Last thread over the bump limit.
How does the last step follow from the one before?
>>8089022
I mean the [math]2\theta = \frac{\theta}{|\theta|}[/'math] where's that from
>>8089024
Additional question: is there a firefox addon that lets me visualise the maths thing before submitting? I know about online renderers, but I'd rather use something more convenient that doesn't ask me to switch tabs
[math]2\theta = \frac{\theta}{|\theta|}[/math]
>>8089022
>How does the last step follow from the one before?
What's the definition of sign(x)? What are the values of x/|x|?
>>8089028
Not that last step sorry :P this one [math]2\theta = \frac{\theta}{|\theta|}[/math] from what was done before
>>8089027
>Click on post number
>"Reply to thread No......" box appears
>Top left hand corner there should be something that says [math] \TeX [/math]
>Click that.
>It's a previewer.
>>8089033
½√θ^-2 * 2θ=½2 * θ/√θ^2 = θ/|θ|
>>8089038
Oh. That's awesome thanks
>>8089033
The last step is [eqn] \frac { 1 } { 2 } \left ( \theta ^2 \right ) ^{ - \frac { 1 } { 2 } } \times 2 \theta = \frac { \theta } { \left \theta ^2 \right ) ^{ 1/2} } = \frac { \theta } { | \theta | } [/eqn]
>>8089048
[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
>>8089088
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.
>>8089115
Oh I see, you're right, I never noticed that X and sigma are always on the right side. Makes sense now cheers
>>8089125
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)
>>8089143
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?
>>8089156
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
>>8089125
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
http://science.nasa.gov/science-news/science-at-nasa/2003/06jan_bubble/
https://en.wikipedia.org/wiki/Local_Interstellar_Cloud
http://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)
>>8089217
Thanks a lot. I'll save this post for sure.
You're a hero anon.
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.)
https://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.
>>8089223
>then how come this hasn't radiated off yet?
Anon, 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.
>>8089231
(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]
>>8089238
are any of alpha, sigma or theta functions of x themselves? If not, it's just a regular affine function.
>>8089232
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: http://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".
>>8089319
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.
>>8089332
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.
>>8089022
What do the vertical bars signify?
>>8089401
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.
>>8089513
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.
>>8089550
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?
>>8089727
>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]?
>>8089957
*On a bundle, that is. I'm interested specifically in fiber bundles atm but I think it should generalize for all types of bundles.
>>8089550
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?
![quadeq1[1].gif](https://i.imgur.com/ptNlGS0.gif "quadeq1[1].gif")
The correct way to solve the root part is
(b^2-((4a)c))right?
>>8090168
>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:
https://www.youtube.com/watch?v=BhnoSREmWVY
https://www.youtube.com/watch?v=r5CQUy3OKL4
https://www.youtube.com/watch?v=hoqF3gjLIyI
https://www.youtube.com/watch?v=4iEshd6izgk
https://www.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?
>>8090210
It's what the paper does
http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
>B. P. Abbott et al.*
>>8090279
>R. Abbott in second position and thus an et-al-pleb
>"Um... call me Bob?"
>>8090316
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.
>>8090506
https://en.wikipedia.org/wiki/Photon_energy
It's actually a significant fact of quantum mechanics.
>>8090506
>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.
>>8089957
pi^{-1} isn't typically a function.
>>8090200
(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
>>8090567
you have to look it up. you are supposed to memorize a few of these.
>>8090561
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.
>>8090653
1) multiply b*b
2) multiply 4*a*c
3) subtract what you got in step 2 from what you got in step 1.
>>8090686
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
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
>>8090657
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]
>>8090695
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.
>>8090700
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)?
![MSP21591h2b2gib18c9dadd000019hc4cifbah123e6[1].png](https://i.imgur.com/y9Q39VR.png "MSP21591h2b2gib18c9dadd000019hc4cifbah123e6[1].png")
>>8090700
Ok yea fuck you, you trolled me. I had it right from the start.
>>8090705
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].
>>8089125
>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.
>>8089156
>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.
>>8089238
>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
>>8089022
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?
>>8090921
This is why I keep a baseball bat in my car
>>8090967
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.
>>8090973
Why do you care what a testosterone-fueled degenerate thinks?
>>8090824
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)
>>8090975
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.
>>8089028
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
>>8091029
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?
>>8091061
insufficient bandwidth
>>8090567
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)
>>8091070
It was a bald white guy, I see your point though.
>>8091029
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?
>>8091118
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
>>8091118
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?
>>8091192
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?
>>8091196
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
>>8091196
24/6-1=4-1=3
h-6=18
h=24
>>8091196
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?
>>8091203
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.
>>8091208
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
>>8091208
Alright, what you are doing is taking a mysterious number h, applying 2 operations to it, and getting the number 3. to express this situation in symbols, you can write ((h#X)#Y)=3, where "#" means "take the number on the left, and then apply the operation on the right to it", and "X" is the divide by 6 operation, and "Y" is the subtract 1 operation. But, you want to figure out what h is based on what you know, so, to do this, use the shoes and socks property, and do this
((((h#X)#Y)#Y^-1)#X^-1)=((3#Y^-1)#X^-1), which simplifies to
h = ((3#Y^-1)#X^-1)
you can figure out the rest
>>8091211
Well yeah. But I shouldn't have to do that.
I just wanna know why the fuck order of operations is thrown out the fucking window for this one equation.
I don't want to bother with math if it's like language where rules only sometimes apply.
>>8091216
This is the most over complicated mess of an explanation I've ever seen for such a simple problem.
>>8091208
For any action X, X^-1 is the action that undoes it. Now stop pissing over the exponents and read what the comic actually says. This doesn't represent your equation, this represents the sequence of steps you are applying to it. You are reversing the process of plugging in a variable to become the process of finding a variable. Because the socks-shoes property described applies to order of operations, we reverse order of operations.
>>8091220
>waah please explain math to me without using symbols and make sure the sentences are short enough for my attention span
>>8091231
I'm not even that guy.
Your explanation was just shit.
Please never be a programmer.
>>8091203
>abstract algebra
>has to resort to shoes and socks
don't change, america.
>>8091234
I'm not that guy either. My explanation is the one that's not shit. It just wasn't much worth complaining about in a math thread.
>>8091236
i'm not elitist enough to care about metaphors used, but i kek'd at the implication that prof wanted students to physically do it instead of mentally consider it.
>>8091227
>>8091235
I just don't understand WHY you reverse the order of operations.
X, X^-1 means literally nothing to me and I don't know what it has to do with this equation.
I just don't see what's different in this equation than any other that requires one to reverse the standard order of operations.
>>8091241
the order of operations is just a tool to remove ambiguity from the "mathy" way of communicating the problem, >>8091196 is this "mathy" way of representing the problem, but writing the equation out in english is "not mathy." You don't need the order of operations for the "not mathy" way of doing it because the order is chronological, so, once you translate the problem to english, forget PEMDAS, and just use the shoes and socks property to figure out how to invert the actions and deduce h based on what you know.
>>8091241
The best "why" you are going to get is to play with symbolic equations and prove to yourself that this the socks-shoes concept of reversing order of inverse operations applies. We are explaining it to you in terms of socks and shoes because those are objects with which you have an intuitive understanding of how to layer onto your feet. Trying to do similar for algebra would result in a wall of symbols you will most likely be unsatisfied with.
>>8091241
Okay, look at it this way. You have h. We don't know what h is. If you know what h is, then you would follow the order of operations and get the answer, 3.
But we don't know what h is. We have to figure out what h is. Instead of being given an equation and told to find the "answer", we are given an "answer" and told to find part of the equation. To find the "answer", you follow the order operations.
Think of this as going from bottom to top.
But, in this instance, we are given the answer and told to find the equation. We are starting at the TOP instead of the bottom. And if this thing we are on top of is the order of operations, we have to work BACKWARDS in order to arrive at the bottom, which is the variable h.
So we start at the top, with 3. We then add 1 to the 3, while removing it from the left side. Then we have h/6 = 4
We "undo" the /6 by multiplying both sides of the equation by 6. 6x4 = 24 and h/6 x 6 = h.
Thus, we have worked backwards to solve for h. It's called retrograde analysis.
>>8091247
So the "why" the order is reversed is because the problem isn't mathy?
Really?
>>8091250
So the why is there is no why, I should just try it and if it works then great but if not retry it in reverse because I wouldn't understand it if it wasn't an analogy?
Really?
>>8091255
Oh. So when trying to solve for a missing part of the equation we use inverse order of operations but if we're solving for a missing answer we use normal order of operations?
That makes way more sense. Thank you anon.
>>8091260
its because you can translate a "mathy" problem to a "not mathy" which could also be described as a "wordy" problem. Again, you don't need PEMDAS after you have translated your equation to english, only during the "mathy" to "wordy" step will you need to use PEMDAS.
if you need help taking an equation, and describing what is going on with that equation with words, then just search google or youtube for people doing step-by-step solutions to these equations, or some crash course videos on arithmetic.
>>8091260
>So the why is there is no why
No, the why is lengthy and abstract as this entire discussion has been. It's easier to tell you to find a proof because it's not particularly hard and that's literally how the math was originally created.
>That makes way more sense.
Literally triggered when your paraphrasing matches
>>8091227
>You are reversing the process of plugging in a variable to become the process of finding a variable. Because the socks-shoes property described applies to order of operations, we reverse order of operations.
>>8091260
>Oh. So when trying to solve for a missing part of the equation we use inverse order of operations but if we're solving for a missing answer we use normal order of operations?
That makes way more sense. Thank you anon.
Somewhat simplistic way of looking at it, but yes, more or less. Now, what the socks and shoes analogy is getting at is that for every operation you do in math, there is an operation to UNDO that operation. You can put on the sock or take off the sock.
Now, if you are wearing socks and shoes, you take off the shoes FIRST, then you take off your socks. Now your feet are bare. Now if you do the INVERSE of that "operation", you put on the socks FIRST and THEN the shoes. They're equal but opposite operations.
The order of operations is more of a guideline to make things less ambiguous, but to solve for variables, you generally would inverse the order of operations, yes, so that you can solve for the variable.
Math is logic. It's taking what we "know", in this case, that the answer is 3, and then using that knowledge to deduce other knowledge, such as what the value of h is.
From all this, I take it you're sort of new at math. It's not a bullshit language, it is the truest language and one cannot do anything with it without correct assumptions. Think less about memorizing steps to solving problems, and more about how you know something, and how you can use that knowledge to deduce something else.
>>8091270
this is a good post.
A computation is just like a plan to build something.
You take the parts and assemble them, screw everything together.
Solving an equation is like looking for a specific part in something that was already built. You need to undo that thing in the opposite order until you get what you were looking for.
h/6-1= 3
means you take h, you divide it by 6, you substract 1 from what you got. And that is equal to 3.
If you're looking for h, you start from 3, you add 1, and you multiply by 6.
>>8091275
When there is a variable on both sides of the equation, generally, you will use some operations to bring all the variables to one side, then use inverse order of operations to solve for that variable.
What level of math have you taken?
>>8091287
Let's just say pre algebra. Since I've technically taken up to geomety and some statistics but that was years ago and I clearly don't remember even algebra aha
I just started getting back into it so my brain isn't quite thinking mathematically yet.
I'll get back into the rhythm of it soon enough.
>>8091292
Alright, well stick with it. Maybe get a textbook and start working through it, or go take a class or two. You aren't doing "real" math yet. You're learning the rules for math - learning how to do operations and deal with variables. This will continue until you finish the calculus series, for the most part. Algebra, Calculus... Those are basically areas to learn how to do operations, so that you can start performing proofs and the like.
It's a long road, but it's rewarding. I very much remember the frustration of not knowing why something works and having to just accept "well that's how we do it."
But as you progress through the levels of math, you will start to see the logic and it will begin to make sense. Good luck.
>>8089022
I know i can get an answer from wolfram but how can i solve this.
>>8091363
what exactly do you know?
Does expansions ring a bell?
If not, use this:
(1+243/h +...)^(h/3) = exp(h/3 ln(1+243/h + ...))
and remember that ln(1+y)/y when y goes to 0 is the expression of a certain derivative.
>>8091363
(1+243/h + 2520/h^2 + 3216/h^3)^h/3 = (1+(243+2520/h + 3216/h^2)/h)^h/3
This form allows you to apply the compounding definition of e, so your answer should be e^81
>>8091363
The easiest way is to write it as exp(h/3 log(...)) and use L'Hopitals but there is another way by factoring and using the limit definition of e.
1+a/h + b/h^2 + c/h^3 can be written in the form (h+p)(h+q)(h+r)/h^3, meaning your limit can be rewritten as
( lim h->inf: (1+p/h)^h (1+q/h)^h (1+r/h)^h )^(1/3) = (e^p e^q e^r)^(1/3) = e^((p+q+r)/3)
The 1/h coefficient of (h+p)(h+q)(h+r)/h^3 is obtained by selecting h from 2 factors and single constants from the other yielding a=p+q+r, so the limit is e^(a/3) or in your specific example e^81.
I have a small insulated room that i need to cool down. I don't have a cooler, but i do have a freezer.
I know warming up rocks in a fire and then putting them in a room makes the room warmer, so the other way around should also work right?
Which material should i freeze and then put in the room to make the room cooler?
Water? Iron? Rocks? Is it about mass?
How is it possible to get either of the [math] a_6>0 [/math] and [math] \frac{a_5}{a_5} \leq 1+c_7(\lambda) [/math] bounds pictured using the fact that [math]P(d) \leq v_2(h) [/math] and [math] d > e^{\lambda h} [/math] for large enough [math] \lambda] [/math]?
It's from page 12 of
http://archive.numdam.org/ARCHIVE/SB/SB_1983-1984__26_/SB_1983-1984__26__309_0/SB_1983-1984__26__309_0.pdf but I'm not sure if I'm missing some obvious thing to do here to get the bound since the author claims its easily shown.
How do you find the minimum area of an ellipse that surrounds the 4 circles in the diagram? they're all of radius 5 and +/- 60 from the y axis and +/- 25 from the x axis
Fucked up this question last thread and it never got answered, so I'll try again.
I know that [math]\frac{∂z}{dx}[/math] can equal [math]\frac{∂z}{∂t}\frac{dt}{dx}[/math]. But can it also equal [math]\frac{∂z}{∂t}\frac{∂t}{∂x}[/math] or [math]\frac{dz}{dt}\frac{∂t}{∂x}[/math] depending on the circumstances?
>>8091419
it's about caloric capacity.
Water is what a freezer is designed for (all food is approximately water)
It has limited power so if you put something like rocks, it will take much much longer to heat up, and longer to cool down as well.
I'd say just put bags of water in the freezer and let them freeze.
If you don't care about humidity, just empty them in a basin in the room. Temperature will drop because the air reheats the water and then some of the water can even evaporate, drawing even more energy. If you can blow some air on the water, it's even better.
If you care about keeping it dry, just leave the bags closed and let them heat up on their own.
Also if there are things you are going to leave in the room (pieces of metal in particular, or ceramic, basically anything that feels cold to touch, too long to explain why), I suggest putting your bags of water on them: they will act as heat exchangers and will store some cold faster, and will keep cooling the room after you take your bags back to cool them more.
>>8091422
on est sensés deviner ce que c'est c7(lambda)?
Oh screw this.
I know that [math]\frac{∂z}{dx}[/math] can equal [math]\frac{∂z}{∂t} \frac{dt}{dx}[/math]. But can it also equal [math]\frac{∂z}{∂t} \frac{∂t}{∂x}[/math] or [math]\frac{dz}{dt} \frac{∂t}{∂x}[/math] depending on the circumstances?
>>8091451
I tried thinking about it last time, but I can't see one instance where this would ever matter. Just apply the chain rule properly every time.
>>8091449
It's not given (that's it's only appearance in this paper), so I suppose it's from some direct manipulation of the two expressions shown. c1,c2,c3 only depend on lambda, psi and M as desired, but a2, a3, a4 all depend on d. It's hard to get a bound on the sum of the real parts of the Gp logarithmic derivatives, but P(d) is the set of primes dividing d excluding the largest one, and so the sum might be limited by the sum of G_p for the first v_2(h) primes.
>>8091442
Thank you anon. This will be extremely useful when summer comes.
Last summer i did freeze a bunch of closed bottles of water and put frozen ones on a desk and set a fan to blow on them.
It worked great, but i had to put a towel below them because water started condensing and dripping down the bottles.
Since dryer air feels cooler and the condensation pulled the water from the air i think this was an extra bonus to cooling the room.
I'll try putting the bottles on a chunk of iron this time like you suggested.
Thanks.
At what point in math does IQ really begin to matter?
Surely given enough time even an average person could overcome most math problems
>>8091651
I guess about 120-130.
Below, you're just a regular person trying to do math, having to put up work to understand and get familiar with concepts.
Above that, you start seeing things as intuitive. The hardest thing to understand for you is how can other people not see how simple it really is.
>>8091202
>Where did you get that top equation?
Just plugged in 24 for h
>>8091217
Because it's not thrown out. Rewrite the equation in the order of how the operations are being done and start stripping the outer branches of the tree.
You have: - (/ h 6) 1 = 3
so
+ - / h 6 1 1 = + 3 1
/ h 6 = 4
* / h 6 6 = * 4 6
h = 24
What the fuck is a binomial coefficient where did that come from
>>8090557
Why not? As I understand, [math]\pi^{-1}(M)[/math] denotes the preimage of the mapping, but doesn't that indicate that [math]\pi^{-1}[/math] is a function itself? Or is it just notation to make the set more intuitive?
>>8091972
>binomial coefficient
fancy wording for n choose k
I have to make an infographic for my technical writing class and I wanted to know what y'all thought of this so far. I'm not done yet, gonna add a little bit about Nuclear being the third most economic source of energy by 2040 in the current gap, but how is the presentation and how convincing is it as an argumentative infographic against coal and gasoline?
>>8091982
does it have to contain sources like that? They take up a lot of space (it's as big as your "keep it clean" section)
>>8092007
Yes, and the sad thing is I plan on adding more. I'll have to make them a bit smaller font.
>>8091982
please put something on the right side of the last part
The Legendre polynomials are normalized such that [math]P_n(1)=1[/math] . Given that [math]a_0 = 0[/math] , use the recursion relation to find [math]P_1(u)[/math] and [math]P_3(u)[/math]
How do I do this guys? I know I'm retarded, I managed to derive the recursion relation but can't use it...
>>8091974
I can put parentheses after any symbol I want; that doesn't make the symbol a function. It's just supposed to be nice notation, in that it agrees with function notation when [math]\pi[/math] is actually invertible and we can say things like
[math]\displaystyle \pi \left( \pi^{-1} (U) \right) = U[/math]
>>8092041
Yeah that's what I was saying, I have one more graphic to put there I'm just trying to figure out a way to frame it. I'll post the update pic in a few
>>8092046
how about adding what it currently costs to produce a TWh with either method?
What about life expectancy? (How long can we still use coal vs how long can we still use nuclear etc)
>>8091982
>ignoring the masses of people that die in the uranium mines as usual.
>>8092076
>send those fuckers into coal mines, problem solved
>>8089957
π need only be a smooth surjection, => inverse need not exist.
(Assuming we are working in the smooth category)
The notation π^-1 denotes only the preimage of π, and not the image of an inverse map.
Sections however are right inverses of the map π. On a general fiber bundle, global sections may not even exist. However due the requirement of local trivializations, local sections always exist.
(for principal bundles global sections exist iff the bundle if trivial)
>>8092076
lol no i'm not, it's not many people and nuclear creates such a large amount of energy that the deaths/twh is pretty accurate. It's actually pretty high compared to most I've seen.
>>8092073
I went more with the cost side of things. We have enough reserves to use coal and uranium for an obscenely long time, so that argument didn't seem too useful for me.
>>8092046
>>8091256
"Calculus With Analytic Geometry" by Simmons and "A First Course in Calculus" by Lang are both approachable for self learners, not excessively rigorous, and explain the concepts and methods well. "Calculus: An Intuitive and Physical Approach" by Kline is similar but with even more hand holding and a far smaller price tag (Dover Books is your friend).
Is becoming a professor hard?
Prove that addition on the real numbers is well defined.
I'm not sure the question makes sense. I thought proving that something is “well defined” meant proving that using different representations of the same number doesn't affect the outcome of the operation. But I only see one representation of a real number here. Does the question make sense?
Pic related is the definition of the real numbers that I was given.
>>8092120
Yeah but what about when something goes wrong and we have another Fukushima or Chernobyl on our hands.
If you think about the devastating consequences just one reactor failure can have it's pretty scary to think what could happen when they start to become more common.
>>8092220
I'd highly recommend you read up on those disasters before thinking that they'd ever start becoming more common. And 3-mile too. If you want to talk about reactor failures, it's best to be at least semi-educated on them.
Chernobyl and 3-mile would never happen now, it would take hundreds of people in collusion breaking federal laws and regulations regarding nuclear plants for anything similar to happen.
Meanwhile, Fukishima was built on a fault line and in a tidal zone, and management of the reactor knew they had to improve their tidal defense but chose not too because they had 6 years until they had to renew their plant and they could wait until then. Guess what everyone did after fukishima? Spent billions of dollars per reactor improving safety against natural disasters.
We've had 3 significant events in the lifetime of nuclear reactors, and only 1 of those had the sort of devastating consequences people think about when they think reactor meltdown
>>8092212
I think it means show that sup(C) can always be written as an infinite decimal expression, and in a unique fashion.
>>8092231
I don't see how you can argue that more nuclear power plants won't lead to an increase in nuclear accidents. Everyone always likes to go on about how many safeguards there are, but then something they didn't account for pops up and none of it winds up mattering. There are always going to be things we don't account for.
Also I don't see how you can say Fukushima didn't have devastating consequences considering it dumped billions of tons of radioactive waste into the oceans and has basically irradiated large swathes of the ocean and coastlines to the point that all the fish are getting nasty tumors and shit.
>>8092220
>classical irrationality
fukushima was designed by morons.
They used numbers like "hurrrr one very big earthquake every thousand years" or whatever.
Maybe nuclear plants failures, IF THEY HAPPEN, can cause a lot of damage.
But coal plants cause much more damage. You just don't say anything because you can't see it.
The numbers are there to help us make rational decisions. And the numbers say coal plants are strictly inferior to nuclear plants (they kill much more people if that's the only thing you care about)
>>8092239
And if we had a nuclear power plant in every major city, you really think that none of them would be "designed by morons"?
Coal plants may cause more damage when both are operating correctly, but at least they are predictable and I know there's not going to be a catastrophic coal meltdown.
>>8092235
Because an increase in nuclear reactors will lead to an even greater increase in safety. As someone who works in a Nuclear reactor, the average person truly does not understand the safeguards that are in place at these facilities. I'm talking like, place a box up 4 steps, hold onto the handrail to climb those 4 steps, and then pick the box up and repeat until you're at the top of the steps type of safety. When these things go wrong, it's not because they haven't been accounted for, it's because someone made the decision to disregard them.
Fukushima may have had some fallout but how does it compare to something like the Valdez Oil spill? or the BP oil spill? Where millions of creatures were straight up dying? It may be devastating but in comparison to the consequences from other energy sources, how is it worse?
>>8092235
Boy, you make this hypothetical incident sound almost as bad for the environment as regular operation of the sources of energy we're using now.
>>8092244
Do I think a 4 billion dollar facility will be designed by idiots? A facility that has to reach the pinnacle of modern engineering to operate? I'd suggest you look into the Crystal River plant and see how plants will shut down entirely if anything at all is wrong with their facilities. I'm gonna have to go with no there
>>8092256
Well either way nuclear power is not sustainable on the large scale. If they tried to put nuclear power plants everywhere the whole system would just fall apart.
>>8092262
It sure is a shame that we need so many nuclear power plants compared to oil wells and refineries to cover the same population.
>>8092120
Not a single of sources is peer reviewed.
>>8092262
So what is your evidence for this statement you just pulled completely out of your ass.
>>8092262
>Well either way
I love watching backpedaling to new rhetoric, abandoning previous ground.
Too bad none of these fucks remember which of their arguments have been torn apart for more than a day before repeating them.
>>8092274
There is FAR more oil out there than uranium, I mean if you figure oil is under $50 for a whole barrelful which is like 300 pounds of oil, whereas that much uranium could cost like $8595.00 according to trusty wolfram alpha.
Not to mention distributing that much uranium would only make it easier for terrorists to obtain it and use it to create nuclear weapons.
>>8092279
>NASA
>US Energy Information Administration
>Both of these agree with, or provide more conservative numbers than those presented
Y'all really just talk out your ears don't you
>>8092299
Both of those sources have a vested interest in pretending the numbers are lower than they are.
>>8092299
Not peer reviewed government owned propaganda websites
>>8092286
>"Oh because 300 lbs of oil provides the same amount of energy as 300lbs of uranium"
>"pfffttthftft as I'm literally talking out of my asshole"
I'll even help you out here, 300 lbs of uranium would actually cost around $250000, not $9000. Unfortunately for you, it produces, at a conservative estimate, more energy than $500000 or 10000 barrels of oil.
>>8092244
>Coal plants may cause more damage when both are operating correctly, but at least they are predictable and I know there's not going to be a catastrophic coal meltdown.
so you're just irrational. That settles it, I don't need to debate you further.
>>8091974
Analogy...
Consider the projection [math]\pi(x,y,z)=(x,y)[/math] from R^3 to R^2, and the the function [math]\sigma(x,y)=(x,y,x^2+y^2)[/math] from R^2 into R^3. Now [math]\pi(\sigma(x,y))=(x,y)[/math]. But [math]\pi^{-1}[/math] is not a function... all points on each line parallel to the z-axis get mapped to a single point. The lines are "fibers", the function [math]\sigma[/math] is a section, and M is the x-y plane.
How do I pay for college ?
I'm on the verge of not passing my trig class. I need to get above an 80% on my final in order to pass, and I failed my last exam, and got a 77% on the first one. I think it's absolutely doable for me to pass though, I just need to bust my balls. I have about 3 weeks until the exam. If you were in my shoes, what would you be doing? What would you're study strategy be? Currently, I'm planning on just going through each weeks homework and redoing it, and supplementing with a bit of Khan Academy and YouTube randoms. This means I'll have to be doing 3 weeks worth of work every week though, and it may be mentally difficult to review older, unrelated material while simultaneously learning new. I also worry I will simply not have enough time in the week for this strategy.
Where can I get the fastest help online? There's so much shit I'm struggling with. It's an online class so I can't just pester my teacher, and I get hung up on the stupidest stuff. I go to SQTs and ask for help, as well as /r/cheatatmathhomework. I might start using stackexchange as well.
Thanks in advance, faggots
>>8092550
FAFSA.
>>8092550
Go to Europe
Declare yourself a refugee from Syria
???
Free shit
>>8092233
That makes sense. Thanks.
Is there an explanation on why 0!=1 ?
>>8089022
I am doing an epsilon delta proof practice that already comes with the answers and for two problems already I have come up with different deltas to the ones the answer set contains.
For example, as x approaches 3, the limit of 2/(x+3) equals 1/3.
I come up with the confirmation that delta is equal to 21 times epsilon, but the answer set says that delta is equal to 15 times epsilon.
Is this possible? I checked my algebra and I cannot notice a single mistake.
Can two different deltas occur for a single limit?
>>8093078
There is one unique way of arranging zero objects by having zero objects.
(n-1)!=n!/n
>>8093078
n! = [math] \int ^{ \infty } _{0} x^n e ^{-x} dx [/math]
0! = [math] \int ^{ \infty } _{0} e ^{-x} dx [/math] = 1
>>8093092
>>8093101
Thanks faglets
>>8093082
You just got a shitter delta
|1/3-2/(x+3)|<ε when |x-3|<δ
so
|1/3-2/(6±δ)|<ε
|6±δ/3(6±δ)-6/3(6±δ)|<ε
|±δ/3(6±δ)|<ε
δ/|(6-δ)|<3ε
δ<3ε|(6-δ)|=18ε-3εδ
δ+3εδ<18ε
δ<18ε/(1+3ε)<18ε
>>8093147
>You just got a shitter delta
But is it valid?
am i missing out if i drop biochemistry and focus on materials science courses for a chemistry major>
>>8091040
Ooookay. I just realized that (after wondering how you could take a sum of two infinite series) that 1/3 can be represented by an infinite series, so an infinite series of 1/3 + 1/3 + 1/3 + ... would be of the same form as the series of T(m). Realizing that kind of opened some doors for me so I'm going to think about this some more afterwards. I've tried constructing the naturals recursively a couple different ways before but I haven't gotten to the rationals yet. Thank you.
>>8091982
gd here,
the coal, gas, and nuclear icons should be vertically aligned, like the icons are in a column and the corresponding names of the icons, arrows, and numbers are all in their corresponding columns.
3% of gas emissions pie char should be moved up by 1-2 pixels
the last row separated by the blue bar, keep the text inside the pie chart for both circles, or outside for both circles- but not both. also, either center or keep it at a 1/3 point (move the entire graphic so it's underneath the barrels in the row above, or center it)
What's the difference between all those integral symbols? How do I tell them apart?
Like for example [math]\int[/math] and [math]\oint[/math], or [math]\iint[/math] and [math]\oiint[/math]. Or even [math]\varointclockwise[/math] and [math]\ointctrclockwise[/math] compared to [math]\int[/math] or [math]\oint[/math].
Also fuck LaTeX previewer for not even supporting half of these integral symbols. Going to bet that /sci/'s LaTeX doesn't, either.
>>8093410
As I thought.
∯, ∲ and ∳ respectively.
>>8090203
Sorry for the late reply (I've doing more research), but I really appreciate you pointing me in the direction of heuristics. Too much of critical thinking seems to be rooted in skepticism through fact checking, breaking things down for analysis, etc. which isn't really practical.
And the correct term for the psychological tactics i was getting at is psychological manipulation. It encompasses everything from confidence tricks, salesmanship, social engineering, political underhandedness, etc. There is a good list on wikipedia for it. Now that i know the keyword and what is associated with it, i know exactly what to look for.
Lastly, i would appreciate it if you could give me your perspective on the current thoughts I've arrived at so far:
As fedora as this sounds i am really just trying to develop my mind to become more accurate and efficient at close examination of whatever is in front of me. In the past i have been strongly swayed by variants of reddit atheists who think they know everything and every religious argument is stupid, theists who are the polar counterpart to reddit atheists, handwaving philosophers who say question everything and claim nothing can be known, media bias whether it be alternative or mainstream, and health/nutrition/fitness experts who use bad science, marketing and whatever else to sell their shit. Not trying to get /lit/ here, but it seems like the only rational and concrete approach to thinking is freethinking, and even then in use the term appears more like thinly veiled atheism and something sjws claim to be. Maybe independent thought is a better term, but it just sounds like a euphamism for confirmation bias or freedom of thought. At the risk of sounding like an intellectual blowhard, if the terms are taken in their literal sense then they seem like the highest form of thinking to me. Correct on that if i am wrong. I'm mentally exhausted after sifting through all this bullshit. Again, i appreciate your help.
>>8091196
>So why is it that I have to add one to both sides before multiplying by six this time?
You don't. Multiply the entire operation by 6 first and then just add the six resulting from 1x6 to the result of 3x6. You don't get to multiply selectively.
>>8093417
The word you're looking for is approaching things with an open mind.
My book says for a complex function [math]f(z) = u(x, y) + iv(x,y)[/math] to be differentiable at a point [math]z_0[/math], the first-order partial derivatives of the functions [math]u[/math] and [math]v[/math] must be continous in the point [math]z_0[/math], and they have to satisfy the Cauchy-Riemann equations.
My question is why bother with the Cauchy-Riemann equations? Doesn't the continuity of the partial derivatives ensure that the Cauchy-Riemann equations are satisfied?
>>8093922
>Doesn't the continuity of the partial derivatives ensure that the Cauchy-Riemann equations are satisfied?
how do you figure? I don't see the steps that would lead from one to the other
>>8093410
>>8093413
I want to say it's the integral over the boundary, but its been a long time since calc 3. notation is blah.
The first one is a normal integral over an interval (since it's missing it's limits it's technically the primative or antiderivative).
The second is a line integral over some closed shape.
The third is a double integral.
Fourth is a integral over a closed surface.
The clockwise and counter-clockwise integrals are used when the orientation of the shape matters...like getting the work in or work out of a pressure-volume diagram
>>8093922
>>8093930
you don't need continuity
I finally figured why you asked.
IF f is a function of two real variables, and both u and v are two functions of two real variables that are differentiable, then f = u+iv is REAL-differentiable with respect to two real variables. The cauchy-riemann equations don't have to hold.
if f is a fonction of ONE complex variable z, then it is COMPLEX-differentiable if and only if the cauchy-riemann equations hold.
What you should remember is that differentiability with respect to 2 real variables is not the same as differentiability with respect to one complex variable.
>>8093922
Complex conjugation is the prototypical example of a non-holomorphic function, and it has smooth real and imaginary parts.
>>8093948
Any examples? Like, say, is there some reason why you need a special integral symbol for line integrals?
>>8093958
Thank you, that makes sense! I had a hard time coming up with an explaination.
>>8093963
> single integral
velocity from an acceleration function
> line integral
Ampere's law
> oriented line integral
work from a power cycle via P-V diagram
> is there some reason why you need a special integral symbol for line integrals?
It tells you what you're integrating with respect to, but I'm pretty sure there's better notation via boundaries, but I'm not that far into my analysis sequence.
>>8093987
Makes sense, I guess. Thanks.
>>8093922
2d derivative (that is the derivative as a linear function from R^2 -> R^2) doesnt take into account the multiplicative structure of R^2 = C.
As you surely know, complex differentiability is defined using complex multiplication. Thats why being holomorphic is a stronger property
>>8093995
Read some pure math texts on analysis.
They're more about making sense, then they are about just calculating a value.
>>8093987
>but I'm pretty sure there's better notation via boundaries
There isn't a specific integral that means boundary.
If you have a manifold-w-b M then and want to integrate over the boundary then you write: [math]\int\limits_{\partial M} {} [/math]
>>8094019
Can you define line integrals using that sort of notation?
>>8094022
It is standard notation. Using [math] \oint [/math] for a boundary is not necessary because all the circle is implying is that the integral is over a closed curve/surface/manifold. But by definition, every boundary is necessarily closed.
I'm double majoring in CS and Maths. Tell me why I shouldn't.
Also, tell me what to minor in between botany, chemistry, economics, philosophy or physics.
>>8094310
Econ will probably be the most beneficial. Physics will probably be the most interesting.
>>8094310
>I'm double majoring in CS and Maths. Tell me why I shouldn't.
Because you're not learning much of anything.
If time travel is possible then why aren't there any recorded instances of time travelers coming from the future?
>>8094362
Some people theorize that Lee Harvey Oswald was a time traveler.
Need help understanding how you get to step 2 from step 1. I understand the first step. But in the second step I don't see how they got the final answer. Explain like I'm a fucking retard, thanks.
>>8094393
first you factor out 8^(x^2+1) since it appears in both terms being added in the numerator
cosx(8^(x^2+1)(ln8)(2x)-8^(x^2+1)(-sinx)
= 8^(x^2+1)[cosx(ln8)(2x)-(-sinx)]
and then subtracting -sinx is the same as adding sinx so
cosx(8^(x^2+1)(ln8)(2x)-8^(x^2+1)(-sinx)
= 8^(x^2+1)[cosx(ln8)(2x)-(-sinx)]
=8^(x^2+1)[cosx(ln8)(2x)+sinx)]
>>8094399
Thanks anon
>>8092043
The Legendre polynomials are normalized such that [eqn] \int_{-1}^{1} P_n(x) P_m(x) \, \mathrm{d}x \, = \delta_{nm} [/eqn]
how the fuck am I supposed to calculate gamma for something travelling at the speed of light? what am I missing?
>>8094535
a proton isn't travelling at the speed of light.
you know its rest mass, you know its energy. You can deduce gamma and the speed from that.
>>8094535
and if the answer is 10^5 years, it doesn't mean it's exactly 10^5 years, maybe it's just very close to the speed of light. A 1 sig fig answer isn't very informative.
>>8094543
the speed is 3x10^8 though
hence it takes 10^5 years to travel 10^5 light years
>>8094547
yeah but idk if my calculator will handle that; it spewed out 3x10^8 exactly for the speed
>>8094553
oohh I have an idea, binomial
-2/2 is -1. 2/2 is 1. You're welcome you retard.
nope.. calculator is still a limiting factor here.. I get t' = 0
>>8094535
I basically find v = c*(1-1/1.066*10^10) which is basically c up until the 10th decimal
This is why the travel time is 10^5 years.
>>8094598
so is it impossible to find t' with my calculator?
>>8094601
I think you need to work it out on paper and use taylor series first. Then you will get something that's useable ( a lot of 10^10 and 10^20 disappear that way)
>>8094610
binomial only gets me so far.. I'll just give up haha
How do you find the proper subgroups and left cosets of the group of symmetry operations on a equilateral triangle?
I believe the proper subgroups are just the two rotations + identity and the three reflections + identity. But I don't know how to work these out other than just by intuition.
>>8094727
you just want to use lagrange's theorem which tells you all the orders of your subgroups have to divide the order of the group (which is 6), so since they're proper either 1,2 or 3 can be the order.
you start with the identity element e.
either your proper subgroup (call it H) contains a rotation or it doesnt. if it does, H has to also contain the rotation applied twice, and so has order at least 3. but it can't be larger than 3 because of lagrange, so that's as you get from this case.
if H doesn't contain a rotation, then it either contains a reflection or doesn't. if it doesn't then it's just the trivial group, and if it does contain a reflection the group has order at least 2. no other elements have order 2 and so there's no way to make a group of order 3 that contains this subgroup. there are three reflections so this gives 3 distinct subgroups.
in total there are then 5 subgroups
>>8094770
Oh, so every reflection has its own subgroup. I see, thanks.
Could you try to explain left/right cosets to a retard with no experience in group theory? I can't grasp the concept at all.
>>8089022
X divided by its magnitude is its sign. What's not to understand about that?
Trig retard striking again:
Looking to find all three complex roots of z^3+1=0 using nth root thereom.
z^3=-1
is the principal third root 1/2 + i[(sqrt3)/2]?
>>8094770
by
>no other elements have order 2 and so there's no way to make a group of order 3 that contains this subgroup.
i meant you can't have more than two reflections in your subgroup without generating the whole group
the cosets just partition your group into different pieces (with respect to some subgroup!)
if your group has order n and the subgroup has order m dividing n then there are n/m cosets with m elements in each. each coset represents a sort of 'shift' of your subgroup i guess
it helps to use the algebraic language for this e.g. if you consider your triangle then its symmetry group (call it G) has order 6 and the subgroup generated by any rotation has order 3. call this rotation R, so that the subgroup it generates <R>={e, R, R^2} consists of the identity, the rotation and the rotation applied twice.
then your cosets are computed by multiplying <R>(say on the left) by each element in G (call one reflection S):
e<R>=<R>
S<R>={S, SR, SR^2}
R<R>=<R>
R^2<R>=<R>
SR<R>={SR, SR^2, S}
SR^2<R>={SR^2, S, SR}
Hence the two cosets are
<R>={e, R, R^2}
{SR^2, S, SR}
Note that this is legitimately a partition, every element in G is in exactly one coset.
This definition is key for eventually coming to the idea of a normal subgroup. algebraically this just means the subgroup is stable under conjugation (gHg^-1=H for all g in your group) but should really be thought of as what it means in terms of homomorphisms between groups. a normal subgroup is precisely the kind of subgroup that can be the kernel (get mapped to the identity) of some other group
>>8094807
oh and what makes normality important is that the cosets themselves form a group!
>>8094807
>then your cosets are computed by multiplying <R>(say on the left) by each element in G (call one reflection S):
this explains a lot, thanks
>R<R>=<R>
>R^2<R>=<R>
Why are these two left unchanged?
>>8094821
R<R>=R{e, R, R^2}={R*e, R*R, R*R^2}={R, R^2, e}=<R>
R^2<R>=R^2{e,R,R^2}={R^2*e, R^2*R, R^2*R^2}= {R^2, e, R}=<R>
>>8094826
of course, my bad. Thanks for taking the time to explain though
Someone please explain Laurent series expansion
I don't understand how to do it
>>8089310
You don't, trust me
Today I've had my last exam of my undergraduate (CS). Towards the end it was quite mathematically heavy (I picked the most maths-y ones like machine learning, computer vision, neural nets, etc.) and although I kept up, I could notice I had a lot of gaps. Is Khan the best way to catch up? I was thinking about going up from pre-algebra and see if there's anything at all that I'm missing but there may be more efficient methods?
>>8094831
it's just like a taylor series except with a different rule for getting the coefficients
https://en.wikipedia.org/wiki/Laurent_series
>>8094794
bump
>>8094794
yes
in general solving z^n=a you can generate all solutions with |a|^(1/n)(cos(arg(a)/n)+isin(arg(a)/n)) where arg is the angle a makes with the x-axis
in which case youve done it correctly
>>8094886
anon please help me before I kill people. After getting this solution, I just plug in other values for which arctan(0)=pi, right? Such as 3pi, and 5pi?
So that
e^i3pi/3
=cos(pi)+isin(pi)
=-1+i0
=-1
?
Then continue with 5pi?
