/sqt/: Stupid Questions Thread

[math][math]\frac { 1 } { 2 } \left ( \theta ^2 \right ) ^{ - \frac { 1 } { 2 } } \times 2 \theta = \frac { \theta } { \left ( \theta ^2 \right ) ^{ 1/2} } = \frac { \theta } { | \theta | }[/math][/math]

Asked this in the previous thread as well. Does anyone know what kind of probability rules are being followed in pic related? I know that P(A,B,C)=P(A|B,C)P(B|C)P(C), but I can't really see what it was used in this case

forget X and sigma^2
call p' = p(. |X,sigma^2).

your pic says: p'(theta|Y)*p'(Y) = p'(Y,theta)
and p'(Y,theta) = p'(Y|theta)*p'(theta)
they just invert the roles of Y and theta to obtain two different expressions.
it's just joint probability, nothing more.

Ok, so I'm fucking stupid.
Like really fucking stupid.
But I wanna not be stupid.
So I looked at the wiki to start learning maths.
But I'm not sure where to start.
I know some basic algebra so I'll definitely relearn algebra and then I assume geometry since that's the order I was told it went in highschool but I'm not sure. I'm also assuming I should learn a good deal of math before moving on to science (calculus maybe?) but I'm not sure.
Also, is Khan Academy a good source for relearning maths and studies of science?
I'm looking at their algebra course and I don't remember there being so much to it.
Basically I need a road map on what order to learn my maths and science. If it matters my goal is to get to physics and if I can theoretical physics/quantum physics but I feel once I get to that point I'll know where I really want to go and how to get there.
Thanks in advance.

Oh I see, you're right, I never noticed that X and sigma are always on the right side. Makes sense now cheers

Kahn seems to be gud. You should start with algebra, yes, but you need a solid grasp on + - * / () and squares first. Then you can and should learn functions and graphs. Then geometry, you can, however learn basic geometry long before. Then Maybe probability as well, maybe... But this should be enough as astart. You dun need to go full university-tier before starting on basic physics (newton' laws, forces, movement stuff)

Yeah, I understand prealgebra pretty well (order of operations, +-*/()^2, functions, graphs, ect.) so I'm fine in that regard.
So I just need algebra, geometry and probability in order to get into physics?
Do I need to know any other sciences before getting into physics, or is science not like math, where I need one before moving onto the next?

Well you don't necessarily need all those math subjects, i just listed the basic math. It won't hurt to learn as much math ap. Other than that, however, maybe learn about the atom

Can't really help you with the mathematics part desu, I can only point you to Khan and tell you to go learn there. I can tell you that you'll need to learn up to at least integration, differentiation, complex and matrix algebra (I think Khan has this last on under "linear algebra", which I disagree with), vector algebra and at least ordinary differential equations. After you have a good grasp on then I can start to recommend books, so I'll start there.

>General recommendations
Mathematical methods for physics and engineering - Riley, Hobson and Bence
A students guide to vectors and tensors - Fleish

>Vector calculus
Div, Grad, Curl and all that - Schey

>Classical mechanics
Classical mechanics - Gregory
Classical mechanics - Taylor

>Electrodynamics
Electricity and magnetism - Purcell
Introduction to electrodynamics - Griffiths
Classical Electrodynamics - Greiner

>Special relativity
Special Relativity - French
Special Relativity - Woodhouse (this is actually written for mathematicians but should still be accessible)

>Thermodynamics
Thermodynamics and statistical physics - Greiner

>Statistical physics
Thermodynamics and statistical physics - Greiner
Introduction to statistical physics - Bromley

>Quantum mechanics
Introduction to quantum mechanics - Griffiths
Quantum mechanics: An introduction - Greiner

Following the above (in roughly the same order as above) should give you a solid intro to physics roughly comparable to someone with a B.Sc. There's a lot more that should be here, but I chose to omit it, since you're starting from scratch.

I was reading about the "local interstellar cloud"/"local bubble" and various websites say it has a temperature of about 7000K, around the temp. of the sun

science.nasa.gov/science-news/science-at-nasa/2003/06jan_bubble/
en.wikipedia.org/wiki/Local_Interstellar_Cloud
www-ssg.sr.unh.edu/ism/LISM.html

How come the temperature of this area is said to be that high?

I get that they probably only measure the temperature of the particles or something, the cloud area is quite low in density, then how come this hasn't radiated off yet? Does it simply take that long?

(Short answers are welcome, I'm only just curious how a cloud that big & old can be at the temp. of the sun)

Thanks a lot. I'll save this post for sure.
You're a hero user.
God speed.

So I've been watching a marathon of these videos and I'm really interested in this theory. (Don't know if it's okay to post links here, but here I go.)
youtu.be/FflcA85zcOM?t=76
He talks about time loops if the universe starts spinning at a certain speed and it made me wonder how fast the universe would have to be spinning to even create a single time loop. That is, the slowest speed to achieve this affect.
If anyone could explain the basic science behind this and if it's possible that the universe is already spinning and has already created time loop(s) I'd be really grateful.

>then how come this hasn't radiated off yet?
user, are you a baka?
How is it supposed to radiate off? There's nothing it can radiate to other than space.
You underestimate how hot things in space can get, ISS is like, 300 fucking degrees when it's in the sun.

(Jump to 1:16 to see where he talks about time loops)

How do you differentiate f(x)/(y) wrt to x?

for example [math]\frac{\partial}{\partial x}\frac{\alpha - x}{\sigma * \theta}[/math]

are any of alpha, sigma or theta functions of x themselves? If not, it's just a regular affine function.

Yeah I'm a baka
That explanation didn't come to my mind, thanks, will read further into that and some basics..

if i want to, say work in big pharma, whats the best way, molecular biology/biochemistry/chemistry?

Can one prove that the ratio of the circumference of a circle to its diameter is a constant without invoking real analysis as in: math.wikia.com/wiki/Proof:_Pi_is_Constant?

Or did the ancient and medieval mathematicians simply take this for granted, as something based on "observation".

if you fill a circle of radius R with a regular polygon with n sides, and increase n, you can see that the covered area increases, and is bound (by the surface of the disk).
So it must converge (this assumes the least upper bound property). It converges to a value S(R) (surface as a function of R). And you can find the surface of the n-gon and express it as the sum of a series.

If you take a circle of radius L, then you can fill it with n-gons that have (L^2/R^2) times the surface of the previous n-gons you used. (Simple property of triangles).
This transmits to the terms of the series, and therefore to the sum.

So S(L) = S(R) * L^2/R^2

Or, written otherwise, S(L)/L^2 = S(R)/R^2

the ratio of the surface and the radius is constant for a circle.
Call this constant pi, and voilà.

and if some fucker is going to bug me about why S(R) converges towards the surface of the disk, just introduce a sequence of disks inscribed in the n-gons.

What do the vertical bars signify?

cardinal, number of elements in a set

Is it possible to get a formula that always makes

1+y = (1+y/X)^X true?

Basically I either apply a factor of 1.1 (for example) once, or I divide the y (10% here) by X and apply the whole factor X times. This is similar to compound vs simple interest but I'm wondering how to always have the right hand side equal the simple one.

In general, you don't, UNLESS y/x is very small when compared to 1.
In that case, the approximation can be good.
It's called a first order expansion.

Double majoring in Math / CS. What should my curriculum look like, ideally? I've heard statistics being useful.

I found how.

All you have to do is take sqrt(x) on both sides, remove one, multiply by X and you get the rate that will equal simple interest.

Basically, I'm wondering what type of math degree would pair best with CS, and what my curriculum should look like. Iv read that statistic is very useful and that pure math isn't, but I've also read that pure math comes in handy farther down the line in academia.

So the fields I'm most interested in are paleontology, astronomy/cosmology and civil engineering.
I think I'm most passionate about paleontology and astronomy/cosmology but civil engineering has way better job prospects.

Any advice?

>1.start with civil engineering.
>2.go for astronomy cosmology to learn how to build a time machine.
>3.Go to ancient times using your time machine and start building stuff there.
>4.???
>5. profit as you fuck with paleontologists of today

What's the difference between a section [math]\sigma \colon M \to E[/math] vs the inverse projective map [math]\pi^{-1} \colon E \to M[/math]? I understand that a section requires [math]\pi(\sigma(x)) = x[/math] for [math]x \in M[/math], but isn't that exactly the same as [math]\pi^{-1}[/math]?

*On a bundle, that is. I'm interested specifically in fiber bundles atm but I think it should generalize for all types of bundles.

It should look something like this

>Fall 1
Calculus I
Intro to Proofs and Abstract Mathematics
Physics I
Chem I or Bio I
Intro to Programming in C++
Technical Writing

>Spring 1
Calculus II
Matrix Algebra
Physics II
Chem II or Bio II
Digital Logic and Automata
Data Structures

>Fall 2
Vector Calculus
Physics III
Electrical Engineering Fundamentals
Computer Architecture
Algorithm I
Combinatorics and Graph Theory I

>Spring 2
ODEs and Dynamical Systems
Probability Theory (Mathematics department)
Mathematical Logic (Mathematics department)
Parallel, Distributed, and GPU Programming
Operating Systems
Numerical Analysis I (Mathematics department)

>Fall 3
Abstract Algebra I
Real Analysis I
Mathematical Statistics
Algorithm II (or Graduate)
Programming Languages and Compilers I
[CS Elective]

>Spring 3
Abstract Algebra II
Real Analysis II
Combinatorics and Graph Theory II (or Graduate)
Numerical Analysis II (Mathematics department)
Computability and Complexity Theory
Compilers II and/or Type Theory

>Fall 4
Complex Analysis, Topology, or PDEs
Computer Graphics/Vision and/or Image Processing
Linear and/or Convex Optimization
Artificial Intelligence and Machine Learning
Internet, Networks and Communication Systems
[Elective]
Professionalism, Ethics, and Conduct (Seminar)

>Spring 4
Control Theory and/or Robotics
Computer Security and Cryptography
Quantum Computing or CS Graduate Elective
Software Engineering Essentials or Elective
Macro and Micro Economics
[Elective]
Personal Grooming and Hygiene (Seminar)

When do university state grants appear? I live in California and going to cal poly Pomona. I just got a pell grant and two loan offers. Nothing else.

Maybe not a stupid question but i don't think it deserves a new thread. Is there a comprehensive guide to honing one's bullshit detector and critical thinking? I am aware of the scientific method, logical fallacies, and cognitive biases, but i never see much about learning how marketers, salesman, con-men, etc. exploit errors and gaps in thinking beyond the superficial "if it sounds too good to be true it probably is." I am more interested in recognizing and identifying more sophisticated bullshit like how debaters win arguments even if they are wrong, how politicians and other public speakers manipulate using half truths , or maybe even how police officers use verbal judo for example. I guess these are more or less psychological tactics. Hopefully I've been clear enough. So is there anything out there like what I'm looking for?

The correct way to solve the root part is
(b^2-((4a)c))right?

>Is there a comprehensive guide to honing one's bullshit detector and critical thinking
>marketers, salesman, con-men

Heuristics: Learn how to do back of the envelope calculations to show quickly and easily that such and such isn't anywhere near the realm of feasibility.
Source check: Where is the verification and who verified it? Is there data and does the data eliminate other contributing factors?

Ex:
youtube.com/watch?v=BhnoSREmWVY
youtube.com/watch?v=r5CQUy3OKL4
youtube.com/watch?v=hoqF3gjLIyI
youtube.com/watch?v=4iEshd6izgk
youtube.com/watch?v=_V6nYLIChUA

>how debaters win arguments even if they are wrong, how politicians and other public speakers manipulate using half truths

Watch a bunch of Hitler rallies, commie propaganda, and the like and practice refuting them. A lot of times politicians just rip them off verbatim.

It's fine to shorten this citation by using "et al", right?

It's what the paper does
journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
>B. P. Abbott et al.*

>R. Abbott in second position and thus an et-al-pleb
>"Um... call me Bob?"

tfw one of your old lecturers makes it in at name #427 or something.

Light travels at the speed it does because it has no mass, but if E = MC^2 wouldn't that mean that light has no energy? And something like UV has gotta have energy for it to be ionising, moving even.

en.wikipedia.org/wiki/Photon_energy

It's actually a significant fact of quantum mechanics.

>but if E = MC^2

That's wrong
E^2 = (mc^2)^2 + (pc)^2

So from de Broglie hypothesis we know p = ℏk and thus have E^2 = (0c^2)^2 + (pc)^2 = (ℏkc)^2 or E=ℏkc=ℏω=ℎν a la Planck.

pi^{-1} isn't typically a function.

(4a)c = 4(ac). associative property of multiplication.

Ok feel like a moron for posting this, but how do you find the answer for this stats problem?

I just need to know the formula or what function to use on a ti-83

you have to look it up. you are supposed to memorize a few of these.

I mostly mean you do the 4ac part before subtracting b^2 right?

How do you go from [math](8+6√2)/2[/math] to [math]1/2[/math] [math]2(4+3√2)[/math]?

Wolfram just says factor by 2 but does not show the work for it.

1) multiply b*b
2) multiply 4*a*c
3) subtract what you got in step 2 from what you got in step 1.

Say b=10, a = 8 and c=2.
1) b*b=10*10=100
2) 4*a*c = 4*8*2=64
3) b^2-4ac=100-64=36
4) sqrt(36)=6

Thanks user. I wanted to be sure PEMDAS was right.

Say you have a set defined as

A = {Mary, John, Mark}

and a function f that is the identity map

s.t.

f: A->A

Can you define the mapping to be

f(John)=Mark
f(Mark)=Mary
f(Mary)=John

or does this violate any rules for functions, if so why?

Because from what I've seen whenever you map an element from a domain to a codomain the element it gets mapped to in the codomain may have multiple elements from the domain mapping to it, so the inverse map may be a many to one mapping.

This shit is confusing me about functions

Almost surely a bait but whatever.
[eqn]\frac{8 \,+\, 6\,\sqrt{2}}{2} \,=\, \frac{2\, \left(4 \,+\, 3\,\sqrt{2} \right)}{2} \,=\, \frac{1}{2} \, 2\, \left(4 \,+\, 3\,\sqrt{2} \right)[/eqn]

Yes you can have that. Then f won't have a well-defined inverse function (as you say, it would be many to one), but f itself is a legit function.

Not baiting. Haven't done math in years,

Where did the [math]1/2[/math] come from?

shouldn't the 2/2 just cancel each other out and the answer be (4+3√2)?

Ok yea fuck you, you trolled me. I had it right from the start.

Yes, any sane person would cancel that and get [math]4 \,+\, 3\,\sqrt{2}[/math]. Also [math]\frac{x}{2}[/math] is the same as [math]\frac{1}{2} \,x[/math] for all [math]x[/math].

>Basically I need a road map on what order to learn my maths and science

Arithmetic -> Algebra -> Trigonometry/Precalculus -> Calculus, Gen Biology, Gen Chemistry, and Freshman Physics -> Linear Algebra and Vector Calculus -> Ordinary Differential Equations, Theoretical Mechanics and Electrodynamics -> Complex Variables and Probability -> Partial Differential Equations, Quantum Mechanics, Thermodynamics and Statistical Mechanics

Geometry is mostly skippable if you know the sum of the angles in a triangle is 180° and A^2+B^2=C^2.

>Do I need to know any other sciences before getting into physics

Usually you go Bio ⇒ Chem ⇒ Phys in high school but logically it's better to go Phys ⇒ Chem ⇒ Bio

>math, where I need one before moving onto the next

Math stops being like that when you get to the university level.

>How do you differentiate f(x)/(y) wrt to x?
f'(x)/y-f(x)y'/y^2

>for example ∂/∂x[ (α−x)/σθ ]

That's a partial derivative so it's just −1/σθ

Anyone ever been followed home?
He started following me only 20 seconds before I got home. Pulled into my spot. He turned his lights off and slowly backed up. I stepped out of my vehicle and heard loud rap music. I closed my door and looked at him, and slowly walked to my front door. Then he sped off.

Roadraged cowardice idiot?

This is why I keep a baseball bat in my car

I'm upset he doesn't know how I feel.
He probably drove home smiling thinking he "got me". When in reality I think he's a coward and degenerate.

Why do you care what a testosterone-fueled degenerate thinks?

don't listen to this faggot. do the elements alongside arithmetic and you'll have a much richer understanding of arithmetic for it. you'll also have an easier time proving things in algebra and trig/calc, etc if you start with the elements because you'll actually be exposed to proofs right from the beginning (instead of fucking 10 years, for fuck's sake)

When his child gets taken away for being a low life.
For when he gets caught stealing and goes to prison.
For when his mother rejects him and he has no place to live except the streets.
For when he gets mugged in a alley trying to score heroin.

I want him to know how fucking pathetic I think he is. Remind him that he is a coward.

That last push he needs to finally leap off the bridge.

Although irrelevant to the post, let me help you.
f(x)=sign(x) is a function that takes in a value of x, and gives the sign, either positive or negative, back.
i.e. sign(56)=1 & sign(-24)=-1

Really struggling with this one Veeky Forums because it just seems like a blatant contradiction and I'm being lied to.

How can you "count past" something you haven't finished counting to begin with? If the natural numbers are infinite, and you can't count to infinity, how can you count "past" it? Or, how can something that has no size (isn't a number) be "bigger" or "smaller" than anything else? Do I not understand what "size" and "counting" mean? What am I missing?

I've been dwelling on this for months, I've read about bijections, surjections, etc. None of it helps. None of the definitions seem to ever address the questions I have. How can you count "past" something you haven't finished counting "to"?

And yes, I've been told so many times, "you just have to leave your intuition at the door". It doesn't work. My intuition doesn't know how to see what I'm reading as anything BUT a contradiction.

And no, this isn't homework. I am just an enthusiast.

For reference, I understand the idea that you can have different sets that can all be counted with the naturals. The naturals are the counting numbers. Anytime you take a list of unique objects and assign a natural number to them in the order that the natural numbers are given (which again, I'm not taking on face value, but thinking in terms of their partitions) I don't understand how you can have a set that has elements that can't be counted with the naturals.

What am I missing? Obviously I am missing something and there aren't any contradiction inherent in the definition of uncountable sets otherwise there wouldn't be entire fields of studies devoted to it. I just want to understand it so bad.

Here's an example of the simplest case:

Consider an infinite series of partial sums S(n) = 1 + 1 + ... + 1 (n times).
As n -> inf, S(n) -> inf
Consider an infinite series of partial sums T(m) = S(n) + S(n) + .... + S(n) (m times).
As n, m -> inf, T(m) -> inf

However, comparing S(n) as n->inf with T(m) as n,m -> inf, T(m) is clearly a "larger infinity".

When something is infinite, processes for sequentially estimating its value are unbounded. But we can still consider "relative size" of infinite sets, using the same intuition above that T(m) is a "larger infinity" than S(n) due to being an infinite sum of infinities. Perhaps you could consider it a second-order infinity.

I can't tell you if that would be correct, as that is essentially the problem of the continuum hypothesis - given the size of the natural numbers and the size of the real numbers, is there a valid size inbetween?

Why Nasa only take pics of Mars instead of filming it? There's no point or not enough technology?

insufficient bandwidth

Within 1.5 SD's means in a normal curve from z = -1.5 to z = 1.5
You got to Distr -> normalcdf(lower = -1.5, upper = 1.5, mu = 0, sigma = 1)

It was a bald white guy, I see your point though.

It's not counting past but having an order with a successor. Imagine an order pair of natural numbers. If you where to count with the dictionary order then it would go

(0,0), (0,1), (0,2), (0,3), ..., (1,0), (1,1), ..., (2,0), ....

(1, 0) is infinitely away from (0, 0) but the ordering still make sense even if you can assign a finite distance to the points.

How would I find the convolution between sin(a*t)/pi*t and sin(b*t)/pi*t?
I tried to use the fourier transform to get frequency domain which gives two square waves, but where do I go from there? Do I just use the usual convolution technique for continuous signals but in frequency domain?

It's 2 ideal low pass filters, the narrower one will win.

ab/|π*max(|a|,|b|)| * sin( min(|a|,|b|) t )/ πt

christ, look at all these fucking nerds

a convolution in the time domain corresponds to a MULTIPLICATION in the fourier domain.

I'm pretty sure you know how to multiply two squares.

How could I rewrite cos(pi/3 * n) such that it ends up in some form like 1 +/- some other term, perhaps with a squared sine?

nevermind kek

Ok. So I saw this posted earlier and feel like a fucking idiot for not knowing basic math.
How the fuck is this 24 and not 19?
Order of operations tells me that I should worry about multiplication and division before addition and subtraction. So why is it that I have to add one to both sides before multiplying by six this time?
How the fuck does that make sense?

It is the shoes and socks situation
First step A happens, then, step B happens
to reverse your actions, step B^-1 happens, then, step A^-1 happens

24/6-1=4-1=3

h-6=18
h=24

What is the shoes and socks situation?
What is step A and step B?
Why do I reverse my actions?
You explained nothing.
Where did you get that top equation?

...

I'm finishing Calc 1 in a few days. I did decently, got a B (my trig is weak, which held me back)

I have 4 weeks to prepare for taking an accelerated Calculus 2 course over the summer. I want to get a head start since it's a full semester of calc 2 crammed into about 6 weeks. Any recommendations on this?

Unrelated - I tried reading spivak's a couple times, but I dont think I have enough mathematical maturity to really understand it well. Is there another textbook I could try that's now Stewart's for self-teaching Calculus?

I don't understand what that has to do with this equation still.
There are no exponents at all and we aren't moving variables.

solve for h

then plug h back in and see if it works

solving for h gives you 24

plug 24/6 = 4 - 1 = 3