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/sci/ - Science & Math

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12771755 No.12771755 [Reply] [Original] [archived.moe]

Formerly >>12750260

Funny rotating numbers and funny spinning vectors edition.

Talk maths.

>> No.12771793
File: 329 KB, 3191x1609, Y3.jpg [View same] [iqdb] [saucenao] [google] [report]

Thank you vector anon

Wtf is y3?

>> No.12772503

Warum hier so ruhig...

>> No.12772601

Topology of logics evolution. In the past, we made linear systems as first descriptors, and perturbed them. Now we start with a description set more flexible than linear

Writing non commutative algebras without indices, and simply using perception of left and right to differentiate ordering, is a non physical notation. There are no ink marking atoms or any other mateials specifying the notation

>> No.12772698
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What the fuck do the weird symbols mean in picrel

>> No.12772703

What are the best Information Theory Textbooks

>> No.12772788

>[math]\partial _0 = - \partial _t[/math]
Fucking relativity and it's near incomprehensible random sign changes.

>> No.12772804
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What's your chess ELO, /mg/?

>> No.12772819

chess is boring unless your opponent is good and a good sport. Finding people like that is hard.

>> No.12772829

I just started learning it, so I'm not good yet but I don't mind losing.

>> No.12772835

Why bother with board games? This is a math thread, right?

>> No.12772840

> incomprehensible
that's just a metric with a (-,+,+,+) signature.

>> No.12772852

Chess is aplied Graph Theory.

>> No.12772861

Dubious. but why ask about an elo rating? No one plays chess while thinking about graph theory, and easily 99% of Strong players don't really know anything about adjacency matrices or anything like that.... Sort of a non sequitur.

>> No.12772871

Chess is a markov chain.

>> No.12772877

chess is a differentiable complex manifold

>> No.12772883

But why is 0 for t

>> No.12772892

the zeroth coordinate is conventionally taken to be time. Some authors label the coordinates 1,2,3,4 for the three spatial and one temporal, but more often you see 0, 1, 2, 3. It's just a convention.

>> No.12772906

I dunno man whys it gotta negative sign

>> No.12772923
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What research topic/area of math for this feel?

>> No.12772933

finding roots of polynomials

>> No.12772946

Hey so a Sum of two subspaces is a direct sum if the only way to write the zero vector in their sum is 0u1 + 0u2 ... 0un + 0w1 + ... 0wm right. This is the same thing as saying that a sum of subspaces is a direct sum if and only if the set of the basis vectors of both subspaces is linearly independent right?

>> No.12772962
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>professor uses microsoft word instead of latex

even handwritten notes would look more professional. i think his undergrad was in computer science which probably explains it

>> No.12772964


For the life of me I dont get what a polynomial is supposed to MEAN

>> No.12772969

Its just a sum of N dimensinal cubes...

>> No.12772985

HOMOlogical algebra.

>> No.12772986

Consider a vector space V over a field F. Say x is a variable that takes on values in V. A polynomial is a function T:V -> V which produces the linear combination of successive powers of x, each power scaled by a 'scalar' f that is in F.

>> No.12772988
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>differentiable complex manifold

>> No.12773000

actually no, i'm retarded. V must be a field as well, not just a vector space since we define multiplication of two of its elements. It must still be closed under addition and multiplication.

Scratch that, V should be a field, and a polynomial is a function T:V -> V that produces linear combinations of scalings of powers of x.

>> No.12773005

Isn’t it the coolest shit how vectors in a vector space f^n represent functions from n->f

>> No.12773010
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quantum computation can in principle solve the halting problem, so is therefore also not limited by the incompleteness theorems.

>> No.12773011
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>> No.12773014

>isn't it the coolest shit how we can add and multiply functions pointwise
Not really.

>> No.12773020
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>> No.12773022

it is cool though, because then you can express derivatives of polynomials as a matrix.

>> No.12773028

>differentiation is linear therefore it's a cool matrix
Woah woah woah, sooooooo amazing.

>> No.12773031

Yeah dude that is so dope. You can also think of exponential functions as the eigenfunctions of the derivative

>> No.12773036

awesome resources. cheers to the OP.

>> No.12773039

Okay then name one simple fact from math that you think is amazing

>> No.12773049

I like the fundamental theorem of algebra.
>add a root to x^2+1=0
>"yup, that's it, you've got all the roots now."
Besides, all of its proofs are pretty sideways, so it doesn't really lose its luster once you know how to prove it.

>> No.12773054


>> No.12773062

listen man, when you learn calculus first it's pretty amazing. Then you learn lin alg and it's pretty amazing. Then you learn the construction of real numbers and that's pretty amazing. Then you look at complex analysis, and integration along lines, and it's pretty amazing. Math is pretty amazing, and the more you learn the more cool it is. Just because you know something very well, doesn't mean it's cool; it just means you're acclimated to how amazing it is.

I bet when you were a kid and the teacher told you about the number e, you were like "shit, that's actually kinda neat". Now dealing with e is like "eh whatever". But you should still realize that's in cool, you're just used to the coolness that youdon't notice it anymore.

>> No.12773078

Oh yeah that is a great one. I’m also partial to complex exponentiation since I discovered that independently when I was a freshman in high school.

>> No.12773098

That is more a physics questions than maths. In general the metric could be anything however the invariant interval for relativistic proper time, in natural units, is [math](dS)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (dt)^2[/math]. That is the same quantity no matter the reference frame and if you integrate you are essentially calculating the "distance between two events". So by inspection you can see the space indices are +ve while the time one is -ve.

>> No.12773155

>I bet when you were a kid and the teacher told you about the number e, you were like "shit, that's actually kinda neat".
Not really because they just gave us the formula and I didn't see the point.

>> No.12773265


Just downloaded this book, this seems to be nicer than Brown & Churchill and the Stein book. It seems to start from the basics and work up, rather than the Stein book, which is nice I guess. It's a more fundamental approach ig.

>> No.12773318

Isn't there a way of simulating quantum computers on a classical computer in exponential time making what you said trivially false?

>> No.12773433

So I'm really stupid help me out. There's a TV game show in which you have to answer a question correctly being given four answers. You can also use a certain number of "lives" in which you choose between two options and one is eliminated. You lose three of this lives if you give the wrong answer no matter how many you used to help you out. What's the best option if you have no clue?

I can go as far as:
using no lives is (0 + 3 + 3 + 3) / 4 = 2.25
using 3 lives is... well 3

Then I went:
using one life is (1 x 0.75 + 4 x 0.75 + 4 x 0.75) / 3 = 2.25
using two lives is (2 x 0.75 x 0.66 + 5 x 0.75 x 0.66) / 2 = 2.98

>> No.12773458


>> No.12773593
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>> No.12773619

i am currently in high school and math is ok

>> No.12773720

HJelo, if Hom(X, X) =0 inn an ycategory then X iso yo 0, yesd?

>> No.12773821

Meruem best girl T_T

>> No.12773836

How do you exponent a vector? Cross product?

>> No.12773844

>Then you learn the construction of real numbers and that's pretty amazing
No I hate this one

>> No.12773851

What if in the future when we get really good at relativity and controlling massive energy sources, we just create warped space time sheets of n dimensinal paper for non euclidean math

>> No.12773889
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>having trouble with trig
Should I just kill myself for being a brainlet?

>> No.12774058

No, you should just practice more trig.

>> No.12774090
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How do people sit like this!?

It hurts my knees!!!


>> No.12774096

>stop posting frogs
>start posting 2hus
you will see results in 2-5 days

>> No.12774206

nah a real manifold works fine

>> No.12774217

Elliptic curves

>> No.12774220

that's not what the paper says at all, retard

>> No.12774229

I’m the guy who didn’t know who mult was last thread, who are these people

>> No.12774236

Dumb frogposter

>> No.12774337
File: 213 KB, 1472x743, janky.png [View same] [iqdb] [saucenao] [google] [report]

I'm trying to do problem 4.72, but I'm having trouble. The current proof I have relies on, in the case of the mapping cylinder, relies on [math] i_ {0} \simeq i_{1} [/math] , but I'm having trouble proving that and finding some other method.

Crossposting from >>12774287 , my question still feels stupid but I'm not sure where to put it. Let me know if I'm out of place.

>> No.12774417

What is the most important undergrad math course?

>> No.12774438

Those names are new and are presumably the same guy trying to avoid a ban.

>> No.12774445

Linear algebra by far.

>> No.12774450

For left homotopy, consider the cylinder diagram with both your standard Cyl(X) and the possibly non-standard cylinder object C. By assumption, there is a left homotopy between f and g, so there will be a left homotopy K: C -> Y. Define a map between h: Cyl(X) -> C by choosing any of the two maps X -> Cyl(X), then taking its homotopy inverse, and then composing that with the corresponding map X -> C. Finally, define H: Cyl(X) -> Y as the composite of h and K. Check commutativity to see that this is a left homotopy, and apply 4.71.

>> No.12774480

Rude. Im Mult and those arent me. I posted on mg as anon for like 1.5 years by now. I just tried a namefag for a bit cause I was havin fun but mg is too filled with little babby autists so Ill just keep it pure math and sweetness

>> No.12774666

[eqn]\bigcap \kern{-0.8em} \mathrel{ \raise{0.3ex}} \subset [/eqn]

>> No.12774669

Fucking mathjax

>> No.12774714

>supposed to portray genius
>doesn't know \left( and \right)

>> No.12774833

Grants and Nature manuscripts have to be written in word

>> No.12774863

Set theory takes [math]\in[/math] as a primitive and derives everything from there but what metalogic field studies the concept of [math]\in[/math] and the alternatives to it?

>> No.12775091

In any category is it true that Hom(X, X) = 0 implies X = 0??

>> No.12775116

they say there are smart pepol here who can help with collectin data from internet?

>> No.12775135

so not science

>> No.12775141

for any object there is at least the identity

and there is one map from emptyset to emptyset

>> No.12775166

>Hom(X, X) = 0
what is 0? empty set?

>> No.12775169

what the fuck are you asking

>> No.12775177

i need to define data from a bunch of people and find out the content they like most...

>> No.12775190

0 means that the only morphism between them is the zero morphism

>> No.12775356

>finished liceum in a typical polish highschool
>now after few years am getting interested with maths
where should i start learning agian, i'm getting trouble with translating all the different fields of math i've been taught
also geometry is fun ngl, making complex figures with just a compass and a ruler is amazing o-o

>> No.12775444

Topos theory

>> No.12775494

You don't know anything about Topos theory.

>> No.12775504

fuck off gaming coomer

>> No.12775513

That's a very productive comment, thank you for enlightening us.

>> No.12775661

hah lame

>> No.12775860
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Help me /sci/, this stupid problem is driving me crazy.

I'm trying to prove the statement in pic related. Basically, I want to "restrict" f(x) along a specific direction h, and prove that, unless the origin is an extremum point, this "restricted" f is monotone.

This seemed a piece of cake in my head, just take the gradient as h and it's done. But this leads to fucking nowhere: clearly the linear approximation is some "sort of" restriction, but I feel like I have no results on the *actual* f_h.

Am I missing something obvious? Or am I just retarded?

>> No.12775938

Yes, you're missing the obvious fact that
[math]D_h f= \nabla f \cdot h[/math]
[math]D_{\nabla f} f= \nabla f \cdot \nabla f = |\nabla f|^2 > 0[/math]

>> No.12775942

You know the derivative of f_h and you know that the derivative is continuous and positive in a neighborhood of 0 (for the h chosen above). We also know that if in an interval a real function has positive (resp negative) derivative, then it's monotone increasing (resp decreasing).

>> No.12775947

Does anyone have the pictures (which I regretfully didn't save when I saw them for the first time) containing a number of books about mahs that should be read in a certain order?

>> No.12775953

I didn't think of using the derivative of f_h, your argument is super nice. Thank you so much!

>> No.12775972

seconding this request, was going to ask something similar but the pics sound interesting

>> No.12776001
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>> No.12776057

I'm going through the introductory probability book by this greek MIT prof, and constantly struggle with problems where parameters of distributions are changing in the course of experiment, or they are themselves random variables, even with given distributions.

Is there a common approach to such problems, or each time there's some clever observation that should be made that makes problem simpler, or am I just being heavily filtered by a fucking Probability 101?

>> No.12776060

Misha fuck off, there's still a line of hung brazilian traps hungry for your ass.

>> No.12776074

And no, it's not about random number of random variables. Better example of what I'm having trouble with is finding PMF of the number of arrivals in the poisson process in the timeframe that is exponentially distributed (with different rate parameter)

>> No.12776376

Functional analysis is a lot, can someone point me to good resources?

>> No.12776507
File: 584 KB, 1080x830, 1582026273574.png [View same] [iqdb] [saucenao] [google] [report]

Hey there, I just got through an Abstract Algebra course but I honestly feel like I didn't learn anything. So I was thinking of using the 15-day break that I'll have to study it deeper. Is it a realistic goal to cover groups and rings (not everything about them of course) in 15 days? Should I use Dummit and Foote? Thanks.

>> No.12776515

Clean. Just went through it, thanks so much!

>> No.12776522

what book is this?

>> No.12776547

y=e^x-x, y is some positive constant >= 1, solve for x

what do i read to learn how to solve this. combinatorics?

>> No.12776589

how do we know that the solution is an algebraic number?

>> No.12776609

You can definitely review the basics if you work diligently every day. Dummit and Foote is good.

>> No.12776623

I mentioned Dummit and Foote because it seems to be the easiest Algebra book and therefore it would be faster if I used it instead of some hard ones like Artin or Aluffi. But if you have any better recommendations please do share. Thank you.

>> No.12776624

It's okay, I wasn't comfortable with trig until I got into complex analysis.

>> No.12776715

Are these the only options?

>> No.12776735

pls help me :c

>> No.12776783 [DELETED] 

Natural logarithms.
If y>=e^x-x and y>=1 then that gives us that x-lnx>=0 which is true for all values of x in the interval x>0
(And I assume that you, by ">=" mean "larger or equal to")

>> No.12776828

There's a thread for stupid questions.

>> No.12776865
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What are some books I can read to make me autistically good at math?

>> No.12776888

Lang, Basic Mathematics
Tao, Analysis
tldr autistic people aren't good at mathematics

>> No.12777006

Is TexMaker good?

>> No.12777201

Works for me well enough. I can't say I've had any issues when using it but I haven't tried many other IDE's to compare it with.

>> No.12777295

>You can also use a certain number of "lives" in which you choose between two options and one is eliminated.
What does that even mean?
You said there were four options.
So which two options do you have to choose between?
And what do you mean by "one is eliminated"?
The one you chose is eliminated? One is eliminated at random?
What does it mean for an answer to be eliminated? Do you now have to choose again between the remaining answers? Can you use a life again?
How many lives do you have?

people aren't answering your question because you didn't explain it clearly

>> No.12777542

what would you pick out of these electives?

>MTH461-462: Graph Theory
>MTH431-435: Topology
>MTH431-432: Geometry
>MTH456: Topics in Combinatorics
>MTH424-425: Elementary Diff Geo & Tensor Analysis
>MTH427-428: Partial Differential Equations
>MTH421-422: ODEs

I'm taking probability, stats, real analysis and abstract algebra sequences as well. math/cs major hoping to get into finance (hence the probability and stats..) but also really interested in math and considering grad school afterward.

im leaning toward PDEs and ODEs, but I also really want to take diff geo. i've self studied graph theory and combinatorics a bit and enjoyed it. it'd be nice to get a taste of topology and higher geometry as well but whatever i don't take I'll just learn myself. i like ODEs and PDEs cuz physics

>> No.12777747

The only sets that exist contain all but a finite number of possible elements.

>> No.12777757

Do you people get any benefits by asking such advices? Like you've described and decided everything yourself. Can we know any better?
Subjects' designations without the syllabus aren't very informative, but I suspect you wouldn't get a taste of topology as you imagine it as it's a point-set one, I assume. Course named geometry can mean too many things.
ODEs and PDEs would be most useful in finance.

>> No.12777763

It's fine. A bit clunky. I would honestly recommend mostly using overleaf and just using TexMaker when you need to (unless you find a better offline editor, I don't know of one).

>> No.12777782

I would usually say topology is necessary. It is especially necessary if you intend on graduate school in pure math. The fact that this isn't required is sad.
If ODEs is a theory-heavy class, that. If it's "how 2 solve second order linear ODEs" then don't bother. Similarly for PDEs. Third choice is definitely diff geo.

>> No.12777814

>unless you find a better offline editor, I don't know of one

>> No.12777837
File: 79 KB, 767x282, Tape Recorder 5.jpg [View same] [iqdb] [saucenao] [google] [report]

Are there any courses on good universities open to the general public or students from other institutions?
Mine allows me to get credits through online courses from other institutions, so I need to know what opportunities are out there.
I'm particularly interested on courses about Algebraic Geometry, Algebraic Curves, Arithmetic Geometry and Commutative Algebra. Nothing too advanced though, I'm still starting on those areas.

>> No.12777936

Non-english speaking professors are the final boss of my degree.

>> No.12777970
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well, I've certainly benefitted by asking this from your topology point. I can supply more info if you'd like. The geometry is
>Topics selected from projective geometry, non-Euclidean geometry, algebraic geometry, convexity, differential geometry, foundations of geometry, combinatorial topology.

which sounds like a hodgepodge desu. there is another course that simply says "topics in euclidean and non-euclidean geometry".

sorry if these questions are asked a lot, getting advice on this is nice though, as i have no idea.

Awesome, the syllabus for the 'theoretical' (should've included that in the title) ODE class is
>Vector fields and phase flows in the plane. Geometric and algebraic properties of linear systems. Existence, uniqueness, and continuity theorems for systems. Additional topics.

can i self study topology and not hurt my grad school chances? I will double check and see if I can fit it in anywhere. you would say that topology is more important than diff geo? I kinda wanted to learn diff geo from pic rel anyway

>> No.12777985

here's the topology descriptions

for the first one
> DeMorgan’s Laws, partially ordered and well-ordered sets, Cardinal and ordinal numbers. The axiom of choice and equivalent formulations. Additional topics.

second one:
>Introduction to general topology with the notions of interior, closure, topological space, continuity, and homeomorphism. Construction techniques and properties of point-set topology, especially connectedness, compactness, and separation.
sounds a lot more topological

>> No.12777989

sorry i should've specified i get to pick TWO. so i was planning on ODE and PDE. boring but practical as a math/cs major, IMO

>> No.12778016

Can anyone recommend a decent tensors book for physics?

>> No.12778098

idk probably look up the Lambert W function

>> No.12778101

I don't think i said it was. plugging it into mathematica gives a "solution" that uses the "lambert w" function (i use solution in quotes because it requires numerical methods to compute so i might as well solve the original equation numerically anyways) and some brief googling i did said it was very useful in combinatorics which is why I aksed if combinatorics is what i should study to understand whats going on.

>> No.12778131

Don't get it twisted, but solving, say, e^x=2 can only be done approximately, that's why we introduce the logarithm function to talk about the solution x=ln(2). Same here with the W function. I imagine one can produce some sort of infinite series expansion giving the solution exactly.

>> No.12778249

That’s like 75% of maths professors. Skip lectures.

>> No.12778258

I wouldn’t bother with undergrad PDE. Do topology and differential geometry.

>> No.12778263

This is the maths general. Just about everyone here will either reply that you should just FUCKING LEARN DIFFERENTIAL GEOMETRY PROPERLY or ignore you.

>> No.12778377

I've looked into DF, but mostly all fluid mechanics in physics is based on tensor analysis, the language is far different than that of most modern DF books. Also MOST PEOPLE CAN GO FUCK THEMSELVES. Good'ay

>> No.12778499

Is it me or does Lang somehow manage to make lines really confusing (Chapter 10, Section 3).
In this chapter there is also a bunch of typos that make it even more confusing (He slightly fucks up Q - P = c(N - M) in the parallelism definition).
I have no idea what the fuck was he thinking with this chapter, think I'm going to need a back up books on basics as a sanity check because this chapter is so fucked up, I can't even tell if something is right or there is another typo.

>> No.12778502
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>> No.12778528


Why determinants

>> No.12778569
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This part is a little fucked for example. He says he wants the line parallel to (1, -5) but actually makes it parallel to (1, -1). Is this an error on the PDF or the book also has little mistakes like this?

>> No.12778638

thanks, I was most attracted to these two anyway so after a lot of consideration, this is what I'll do. I may still take Theory of ODEs for fun though.

>> No.12778690

How is Texstudio better? It looks very similar to me.

>> No.12778696

yeah, that's a good ODE class. topology and differential geometry are both nice, but if you want to go to grad school for pure math, unless you did a significant amount of metric space topology in real analysis, then you're not going to be in a good position if you have no formal topology background.
is your differential geometry a class on curves and surfaces, or a class on manifolds? no grad school will care about a class on curves and surfaces.
the second one is the only one worth taking.... the first is a fucking set theory class.

>> No.12778698

you should aim to take all three of them.

>> No.12778701

i'm just gonna be straightforward with you: if you're just doing the bare minimum major requirements for math, you are not going to be admitted to a pure math phd program which is worth going to. not a chance.

>> No.12778731

what makes you think I'm doing the bare minimum? do you mean bare minimum credit number? I never heard of people taking more. I'd like to, just thought it was dumb to pay more time and money for the same paper. I am trying to skip some "intro" courses so I can fit more real stuff in my degree.

I'd like to take as many as I can, I hate having to cut out topics I think every math grad should know. do people do this? just linger around a bit before getting the degree?

could I skip the first one, you think? email a prof and see what happens or..?

thanks for the advice guys, there's a consistent message in all the replies I was given but I'm not sure how to apply it

>> No.12778744

>is your differential geometry a class on curves and surfaces, or a class on manifolds?
this is the description of the first course:
>Differential geometry of curves and surfaces; elementary Riemannian geometry; the Gauss-Bonnet theorem; applications from mechanics and field theory.

and the second
>Surfaces of constant curvature, the Gauss-Bonnet theorem; spherical and hyperbolic geometry, elementary Riemannian geometry applications from mechanics and field theory.

does it look good? they're talking surfaces so i assume it's alright? there aren't any prereqs beside applied diff eq (which has prereqs of linear alg and calc i think)

>> No.12778751

What does mg think of fencing? Spherical geometry...

>> No.12778760

this is what I'm looking at now then guys
>MTH 311, 312, Introduction to Mathematical Analysis I, II (sub with Real Analysis I, II (461,462)?)
>MTH 344, 345: Group, Ring and Field Theory (sub with Abstract Algebra I,II (435, 436)?)
>MTH 431, 435: Set Theory and Topology I, II (skip set theory intro course?)
>MTH 424, 425: Differential Geometry & Tensor Analysis
>MTH 421, 422: Theory of Ordinary Differential Equations I, II
>MTH 464, 465: Numerical Optimization I, II
>STAT 461, 462: Applied Statistics I, II
>STAT 467, 468: Applied Probability I,II

pls tell me how to not do the bare minimum and help me enhance my chances of getting into a pure math phd program that's worth going to. i don't want to cut stats and probability as I'm taking a lot of CS classes too and trying to keep software development as a fall back

>> No.12778762

This is gonna sound weird but do you regulate your emotion when you work on problems?
Or do you just feel numb?

>> No.12778915
File: 29 KB, 232x469, VisuBinaryTetGrp.jpg [View same] [iqdb] [saucenao] [google] [report]

Does anyone know which vertices of the 24-cell these GL(2,3) matrices relate to? I have the 2T version worked out already, but I don't understand how GL(2,3) works.

>> No.12778981
File: 14 KB, 326x499, 315wfVckycL._SX324_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google] [report]

so many definitions ...

by the time I would need to regulate emotion be it frustration anger etc. I find that it's best to just take a break and work on something else for a bit.

>> No.12779056

I didn't assume you seriously consider a math grad aftewards, like it may not really be helpful with finance. Do you have an endgoal?

I guessed right that the curriculum is only about point-set topology. That is a standart intro, but it doesn't scratch the surface of what people mean by "topology" aka algebraic topology, like no homology or homotopy. Point-set is the boring cornerstone everybody has to go through first though.
Geometry curriculum sounds more fun.

>can i self study topology and not hurt my grad school chances?
Why not. Munkres' book is a great introduction. It also has a good overview of basic set theory, like choice, cardinality etc.. In case you're not yet familiar with those, it's a comfy introduction.
Then comes much more fun algebraic topology. Hatchers' book seems to be the most renowned introduction http://pi.math.cornell.edu/~hatcher/AT/AT.pdf
That text is a lot more straightforward, but it's not fit for first read https://lniat.sitehost.iu.edu/m621notessecondedition.pdf#theorem.4.10

Gauss-Bonnet theorem requires some familiarity with algebraic topology, unless it's left without proof or used in special cases only in "engineering" fashion. Its proof actually requires lots of stuff beyond your previously mentioned courses, like you're supposed to be fluent with manifolds. So either that elective has more advanced prerequisites or it's meant for the applied math folks.
In case you're interested in that stuff, check out Lee's introduction to smooth manifolds or the more brief Tu's introduction to manifolds.

>> No.12779089

The only emotion with math is fatigue or curious energy, and the general pull of conceptualization towards correct energy minimum

>> No.12779094

>I'm taking a lot of CS classes too and trying to keep software development as a fall back

Life is only that long.
What are your interests exactly? Why pure math PhD?

>MTH 431, 435: Set Theory and Topology I, II (skip set theory intro course?)
Skipping a course because some random people advised you to do so may not be the wisest idea. That intro stuff is pretty basic, but we don't know your level. Try learning it yourself and see if it's something you may skip.

>> No.12779142

The number one is getting to study math longer in grad school. If that flops, I'd like to pivot to development in areas I'm interested in, and finance seems interesting and high paying.

The geometry cirriculum did sound fun, but I'd worry with so many topics crammed into 8-12 weeks I'd only have a first impression of all the stuff, I'd rather go deeper and do less, but what do I know.

Thanks for the topology books. I know I can self study, but I'm not sure if not having topology courses on a transcript is a big negative despite self studying.

I've learned set theory, I read that little Naive set theory book too. I don't know how deep set theory goes, but I'll take the intro. It'll surely introduce topology at least.

I like doing math. Well, I enjoy studying it in my free time anyway. Not sure if I'd like doing PhD work necessarily, but I have this feeling I'll regret not trying. I like proof based stuff a lot more than the mostly computational stuff I've done so far in my undergrad, I'm really looking forward to these more theoretical courses.

I'm not taking that many CS classes; I was going to double major, since I've filled all the lower division requirements, but at this point I'm just going to take a few more that I think are relevant to the work I'd like to do. Being that a lot of people drop PhDs, I think a fallback isn't a terrible idea.

>> No.12779208

I just feel that math PhD isn't the most productive way to get into finance.
If you're not in a rush for it and planning to spend more time on math, then you may not need superficial courses related to stat.
Instead you can begin with measure theory which is behind the framework of (formal) probability theory. Then you can take a course/read a book which treats probability mathematically. I don't know if it gives a huge advantage for applications, but as a mathematician you'll have to know it anyway.
Some economists use quite advanced measure theory in their papers.
https://www.math.ucdavis.edu/~hunter/measure_theory/ is a good overview.

Basically you should ignnore everything applied and take only mathematical courses in that case.

>> No.12779259

that's good advice, thanks. i don't think my uni offers measure theory to undergrads, so what should I do then? I'll probably still take stats and probability if it's advisable, their good fall back classes IMO. but i don't want to stuff my degree with plan B stuff either.

>> No.12779263


>> No.12779299

There's no a specific need to go into measure theory too deeply, just try to learn the stuff needed for probability, that's really not a lot.
If your course doesn't treat probability in its generality, then you can take a book which does and read on the topics they've told you about.
The basic concepts like probability space and random variable are defined in terms of measure theory. The whole apparatus of probability is build on measure theory.

>> No.12779337

>>>MTH427-428: Partial Differential Equations
>>MTH421-422: ODEs
for finance

the rest is for being an alpha math graduate. You cant'be good at finance and general maths at the same time. THe maths are jsut too different. you have to choose.

Also dont forget that

maths is useless to get rich. Math is only used because
-atheists think that using maths will turn any field as a ''''''''''''''science'''''''''''
-atheists think that an asset has ''''''''''''''fundamental value'''''''''''''(see the brainlet like graham and so on)
-atheists already in finance use math already and value everything with their formulas, but it doesn't mean the value they output is actually the '''''''''''''''''fundamental value''''''''''' of the asset. it's just that everybody right now uses the same formulas, so they just cling to the same delusion and pass it as reality and they price the same asset with the same formula at the same time so they agree the ''real'' price of the asset is the output of their formula.

Sinice you want to do finance, start day trade casually to know the tools.
If you want to earn money with finance, then buy nasdaq and an etf world.
If you want to trade, do it every day and just follow the herd. You sell what other people sell and buy what other people buy.
Dont try to invent some crappy martingale or go against the herd.
Once you keep day trading for a few months, you try to time the market and also follow the herd.

>> No.12779341


it just is

>> No.12779383

Based. Atheists would be btfo if they attempted to study math.

>> No.12779407

Is this his basic math book or geometry book?

Yeah, most math books have errors. I wish someone would make an erratawiki to catalogue them all.

>> No.12779447

go on libgen and start reading big books on finance, like ''hull''

Finance uses Stochastic Calculus and integrals.
Go on amazon and look for such books, read the reviews and buy 5 books about this.

>> No.12779460

>>I like doing math. Well, I enjoy studying it in my free time anyway. Not sure if I'd like doing PhD work necessarily, but I have this feeling I'll regret not trying.
You know there are Phd in financial maths. You can be phd and do a thesis on mathematical finance. But again, it's not general maths, but in universities specialized in that.



>> No.12779639

A simple PDE [math]y^2 u_{xx} - u_{yy} = 0[/math]. I'm trying to put it into canonical form. I tried change of variables by the characteristic equation but that left me with 0=0 which made me sad. Explictly, [math]\xi = \frac{y^2}{2} - x [/math] and [math] \eta = \frac{y^2}{2} + x [/math]

>> No.12779647

Ive read a few, but never got that into it. I was able to see myself enjoying working on the kind of stuff Jane Street does, but I'm not deadest on it. I'd like to just keep studying maths for now, I think, it seems like it's easier to get into finance at the grad level anyway.

Thanks for the links. Though maybe I shouldn't have said finance initially, I just thought if shit doesnt pan out the way I want with grad school I'd try to pursue that somehow.

>> No.12779661

I did some of this in discrete math, and bought a cheap little probability book I read maybe half of. Would you recommend taking probability/stats as an undergrad, or would you say it's "superficial" at this level?

>> No.12779809


Before you take a class in voodoo ''economics'' you should take a coruse in finance. It's like taking a logic class before doing maths. It helps a lot for seeing who talks rubbish or not.
Economics of Money and Banking

This document contains redacted course notes of the second part of the course Economics of Money and Banking by Professor Perry G. Mehrling of Columbia University in the United States that is available on Coursera.org. This course explains the basics behind money and banking that are essential in understanding the financial system. According to Professor Mehrling, the financial system is about balancing flexibility and discipline.

Professor Mehrling builds on his own background in the history of monetary economics and financial economics. He sees himself in the American tradition of monetary thought that is based on the tradition of British central banking thought. Each generation had to rethink the underlying issues for themselves in order to make sense of the conditions of their own time. The current challenge is to work out the implications of financial globalisation for money, banking and central banking.

>> No.12779813


The Economics of Money & Banking

The last three or four decades have seen a remarkable evolution in the institutions that comprise the modern monetary system. The financial crisis of 2007-2009 is a wakeup call that we need a similar evolution in the analytical apparatus and theories that we use to understand that system. Produced and sponsored by the Institute for New Economic Thinking, this course is an attempt to begin the process of new economic thinking by reviving and updating some forgotten traditions in monetary thought that have become newly relevant.

Three features of the new system are central.

Most important, the intertwining of previously separate capital markets and money markets has produced a system with new dynamics as well as new vulnerabilities. The financial crisis revealed those vulnerabilities for all to see. The result was two years of desperate innovation by central banking authorities as they tried first this, and then that, in an effort to stem the collapse.

Second, the global character of the crisis has revealed the global character of the system, which is something new in postwar history but not at all new from a longer time perspective. Central bank cooperation was key to stemming the collapse, and the details of that cooperation hint at the outlines of an emerging new international monetary order.
Third, absolutely central to the crisis was the operation of key derivative contracts, most importantly credit default swaps and foreign exchange swaps. Modern money cannot be understood separately from modern finance, nor can modern monetary theory be constructed separately from modern financial theory. That's the reason this course places dealers, in both capital markets and money markets, at the very center of the picture, as profit-seeking suppliers of market liquidity to the new system of market-based credit.
Perry G. Mehrling

>> No.12779831


YouTube links to download with jdownloader

The Four Prices of Money

The Natural Hierarchy of Money

Money and the State: Domestic

The Money View, Macro and Micro

The Central Bank as a Clearinghouse

Federal Funds, Final Settlement

Repos, Postponing Settlement

Eurodollars, Parallel Settlement

The World that Bagehot Knew

Dealers and Liquid Security Markets

Banks and the Market for Liquidity

Lender/Dealer of Last Resort

Chartalism, Metallism and Key Currencies

Money and the State: International

Banks and Global Liquidity

Foreign Exchange

Direct and Indirect Finance

Forwards and Futures

>> No.12779973

Maybe a simpler and more direct question is how to convert the coordinates 1,0,0,0 into a 2x2 matrix with values [1,0,1,0]. Coords [0,01,0] to [1,1,1,-1], [0,1,0,0] to [0,1,-1,0] and so on?

>> No.12780319
File: 1.22 MB, 1200x1200, 1609141491870.png [View same] [iqdb] [saucenao] [google] [report]


> actually got accepted to the PhD program I applied for
> had very low expectations and was training to join the military

>> No.12780380

Not the OP, but I'm interested nevertheless. I don't quite understand what you mean by the "corresponding map X -> C"

>> No.12780565

Let's say you have maps i_n: X -> C and j_n: X -> Cyl(X) for n=0, 1. Choose your favorite n and use it for both.

>> No.12780604
File: 8 KB, 579x182, qerqefweflo.png [View same] [iqdb] [saucenao] [google] [report]

help bros what does vector*nabla even mean?? i dont get why the 4rth term is supposed to be 0 given that v is cosntant (i do get why the 1st is 0 though)

>> No.12780654
File: 2.45 MB, 4000x3000, 20210303_160320.jpg [View same] [iqdb] [saucenao] [google] [report]

If I've understood you correctly, then the diagram I've included should commute. But it's not apparent that it does.

>> No.12780659

GNU Emacs.

>> No.12780670

Maybe it doesn't, idk. I haven't done homotopy for a few years.

>> No.12780688

Aren't vectors just the coolest shit ever?

>> No.12780743

18+ website

>> No.12780810

A lecturer I have many courses with and will probably deal with a lot if I do post grad lists making question using the binomial theorem, Taylor series and series in general. What's a good resource to really master series and sequences?

>> No.12780824

Take (j_0^-1, j_1^-1) instead. That is from Cyl(X) to XUX.

>> No.12780834


>> No.12780893

The domain is incorrect. It would have to be a map from Cyl(X) U Cyl(X) to X U X. Although this might be helpful, let me think about it.

>> No.12780922

Infinities, zeroes
All those special cases where there are no new thoughts.
Build a bunch of new axioms and here you go

>> No.12780956

No I don't think it is incorrect. Take something from Cyl(X) and plug it simultaneously into both of the maps.

>> No.12781168

So a point x -> {j^-1_0 x, j^-1_1 x}. This is not a function, you can't map one point in the domain to two points in the codomain.

>> No.12781177

The universal property of the coproduct allows you to map out of it, not into.

>> No.12781223

True I guess.

I don't know CT.

>> No.12782346

what's the scoop on undergrad numerical optimization?

I'm not taking any economics or finance courses. But thanks for the links. Surprised you didn't drop Wildeberger's series on it :^)

>> No.12782898

if i know limits, differentiation, and integration, do i basically know calc 1?

>> No.12783449

Remember for linear algebra:
A singular matrix is non-invertible and the determinant is 0.
A non-singular matrix is invertible and the determinant is not equal to zero.
An analogy would be if you are single, you don't have the inverse of your gender, and therefore it is determined you will have 0 offspring.
If you are non-singular, you have the inverse of your gender and you will have offspring.

>> No.12783717

how important is Complex Analysis if I want to get into grad school?

also, my uni requires Analysis I, II and Abstract Alg I, II but they have a third class for each. same goes for the electives Topology, Diff Geo, and Theory of ODEs. how important is it for grad school to take these third and final courses?

>> No.12783761

samefag from the other day (obv). here's the total list of courses I plan on taking

CS (5):
>CS 350: Algorithms and Complexity
>CS 445, 446: Machine Learning I,II
>CS 480: Randomized Algorithms and Probabilistic Analysis (skip stats requirment?)
>CS 549: Computational Geometry (pls?)

Math (15):
>MTH 311, 312, Intro to Mathematical Analysis I, II (sub with Real Analysis I, II (461,462)?)
>MTH 344, 345: Group, Ring and Field Theory (sub with Abstract Algebra I, II (435, 436)?)
>MTH 434, 435: Set Theory and Topology I, II
>MTH 424, 425: Differential Geometry & Tensor Analysis, I, II
>MTH 421, 422: Theory of Ordinary Differential Equations I, II
>MTH 420: Complexity Theory
>MTH 461, 462: Graph Theory I, II
>MTH 464, 465: Numerical Optimization I, II

turns out there's a third course in the series offered in all of Analysis, Abstract Alg, Diff Geo, Topology, and ODEs, and I'm unsure how important taking any / all of those would be. I can tack a couple extra classes on nbd, but much more than that and I'm looking at potentially taking another term.

>> No.12784545

>So which two options do you have to choose between?
Each question has 4 options to answer
>And what do you mean by "one is eliminated"?
You choose two and a wrong answer is eliminated. You then have 3 options to answer
>Can you use a life again?
Yes you can use up to three lives - giving you the right answer without answering
>How many lives do you have?
9 but that doesn't really matter for the problem

Hope this clarifies it

>> No.12785689

I think I got it now.
And what is the goal? To get as many correct answers as possible before your lives run out?

And just to be clear, if you've used 1 live on an answer for example and then get it wrong, do you lose an additional 3 lives, or do you lose an additional 2 lives, making a total of 3 lives?

>> No.12785967

The Gauss–Bonnet theorem, or Gauss–Bonnet formula, is a relationship between surfaces in differential geometry. It connects the curvature of a surface (from geometry) to its Euler characteristic (from topology).


>> No.12786099

I cut complexity theory and graph theory, added complex analysis.

>> No.12786423

>professor is foreign but brilliant and actually pretty great and explaining difficult concepts in person
>insists on communicating by email rather than meeting face to face.
>send him questions
>"is it x or y?"
>"yes, exactly"
Everytime, I really like the dude but goddamn.

>> No.12786617

Its x and y

>> No.12786629

It means how much exterior angle your polygon can have is related to how many holes there are in your manifold

>> No.12786712

I'm studying Spivak's Calculus and I've got a good grip on maybe half of the exercises. Then I'm washy on the half of the rest and totally lost on everything else. Is this normal? What should I go back and study to cure this stupidity?

>> No.12786867

How so?

>> No.12787267

>To get as many correct answers as possible before your lives run out?
Just to answer correctly to go up the prize ladder (wrong answers make you fall). These lives just help you achieve that
>if you've used 1 live on an answer for example and then get it wrong, do you lose an additional 3 lives
No matter using one or two lives if you get it wrong you lose three additional lives

>> No.12787430

Do you think graduate schools will be understanding about 2020-2021 being a shitshow in undergrad? No research opportunities and what not?

>> No.12787479

Might want to take a gap year for research opportunities.

>> No.12787504

The system needs to die

>> No.12787543

Is L Hopitals applicable to complex numbers because it sure looks like it does

>> No.12787566

Yes. You are looking at the behaviour of the function about some point and that point could be complex.

>> No.12787612


>> No.12787840
File: 172 KB, 1000x766, 1_C8iI2z3HCzLSSH7hgOjpPg.jpg [View same] [iqdb] [saucenao] [google] [report]

Does "no real solutions" have the same meaning as "no analytical solutions"?

>> No.12787861

I think they probably won't be, there are so many people applying and I've had it explained to me that they don't want to take risks on people. So the really good schools will probably stick with people who utilized that time well.

>> No.12787871

No. Generally, no real solutions means that there doesn't exist a solution in the Real Numbers. On the other hand, no analytical solutions means that no "plug & play" type solutions exist, but it might still have solutions in the Real Numbers. The typical approach then is to solve such solutions numerically often with the use of a computer.

>> No.12787873

>there are so many people applying


>> No.12787879

I really like Konrad Knopp's book for this

>> No.12787901

thanks friend

>> No.12788115

If you're talking about big name programs, there are several hundred people applying for maybe a dozen or two dozen spots, depending on the school. sure, if you want to go somewhere meh for grad school then it probably won't be a big deal. but i think many would hazard that it is not a good idea to try to pursue mathematical academia if you aren't in a position to go to a rather highly regarded grad school.

>> No.12788158

I see. There's just one more thing that wasn't clear to me.
When is the game over?

>> No.12788343
File: 13 KB, 474x234, Rudin_2_7_wtf.png [View same] [iqdb] [saucenao] [google] [report]

Quick question about Rudin question 2.7. A solution/statement is here (Theorem 2.27 is the Heine Borel Theorem):

See pic related. How does the infinite union follow?

>> No.12788593

>How does the infinite union follow?
It's so obvious that I don't even know how I'm supposed to answer that.

>> No.12788638

>How does the infinite union follow?
by definition of the infinite union and of the subset

>> No.12788693

When I start my masters, should I
A. take a bunch of different classes or
B. focus on two subjects that really interest me.
I want to apply to PhD programs after I finish my masters. Plan A sounds more fun, but Plan B seems like the better choice. If I focus on two subjects (say, Algebra I, Algebra II, Topology I, Topology II, plus the real analysis requirement), I should have an easier time passing qualifying exams when I start my PhD, right?

>> No.12788836

if a bunch of sets are contained in some set, then the union of the sets are also. think for 5 seconds before posting.

>> No.12788841

you should focus on the material where you want to do research. are you really asking this question? this isn't fucking high school.

>> No.12788928

does [math] arcsin(c\sin(x)) = cx[/math]?

>> No.12788955


>> No.12788978

After the 12th question

>> No.12788979

I think people recommend a precalc book like the one in /sqt/'s OP. BM is suppossed to be full of errata

>> No.12789089

>Can't do difficult problems when I'm too stressed
>Procrastinate when I'm too relaxed
Is anyone likes this?

>> No.12789143

900 blitz, I suck

>> No.12789157

kek but probably true

>> No.12789168

Is there any benefit to using C over R^2?

>> No.12789185

>by definition of the infinite union and of the subset
Where is this definition?

>if a bunch of sets are contained in some set, then the union of the sets are also
They are contained in a metric space, and the two are equal if finite (question a), only when infinite is one a superset of the other (question b, the one I am asking about).

>> No.12789260
File: 55 KB, 512x512, 52390064_387100171871404_3864791056470770776_n.jpg [View same] [iqdb] [saucenao] [google] [report]

when is it true that something like [eqn]\min_{y} f(x,y) g(x,y) = \left[\min_{y} f(x,y) \right] g\!\left(x, \operatorname{argmin}_{y} f(x,y)\right)[/eqn] holds? that is, you can minimize the functions separately.

>> No.12789310
File: 19 KB, 369x387, 3r72966g68e11.jpg [View same] [iqdb] [saucenao] [google] [report]

got my fluid dynamics exam tomorrow, still don't get it at all. man i'm so close to getting a first and i'm gonna fuck it in my last semester

>> No.12789382

Not maths

>> No.12789483

maths degree, fd module

>> No.12789536
File: 29 KB, 828x149, 38FBE0E1-BC00-4B40-83C4-E6FB018150F0.jpg [View same] [iqdb] [saucenao] [google] [report]

Someone explain I’m retarded

>> No.12789539

read that brainletanon

>> No.12789558

I want to specialize in vectors
I'm writing a thesis on vectors with hundreds of elements. advanced computer calculations required but I'm doing lots with my bare hands too. which department I should send it to? or in other words what math department in america has the most prestigious vector research unit?

>> No.12789568

They gasses just swirl bro

>> No.12789877

Well the LHS is the Jacobi theta function [math]\theta_3(x)[/math] and there is an identity [math]\dfrac{\theta_3(x)}{\theta_3(x^{-1})}= \dfrac{1}{\sqrt{x}}[/math] but I'll be fucked if I can prove it. I always detested number theory.

>> No.12789900

Got it. Interesting problem.
The following numbers show the average number of "points" gained per live used, when applying the different strategies.
So it basically shows how efficiently these strategies convert lives to points.
>Using 1 live:
1*1/(1*1+2*4) * 1/1 + (2*4)/(1*1+2*4) * -1/4 = -1/9
>Using 2 lives:
1*2/(1*2+1*5) * 1/2 + (1*5)/(1*2+1*5) * -1/5 = 0
>Using 3 lives:

I'm having trouble explaining the calculations cause it's actually pretty tricky.
But I ran some simulations and they gave the same results.
Using 3 lives seems to be the best strategy.

We still have to show that it's better than using 0 lives though.
So the following numbers show the expected number of points gained when using 0 vs 3 lives:
>Using 0 lives:
1/4 * 1 + 3/4 * -1 = -1/2
>Using 3 lives:

So yeah, using 3 lives is the best strategy.

>> No.12789913

thanks bro, turns out it's next week rather than tomorrow

>> No.12790029
File: 17 KB, 779x99, rudin_2.png [View same] [iqdb] [saucenao] [google] [report]

So it turns out that I didn't ask my question clearly and was so confused why you all thought I was a brainlet. I meant to ask was why the infinite union was not possibly equal to B (proper subset?). The solutions manual had it differently and this one I understand. Thanks for making me feel bad about myself because Rudin's assblasting isn't already doing a great job of it. I'll be clearer next time, /mg/ has actually helped me out in the past.

>> No.12790132
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has there been any formalization/generalizations of this?

>> No.12790222
File: 106 KB, 678x417, 1611011999352.png [View same] [iqdb] [saucenao] [google] [report]

What proportion of exercises should you be able to comprehend to say you understand a book, roughly? I only feel solid on half of my calculus exercises. I still get the gist after I read the solutions, but I'm definitely not at 100% comprehension. Is that abnormal?

>> No.12790286

use Poisson summation formula

>> No.12790309

and not the meme curve the paper round type of tricks

>> No.12790502

you are facing this problem at the right time. Each solution should make sense to you. each. single. one. Because it's gonna get worse, so you better get your shit right on right now. That means that you don't let the problem go until you get it, and utilize all your resources to understand it.

>> No.12790985

It depends what you've been taught in class or what you have studied beforehand, dunnit?

>> No.12791056

I'm trying to prove that the projection of the first coordinate of a pullback of a homotopy equivalence along a fibration is a homotopy equivalence. Here's what I have so far. Let [math] f: A\to B[/math] be a homotopy equivalence and [math] p: E\to B[/math] be a fibration. Since f is a homotopy equivalence, there is a map [math]g: B\to A[/math] such that [math] fg\simeq 1_B, gf\simeq 1_A[/math]. Let [math] \tilde{f}: E\times_BA \to E, \tilde{p}: E\times_BA \to A[/math] be the projections respectively. Since [math] fg\simeq 1_B[/math], there is a homotopy [math] H: B\times I \to B[/math] such that [math] H_0 = 1_B, H_1 = fg[/math]. Composing by p, we get another homotopy [math] H^p: E\times I \to B [/math] such that [math]H^p_0 = p, H^p_1 = fgp[/math]. Let [math] E\to A[/math] be the map gp and let [math] E\to E[/math] be the map [math] H^p_0: E\to E[/math]. By the universal property of the pullback, there is a map [math]\tilde{g}: E\to E\times_B A[/math] that makes the pullback diagram commute. Clearly, [math] \tilde{f}\tilde{g} \simeq 1_E[/math]. However, I cannot show for the life of me that [math] \tilde{g}\tilde{f}\simeq 1_{E\times_B A}[/math]. please halp :c

>> No.12791093

How much of your math knowledge came from self teaching at your own direction as opposed to classwork? I feel like I don't self study nearly enough.

>> No.12791252

One of my professors once told me that you understand a subject when you're able to pick up an arbitrary book on it and do all the exercises. I'm not sure where the line is when it comes to roughly understanding the book, probably depends a lot on the class and who you are.

>> No.12791281

It is pretty cool, you're jaded anon.

>> No.12791311

> I meant to ask was why the infinite union was not possibly equal to B
It is possibly that it’s equal to B, which is why rudin didn’t use the proper subset symbol

>> No.12791317

sorry I didn’t look at the first image you posted. But yeah that pisses me off too, some people use the proper subset symbol to mean regular subset, then they use a retarded symbol with the equals sign crossed out to mean proper subset

>> No.12791555
File: 18 KB, 675x598, Graf.png [View same] [iqdb] [saucenao] [google] [report]

>> No.12791560

Post the smallest non planar graph

>> No.12791790

I'm on chapter 2 of baby rudin and it defines metric space as any set with a distance function. Then they prove the theorem "every neighborhood is an open set". Their proof makes sense but doesn't it assume some sort of continuity to the metric space? the definition seems to allow for discrete sets. The integers form a metric space and the neighborhood about 0 of radius 2 contains a finite number of elements (3 exactly) and is obviously not open. did i miss something that said the space has to be continuous?

>> No.12791809

nvm i just needed another minute to think about it. somewhat counterintuitively, my example is an open set because every point is an interior point, since all neighborhoods of radius 0.5 contain only the center point, but a limit point needs to contain at least one other element in every neighborhood.

>> No.12791907
File: 38 KB, 588x357, Anglo1.jpg [View same] [iqdb] [saucenao] [google] [report]

When a nigga learns the union of a buncha rectangles can equal a circle

>> No.12791917

Nvm thats not even hard to visualize if you imagine smearing a rectangle along a continuum to trace the 4 quarters of the circles edge

>> No.12791923

Afaik there can be metrics on discrete things or metrics can be discrete

>> No.12792041

>Using 3 lives seems to be the best strategy.
What? Using zero lives equals a 75% chance of losing three lives, using three lives means a 100% chance

>> No.12792072

same as finitist

>> No.12792089

anything involving hard arithmetics and not some flabby french math bullshit

>> No.12792147

>d instead of Δ
why? do they mean different things?

>> No.12792153

This is kind of interesting


>> No.12792173

[math]\Delta[/math] means some small change or difference and is an actual real number. d is an infinitesimal and if you are being precise isn't a standard number.

>> No.12792215

There was a chart with 3 books to get into finance-related math. Can anyone share it here? I started with measure-theoretic approach to probability, then a book on stochastic processes culminating in applied math for finance book. I just can't remember particular books mentioned.

>> No.12792614
File: 272 KB, 1200x675, 1613425567292.jpg [View same] [iqdb] [saucenao] [google] [report]


(a mod p) = (b mod p)
(a-b) mod p = 0

>> No.12792618

(a mod p) = (b mod p)
(a-b) mod p = 0

>> No.12792723

When answering a single question, the goal is not simply to lose as little lives as possible on that question.
Nor is the goal to have the highest chance of getting that question correct and moving up the prize ladder.
The ultimate goal is to be as far up the price ladder as possible once the game is finished.
To achieve this, the two previously mentioned goals are both important.
You need to have the right balance between minimizing life loss and maximizing points gained.
I took all of that into account.

>> No.12792898

Don't make fun of my flabby sheaves. ;_;

>> No.12792941
File: 212 KB, 1200x1200, 1602161976048.jpg [View same] [iqdb] [saucenao] [google] [report]

Hey guys, mathlet here. I want to git gud at math for computer science, and I was adviced to read "Basic Mathematics" by Serge Lang. While I can read the book, and do most of the exercises, I struggle a lot with the "proofs". Should I go and do something like "Khan academy" precalculus, then come back to this book, or should I just tough it out, and finish the book?

>> No.12792947
File: 157 KB, 676x454, JackParsons3.jpg [View same] [iqdb] [saucenao] [google] [report]

>spinning vectors
Don't get me started

>> No.12793481

I think I see what you mean but shieeet then I should add that when you run out of lives you drop in the ladder - that is, if you have 2 lives and get it wrong you go down one spot, if you have 1 live you go down two spots, if you have no lives you go down three spots

>> No.12793494
File: 850 KB, 1920x1080, Untitled.jpg [View same] [iqdb] [saucenao] [google] [report]

This is the ladder btw

>> No.12793619

by definition yes

>> No.12793868

This is always true right?
Let a, b and c be lengths of an obtuse triangle and c b the longest edge.
We will always have a + b < c\sqrt(2)

>> No.12793874

I meant to use math /math but somehow I hit control+s.

>> No.12793898

Can anyone recommend me some good book focusing on inequalities?

>> No.12793909

>and is obviously not open
no, they are open. actually a space is discrete iff the singleton sets {x} are open. you're mixing your intuition about openness with the actual definition.

>> No.12794066

A set and the compliment of a set contain the exact same information.

I think it goes Durrett -> Karatzas and Shreve-> Karatzas

>> No.12794067

additive combinatorics is going to give me autism for the symbol A-B which some people use in a hurry to denote set difference which in reality should be denoted A\B

>> No.12794323

Wilderberg, go home. You're drunk.

>> No.12794586

from henceforth I introduce the all encompassingly inportant concept of the anti-element
an example as follows will demonstrate its function
let a set A contain the element x and set B contain only the counterpart anti element nega-x (B = {nega-x})
now taking the intersection of A and B will yield the expected empty set, however the union of two such sets produces A\{x}
x and nega-x are distinct objects and can not be contained in the same set and any attempt to do so will destroy both

>> No.12794593

How do you guys find math study buddies?

>> No.12794736

Please remember that algebraists are people 2, even if they think 2 is a prime.

>> No.12794744

Congrats you invented fuzzy sets

>> No.12794789


>> No.12794837

I guess that strictly speaking fuzzy means [0,1]-valued, so instead I'm gonna say your generalized sets are elements of an algebra with coefficients 0, 1, or -1 satisfying 1+1=1, 1+(-1)=0, and so forth. If you choose your coefficients in an actual ring you can have even nicer behavior.

>> No.12794989

tell me why 2 shouldn’t be a prime

>> No.12794995

>vector anon
i love this place at times

>> No.12795064

flabby sheaves are soft!

>> No.12795832

Given a set of (finite) N elements, how many possible topologies can be on it?

>> No.12795903

So a subbasis is the same shit as a basis except in bases the intersections are forced to be in the collection and in the subbasis they get to be generated? Whats the significance of specifying the distinction?

>> No.12796054

Applications are up 50% at top places this year. Not exactly sure why though.

>> No.12796073

Gilbarg and trudinger

>> No.12796090

How the fuck do I calculate residue at [math]z_0 = 1[/math] if my Laurent series is different for [math]|z| > 1[/math] and [math]|z| < 1[/math]? Is it still the [math]c_{-1}[/math] co-efficient?

>> No.12796133
File: 352 KB, 480x486, she-will-prove-abc.png [View same] [iqdb] [saucenao] [google] [report]

>do you want my prime strip in your hodge theater?
>There's about to be a non-zero torsion map into your left module
>spread my morphism around your body like it was étale

>> No.12796137
File: 198 KB, 512x512, 0ySNtlu.png [View same] [iqdb] [saucenao] [google] [report]

>Call me tooker because I'm inside your neighborhood of infinity
>Why not just a neighborhood of 2^200?
>My big Picard says I can find it near your essential singularity anyways
>[Zoom into her hairy asshole]
>It looks like your fiber bundle has nontrivial structure. Let's see what happens after an action from my D-module

>> No.12796141
File: 100 KB, 797x447, 1587440831955.jpg [View same] [iqdb] [saucenao] [google] [report]

>Suck on my snake charmer
>It looks more like a triple integral because it's so hard!
>I won't tell anyone if you use Barnett-Perelman theory

>> No.12796181
File: 542 KB, 680x974, 2c5.png [View same] [iqdb] [saucenao] [google] [report]


>> No.12796309

We have schizophrenia

>> No.12796347
File: 1.72 MB, 2160x3840, 1592937856654.jpg [View same] [iqdb] [saucenao] [google] [report]

I got you senpai

What's your plan? Make your own bot or join a hedge fund? If you make some money you have to come back and tell us.

>> No.12796349
File: 15 KB, 397x600, 21146234z.jpg [View same] [iqdb] [saucenao] [google] [report]

I got owned by Spivak's Calculus so I'm back to pic related like a brainlet. Then I'll do Book of Proof by Hammack and then back to Spivak.

>> No.12796402

how? this ain't a roguelike, nigga. you don't have to start over just because you failed once.

>> No.12796529


>tfw stuck in multiplication table hell

>> No.12796535


>> No.12796674

new >>12796673

>> No.12796935

It is easier to show that a basis having a property implies the toplogy has the property than to show that the subbasis having it implies the topology has it.
So often times it's easier to use a basis instead of a subbasis if you can get away with it

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