-standard analysis.

• Computability and incompleteness: Models of computation, classes of computable functions, decidable and irreversible problems, Gödel coding and Gödel’s incompleteness theorem.

>>9263973
>mathematical logic
What's the point?

Fun things are fun

>>9263976
Fun things are fun

can someone walk me through this one?

>>9263973
Kunen The foundations of Mathematics and Enderton Intro to Mathematical Logic.

>>9263980
https://www.symbolab.com/

>>9263438
England? I'm on the same boat
someone pls respond

>>9264064
Yep thats me
Looks like we're fucked. Why would they announce it so close to the actual fucking date of the competition.

Studying category theory and everything is indexed by sets and sometimes the objects of categories. Can someone explain why? Why add the extra layer of abstraction when it can just be indexed by intigers, does it serve a purpose later? I know technically it can be something with a higher cardinality than integers, but I haven't found a single time it's used that way

Can someone give me an example of when a index with higher cardinality than the integers is used in cat theory pls

>>9264086
>when it can just be indexed by intigers

>>9264086
What if you wanted to do something with the category of all sets? Could that be countable? Note that every subset of [math]\mathbb{Z}[/math] is an object there.

>>9264086
Because from the standpoint of category theory, integers are on a much higher level of abstraction than sets are; integers are often constructed (via the peano axioms) from sets, not the other way around. Since set theory can be defined from category theory, sets are far more naturally accessible than the integers are. Now, I haven't studied category theory deeply, but what would be the advantage of using integers? Why would you restrict your domains to be countable?

I have what should be a super straight forward question but I'm not really grasping it, is anyone here familiar with quantification in predicate logic?

It's just finding a counter-example for ∀x∃y (3 · y = x) where the domain is the set of all positive whole numbers

>>9264086
>Can someone give me an example of when a index with higher cardinality than the integers is used in cat theory pls
The category of all axioms

>>9264126
>It's just finding a counter-example for ∀x∃y (3 · y = x) where the domain is the set of all positive whole numbers
the claim is that every positive whole number is a multiple of 3 (for all x there exists y such that 3y=x)

it's false since it's not true for x=1

>>9264126
x=1, so you would be claiming there is some positive integer y such that 3y=1. You do understand what it's saying, right?
>for every x there is a y such that 3y=x

>>9264141
>>9264136
I see, so the counter example to this statement is an whole number that is not a multiple of 3? 2, 4, 5 are also acceptable counter-examples?

>>9264150
>I see, so the counter example to this statement is an whole number that is not a multiple of 3? 2, 4, 5 are also acceptable counter-examples?
yes and yes

>>9264154
That makes complete sense, thanks. What if the variable y hasn't been given any implicit value like 3, and it's just something like y^2 for example?

>>9264156
Every positive integer x has some positive integer y such that x=y^2, choose x=2 and get into trouble.

>>9264159
I see, x=2 serves as a counter example to y^2 as as the square root of 2 is 1.41, and 1.41^2 is not equal to x?

>>9264178
Nope, it's because then y wouldn't be an integer. If you have any claim of the form "for every ... there is some ...", all you need is one counter-example. In this case it would be any positive integer whose squareroot is not an integer, 2, 3, 5, 6, 7, and so on. The order of words is important, too. You can have "for every integer x, there is an integer y such that x-y=0", and you can have "there is an integer x such that, for every integer y, x-y=0". The first one is true, but the second one is false.

>>9264193
Oh, that makes sense! So it invalidates the statement because it violates the "positive whole number" domain?

>>9264199
In this case yes. In general, you want some contradiction, which in this case is the domain.

>>9263266
>>9263810
>>9264090
>>>/r/taiwan/
Subhuman attention whoring is not welcome here.

>>9264049

its says it can't solve this problem,

I OBVIOUSLY would have already tried that website

>>9263973
>Equivalent formulations of the axiom of choice
Just pick anything false.

Are you still here based anime quantifier guy?

With a compound like ∀w∀z (w < 2z) can I assign separate values to both w and z, such as w = 3 & z = 1 to serve as a counter-example? (assuming we're using the same domain)

>>9264238
Yeah
t. not based anime quantifier guy

>>9264248
So I'm assuming we're allowed to apply values to Universal quantifiers but NOT existential quantifiers then?

>>9264205
>Subhuman attention whoring is not welcome here.
Where does it say that?

>>9264238
Yes. As long as they are in the same domain, like for example positive integers. Since it says "for all w and for all z", you can pick any two elements in the domain in order to find a counter-example. It could also be, for example animals. For each animal w and each animal z, the animals w and z are of the same species. Then you choose a walrus and a zebra.

t. based ∀nime quantifier guy

>>9264254
Okay, this is starting to make complete sense to me now, thanks a lot for your help. I'm sure I've done got most all of the rest correct, but there's one that's still tripping me up a little:

∀x (x > 0) → ∃y (y < x),

I can't think of a counter-example here as it seems like it always holds to me. Even 1 would still set y as 0 which is a positive integer - what am I missing here?

>>9264251
You can "apply" values to both but order matters [math]\forall z \exists t [/math] and [math]\exists z \forall t [/math] are two very different statements

>>9264263
>0 which is a positive integer
No it's not.

>>9264266
You're right, I'm fucking retarded and was taking the "whole number" definition in the domain way too literally, absolute brain fart. So x =1 would be the only actual counter-example in this case then?

>>9264263
Have you tried to simplify it to english? For all x larger than 0 implies that there is a y that is lesser than x

>>9264263
That one is correct. Choose [math]y = \frac{x}{2}[/math]. Then we have [math]0 < y < x[/math], as claimed. 0 is not positive, though. It's only non-negative.

>>9262707
>>9264252
>>>/r/dogs/

>>9264268
>So x =1 would be the only actual counter-example in this case then?
If you're restricted to natural numbers, yes.

>>9264276
>>>>/r/dogs/
What about dogs?

>>9264278
Proof?

>>9264278
Oh, of course this restriction makes 1 a counter-example indeed.

>>9264282
>Proof?
For any other natural number x, take the natural number y=x-1.

>>9264251
also not based animeman, but i'll try to connect this to the formalism a bit more to explain.
if we find an object [math]x[/math] such that some proposition[math]P(x)[/math] is true, then we've proven the existence of such an object, so [math]\exists x\,P(x)[/math] is true.

now let's say we have a proposition of the form [math]\forall x\, P(x)[/math]. proving a statement like that is usually harder, but disproving it is much easier than for the [math]\exists x[/math] quantifier.
to find a counterexample is to find an x such that [math]\neg P(x)[/math], which proves that [math]\exists x \,\neg P(x)[/math].
now, the statements [math]\exists x \,\neg P(x)[/math] and [math]\neg\forall x\,P(x)[/math] are equivalent, and so the proposition is false.

as such, you can 'apply' values to both quantifiers, but doing so can only prove [math]\exists x[/math] and disprove [math]\forall x[/math], not vice versa.

>>9264295
>the statements [math]\exists x \,\neg P(x)[/math] and [math]\neg\forall x\,P(x)[/math] are equivalent
Only in retarded logics.

>>9264303
idiot

>>9264303

Okay, retarded quantification guy back again - what's the best process to find a formula that is logically equivalent to the negation of some given formula* AND has no negated quantifiers:

*∀x ¬(P(x) ∧ ¬Q(x))

I'm assuming I might be able to use standard predicate transformation laws like DeMorgans? I'm not sure how to apply them to quantified formulas, though.

>>9264304
Yes and so are you.
>>9264305
Don't be hasty, anon.

>>9264303
>trying to explain a set of rules
>yeah but your rules are stupid
that's not the point, mr pisserwasser

>>9264315
Might as well explain rules which are not retarded, especially when using retarded ones simply isn't necessary in that case.

Any recommendations for resources like symbolab?
I'm still pretty early in my math education. Planning to do CS.

>>9264303
You might now as well go full hardcore finitist route and say that quantification over infinite sets itself is meaningless and that infinite sets themselves don't actually "exist".

>>9264311
That's simply [math](\forall x \neg(P(x) \land \neg Q(x))) \Leftrightarrow (\forall x (\neg P(x) \lor Q(x)))[/math]. You could also have [math](\neg(\forall x P(x)) \land \neg Q(x)) \Leftrightarrow ((\exists x \neg P(x)) \lor Q(x))[/math]. You can use de Morgan like you would do in propositional calculus, but you must apply these rules for the negations of quantified statements >>9264295

>>9264311
yes, that's perfectly allowed; [math]P(x)[/math] and [math]Q(x)[/math] are predicates just like any other. predicates taking a variable are just functions from objects to no-variable predicates, so any rules that hold for no-variable predicates also hold for parametric predicates with specified arguments
>>9264317
or maybe you could explain it, since you're the only one wildbergering about standard logic being retarded

>>9264324
Would you be able to expand a little on your process? I'm a bit brain dead when it comes to logical equivalences.

>>9264322
You might, but I won't. And in that case those two would actually be equivalent.

what is the best basic math book?

>PreCalc, Stitz & Zeager
>PreCalc, Axler
>Basic Math, Lang

I'd like to have a nice desktop reference and I'm getting fuck SICK of making algebra mistakes and having to resort to Khan for quick brush ups. So I'm looking for something niggorous that would make a good reference, but also can be read enjoyably cover to cover (though the former is much more important).

>>9264335
The first one is obtained by applying de Morgan's law to [math]\neg(P \land \neg Q)[/math], which gives [math](\neg P \lor \neg\neg Q) \Leftrightarrow (\neg P \lor Q)[/math], and this can be done because that whole thing lies within the scope of the universal quantifier. In the second one, we apply de Morgan the same way, but now we must negate [math]\forall x P(x)[/math], which is equivalent to [math]\exists x \neg P(x)[/math], and this is because only [math]P[/math] lies within the quantifier's scope (notice the parentheses!), and things are a bit different. I hope this helped, I'll sleep now.

>>9264345
It has helped a lot, I appreciate it. Thanks anime quant guy.

>>9264344
Also, I'm not limited to those I mentioned, those are simply recurring recommendations.

Axler's seem nice because the solutions are worked out, Stitz's seems more rigorous and free, and Lang's seems rigorous as well.

>>9264345
It seems the parentheses are wrong there, oops. [math]\neg((\forall x P(x))\land \neg Q(x))[/math] is what I wanted. Now, bye bye!

Hey guys, do you know of a program/ script that will help me review what I've learned? Or even just through a random olympiad problem at me?

How big is the category of axioms?

>>9264449
>big
>category of axioms
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9264472
>I don't understand what you're saying.
Please learn some basic category theory before replying to posts that are above your mathematical maturity level.

>>9264475
I am one of its creator's successors though. I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9264480
>I am one of its creator's successors though.
Irregardless, please learn some basic category theory before replying to posts that are above your mathematical maturity level.

>>9264482
My choice of using "successor" implies I know some basic category theory, and I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9264487
>My choice of using "successor" implies I know some basic category theory
It's clear you do not, otherwise you would understand what I'm saying.

Irregardless, please learn some basic category theory before replying to posts that are above your mathematical maturity level.

>>9264482
>>9264475
>>9264449
>I'll ask a meaningless question and claim it needs mathematical maturity to grasp

>>9264488
>what I'm saying
It doesn't sound rigorous, whatever it is.

>>9264492
>>I'll ask a meaningless question and claim it needs mathematical maturity to grasp
Who are you quoting?

>>9264495
>It doesn't sound rigorous, whatever it is.
Irregardless, please learn some basic category theory before replying to posts that are above your mathematical maturity level.

>>9264497
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

>>9264502
>Right and wrong.
Only right actually; replying to posts that are above your mathematical maturity level is frowned upon here.

>>9264507
Physicists of the older generation are more likely to reject fancy mathematical constructs, but I'm sure this is about to change.
Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.

>>9264513
>Physicists of the older generation are more likely to reject fancy mathematical constructs, but I'm sure this is about to change.
>Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.
Irregardless, please learn some basic category theory before replying to posts that are above your mathematical maturity level.

>>9264488
>basic category theory
>mathematical maturity

>>9264524
>>basic category theory
>>mathematical maturity
It's fairly simple, if you don't even know basic category theory, don't reply to questions about it purely for the sake of displaying your confusion.

Go gain some mathematical maturity, then come back.

>if you don't even know basic category theory
You would know it doesn't require any mathematical maturity if you actually knew it yourself.

>>9264449
>>9264475
>>>/r/taiwan/
>>>/r/dogs/

>>9264531
>You would know it doesn't require any mathematical maturity if you actually knew it yourself.
That's what makes your confusion about my question so truly embarrassing.

You claiming it requires "mathematical maturity" (even a small amount of it) implies you don't actually know it.

>>9264538
see >>9264537

>>9264527
>>9264537
>>>/r/taiwan/

>>9264534
?

>>9264449
>category of axioms
What are the morphisms?

>>9264541
>>9264534
?

>>9264544
>What are the morphisms?
see >>9264475

>>9264548
I'm trying to learn from you since you seem to be quite advanced at it

>>9264559
>I'm trying to learn from you since you seem to be quite advanced at it
Advanced category theorists such as myself are not responsible for the education of the mathematically immature.

Not sharing your advanced knowledge with people who are interested is frowned upon here.

>>9264565
>Not sharing your advanced knowledge with people who are interested is frowned upon here.
Advanced category theorists such as myself are not responsible for the education of the mathematically immature.

Go read all of nLab, then come back.

Link to the articles relevant to understanding your deep question?

>>9264568
It doesn't seem to have anything on the category of axioms. Why is that?

>>9264572
>It doesn't seem to have anything on the category of axioms. Why is that?
Not every category has its own page.

Advanced category theorists such as myself are not responsible for the education of the mathematically immature.

>>9264578
Is it a part of your research then? It doesn't seem to be known to anyone except yourself.

>>9264586
>Is it a part of your research then?
All of mathematics is my research.

>>9264578
>Advanced category theorists such as myself are not responsible for the education of the mathematically immature.
Where is that written?

>>9264669
>Where is that written?
In the post you quoted.

>>9258236
Is this loss?

>>9264109
> Why would you restrict your domains to be countable?
Because every single example or problem I've found where an index is used, like calculating limits, the index is countable. It seems like a definition that's useless, yes it can be generalised to uncountable sets, but there's no application of it so all it does is make you have to specify in every single theorem and problem that the index is countable.

>>9264102
Ive never seen an index be Set, can you give an example of when it's used?

>>9258236
Wheel theory...

Read the wikipedia article

Are things like this kind of bullshit special cases of generalizations with no real purpose or are they valuable

>>9264898
I don't know about category theory, but transfinite induction is used when dealing with ordinals in set theory. Maybe there's an analogy with categories?

>>9264898
>Ive never seen an index be Set, can you give an example of when it's used?
Fuck indices.

why is there so much avatarfagging in these generals?

What's the best supplemental book to baby Rudin? I'm using it for a class

>>9265763
Tao's Analysis I and II

>>9265763
lay's intro analysis is ok. maybe rosenlicht if you dont like lay

>>9265763
Rudin is a meme.

>>9265564
>why is there so much avatarfagging in these generals?
There isn't.

>>9259763
we used Classical Mechanics by Goldstein
totally worth it

>>9260015
complex analysis was the most fun i had in math, ever

What was the last legit important mathematical publication?

>>9265564
>why is there so much avatarfagging in these generals?
reaction images != avatars

>>9266120

http://www.foxnews.com/us/2017/10/24/white-privilege-bolstered-by-teaching-math-university-professor-says.html

What are some of the weirdest metric spaces?

>>9266150
There aren't any weird ones. The definition of a metric space is restrictive as fuck.

>read and understand all the theory before doing the exercises
vs
>skim the theory, begin the exercises and get back to it when needed

What is your approach /mg/?

>>9266197
Develop the theory by doing the exercises

>>9265922
Well I didn't pick it

>>9266150
discrete metric induces some pretty unintuitive shit

>>9258359
>>9258365
>>9259076

wtf kind of math are yall doing where you unironically use a calculator?

I'm doing EXPERIMENTAL physics and the only reason I ever use a calculator is because I don't want to round my measurements, but for all practical purposes I dont ever need one.

>>9259763
>no Landau-Lifshitz

Modern right wing:
Armin Mohler
Alain de Benoist
Paul Gottfried

Conservative revolution:
Oswald Spengler
Ernst Junger
Martin Heidegger
Edgar Julius Jung
Carl Schmitt

Traditionalist school
Rene Guenon
Julius Evola
mircea Eliade
Emile Cioran
Titus Burchars

Religious:
Augustine of Hippo
St. Thomas Aquinas
St. Gregory of Nissa
St. Hyeronimous
G.K Chesterton
Joseph Ratzinger

Conservative:
Edmund Burke
Joseph de Maistre
Louis de Bonald
Juan Donoso Cortes

Interesting leftist:
Zygmunt Bauman
Slavoj Zizek

>>9266526
seconded

For more introductory content, Feynman lectrures are a classic

>>9266528
Fuck off back to /pol/

>>9266536
>Fuck off back to /pol/
There's no need for profanity.

>>9258236
Writing Women in Mathematics into Wikipedia

https://arxiv.org/pdf/1710.11103.pdf

In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present the rules for creating a biography on Wikipedia and relate my personal experiences in creating such articles. I hope to provide the reader with the background and resources to start editing existing Wikipedia articles and the confidence to create new articles. I would also like to encourage existing editors to look out for and protect new articles about women mathematicians and submit new articles.

>>9265157
yes, existence of limits indexed by an arbitrary set are important in category theory. however, a similar issue shows up just at a "larger" level.

Which conjecture are you most convinced is probably true?

For me, it's the Bombieri-Lang conjecture

https://en.wikipedia.org/wiki/Glossary_of_arithmetic_and_diophantine_geometry#B
https://terrytao.wordpress.com/2014/12/20/the-erdos-ulam-problem-varieties-of-general-type-and-the-bombieri-lang-conjecture/

>>9266316
discrete metric spaces are effectively just sets. in fact you can characterize them like this: a function X-->|M| from any set X to the underlying set of a metric space M (or any space) is continuous wrt the discrete topology on X. There's really no magic.

>tfw /sci/ is now filled with brainlets who know LaTeX but not math

>Mathematics Stack Exchange

Im working through Axler's LADR
some of my proofs on paper are shoddy with all the tiresome indexing needed, though clear in my head with a little intuition
It's not that big of a deal right? It's already taking a long time doing all the exercises

Need some help with some game math

Didn't get much past algebra in school because I was lazy but there's my formula for determining chance to hit

The attack roll is base 100, but I'm taking it down to 80% because the Defense Roll is from 1-100

so I want there to be a chance to block if the defense roll is 0-15% better equal or greater

and if it's 16% or above then you evade and avoid all damage

basically a 5% chance to evade, 20% chance to at least block.


You gain stats in base 10, so 110, 120, ect. basically adding 10 to your rolls. I'm trying to get it to where you have diminishing returns on block/evasion, that way your defense isn't much better than having offense. So how do I maintain that if it's not already functional?


Going to be doing some more testing, did that make any sense?

2nd post will have tl:dr I guess

>>9267006
Basically

how do I get diminishing returns for defense rolls, and keep it closer to 0-15% is a block, and 16%+ is evasion?

Like at the end you have +20 to defensive rolls, but with this system each + 1 is +1% gained, how do I make so each addition +1 is less than a +1% gain?

So you only have to roll a 60 instead of an 80 to block. which is going to be way too strong of a gain.


Surely someone gets it now right?

>>9266739
>he doesn't respect the beauty of MSE

I bet you dont even think of math as a hobby

>>9267006
>>9267020
Taking a guess, but I need to balance it for

100 * .3
vs
80 * .5

and do the same balancing in the check sum thing, so that 80 is a block and 96 is an evade.

>>9267058
Figured it out, that was the solution I think, now every + 10 is only .3% gained for a better chance to evade, might need to go a bit higher, maybe every 5 points should equal + .5%

>>9267065
>>9267058
Wait I may be retarded, I'm going to sleep...

Need help with my Category theory homework.

Pic related is the question, the thing is at least 2 other questions have obvious errors in them, so now I don't know if im being an idiot, or if this question is also fucked.

First, the functor [math]\Delta[/math], should that be [math]{\Delta}:Set \to Set^C[/math]? Im pretty sure about that, but then [math]P[/math] isnt the representation of [math]hom(\Pi,\Delta(-))[/math], its the representation of [math]hom(\Delta(-),\Pi)[/math]. unless they are the same or isomorphic to each other. I didnt work it out yet, but Im quessing [math]P[/math] should actually be [math]\Pi(0) +_{\Pi(4)} \Pi(1) +_{\Pi(4)} \Pi(2) +_{\Pi(4)} \Pi(3)[/math].

I just need to know if the question is correct or not.

So I'm being asked to find all bs such that the linear system is consistent.
But all the examples in the lectures have the constant terms, well, constant.
I tried solving the system and got solutions for the xs in terms of the bs and a free variable t, but I don't really know what to do with that result.
I have no idea how to go about this kind of problem. Can anyone point me in the right direction?

>>9267070
I am assuming "constant functor" means it takes every object to the same object and every arrow to identity. For every [math]i\in \{ 0, 1, 2, 3, 4\}[/math], let [math]S_i := \Delta(i, 0)[/math]. For a fixed object [math]i[/math], you would then have a contravariant functor [math]\text{Hom}_{\textbf{Set}}( \Pi, S_i)[/math], which would then turn the arrows around. Try this, it could help.

>>9267446
Assuming its behaviour with a varying [math]\Pi[/math] is what you are really interested in.

>>9267403
Just find the image of this matrix [math] \left( \begin{matrix} 1 & -2 & 5 \\ 4 & -5 & 8 \\ -3 & 3 & -3 \end{matrix} \right) [/math] .
It is the span of its columns.

>>9267483
by the way that's the whole [math] \mathbb{R}^3 so all b's work.

For LA I, I'm supposed to show that for a linear map f between a finite set A and the set A itself, the statements "f is injective" and "f is surjective onto A" are equivalent. I think I've done that, but now I'm supposed to show that neither implication holds for a linear map between infinite sets.
Can I just pick two linear maps between the set of natural numbers, like n->2n for an injective function, and say that the implication doesn't hold and be done with it? This doesn't feel right.

>>9267519
First of all the Naturals can't be a vector space (e.g. no additive inverses).
Linear Maps are a name for homomorphisms between vector spaces.
This makes me think that you didn't get the part with the finite sets right.

Also, f injective <==> f surjective holds in any finite-Dimensional space (as a set it can be infinite).
But, it may not hold for infinite dimensional spaces.
Some examples are here:
https://math.stackexchange.com/q/2091104

>>9267559
Oh and f:V-->V .

>>9267559
We only just introduced the concept of a vector space, it's just that the set should be the natural numbers. Maybe I translated something incorrectly. It's fairly close to ehat I was looking for, though, thanks.

>>9267709
And your professor calls them "Linear Maps" just because f(u+v)=f(u)+f(v), f(λv)=λv?
Tell him that he is a fucking retard.

>>9267716
That was me being the retard, it's just supposed to be a plain ass function.

>>9267716
Thats what linear means

>>9267519
Let f: A->A be any function with A a finite set. (1) Suppose f is injective. Then there is a bijection A -> im f. Consider the set B of elements not in the image of f, and |A| = |im f| + |B|, but the bijection gives |A| = |im f|, so we have (by finiteness) |B| = 0. (2) Suppose f is surjective but not injective. Then we have some x and y on A such that f(x) = f(y), but this implies |im f| < |A|, by finiteness, contradicting surjectivity.

>>9267746
Shit, I didn't even consider using cardinality for this. Thank you.

>>9265564
There was until the subhuman dog-eater's posts weren't regularly deleted.

>>9266590
All I ever see here is people who know neither.

>>9267559
"Linear maps are the name for homomorphisms for vector spaces" is kinda b.s. Linear maps are maps that are linear. Aka f(ax+by)=af(x)+bf(y). This happens to be homomorphisms for vector spaces, but you can speak of it for other spaces aswell..

hey guys how do i prepare for a university math competition in less than 2 weeks

>>9267846
>There was until the subhuman dog-eater's posts weren't regularly deleted.
What's wrong with eating dogs?

>>9267716
that's literally the definition of a function being linear

>>9268253
Yes and the definition makes sense for other things than vector spaces. For instance for associative algebras, but then the notion of a linear map is not the same as the notion of homomorphism.

>>9258236
Wheel theory is quality, but I'm reading up on computability logic.

>>9267020
>>9267069
I am for sure retarded

forgot that in a D100 system every +1 is 1%, would need to go to D1000 to make it tighter, but I just divided the stats by 5 and it looks fine

>he/she comments their code

>>9268626
>Making your code completely unintelligible in order to fuck over your employer if they ever decide to fire you

>>9266120
IUTT

>>9263973
1-2 are in Chang and Kiesler; can't remember how much of (3) is

Please help, I'm retarded and probably overthinking this.
How would I integrate the area between two cardioids? The problem I'm doing has R =1+sinθ and R=1+cosθ

Hello /mg/.
I was reading the recommended math books page at wiki, but I got confused.
Should I learn Linear Algebra after studying multivariable calc?

What does it mean to say a set ≤ a set?

>>9258240

>>9270317
You can't actually do multivariable calculus if you don't know linear algebra

>>9270338
I see
Thank you anon

>>9270317
>Should I learn Linear Algebra after studying multivariable calc?
You can't study Multivariable Calculus without knowing Linear Algebra.

>>9258238
What's it like to be a brainlet?

>>9261165
>integrating over (theta, theta plus epsilon)....with respect to theta
Disgusting

>>9270322
>What does it mean to say a set ≤ a set?
Depends on the context. It could be a partial order, or just a quick way to say every element in the left set is <= every element in the right set

>>9270452
I thought it was used in the context of set cardinality and if you can construct a bijection between sets or not, e.g.
[math]\mathbb{N} \leq \mathbb{Z} \leq \mathbb{Q} < \mathbb{R}[/math]

>>9270317
Multivariable calculus introduces some linear algebra that it needs. You can learn linear algebra before or after multivariable.

>>9270476
It's really not enough if you actually want to understand Multivariable Calculus. And they usually explain LA there in an unintuitive engineer-tier way.

>>9270470
>I thought it was used in the context of set cardinality and if you can construct a bijection between sets or not, e.g.
I've never seen it used that way, it seems strange since you would also be able to write Z <= N in that case.

>>9270510
That's because [math] \leq [/math] needs to be defined on a set, and there isn't a set of all sets. That's why we compare cardinalities instead of sets.

>>9270322
there is an injection from the left set to the right set

For example Schroeder-Bernstein says [math]A\leq B[/math] and [math]A\geq B \implies A=B[/math]

>>9270510
>>9270452
retard

>>9270809

I need the most rigorous probability theory book followed by the most rigorous statistics book. Intuition not required

>>9270812
>retard
?

>>9270809
>there is an injection from the left set to the right set
Then here >>9270470 it would be N <= Z <= Q <= R instead of N <= Z <= Q < R.

>>9270826
Well, "[math]<[/math]" means "[math]\le[/math] but not [math]=[/math]", so you indeed have both [math]\mathbb{Q}\le\mathbb{R}[/math] and [math]\mathbb{Q}<\mathbb{R}[/math], since there is no injection [math]\mathbb{R}\to\mathbb{Q}[/math].

>>9270862
Interesting, this worked in the preview. Q < R and R -> Q

>he/she reads textbook proofs before trying to prove the theorem himself/herself

>>9270933
>gorillas
>>>/r/eddit/

>>9270935
That's a frog, not a gorilla.

>>9270322
Inclusion viewed as a partial order

Any good alternative to MIT OCW's DiffEq course?
pretty bad quality of the lectures desu
I got the meme book from wiki too

>>9263426
Had an infatuation period with math too, got into uni and i'm still thrilled when I learn new stuff but I can't sit down to study even if my life depended on it.

>>9263980
[math]2(x-2)^{-1/3} - \frac{2}{3}x(x-2)^{-4/3}
= (2(x-2) - \frac{2}{3}x)(x-2)^{-4/3}
= (\frac{4}{3}x - 4)(x-2)^{-4/3}[/math]
brainlet

>>9258236
In vector calc right now, having a hard time understanding graphing in 3 dimensions. I'm doing fine in the class, but it's not intuitively making sense to me. What can I read or watch to help make this more sense?

>>9271788
all you can do it work through examples. graph a lot of shit, and you'll start to get intuition on it

>>9271788
What do you mean? You can't read the graph of a function f(x,y)?

>five (5) years since IUTT papers released
>still no consensus

Guys, is this >>9272130 correct?
I mean it "seems" correct, but if you put m=n you don't get n*(1/d)^n ...

>>9270300

>>9263426>>9263426
>>9270970

same thing, and it happened during the phd which made it hard to finish. Now I just relax at home watching tv.

>>9268626
Are you retarded?
You comment the trivial parts:
i++; //adding 1 to i
and when it gets complicated you comment nothing.

>>9266543
Historical revisionism through sexism is not a nice thing anon :(

>>9272580
Oh wow, that makes much more sense.
Thanks!

>>9272637
Why the fuck did you post a random. Tinder profile you fucking weirdo

>>9273096
>you fucking weirdo
cringe

>>9273096
I don't know why he did it but you have to admit it is funny
>I'm used goods
>I EXPECTS FLOWERS AND EVERYTHING FROM A FAIRY TALE
>single mother
>I have a 5 year old from another man, who will cost you money
>CAN'T HANDLE IT HUH? CAN'T BE A GROWN UP? DON'T WASTE OUR TIME!

Single mothers are so delusional. No one is ever going to buy them flowers again. You have to be the greatest cuck alive to raise a child from another man.

>>9273097
Incel spotted
>>9273099
And yet a beta will do exactly that, giving girls high standards,making it impossible for uggos to ever find an attractive girlfriend.

>>9273105
>And yet a beta will do exactly that, giving girls high standards,making it impossible for uggos to ever find an attractive girlfriend.

No. I'm pretty ugly from many fronts and I have a girlfriend right now. It is possible to find an attractive girlfriend.

>>9272580
I guess I still don't get it. Also, whenever I graph it by hand or using a graphing program, I end up with a small area from pi to 3pi/2.

>>9273107
Wrong. Enjoy your hand uggos, or your butter faced troll

>>9266517
This

>spend 2 years idling thinking about the problem of ranking forecasters, convinced I'm stumbling upon an entirely new branch of mathematics
>ayy lmao, Brier was here 1950
At least I can actually write a decent research paper now, but fuck, I was ready to get my own formula.

>>9264578
quit baiting, you're a faggot

>>9266197
> skim the theory and skim the exercises

>>9266543
this won't get you laid, stop this idiocy

>>9263432
Fuck off brainlet

Good books for limits by definition?

Is abstract algebra worth learning? Does it help you understand math better overall?
Also, say I wanted to study abstact algebra, topology and real analysis. Which one should I learn first and why?

>>9274559
>Which one should I learn first
Abstract algebra and topology. You can safely ignore analysis, since it's known to be garbage.
>why
Any even remotely interesting field of mathematics requires them.

Few years into college changing majors and all that and I like mathematics so I settled with that. Mainly because I like solving problems. However I suck at showing my work and it brings me down in the upper maths because I seriously suck at showing work despite getting correct answers.
Maybe math isn't for me career wise? What would be a close alternative major where maybe the fact I can solve problems but not really show why would work out better?

>>9274620
>I seriously suck at showing work despite getting correct answers.
if your prof doesn't follow your proof you don't have correct answers