/mg/ math general: Poppin' Wheelies Edition

>blaming the tool
yeah okay

get a ti 84 if you must

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

this puppy

FX 115es plus or FX 991ex

Patrician here.

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

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?

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?

Get the TI 36x pro engineering calculator.

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

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|

So how do you define set, /mg/?

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?

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

>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?

Also, Veeky Forums 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?

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.

fuck off

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

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

I was 2nd semester freshman but out of 150 ppl taking it I was one of

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

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

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

cool,thx

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.

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.

t. dumbass

good if you're undergraduate??
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

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.

Axler

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

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

Residues are awful, just keep practising.

>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.

>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

just wake up user

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?

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

it's /math not \math

Thanks.
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?

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.

because a circle is "flat" locally

Thanks !

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?

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

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.

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.

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.
en.wikipedia.org/wiki/Categorical_distribution#Bayesian_inference_using_conjugate_prior

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

>faggots
Why the homophobia?

so that you ask and bump the thread again, faggot

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

An answer for this?

>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: 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?

god dammit, good*

Has anyone here studied Differential Algebra? Any book suggestions?

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

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

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?

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

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

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].

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).

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

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

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.

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

Alright, I'll add physics to it then.

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

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.

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

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

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?

>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?

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.

>mathematical logic
What's the point?

Fun things are fun