/sqt/: Stupid Questions Thread

That's one way of solving the problem, here's another:

Let's call P(A) the probability that Alice eventually wins the game given that it's her turn now.

There is a 1/2 chance she wins immediately and a 1/8 chance she gets another turn.

So P(A) = P(flipping heads) * P(victory | given heads was flipped) + P(getting another turn) * P(victory | getting another turn) = 1/2 * 1 + 1/8 * P(A).

P(A) = 1/2 + 1/8 * P(A) and so P(A) = 4/7.

Same for P(B) and P(C).

A wins P(A) of the time, B wins 1/2 P(B) of the time, and C wins 1/4 P(C) of the time.

Alternatively you can see that P(A) = P(B) = P(C) by symmetry and that P(A) + 1/2P(B) + 1/4P(C) = 1 and calculate from there.

Thanks that's a nice way of solving it

math.stackexchange.com/questions/170331/why-is-int-0-infty-frac-ln-x1x2-mathrmdx-0

Split the interval [0,∞) into [0,1) and [1,∞). For the latter, use integration by substitution with u=1/t.

You don't need to actually evaluate the integrals, because one half is just the negation of the other, so their sum is zero.

Anyway to answer the question you actually asked, sum(1/2^(3n+1)) = 1/2sum(1/8^n) = 1/2 (1/(1-1/8)) = 4/7.

because sum(1/a^n) = 1/(1-a) when a

There doesn't necessarily need to be a cosine, especially when the basis vectors are not perpendicular.

thankyou guys

can somebody please explain why this holds

so a matrix, R 100x100 has the diag
d1=8, d2=6, d3 = 4, d4 = 1.5, d5 = 1.4, d6 = ... , d100=1

i just cant find the pattern...

second q:
in iterative methods, like matlabs/octaves pcg function, what is the energy norm and how can i compute it?

Here's a third way. Going by pic related if we let X ~ Geom(0.5) then
[eqn]\text{P}(\text{Alice wins}) = \text{P}(X = 0, 3, 6, ...) = \sum\limits_{n=0}^{\infty}\text{P}(X = n) = \sum\limits_{n=0}^{\infty} \left(\frac{1}{2}\right)^{n+1} = \frac{4}{7}[/eqn]
similarly
[eqn]\text{P}(\text{Bob wins}) = \sum\limits_{n=0}^{\infty}\text{P}(X = n + 1) = \frac{2}{7}[/eqn]
[eqn]\text{P}(\text{Charlie wins}) = \sum\limits_{n=0}^{\infty}\text{P}(X = n + 2) = \frac{1}{7}[/eqn]

Shit, P(X = n ...)'s should be P(X = 3n ...)'s

Also (1/2)^{3n + 1}. I should proof-read a little better.

How would I show that for all natural numbers n and m, if [math]\mathbb{Z}^n \cong \mathbb{Z}^m[/math], then [math]m = n[/math]?

I have a hint to write [math]P = \mathbb{Z}^n[/math], [math]Q = \mathbb{Z}^m[/math] and compare [math]Q/2Q[/math] with [math]P/2P[/math] but I'm not sure what to make of it.

If x is a scalar, then A.xI = x.A so M^-1.xI.M = x.M^-1.M = x.I

Not really a question but doesn't deserve it's own thread.

Physics major here, junior. Have become pretty disillusioned with the study of physics.
Tangent: I got into it in some desire of a theory of everything, some sort of objective truth, everything is a manifestation of these simple principles and we can quantify it blah blah blah, but GUESS WHAT GUYS WE HAVE A BUNCH OF disconnected theories that are EMPIRICAL, only fit in specific situations, and don't work with each other. Literally every step in physics is "hey guys, what we taught you last semester was just an approximation, here's the truth" (repeat every semester). Might as well be an engineer -- at least then you aren't pretending to be studying some objective truth, and you may actually publish something useful at some point in your life. The only reason physicists think that there is some TOE is that they WANT there to be one, because it's a friggin cool concept. That doesn't mean it exists or that it's possible to study.
/rant

Anyway, what I have learned is really a set of problem solving skills. How to approach and solve problems. I also love chemistry, and enjoy working with and learning about the human body. Before undergrad I went and got my massage license, but it wasn't fun after it was my actual job, lol. Contrary to what my writing probably portrays, I'm quite smart.

So... med school? Anybody? Is it just a meme? I only would have to take a few extra bio courses to be eligible, and I have plenty of room in my schedule my senior year.

Any opinions on med school from people with experience?

Okay so I gave this it's own thread, but it only seemed to attract shitposting, so I'll try again here:
>How do I work out correlation functions in QFT?

Is it really just talking a series of functional derivatives wrt the source terms? So if I had a Lagrangian like [eqn] \partial ^{ \mu } \phi _1 \partial _{ \mu } \phi _1 - m^2 \phi _1 - \partial ^{ \mu } \phi _2 \partial _{ \mu } \phi _2 - m^2 \phi _2 - \frac { g } { 4 } \phi _1 \phi ^2 _2 [/eqn] Would the 2-point correlation function (after going through the standard fare of splitting up the Lagrangian into some source terms) just be [eqn] \langle 0 | \phi _1 ( x) \phi _2 ( y ) | 0 \rangle = \frac { 1 } { i } \ frac { \delta } { \delta J_1 (x) } \left ( \frac { 1 } { i } \frac { \delta } { \delta J_2 ( y) } \right ) Z [/eqn] where [math] Z [/math] is the generating functional for the interacting theory.

Woops, that last line should be:
[eqn] \langle 0 | \phi _1 ( x) \phi _2 ( y ) | 0 \rangle = \frac { 1 } { i } \frac { \delta } { \delta J_1 (x) } \left ( \frac { 1 } { i } \frac { \delta } { \delta J_2 ( y) } \right )^2 Z [/eqn]

wolframalpha.com/input/?i=sqrt(2)/(sqrt(2sqrt(2)+3)) - sqrt(6-4(sqrt(2)))/(2*sqrt(2)-3)

How does this simplify to 4? I don't have Wolfram Alpha Pro account so I can't see how they done it.

If I'm reading Apostol, is there any reason to read Spivak after finishing Apostol? Also, what to read after Apostol? Rudin?

How easy is it to describe an irregular, natural surface as a function, Veeky Forums?

Was thinking about how integral calc can be applied to physical scenarios. For example, say you've used sonar to map the bottom of a lake, and you want to calculate the volume of water in it using integration.

How do you turn that sonar data into an integrable function?

Not really. But if you're getting stuck on something in Apostol, try looking it up in Spivak. And if you need more exercises, again, try Spivak.

>what to read after Apostol? Rudin?
Yup. Apostol also has a real analysis text, if you'd prefer that.

I don't really have any experience with this kinda stuff, but I think you would evaluate the integral using other, numerical methods. You wouldn't try to come up with a function to describe the height of the water because it would be too complicated to evaluate.

I see thanks. Also, there are some exercises in Apostol that is not starred that I find quite hard so I skip them, but I keep wondering if I should try until I was able to resolve them. It's okay for me to skip them for now and try them later on when I feel like I can do them? I'm used to easier textbooks so never had to skip exercises until now.

pastebin.com/8mB8XeQz

That's really up to you and what your goals are. Personally, I don't think it's necessary to solve every single exercise, especially in Apostol where he gives you a wealth of material to practice on. I would do as many exercises as I need to in order to feel comfortable with the concepts. If I'm spending a reasonable amount of time on a problem and I still can't figure it out, I'll skip it, and if I remember to, I'll come back to it later. But I would persevere as long as I can, maybe up to a few days.

But that's just me. I don't have a ton of time to devote to mathematics, so I don't try to learn absolutely everything. If you want to become a mathematics mastermind, then maybe you do want to do all of the exercises. Depends.

I want to have a solid foundation in Calculus to take harder subjects like Real Analysis without suffering too much on it.

Make sure you at least give all the hard problems an honest shot (meaning let it sit for at least a few hours, preferably at least a day or two). The hard ones are what are you going to build up your skill.

That said, if you don't get it, you should try to find a solution somewhere, either in the manual or by googling (google the whole problem, or maybe just the part you're stuck on. Stackexchange already has answers for most of your undergraduate questions).

There's nothing wrong with seeking help if you've already tried and failed. It's better than just leaving the question as something you don't understand.

Yeah, I don't just ignore it. I really for some time and when I see that I don't know how to do it after trying everything I know, I skip it. But will search for a solution(or some hints to solve it) now, thanks user.

Are there any self-inverse functions (i.e. Involutions) from the Riemann Sphere to itself (alt: from C without 0 to itself) which is continuous and has no fixed points?

I really try for*

Someone can help me for this ?

Hey everyone, i am currently in a first semester course called experimental physics, it's all about kinematic, dynamic, basic stuff often backed up by simple experiments.
I know that there will be a rather random test tommorow and i suspect it will have differential equations again.
Any idea what type of differential equations i can take a look at in before?

is this as rings, groups,modules...?

Maybe you are thinking about this?
[eqn]x^Ty = x \cdot y = |x||y|\cos (\theta)[/eqn]
You can start reading more about that by searching dot product.

Thank you, man.

Uh, sorry. Finite abelian groups

finite? did you mean to write Z/mZ and Z/nZ?

This is where it first comes up. You can really tell that it's the end of term and I did less work that I should have for this final part of the module..

In the previous thread (), I asked the same question, but I didn't feel like I explained my concerns fully.

I mostly want to know where I can input the function and find all the points listed.. I've tried some sites like

desmos.com/calculator
fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--

but they don't quite work as well as I want to. They're very fiddly and don't show the points in the (x,y) format as a list.

If the dimension of your space goes down, it's a projection. In general,

en.wikipedia.org/wiki/Projection_(mathematics)

>In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).

Assuming [math]x^T[/math] is a row vector, you have a projection of your space onto [math]\mathbb{R}[/math]

310 > 300 so if it's over 310 it's over 300.

What does my statics prof mean by this?

The answers for both are either integration, subtracting, or adding.
Maybe I am overthinking this.

Please help, thanks.

If trillions of years from now, at effectively the head death of the universe, if you were on the last planet orbiting the last star, what would the night sky look like?

Would it be black?
Or would you still be able to see the echoes of the universe?

And this too pls k thx

It would be completely pitch-black because there's no more energy.

Also the last "planet" would be practically formless. And you wouldn't exist.

I watched this video on youtube and now I have a stupid curiosity question, because i'm stupid.
>youtube.com/watch?v=CVL99yIB3NQ

What is the speed of the air going into a vacuum such as in the video?

He also said 300 is equivalent to the bump limit.

In the second part of the question, where they want you to determine the mass that needed to be bleed off, can someone please explain why they use P_1 to determine the m_2?

Why did they use P_1 twice?

I was going to do

delta m = m2-m1 = P_2V/RT_2 - P_1V/RT_1

A higher Young's modulus means reduced toughness, right?

lmgtfy.com/?q=how do i crop an image

is sci-hub down?

downforeveryoneorjustme.com/

Do you guys have any resources on how to study effectively, and more importantly, how to take good notes?

I just cannot stop procrastinating, I'm 22 and I could be doing so much more with my life if I could just write down a schedule for personal studies and stick with it, I don't want to turn 40 and wonder what I could have studied and understood in my youth. I already feel so far behind.

Is there any good software for note-taking and/or making a study schedule?

if you just need the function to be continuous, then identify the Riemann sphere with the unit sphere [math] S^2=\{(x,y,z)\in\mathbb{R}^3: x^2+y^2+z^2=1\}[/math] and consider the map that takes (x,y,z) to (-x, -y, -z)

"How much" math can you learn in the time-span of 4 weeks if you invest for example 8 hours a day in it? Can you cover Calc 1-3 for example in this time? Complete LA on University level?
What's your guess?

Yes. Just do it.
Make It Stick, The War of Art, A Mind for Numbers are great books. Anyway, just start.

Thank you.

If you can learn a fuckton of math course in math55, I guess you can learn cal 1~3 in 4 weeks using that time.

M^(-1) x I M = x I

>don't know what math55 is
>google
>Math 55 is a two-semester long first-year undergraduate mathematics course at Harvard University, founded by Lynn Loomis and Shlomo Sternberg
>Shlomo Sternberg

f(z)=-z

Supposedly, the hardest math course in USA. This shit even has a wikipedia page.
"In 1970, this demanding course covered almost four years worth of mathematics classes in two semesters"

>tfw such a brainlet I'm probably going to fail calc 1 that was over 16 weeks

;_;

whats the science behind the health of the sperm in your ejaculation?

is there any known relation between say 'quality of sperm' and time since last ejaculation?

What is an electron's energy?
I'm aware of the macroatomic analog, temperature, but with a single hydrogen atom there's nothing to allow the electron to vibrate.

Also, what causes an electron to have energy levels?

>what causes an electron to have [finite, bounded] E levels?

it is bound to a proton, and it can only have distinct energy states described by the hamiltonian. when it is free, it has infinite energy levels.

i don't know how to answer what an electron's energy is

it's kind of tricky because we only arrived at the math because we saw it experimentally. i dont know if we have a real answer for why the electron has energy levels other than because the math says so and because it can be observed.

Kek

>math
>hard

Pick one and only one

Problem is that whether or not a real answer exists, ability to find such an answer is the same since for every person who will give you a real answer to something complicated, there's a hundred who will give you the "the math says so" explanation.

is there a way to make a healthy homemade alternative to energy drinks/coffee?

Yes. Guarana. Get some guarana powder and mix it with orange juice. Best coffeine you can get in a healthy way. Energy drinks ar emaking you fat and your teeth bad. Coffeine kinda as well. Guarana is natural coffein.

>guarana powde
See for example
amazon.co.uk/Sevenhills-Wholefoods-Organic-Guarana-Powder/dp/B00AO1UYL0/ref=sr_1_1_a_it?ie=UTF8&qid=1480918488&sr=8-1

thanks

if you brush your teeth immediately after drinking an energy drink does that prevent the associated tooth decay?

Brushing your teeth is just removing the plaque and sticking food parts out of your mouth.
I'm not a dentist but I would assume it's varying from your teeth properties, how much you drink and keep in check that your dental enamel is weakened after consuming energy drink. So your'e brushing enamel off what's basically the only thing protecting you from caries. Its the same like not brushing immed. after drinking orange juice.

So in short: Just drop the energy drink and try out Guarana. In the long term healthier and cheaper.

you should not brush immed.* after drinking such things

You should watch the docu.
youtube.com/watch?v=6uaWekLrilY

You might reconsider consuming a lot sugar after that

...

well in the end all it is is math

orbitals don't exist and we only keep them around because they are convenient to chemists

real QM computations/functions don't even use orbitals and can approximate the energies of any atom or molecule to any desired degree of certainty, essentially to perfect exactness

this is what the math does, while our imaginations can only go so far.

bump for answers.

We can blow the vacuum? (not false vacuum)
Blown up by vacuum energy detonation

You will need: some means of extracting huge amounts of energy from the vacuum.

Method: Some scientific theories tell us that what we may see as vacuum is only vacuum on average, and actually thriving with vast amounts of particles and antiparticles constantly appearing and then annihilating each other. It also suggests that the volume of space enclosed by a light bulb contains enough vacuum energy to boil every ocean in the world. Therefore, vacuum energy could prove to be the most abundant energy source of any kind. Which is where you come in. All you need to do is figure out how to extract this energy and harness it in some kind of power plant - this can easily be done without arousing too much suspicion - then surreptitiously allow the reaction to run out of control. The resulting release of energy would easily be enough to annihilate all of planet Earth and probably the Sun too.

Earth's final resting place: a rapidly expanding cloud of particles of varying size.

Why do you need to split the region?

How come the shit they teach at uni classes is completely different from the notation used in most resources online?

For instance I'm taking a numerical fluid dynamics course and the general differential equation used is fine to understand, but when I look up Navier-Stokes for instance on wikipedia, its completely greek to me. How come? Why dont they all use the same notations and shit?

What the fuck is flux?

I've learned that it's ∫F•n ds, but I'm having trouble understanding the geometric interpretation of it... Does flux (in 2-D) go outside of a boundary, or through it?

Thanks Veeky Forums!

What the fuck is flux?

I've learned that it's ∫F•n ds, but I'm having trouble understanding the geometric interpretation of it... Does flux (in 2-D) go outside of a boundary, or through it?

Thanks Veeky Forums!

>Hard
>Always

Wiki is your friend, pleb:
en.wikipedia.org/wiki/Flux

Thanks for the link! I think it helped clear some confusion, but I have a bit of a question:

So is the Surface Integral for Flux the flux in 3-D (liquid going through a surface), while the Line-Integral for Flux could be thought of a as a liquid expanding outward/inward ?

You can think of flux through a line as for instance water spilling onto a table, then you measure the amount of water that passes a line per second, since the water on a table has almost no thickness, so you can approximate it to be two dimensional.

You can also just say that if you have a 2D vector field, the flux through a line is "amount of field" through the line per second.

this is such a good picture

When is something a hypothesis in Natural Deduction?
For example the argument E |- F->E
The proof is:
E
-----
F
E
-----
F->E
Where E on line 3 is a hypothesis. Where does it come from and when should you know when to use one?

I need to find the volume of the sphere x^2 + y^2 + z^2 = 9, bounded by z=0 and z=2. Preferentially using a double integral. I'm having problems with the limits of integration. Can someone help me?

At a constant P(O2), the blood's oxygen saturation curve is inversely proportionate to its temperature. The skeletal muscles will contract to generate heat, which warms up the blood and allows for more oxygen to be distributed to the tissues.

I know that shivering has something to do with skeletal muscle movement to warm up the body. Is the aim of shivering what I described, or is it a different mechanism?