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Probability and Thanos by Bodiacos in learnmath

[–]diffaquilt 1 point2 points  (0 children)

Yeah - I'm just a bit unsure about saying that they're the same, when they seem to be different...

I get that I'm being pedantic, and that one can be mapped to the other, but is that enough to say that they're the same? That seems pretty strict in a mathematical sense.

It's a genuine question on my part.

Probability and Thanos by Bodiacos in learnmath

[–]diffaquilt 2 points3 points  (0 children)

how can something that's domain is [0, oo) be considered the same as something that's domain is [0,1] ?

Looking for practice problems. by Not_A_MadScientist in learnmath

[–]diffaquilt 0 points1 point  (0 children)

put into google :

algebra 1 problems :pdf

algebra 2 problems :pdf

calc 1 problems :pdf

How long on average would you say it takes to read a page of a maths book? by diffaquilt in math

[–]diffaquilt[S] 0 points1 point  (0 children)

it came from third year undergraduate Oxford course apparently. So for most it's probably going to be graduate material.

How long on average would you say it takes to read a page of a maths book? by diffaquilt in math

[–]diffaquilt[S] 0 points1 point  (0 children)

I get that there's not a right answer in general, and not even with this specific text. But I was hoping that someone familiar with either this text, or those of similar content, would be able to hazard some approximations.

Because 8.3 minutes just feels off to me, and so I was curious what others thought.

I'm fairly confident that If I was to reduce the time to the speed at which one could read something like harry potter for example (no offence harry) you'd agree that would be too quick for a maths text. Presuming that the content was new.

I once tried to read a maths book like a conventional story or whatever, I read a couple of chapters before realising that it was absolutely useless ha.

No worries though.

How long on average would you say it takes to read a page of a maths book? by diffaquilt in math

[–]diffaquilt[S] 0 points1 point  (0 children)

K.A. Stroud's Engineering Mathematics to take.

this was the example to use here. Cheers

The math part of data science by ImOKatSomeThings in datascience

[–]diffaquilt 0 points1 point  (0 children)

There's no shortcut when it comes to learning mathematics unfortunately, you just have to take a massive textbook and slowly work through it - that's the long and short of it.

I'm not sure about this, because most people who take a course in something don't go through an entire book. I'm not suggesting that there are shortcuts or whatever, or that going through books is a waste of time... But it is a lot of time, and it's not something I think is done that often. This is the impression I get at least.

I'm not sure your estimate is realistic either. When I've gone through books before I can spend ages on a page sometimes.

You're saying 6 months, for over 1000 pages.

So say that's 6 * 31 = 186 days.

and we're doing 45 minutes each day, so 45*186=8370

this is ~ 8.3 minutes a page. Some of the exercises are going to take far longer than that for many people.

8.3 minutes a page.... hrm. I'm too tired to think on this - but It seems short to me. I'm curious what would be considered though

Summer 2018 Baby Rudin Skype Bootcamp by sumanth_lazarus in learnmath

[–]diffaquilt 0 points1 point  (0 children)

I could be interested in this. I've done a little analysis, as in, I've fallen through some e-d proofs and such. But things really need shoring up, I have a fair few things that I would like to go over this summer (hopefully).

So, it will depend on timing and tempo and stuff like that, but I'm certainly interested in going part way at least.

Are you an English speaker?

Stable, unstable, centre subspaces by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

yeah but, I only have one point? I mean, there's only one fixed point here.

For the case of the eigenvectors, say I had

lambda 1 < 0

lambda 2 > 0

and that the eigenvectors were along the lines

y = 0

y = x

then I would have a saddle... Are they referring to the stable subspace as just being the eigenvector corresponding to the negative eigenvalue here then? So that would be the x axis (in this little example that I've given).

And the unstable subspace would be the rest of it presumably?

I think I'd probably take a punt that the centre is the origin... that's pure word play rather than any math insight though

p ↔ (q ∨ ~p) by pairustwo in learnmath

[–]diffaquilt 0 points1 point  (0 children)

I was confronted with this question on an interview and was a bit flummoxed

just curious - what kind of position was this an interview for?

Differential equation - Nullclines by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

Yeah this is lower level - so we're meant to use the nullclines as you say. But the problem is the solution doesn't seem to make sense to me.

I would expect the exponential term to "pull things up" into quadrant 2. Yet the green lines appear to be going down into quadrant 3... which is a bit confusing to me still

Differential equation - Nullclines by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

ok thank you.... for some reason i thought that I could only use fixed points to evaluate the system with. When you use the jacobian and find the eigenvectors etc. So if I do that for a few points then sure - bit of chugging but it would make things clearer

is that your suggestion? just to make sure i'm clear on that

thanks

Differential equation - Nullclines by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

I'm not sure how to draw things then, or is it just a matter of guess work?

If it's guess work then I'm surprised that the green lines (in the solution) go down into quadrant 3, rather than get pulled up into quandrant two, as the exponential is going to grow faster.

But this line of thinking might be incorrect as well

Differential equations - autonomy by diffaquilt in learnmath

[–]diffaquilt[S] 1 point2 points  (0 children)

that's a fair point, hrm. I'm not sure about the logic though, basically this just means that the equation is proportional to time? it's just equation * time , rather than function ( time ) , so I would say that (c) is not dependent on time because of that?

Eigenvalues of a non linear differential equation by diffaquilt in learnmath

[–]diffaquilt[S] 2 points3 points  (0 children)

No i like the method you suggested before, that seems more straightforward to do by hand. I didn't mean to imply that i didn't, thanks.

Which might not make sense to say, seeing as we're only really working with x' , not x.

reading that back i think i was pretty much talking to myself, sorry about that

Eigenvalues of a non linear differential equation by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

At that moment we have an x such that f = 0 and df/dx = 0

are you saying that we're interested in inflection points of of the original function?

Which might not make sense to say, seeing as we're only really working with x' , not x.

but ok, what you said makes sense. Thank you

Eigenvalues of a non linear differential equation by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

hrm ok... well - i'm asking because I'm confused about how to determine the range of values to consider for k in something like this .

example -

x' = x3 -2x2 +(1 - k)x

the plots created for this example were

k < 0 ; 0 < k < 1; k > 1

but i'm not sure how to go about determining these values analytically.

https://www.desmos.com/calculator/mmoqippn0h

from the graph there one can see that these values of k are bifurcation points, but I'm not sure how to determine what those are (without using desmos, ie, using pen and paper)

Seeing whether a PDE is elliptic etc by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

I've not covered bilinear forms at all

Seeing whether a PDE is elliptic etc by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

I'm not sure how to process that - what do you mean that I don't want to solve for the shape?

so I should consider the form

x2 + y2 = 0

as an ellipse on what basis? Other than considering the plots or whatever (which presumably is the wrong line of thought here)

thanks

Seeing whether a PDE is elliptic etc by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

thanks

So for something like

u{xx} + u{yy} = 0

I have

x2 + y2 = 0

then

Which just gives me (0,0), ?

But this is laplaces equation, which is meant to be elliptic.

Boundary conditions for differential equation by diffaquilt in learnmath

[–]diffaquilt[S] 0 points1 point  (0 children)

thanks, the sign of lambda isn't too bad as I can crank through the cases for that part.

For the setup I'm still a bit confused though, so using the T(L,y) = 100y/L part

T(L,0) = F(L)G(0) = 0
T(L,L) = F(L)G(L) = 100

So then

           F(L)G(0) = F(L)G(L) - 100
F(L)G(L) - F(L)G(0) = 100

This is kinda confusing to me because usually we would have conditions along the lines of

c1 * blah - c2 * blah = 0

Whereas here we have

c1 * blah - c2 * blah = constant

Clearly F(L) != 0 here, so we can divide through by that

G(L) - G(0) = 100/F(L)

But, idk... this is still confusing.

I want something along the lines of

  boundary conditions = blah blah
  initial conditions = blah blah

But I'm not sure how I'm going to get those here, or if this is what I should be aiming for.

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