/sci/ - Science & Math

In game theory, I understand why mixed strategies are represented like {(a, b);(c;d)] but how come pure strategy Nash equilibria also have to be represented in the same way? Can't they just be given as the initial value? I don't get why they're always like (1, 0) or (0, 1) either since the lecturer never explains anything, what's the deal with this? Thanks

Im going insane over this stupid question, and I know the answer is gonna be trivial, but please help me out:

Let [math] \mathbb{R}^n [/math] be a vector space (with [math] n \geq 2[/math]), with [math] e_1, ...,e_n[/math] being the base of [math] \mathbb{R}^n [/math].
Now there is a [math] w = (1,1,...,1)\in \mathbb{R}^n [/math] and i need to show that [math] w-e_1,...,w-e_n [/math] is also a base of [math] \mathbb{R}^n [/math].

How do I show that every [math] v = \sum_{i=0}^n a_i e_i [/math] can be expressed as [math] v = \sum_{i=0}^n a_i (w- e_i) [/math]?

>>10138222
One way is to show that each standard basis element e_i can be written in that way.

>>10138222
just let [math]a_i = (\frac{b_iw}{e_i}-b_i)[/math] for any b_i in K?

Can somebody show me an example of a hypercentral group (i.e. a group G with an infinite upper central series such that the limit of the series is G)?
None of the sources I can find online actually give any examples of these.

>>10138253
Any abelian group should be a trivial example

>>10138253
>>10138308
Oh, you want an infinite series. Hmmm

>>10138308
The upper central series of an abelian group is trivial. That's why I asked specifically for one with an infinite series, i.e. a group that is hypercentral but not nilpotent.

>>10138253
The group of permutations of the naturals.
S_1, S_2, etc.

>>10138253
Any inverse limit of nilpotent groups (such as p-groups) will do. E.g. infinite matrices over F_p with finitely many entries nonzero.

>>10138325
(provided that the nilpotency class is unbounded, that is)

>>10138222
>>10138222
[math]w[/math] could be nigh-arbitrary and it would still hold. In your particular case:
let's call your new basis [math]\{b_j\}[/math],[math]w_j[/math] being components of [math]w[/math] in the original basis
[eqn]\sum_{j=1}^n w_jb_j=\sum_{j=1}^n (w-e_j) = nw - w = (n-1)w[/eqn]
Thus, you can express [math]w[/math] in your new basis as
[eqn]w=\sum_{j=1}^n \frac{1}{n-1}b_j[/eqn] and express your [math]e_j[/math] as [eqn]e_j = -b_j + w = \frac{-n+2}{n-1}b_j+\sum_{k\ne j}^n \frac{1}{n-1}b_k[/eqn]. The rest is re-shuffeling sums now that you expressed each [math]e_j[/math], but you're done basically.

>>10138325
>infinite matrices over F_p with finitely many entries nonzero.
I don't think this is even a group, unless you modify the definition. You need an infinite diagonal to have an identity.
Maybe finitely many entries in each column?

>>10138347
Sorry, yeah, that should say that each matrix is invertible and acts as the identity on everything outside of the first n rows and columns.

>>10138361
Except...those groups aren't nilpotent. Never mind.

>>10138357
pls hlpe

>>10138345
on a sidenote: what I meant by nigh-arbitrary was that
[eqn]\sum_{j=1}^n w_jb_j=\sum_{j=1}^n w_j(w-e_j) = \left(\sum_{j=1}^n w_j \right)w - w = \left(-1+\sum_{j=1}^n w_j \right)w[/eqn] is only an invalid construction if
[eqn]1=\sum_{j=1}^n w_j, [/eqn] in which case we found a nontrivial representation of [math]0[/math] and are done.

where does /sci/ get their physical textbooks from? obviously i know of abebooks and amazon, but is there anywhere cheaper and more academically oriented? i dont care about the condition or if the books are falling apart as long as theyre cheap

>>10138426
I use isbn.nu to find all the cheap books

>>10138378
>>10138345
im thankful for the help, but seeing this task on a linear algebra testing sheet as the simplest task makes me wonder if that is really what im supposed to do lol
still thanks bud

How do you study operational topics? I mean stuff where you have to make calculations. Yes, you solve problems, but do you use a textbook? Do you solve past tests? What do you do if you can't solve any? How often do you do it? What do you do when you make a mistake? Do you solve lots of problems before your exams, or do you focus on solving some problems every day?

>>10138575
The required notation makes it seem way more complex than what's actually going on. It makes sense for it to be the easiest question.

In reality all you are doing is applying the fact that the basis of a vector space is a maximal linearly dependent set, or also a minimal generator for the space.

>>10138377
do all the interesting looking problems. if two problems are very similar, dont do one of them. if you want to do better in your exam, do more exercises in the book. if you want to learn physics better, get a better textbook on whatever subject you're covering

>Let [math]f\in\mathcal{L}[a,b] [/math] and [math]\{A_{n} \}_{n=0}^{\infty} [/math] be pairwise disjoint and measurable subsets of [math][a,b][/math]. Prove that [math]\displaystyle \int_{\cup A_{n}} f = \sum \int_{A_{n}} f[/math]

I know that [math]f = f^{+} - f^{-}[/math], so it should suffice to show that [math]f^{+}[/math] and [math]f^{-}[/math] are integrable over each subset.
I'm thinking that [math]\displaystyle \int_{A_{n}} f^{+} = \int_{A_{1}} f^{+} + \int_{A_{2}} f^{+} + \dots = L < \infty [/math] (similarly for [math]f^{-}[/math]) since [math]A_{i}\cap A_{j} = \emptyset[/math]. This step I'm not sure about.
Then, since I know both [math]\displaystyle \sum \int_{A_{n}} f^{+}[/math] and [math]\displaystyle \sum \int_{A_{n}} f^{-}[/math] converge,
[math]\displaystyle \int_{A_{n}} f = \int_{A_{n}} f^{+} - \int_{A_{n}} f^{-} = \int_{A_{1}} f^{+} + \int_{A_{2}} f^{+} + \dots - \int_{A_{1}} f^{-} - \int_{A_{2}} f^{-} - \dots [/math]
[math]\displaystyle = \int_{A_{1}}\left(f^{+}-f^{-}\right) + \int_{A_{2}}\left(f^{+} - f^{-}\right) + \dots = \sum \int_{A_{n}} \left(f^{+}-f^{-}\right) = \sum\int_{A_{n}} f[/math]

>>10138815
should be [math]\cup A_{n}[/math] where applicable.

>>10138815
You know, people have the bad habit of invoking theorems when they don't need to, and invoking the definition when they don't need to. But mostly the first one.

>>10138831
hm?

>>10138839
The measure function on a union of disjoint sets is the sum of the measure functions.

>>10138851
Yes, but I'm assuming I have to show this explicitly.

>>10138857
Yes, but showing that first and using it as a theorem is cleaner.

>>10138871
Perhaps so, but I'm curious as to the validity of my original attempt too.

>>10138877
It works, yeah.

>>10138885
Thanks, based and redpilled.

>>10138890
why are you pretending to be me? utter cretin.
>>10138885
thanks, I'll consider your way as well.

>>10138896
Why are you pretending that I'm pretending to be you? This is me: >>10138815

don't know what kind of autism you have, but it's pretty annoying.

>>10138928
You used inspect element.

>>10138165
I started university and my math teacher is fucking brainlet.

anybody can recommend me books for fundaments of math pls?

If I have an object moving in an ellipse, and I know the circumference of the ellipse and the speed, how do I find the (x,y) coordinates of the object at any arbitrary time?

>>10138974
post your syllabus.

>>10138983
Introduction to Mathematical Logic
Introduction of set theory
Real Numbers
Real functions
Complex Numbers

>>10138987
Abbott's analysis might do the trick.

>>10138994
thx anon

meant to post >>10139206 here.

I'm the idiot from >>10136951, I think I finally got it but now I have a question about the solution.

It is easy to prove that [math] f(0) = 0[/math], and also since the function is differentiable in 0, I know that [math] \frac{ \partial f(0)}{ \partial v } = Df(0) \cdot v [/math] is the directional derivative of v in 0.
[math] f(v) = \frac{ \partial f(0)}{ \partial v } = Df(0) \cdot v [/math]
[math] f(v) = Df(0) \cdot v [/math], where Df(0) is just a vector in a dot product, and that means that f itself is a linear form.

But my question is, I never really used that the function f was differentiable everywhere, I just needed differentiability at the origin. Am I fucking up somewhere?

How do you get used to this sort of thing? I can't do them on my own yet and I have to work through them with the answers, I just don't intuitively get extensive form/normal form conversion at all. Is there some way to understand this sort of thing easier?

I have to break down Black Peppercorns.
The strongest acid I can buy is household hydrochloric acid.

Will that be enough?

How best to show that given [math]f:[0,1]\to\mathbb{R}[/math] defined by [math]\displaystyle f(x) = \begin{cases} n(-1)^{n} &, \frac{1}{n+1} < x \leq \frac{1}{n} \\ 0 &, \text{otherwise} \end{cases}[/math] is Riemann integrable on [math][t,1][/math] for [math]t\in (0,1)[/math]? Is there any way I could use Lebesgue dominated convergence theorem?

Trying to show that given a sequence of lebesgue measurable functions with [math]\lim_{n\to\infty} \int_{a}^{b}f_{n} =0[/math] that [math]\liminf_{n\to\infty} f_{n}(x) =0 [/math] a.e.
Is it safe to assume [math]f=0 = \lim_{n\to\infty} f_{n}[/math] a.e and try to apply Fatou?

I know that for symmetric matricies, eigenvalues are real and eigenvectors are orthogonal. Are there any special facts about eigenvectors if for a square matrix [math] a_{ij}=-a_{ji} [/math]? And also for lower triangular matrices?

>>10139410
eigenvalues are on the diagonal
>for triangular matrices
sorry dude, best I can do

Lets go Dumb question!!
Why in machines the infinite make back forward the system?

>>10139345
Whats n supposed to be?
Just a given constant?

Then it is pretty much obvious, the function is continuous almost anywhere and bounded, thus it is Riemann intolerable on a compact set, or am I missing something?

>>10139359
>Is it safe to assume [math]f=0 = \lim_{n\to\infty} f_{n}[/math] a.e
This is an even stronger claim then what you are trying to prove, or am I missing something?

LetT(n) be a function such that T(n) =T(n−1) +T(n/2) +O(n^2000) and T(1) = 1.

Show how T(n) = 2Θ(logn2).

>>10139410
Lower triangular matrices are just like upper triangular matrices. Skew-symmetric matrices have imaginary eigenvalues and their (complex) eigenvectors are also orthogonal

I just need a straight answer.
Can 500mg amoxicillin cure gonorrhea?

trying again

Should I go for math master or theoretical physics master?
I want to work with physics but I also want to learn lots of maths that can be used in physics. (including group theory)

>>10139762
Physics. Math is easier to learn on the side, and physics nets you access to computer simulations and stuff.

so if you have a 3x3 lower triangular matrix of all 1's, is the set of all eigenvectors a line? The problem asks to find three linearly independent e-vectors but I'm only getting (0,0, a), is the problem wrong?

I saw a formula that went something like

Πzi = Πri [cos( Σ φi) + i sin (Σ φi)]

What kind of math is this? When is it normally taught in school?

>>10139881
It's just multiplication of complex numbers. I learnt it when I was 16.

>>10139884
Alright, I see. I stumbled upon it and it seemed familiar so I was debating whether I had done it in high school or it's some scary hard math.

Where do I even start with this? I know energy level in a 3D infinite well is given by E=(n^2_x+n^2_y+n^2_z)pi^2hbar^2/(2mL^2)
But where do I go from there as I am completely lost.

>>10139280
how did you get [math]f(v) = \frac{ \partial f(0)}{ \partial v } = Df(0) \cdot v[/math]

>>10139345
You mean f to be the limit of that sequence of functions as n tends to infinity?

Every asshole in STEM is getting into machine learning, biotech and other hot subjects. Are there any niche fields of science that aren't overcrowded yet still in-demand?

>>10138165
How the hell am i supposed to find the awnser to these questions without memorizing them?

>>10139920
The energy of the photon emitted is just E3-E1 and you can calculate the wavelength from E=hv.
You can try out some combinations to see what the energy levels are, there's a good visualization here: http://www.physics.csbsju.edu/QM/square.13.html

When i need to solve the compound inequality where

V<-2 AND v<4

I need to write the solution in interval notation so the awnser imo would be:

(-∞ ,-2] but according to the awnser sheet it should be (-∞ , -2)

why do you not use the bracket at -2?

>>10139840
The only eigenvalue of that matrix is 1. If it had three linearly independent eigenvectors, they would span R3 which would make it the identity map. So its eigenspace must have dimension 1 or 2.

>>10139993
>without memorizing them?
Or using my calculator.

I would like to know how to do this on paper instead of blindly using a calculator

>>10139998
This ] bracket means -2 is included, this ) means it isn't. So if it was v <= -2 it would be the first one

>>10139993
See pic related.

>>10140031
Oh thats way less complicated than i thought.. thanks man

>>10140008
>on paper
If you have compass and straightedge, you can draw a triangle with the given proportions and measure it.
Otherwise....
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Infinite_series

>>10139969
Using the definition for directional derivatives at 0, I got
[math] \frac{ \partial f(0) }{ \partial v} = \lim_{h \rightarrow 0} \frac{f(0+hv)-f(0)}{h} [/math]
[math] \frac{ \partial f(0) }{ \partial v} = \lim_{h \rightarrow 0} \frac{f(hv)}{h} [/math]
Differentiability at 0 implies that the partial derivative exists, and so the limit must exist (and thus be unique), and also implies continuity (so I can evaluate the limit through a sequence). Then, I should be able to find the limit by analyzing h through a particular sequence that also tends to 0. I chose the sequence [math] (x)_{n \in \mathbb{N}} = ( \frac{1}{2^{n}})[/math]:
[math] \lim_{h \rightarrow 0} \frac{f(hv)}{h} [/math]
= [math] \lim_{n \rightarrow \infty} \frac{f( v/2^{n} )}{ 1/2^{n} }[/math]
And using the property I'm given about the function (n times) I can just
= [math] \lim_{n \rightarrow \infty} \frac{f( v ) /2^{n}}{ 1/2^{n} }[/math]
= [math] \lim_{n \rightarrow \infty} f(v) [/math]
= [math] f(v) [/math]
But then again, I just end up using differentiability at 0, and not everywhere

Does every linear transformation have an adjoint? Is it unique?

>>10140084
Yes. Rudin's Functional Analysis, page 93:
Suppose X and Y are normed spaces. To each T in the space of linear transformations from X to Y corresponds a unique T* in the space of linear transformations between X* and Y*, that satisfies <Tx, y*>=<x, T*y*>.

>>10139985
Mathematical biology

>>10140117
Isn't that boring as shit and glorified computational biology + a lot of statistics?

>>10140008
think that sin is the function that plots your y coordinates when you imagine yourself walking on the unitary circle counterclockwards, and project your position on both axes
sin(0) and sin(90°) become obvious, sin(45°) is you forming a square whose diagonal is 1, while for sin(30°) you slap >>10140036 such that its height is one axis and that the unitary circle circumscribes it

>>10140124
Ok that makes is clearer, thanks!

What exactly is computer science? Like if you were to find a job in the CS field, what are you doing? Just programming? Why couldnt you just become a software engineer?

>>10140163
get the idea that all of CS is just programming out of your head right now

>>10140190
So what exactly do CS people do?

>>10140274
code monkey

>>10138165
Does this synthesis make sense?

>>10140546

>>10140274
Write blog spa with angular and php.

>>10140546
Not sure how well that cross coupling would work, but it makes sense
you could probably do it in a kumada way, for which you would only have to use the grignard, that would save you a step

>>10140573
I think the triple bond is too unstable...would you have any idea how to do this synthesis?

I'm really stuck on it. I think you have to do something with Grignard and epoxides, but Idk the exact steps. Could you draw out what you think?

>>10140573
>>10140587

>>10140590
>>10140587
the second one is pretty clumsy and kind of dumb, but it should work
I hope you can figure out the reaction conditions for yourself

>>10140632
Thanks anon!
>I hope you can figure out the reaction conditions for yourself
I'm trying to, but can you at least tell me how you just formed the epoxide in the first reaction?

Also, what did you do the OH to make it OR? Did you just protonate the alcohol and the Oxygen is suppose to be negative? Or was it suppose to be OH the whole time?

Thanks so much for help anon

>>10140642
Also, I made a dumb for the first one, you could probably also do it the first way you proposed, if you brominate the cyclohexane and then eliminate,you will arrive at the bromocyclohexene we need for the cross coupling which makes the whole cyclohexyne business a moot point

>>10140642
>how you just formed the epoxide in the first reaction?
you would use some peroxoacid for that transformation, something like HCOOOH or mCPBA

>Also, what did you do the OH to make it OR? Did you just protonate the alcohol and the Oxygen is suppose to be negative? Or was it suppose to be OH the whole time?
No, I would introduce a protecting group(which I just called R), in order to avoid the competing reaction of the deprotonated alcohol attacking the epoxide(in the grignard step)
For this, I would use some silyl protecting group like TMS or TBS

>>10140649
>if you brominate the cyclohexane and then eliminate
cyclohexene* of course

I'm trying to solve this problem using only the laws of logarithms (no chain or product rule allowed), and I don't understand what to do with ln(e^-3t). The first part ln(t^3) is easy enough, its 3/t, but I don't know what do when (t) is in the exponent.

>>10140649
>if you brominate the cyclohexane and then eliminate
If you do an elimination because of antiplanar addition, then wont you just end with the same cyclohexene?

Can you explain exactly what you mean? Thank you again!!

>>10140652
look up the definition of a logarithm

>>10140649
Not that anon, but you are using this protecting group after you protonate the alcohol?

>>10140652
Separate it into a difference of natural logs ln(t^3)-ln(e^3t).
Remember, the derivative is just one over the thing inside, multiplied by the derivative of the thing.
You get 1/e^3t * 3e^3t, or rather just 3.
The answer is (3/t) - 3.

>>10140652
Anon you better be fucking memeing me.

>>10140683
Anon you better also be fucking memeing me.
ln(t^3)-ln(e^3t)=3ln(t)-3t ln e=3ln(t)-3t.

>>10140683
Ahhhhh, OK, I get it now, thanks.

>>10140693
>>10140690
The whole reason I'm doing this stuff is to brush up on my reasoning, algebra, logarithms exponents before I start calc.

>>10140694
Calculus isn't wizardry or anything, relax.

>>10140667
>If you do an elimination because of antiplanar addition, then wont you just end with the same cyclohexene?

yeah, I'm stupid
if you really want to do it the cross coupling way, you could get the 1-bromocyclohex-1ene another way ,but I think the second way is much easier

>>10140677
>but you are using this protecting group after you protonate the alcohol?
that's a good point, dehydration with acid might get a bit messy there
you might actually want to think about which protecting group you use, or do the dehydration in a different way (perhaps make the OH into a triflate or tosylate and then use base)

>>10140652
Just remember that ln(x) = log\/e (x)
Any logarithm is f(x): log\/base (x) = a
f^-1(x) : base^x = a
So what does composing these two functions do?

>>10140632
how do you add a bromine to the cyclohexene

What is discrete math? Is it like calculus? Is there a calculus difficulty level equivalent for discrete math?

>>10140632
what did you draw this shit in anon?

>>10140775
NBS that shit buddy boyo

>>10140793
Discrete math is number theory.
It's different from calculus. In Calculus, you can draw things out from the definitions without much effort, while proofs in number theory require some creativity. It's usually harder than calculus.

>>10140809
yup, this
radical bromination

>>10140802
chemdraw

>>10140810
Where does one usually start? Is there a specific class for undergrads?

>>10140632
>>10140809
>>10140812
Sorry, I'm the other retard anon, how did you go from the bromine to MgBr, and the epoxide to the alcohol as well as MgBr to alcohol and alcohol to the final product?

Suppose a new spam filter can detect a spam message correctly with probability .99. However, it also tags a non-spam message as spam with probability .02. If 30 percent of the traffic to your mailbox is spam, what is the probability that it will tag an incoming message as spam?

>>10138650
thanks anon!

>>10140837
Unsolvable.

>>10140841
I misread your question, sorry.
The message has a 0.3 chance of being spam, and 0.99 chance of not making it through. The other 0.7 has 0.2, so it's 0.3x0.99+0.7x0.2=0.437 according to my calculator.

>>10140845
This anon is right except the other 0.7 has 0.02*

So answer is 0.3x0.99+0.7x0.02=0.311

>>10140845
>>10140847
Thank you anons. Follow up question, an incoming message is marked as spam. What is the probability that it's actually spam?

Actually spam is .30, marked spam is .311.
So, is P = .30/.311 = .9646?

Is it normal to feel like you're a fucking idiot, despite constantly being told otherwise?

>>10140632
How would you do the second synthesis without leaving groups?

>>10140886
No, I wish I were better and smarter because they're the same.

Is Grad School worth it? When should one consider grad school?

>>10141114
>>10140381

>>10141116
I was thinking Masters rather than a PhD

Why is this wrong?

>>10141217
they won't be as horny

>>10138165

DID YOU KNOW?

The United States' 50 states are divided into exactly 3141 counties and county-equivalents. 3141 is equal to [math]\lfloor 1000 \pi \rfloor [/math]. The above count includes things like the Parishes of Lousiana, Virginia independent cities etc, and excludes D.C., Puerto Rico and so on.

I'm going to fail an Advanced Calculus course with Baby Rudin.

We're six chapters in right now.

How do I recover after a blow like this, I'll have to wait until next fall to retake it because it's part 1 of a 2 part sequence.

I have a rare autoimmune disease and commute to university. I overdid myself and I come home so tired I can barely study from chronic fatigue issues. Lesson learned and am taking an easier schedule next semester to accommodate this. I wanted to push myself and I did. I finally hit my limit in terms of scheduling.

within the past couple days, someone posted an image with a greentext stitched together outlining how they were working with a 6(?) year old boy to get them to enjoy math and their method. Involved getting rid of screen time, multiplication table up to 20 and a bunch of other stuff.

Does anyone have this image? I meant to save it and can't find it again

How the fuck do siphons work, bros
I need answers

Why don't we just harvest lightning for energy?
>it's a lot of power!!!
Transformers exist you can just put a kilometer of wrapped coil to lessen the charge that you distribute to a storage warehouse. Or hell why even transfer it? Why not store that energy from plasma (lightning) to plasma and have plasma energy storage? Am I retarded? It seems like plasma has a lot of energy in it so you could just use it as storage for high amounts of energy.

Two gamblers each toss a six sided fair die. The gambler who rolls the lower score pays that many dollars to the other gambler. For example, if gambler A rolls a 3 and gambler B rolls a 5, gambler A pays 3 dollars to gambler B. If there is a tie, no money exchanges hands. Compute the distribution of gambler A’s winnings (losses are negative winnings) from this game.

can someone explain jealousy to me and what causes it?

i don't think i've experienced the emotion post grade school and i just can't understand jealous individuals and why they are so bitter and vindictive

Is this as simple as taking [math] x = \frac{2}{\pi} [/math] and [math] x' = \frac{2}{3\pi} [/math]. Then set [math] \delta = \frac{4}{3\pi} [/math] which gives us the desired result?

>>10141460
Uh. The pressure in a container depends on height. Gravity and vacuum suck shit from a high pressure to a lower. Siphon will stop working when height of two containers becomes equal. Now someone can call me a retard and give a hopefully less retarded answer. I doubt it.

>>10140820
yes, it's usually discrete math / discrete structures / intro to proofs / intro to higher level math
sometimes it's split into intro to number theory and combinatorics, since those are generally the two main sections
the typical discrete math class covers introductory mathematical logic, sets, and proof techniques, basic elementary number theory and modular arithmetic, combinatorics, (discrete) probability theory, and graph theory.
some classes also do a bit of algorithms and orders of growth, if the class is a little more applied.

>>10141322
rudin is a meme

>>10141889
you don't get to pick delta. it says "for any delta > 0". you want x and x' to be in terms of delta.
you're on the right track though!

>>10138165
any thoughts on this? These all look to be strong nucleophiles, and the halide is on a secondary carbon
The left reaction is a E2 reaction, because EtOH is a base, and right side is SN2 because I-

Is this correct?

>>10141912
so am I gonna get some nasty arcsin bullshit here or am I doing it wrong?

Does anyone have the /sci/ major guide meme?

>>10140793
>>10140810
It's not only or even primarily number theory, it also involves combinatorics and other things that are relevant to computing.

What's a good book/resource for an introduction on Stochastic processes?

>>10142046

>>10142447
https://4chan-science.wikia.com/wiki/Mathematics#Stochastic_Processes

>>10140793

Does a^n * b^n make ab^n?

So -1 * (1 - n)^-1 = -1^-1 * (1-n)^-1 = (n-1)^-1 ?

I need to find out the amount of irradiance at a given coordinate per day, what would be a good way of doing this?

http://solarelectricityhandbook.com/solar-irradiance.html
Similar to what this has, but without using actual meteorological data? I can choose a single coordinate to make it easier, and this is assuming a flat surface (horizontal to Earth) From a first principles approach, would taking an average expected (per hour) and reducing due to the angle (plus all the other deductions) form a fairly reasonable estimation? I'm a little stuck as to how, by using coordinates, I can come to number per day? (due to the yearly rotation)

brainlet here, the gen chem lectures (Berkeley) are no longer working. whats the next best thing to watch?

I need some ideas for a biology presentation I need to give next month. It's a very entry level course and I think pretty much anything would do, but I'm looking for something interesting.

I know this is broad, but it sort of can be.

This is basically a google question but IDK how to word it properly:
I've got 8000 cells in excel, but I need to sum all of them (chronologically) into groups of 20. How can I easily do this?

>>10138165
what happens when you read all of the books anons?

https://www.ohmsha.co.jp/english/manga.htm

>>10142929
The only ones I could see you actually learning from are the linear algebra, statistics, regression, calculus, differential equations and bayesian statistics ones, because those are all pretty trivial subjects.
So you'll know that much. Maybe the immunology one is also somewhat good.

How much global warming is due to waste heat, not the greenhouse effect?

>>10142626
Have you tried reading your book you fuckin brainlet. Or asking your peers/professors?

>>10142929
I found one of these in my school library. It’s not that good for learning a subject. It was fun to read, though. It’s basically just a story and inbetween they teach you something.

Can someone explain how they simplify the root of 52 to the root of 13 by dividing by 2?
I mean how do i do this without a calculator?

>>10143051
We can decompose 52=26x2=13×2^2.
sqrt(52)=sqrt(13)x sqrt(2^2)=2 sqrt(13).

>>10143068
ohhh jesus, thanks man!

This is an especially stupid question. How do I factor 0.03x^3-4.5x^2+225x+250 without using a calculator or pic related? The rational zeros theorem doesn't seem to help (or I'm using it wrong).

>>10143086
>This is an especially stupid question
>I ask how to divide a sqrt by 2 one post up

>>10143086
You don't, suck it up and solve hyper-baskara for the roots.

>>10143088
Lol that's what this thread is for

>>10143091
Did the source material just want me to whip out a calculator real quick? I figured practicing factorization was part or the exercise

>>10143103
Maybe it expects you to use Newton's method.

What do you name this compound?

CH3-CH2-O-CH2-O-CH3

>>10141217
because all the elephants are dead after they get the tusks removed.
Cant pass on the anti poach gene

Why is x=-256 wrong when x^0.25 =-4 ?

>>10143185
I wanted to ask why my calculater says -4^4 is -256, do i throw this thing in the trash or what

>>10143193
I'd throw it.

>>10143185

x^0.25 equals the forth root of x

You can't take an even root of a negative number, because any number multiplied by itself an even number of times is always positive
>>10143193
Now try (-256)^0.25 and if you don't get Math Error, then yes, throw it in the trash.

>>10143193
>>10143217

Also, I gotta add that you have to use the parenthesis if you want to calculate that because if you input -4^4 the calculator evaluates

-(4^4) which is clearly -256

Any idea how to calculate the speed of a small wooden boat that has a certain velocity, but the person in it starts moving opposite to the boat's direction. I'm supposed to calculate the change in boat's speed. I have no idea where to even begin.

>>10143226
>>10143217
Thanks, i think i might be retarded.

>>10143231
No wait, he moves in the boat's direction. But that affects the boat's speed. Still don't know how to solve though

>>10140826
in case you are still looking for the answer:
the reaction of the bromide with elemental magnesium in ethereal solvents yields the grignard reagent(MgBr), the epoxide to alcohol step is a simple nucleophilic substitution in which the grignard attacks the carbon of the epoxide and you have an alkoxide leaving group
the reaction from the alcohol to the product can be done in multiple ways, simple dehydration with a strong acid might work

>>10143231
>>10143234
Conservation of momentum

>>10143270
>Conservation of momentum
Thank

>>10142702
how long do you have to present? last year i did a short presentation on poisonous mushrooms, others did certain animals (seahorses, jellyfish, lions), some did genetics and diseases. whatever interests you.
i think mimicry is a good theme, you can add a few images and easily engage with others to make them find the animal and such.

>>10143231
The boat's velocity shouldn't change. Think about reference frames.

>>10138165
So I have a test about EM plane waves and I dont know a shit what all these variables mean. Anyone haves a summary with all the formulas so I plug them in the test and forget about it?

Im trying to determine if a series converges or diverges. An (read as "a sub n") is 1^n/(2n-1)

So the series is Sigma 1^n/(2n-1) where n starts at 1 and goes to infinity.

This would be really easy if I could view this as a p-series of the form 1/n^p where p is a constant. What I dont know is if it is still a p-series if you have 1/2n^p

I am pretty sure you can add or subtract a constant from the denominator and still consider it a p-series, but I dont know if you can multiply by a constant as well.


TLDR: is the series 1/(2(n^p)-1) considered a p-series where p = 1? what about 1/2n^p? What about 1/(n^p)-1?

>>10143402
>What I dont know is if it is still a p-series if you have 1/2n^p

Multiplying a series by a nonzero constant (in this case 1/2) doesn't change whether it converges or diverges.

>>10143419
cool, thanks.

Why did some fucker call imaginary numbers imaginary when they clearly exist?

>>10143426
Because they're not in the Real set. What's the opposite of real? Imaginary.

The MikTEX server seems to be down and I really need to install a package. Is there some other way to get them?

>>10143426
>"clearly exist?"
define existence

>>10143483
define "define"

>>10143489
They are actual numbers that work. You can graph phasors with them and imaginary implies they dont exist.

One of my exercises is to compare the topologies T1, T2 on [-1,1] where T1 is the topology with subbasis C={[-1,b),b>0} union {(a, 1], a<0} and T2 is the euclidean topology

I got so many questions on this. The closed interval [-1,1] must be open with the euclidean topology because that's the set on which we have the topology, and on a topological space (X, T) T must have the null set and X, but how do we construct [-1,1] with open balls? Also, what's the topology T1? It seems like every open interval can be constructed with unions of intersections of elements of C, along with [-1,1]. What about semiopen or closed intervals? Am I missing a way to construct them?

>>10143132
however stupid the article is, you've topped it
your reply literally gave me -30 iq points

>>10141954
you're doing it wrong
the idea is: close to 0, the sin function is going to go up and down a lot, faster and faster as you approach 0. In particular, these correspond to peaks of the sin function. Given a delta, you want to go close enough to zero so that you can find a peak and a trough of sin that are less that delta from each other. Since they take the values +1 and -1 respectively, they have distance 2 between them.

>>10142600
yes

>>10143086
The rational zeros theorem would only tell you if theres a rational zero, obviously. Other than the cubic equation, there is no way of finding zeros, other than numerically. You can always graph it and check where it's zero, given that trying rational root theorem on a monster like yours with hundreds of divisors is gonna take ages.

>>10143232
>think
you are, bucko

>>10143451
how would you like my fat package in your mouth, bitch

>>10144003
For starters, T1 is not Hausdorff. There are many ways to show this, but the easiest would be to use: If X is Hausdorff, then every singleton {x} is closed. In T1, {0} is not closed since every open subset contains 0.

They are both connected and compact.

I don't see what you want to "compare", or why you're looking for open balls.

How the fuck do I draw a tanx graph/wave in excel?

I used the same method for sinx and cosx (both of which came out fine) but I get this shit...

How the fuck does undergraduate research work? A professor offered me some research for next semester and it will count for some academic credit. Is this any different from my friends who help out in labs but receive no credits? Since it counts for credits, will I not be a "real" research assistant but simply taking another course? Am I through with this lab after the semester is over, or do students usually stay in the same lab during their whole university experience? And what do people actually do in a lab? I'm so fucking confused.

>>10144143
Compare which is coarser.

>>10144202
well clearly every set in the subbasis of T1 is open in T2, so T2 is finer

>>10144143
I'm looking for open balls because T2 is not a topology on [-1,1]. If it were I could construct the whole interval [-1,1] union-ing open balls.

>>10144212
Not every set, since [-1,1] is open in T_1. But yes, I ended up with T2 being finer, my confusion isn't there.

>>10144215
When it says, [-1,1] with the Euclidean topology, it means implicitly with the subspace topology, when considered as a subset of the reals. Hence, every open set in T1 is of the form:
>[-1,x) with -1< x <= 1
>(x,1] with -1<= x < 1
>(x,y) with -1<x<y<1

And YES, [-1,1] is OPEN in [-1,1]
>>10144223
>>10144223
>>10144223

>>10144226
(x,y) with -1<x<y<1
Wait really? How do we construct (1/3,1/2)? Am I missing something?

>>10144236
>>10144226
shit I meant T2

>>10138165
Is first semester physics supposed to be a class where the average on tests is about 60%? Or is the professor at my uni for it just really hard? I am in an engineering club at my uni and a lot of really smart people in that group say they had to retake the class because the professor is so difficult. It's the first semester physics class and he puts super theoretical things on the exam that he doesn't go over in class. For the midterm he doesn't have a study guide. You arent allowed a formula sheet even if the test covers a lot of topics some of which he literally just covered a day or two ago. He just says everything from this chapter to this chapter is fair game for the test. I spend hours each day studying and I have a 5 in classical mechanics on brilliant and even I'm not getting an A in his class. He even admitted he couldn't get 100% in his own class. Why are professors who have such a high fail rate allowed to teach that class? I'm not saying it should be a cake walk but its pretty ridiculous the things they get away with.

>>10144244
Yeah that makes sense, we didn't get taught subspace topologies yet though so I got confused. Thanks for the clarifications.

>>10144251
>no country
check
>no university
check
>no syllabus
check
>no distribution/variance
check

How the fuck do you expect anyone to answer your stupid fucking brainlet question, you fucking retard?

And what do you expect, that every class should be there for easily getting As? I know american education is a joke, but complaining that it is hard for you to literally get the top fucking mark is insulting to humanity

>>10144259
that's dumb.
asking that question without learning about subspace topologies is as stupid as asking if two spaces are homeomorphic without having learnt about continuity

>>10144271
That's what happens when you're bored to lecture and make students study and present the lectures along with exercises.

>>10144265
I did say that the first test had a average of about 60%. I got 86% and the highest was a 90%. I am not saying it needs to be an easy A. But not telling us what will be on the exam and then the topics he does have he asks really theoretical questions about is kinda ridiculous. And yes I'm from America. We have a booming economy and there isnt really a reason to make it overly difficult. This isnt India where you need to be the next coming of ramanujan to become an engineer but yet for some reason they still shit in the streets and only have a handful of nukes but that's besides the point. I'm not bitching about economic institutions and the bootstrap theory here. I'm talking about this first fucking semester physics class were the tests look nothing like the lecture or the homework and where even the professor himself admitted he couldn't get a high A in his own class. No study guides. No hints as to what might be on the exam. Has really theoretical stuff on the exam. Theres a reason there is a whole class for statics. Mechanical engineers have to learn only the basics of electricity but for an electrical engineer to learn about electricity we have to do all this shit that only MEs will ever use? What the fuck is that about?

>>10144265
He doesn't even let us keep our tests. And the exams have typos. A lot of typos. I talked to other students doing the same course and they are doing great.

What's the negation of a proposition like this one?
[math] \left( \exists r_0, \dots , r_n \right) P(r_0, \dots , r_n) [/math]

>>10144379
For all (r_0,...,r_n) NOT P(r_0,...,r_n)

>>10144316
>I did say that the first test had a average of about 60%
I'm in the UK and I've sat tests where the average was about 30%, but obviously curved upwards. I have friends in Spain and Germany where most people failing is the average.

>I got 86% and the highest was a 90%
so what are you complaining about?

>But not telling us what will be on the exam
What, you want him to tell you the questions? You already said
>He just says everything from this chapter to this chapter is fair game for the test.

>We have a booming economy and there isnt really a reason to make it overly difficult
I dont think you understand what the university is for, nor the reason why degrees are worthless

>This isnt India where you need to be the next coming of ramanujan to become an engineer
Yeah, because you face actual competition at admissions and every step of university. Universities now foster the idea that everyone should do well and get high grades, and entry is a joke. You just have to show that you're willing to pay the incredible tuition, and if you don't get in there's 300 more universities looking out for your money.

>I'm talking about this first fucking semester physics class
I don't understand why you keep mentioning first semester. You think that because it's the first class you have, it should be easy? In many countries, pass rates for first year are under 50%. He's preparing you for second, third, fourth semester physics, and he's actually giving you a challenge.

>tests look nothing like the lecture
Why don't you look at previous tests then?

>No study guides
I still don't know what a study guide should be or why you should be guided to study

>Has really theoretical stuff on the exam
I'm failing to see what could be "theoretical" in first semester physics, and I don't see how computational anything could be other than literally telling you to plug in numbers to equations

>...
The rest (and the previous too) is just so stupid I'm gonna stop right there

if male patern baldness is caused by clogging of the hair follicles with keratin, isnt it possible to make a liquid that disolves or dilutes keratin?

I'm learning integrals and I'm supposed to find the area between y=tanx and y=2sinx between -pi/3 and pi/3. Can someone explain why this answer isn't 0? I thought on the -pi/3 to 0 interval would give a negative answer and 0 to pi/3 interval would give a positive answer, canceling each other out since sin is greater on one interval and tan greater in the other.

I have a problem that I have to prove that an AR(2) Process Yt=B1*Yt-1 + B2*Yt-2 + epsilon has an expected value of zero, given that it is assumed to be weakly stationary.

I get E(Yt) = E(B1*Yt-1 + B2*Yt-2 + epsilon), or E(Yt)=B1*E(Yt-1) + B2*E(Yt-2), and given weak stationary, E(Yt)=E(Yt-1)=E(Yt-2)=Mu (expected value), so we get Mu*(1-B1-B2)=0. Thus either Mu=0 or B1+B2=1. Can we by some argument say that B1+B2=1, thus proving that Mu=0?

>>10145257

>>10145257
>I sure wonder what the integral of two skew-symmetric functions through two points at equal distances from zero looks like
This is the kind of stuff you honestly shouldn't have to solve.

Why are the mole, Kelvin and candela base units, and why is it the ampere instead of electric charge? None of these are fundamental quantities; they are all composed of and determined by other units.

Especially mole. It's a fucking number. Write it down and use that as the definition.

>>10145393
Convenience. It's far easier to work with temperature at the macro scale by treating it as its own thing than as the vibration of molecules, for example.
Moles also give us some nice round (or close enough that we can round them without much issue) numbers when measuring how many particles of X are in Y mass of something.

>>10145180
yes, try kerosene

We just had this on semester and I'm going to kill myself for not being able to do it, since I've done a lot harder examples on my own, yet this simple shit made me fucking retarded, somebody please show me how to do it.

Basically prove with induction that for all given natural numbers, 1^2 + 2^2 + ... + n^2 > ((n^3)/3)

So apparently people had observed sunspots as early as 600BC. How? Isn't the sun too bright to observe with the naked eye?

>>10145606
If n=1, then 1=1/3
You've got the wrong statement, of course you can't do the induction.

>>10145656
>1 > 1/3

what a shocking, outrageous falsehood!

>>10145656

It's >, not =.

if n = 1, 1 > 1/3

>>10145667
>>10145669
Ooooh, it's a larger than sign, I thought you'd mistyped the sum of squares formula.
Can't you just show that one is larger than n^3/3?

>>10145674
Here. https://en.wikipedia.org/wiki/Faulhaber%27s_formula

>>10145677
oh for fucks sake, from all the fucking examples I did and we've done in school, never have we done n^3 and then slice it into n^2 + n.

I don't know whether to hate the teacher or be mad at myself to be honest, I felt really comfortable with my induction skills.

fuck me, so dissapointed :(

>>10145684
Well, you could also have forced it.
n^2>[n^3-(n-1)^3]/3 isn't hard to show, it's just boring.

>>10145606
trivial base case

suppose it's true for all numbers <n

then 1^2+2^2+...+(n-1)^2+n^2 > ((n-1)^3)/3 + n^2 by induction hypothesis

But
((n-1)^3)/3 + n^2 = (n^3-3n^2+3n-1)/3 + n^2 = (n^3 + 3n-1)/3 > (n^3)/3 since 3n-1 > 0 for all n natural

QED

>>10145636
>doesn't know about sungazing
guess how i can tell you're a dumb euronigger

>>10145697
I'm literary pajeet

>>10138165
does time go slower and slower the closer you get to t0 of the universe?

>>10145606
Even simpler solution
The formula to the sum of the squares of natural numbers is n(n+1)(2n+1)/6. From there you can see that you'll get a grade three polynomial of all positive terms with the grade three term having a coefficient of one third.
Add a positive to something, you have a bigger thing than it.
QED

>>10145726
>step 1: know the solution
>step 2: use the solution

>>10145726
the thing is I didn't knew I just add n^2 to the both sides and then go from there on

Is dyslexia real?

So is there going to be an even bigger economic crisis like we had in 2006?
It seems like everyone forgot what happenend.

The housing prices have never ever been this high in my country nor have they ever risen this fast, seems like a pretty obvious red flag to me but all around me people are buying houses or apartments for ridiculous prices with 100% mortage.
What is going on?

>>10146142
Economist here.
If we told you, the crisis would be worse, so it's better if you don't know. Just trust us to do the best we can.

>>10146165
Seems like you arent doing a great job

>>10146181
You thinking like that isn't helping.

>>10146184
How do i make money out of the next crisis?

Physics student taking a course in topology here. [math]S^1[/math] being homotopic to [math]\mathbb{Z}[/math] makes sense because a loop can be wound any integer number of times around the circle. Is there any intuistic way of understanding the appearance of the set of [math]\mathbb{Z}[/math] in homology groups? For example, [math]H_1(K) = \mathbb{Z}[/math] tells me that K has a hole in it, but that is due to the multiplicity of [math]\mathbb{Z}[/math], not due to [math]\mathbb{Z}[/math] intrinsically. Can someone make sense of it?

I'm going crazy over this and I know its really fucking stupid.

Say I have a function like:
[math]I=\cos({\varphi(t)})[/math]
And I want to differentiate w/ respect to time.
[math]\dot{I} = \dfrac{\partial I}{\partial \varphi} \dfrac{\partial \varphi}{\partial t}=\dfrac{\partial I}{\partial \varphi} \omega[/math]
Is the 2nd time derivative this:
[math] \ddot{I}= \dfrac{\partial^{2} I}{\partial \varphi^{2}} \omega^{2} [/math]
or this:
[math] \ddot{I}= \dfrac{\partial^{2} I}{\partial \varphi^{2}} \omega +\dfrac{\partial I}{\partial \varphi} \dfrac{\partial \omega}{\partial t}[/math]

>>10146363
The latter, although omega in the first term of it should be squared. Both I and omega are functions of t, so you have to apply the product rule. The second term is fine, but for the first you take the derivative of dI/dphi to t. Here you would want to use the chain rule again, creating a second derivative of I to phi, but also producing a new omega.

>>10146380
Thank you based anon

>>10138165
>be me
>27
>My younger self was really lazy and unmotivated
>wasted time on video games and hanging out with friends
>didn't learn shit
Is it worth trying to be better now that my prime years of high neuroplasticity are gone?

>>10146328
>S^1 being homotopic to Z
S^1 is not homotopic to Z, it's fundamental group is Z and its homology in degree 0 and 1 is Z, which is something completely different to that.

Homology groups in degree n tell you about how many n dimensional holes there are in your space, and how they behave.

When looking at homology with integer coefficients (what you're doing), the 0th homology tells you about the amount of path components, that is, how many distinct points are there that you can't draw a path between them. The 1st homology tells you about 1 dimensional holes, and S^1 has one "hole". The homology is Z because of the way you build chain complexes. If you were to have homology with coefficients in an arbitrary abelian group G, you'd get that the first homology of S^1 would be G.

You shouldn't think of Z in the same sense as the fundamental group. Instead, look at the exponent of Z. If you had a space with [math]H_0(X)=\mathbb Z^3[/math] and [math]H_1(X)=\mathbb Z^2[/math], then you can exactly say that your space has 3 path components, and roughly two 1 dimensional holes. An example of a space that gives this is if you had an isolated point, and two isolated circles, or two isolated points and a space that looks like an 8. A final example is an isolated solid disk, an isolated point, and a torus (the latter has one hole in the crosssection and another going around it).

But homology doesn't just capture holes, it also captures "twist" or torsion. For example, projective 2-space is defined as the sphere with opposite points identified. Hence, when you look at the equator of this sphere, going around halfway around the equator is actually the same as going around the equator once, so going once around the whole equator is the same as going around the equator twice. This "degree 2" idea is captured in the fact that [math]H_1(\mathbb RP^2)=\mathbb Z/ 2\mathbb Z[/math], and similarly if you had "degree n" maps you'd get [math]\mathbb Z/n\mathbb Z[/math] terms.

>>10146403
Yes. Your "prime years of high neuroplasticity" were already past by the time you were 10.

>>10146403
Yes, but start now before you let more time slip away! Start small too, read 30 mins every day, and then increase the amount you read little by little, kinda like working out, you build your way up. good luck.

My tooth crown accidentally fell off, after 4 years I guess.
Since I moved to other place, I visited nearest dentist and got it put back... But it didn't last at all.
How fucked is it? Considering those ass-handed 'dentists' used UV-curing filler for some reason (I guess it is visible on pic), and had cut crown pretty significantly...
Dunno, it seems just wrong to me, some of filler should be cut, and post (or how this shit is called) will be exposed more, thus there will be more surface for adhesion, and I guess new crown is requires, since this is pretty fucked up now I guess.

(I'm sorry if this pic is somehow disturbing)

>>10145606
Let
f(n)=1^2+2^2+3^2+...+n^2
g(n)=n^3/3
d(n)=f(n)-g(n)
=>
f(n)-f(n-1)=n^2
g(n)-g(n-1)=n^3/3 - (n^3-3n^2+3n-1)/3
= n^3/3 - n^3/3 + n^2 - n + 1/3
= n^2-n+1/3
d(n)-d(n-1) = (f(n)-g(n))-(f(n-1)-g(n-1))
= (f(n)-f(n-1))-(g(n)-g(n-1))
= n^2 - (n^2-n+1/3)
= n-1/3 (which is >0 for n>=1)
d(1) = f(1)-g(1) = 1-1/3 = 2/3
IOW, d(n) starts out positive at n=1 and only increases, so d(n)>0 => f(n)-g(n)>0 => f(n)>g(n).

helpings

>>10146708
by the way saying "flip bits and add 1" is not a circuit diagram........

>>10138165
I remember there's a paper about how to write papers. Link me to it please.

>>10146428
Thank you, I haven't quite grasped the terminology yet but I should have known that. Does that also mean that if we were to work in an arbitrary group G (the reals, for instance), would the fundamental group still be [math]\mathbb{Z}[/math]? Since the integers actually have meaning here in counting the number of winds.

>>10146734
>>10146734
Are you a CS brainlet?

>conditional flip bits
<b,c,d,e,f,g> xor_bitwise a = <t1,t2,t3,t4,t5,t6>
>carry the one
c_6=a
c_n=c_{n+1}&t_{n+1}
>sum
t_n xor c_n = m_n
s=a

How is this true? If m=n=2, isn't there only 2 functions? n^m would = 4 functions which means either an element in the domain maps to two elements in the codomain or an element in the domain doesn't map to anything which aren't functions.

Am I lower than a brainlet, missing something really simple?

>>10146741
Interested in this too.

Can all non-repeating decimal numbers be represented as a rational number?

>>10147733
Those are specifically the ones that can't be represented as rational numbers.

>If your latex isn't working, it's because your adblocker is blocking it.

how to use with ublock origin on firefox, do I whitelist a certain url?

Is there a name for the equation sin(ax)=sin(bx) where a and b are constants?

I've been working on this problem for an hour now. Not sure how to arrive at the final result. Problem is worded as follows:

The rigid bar is supported by the pin-connected rod CB that has a cross-sectional area of 13 mm^2 and is made from 6061-T6 aluminium (E = 68.9 GPa).

Determine the vertical deflection of the bar at D when the distributed load is applied.'


Using the sum of moments about A, I found the force along the rod to be a 1200 tensile force and using dL = FL/AE I found the deformation of the rod due to stress to be 5.58 mm.

How then do I proceed to get the displacement of D? I tried using law of similar triangles and I might just messed it up somehow but I got the vertical displacement of B to be 3.35 mm and vertical displacement of D to be 6.70 mm.

Anyone else with an interest in Engineering wan to have a go at this?

>>10147839

Correction: I got the force along the rod to be 2000 N tensile. 1200N was the vertical part of it.

>>10147324
As far as I'm aware, homotopy groups (ie the fundamental group) works very different that homology, so you cant "work" with an arbitrary group G. You can do so because in homology because the way you build the chain complex is determined by what group you assign to an arbitrary (singular) simplex, but in homotopy groups, there is no mention of assigning a group to anything. It just so happens that Z pops out for circles.

However, there is Hurwitz' theorem that says that the abelianisation (roughly, turning a non-abelian group into an abelian group by quotienting out the "non-commutativeness" out of it) of the fundamental group is the first homology group with integer coefficients, and it does make sense because both roughly count the amount of 1D circles. It doesn't work in higher dimensional homotopy groups because they dont count how many n-holes there are, but rather, how many ways you can map an n-sphere into your space in a continuous way.

>>10147774
yeah, the 4chan one. You could use the "element zapper" option on ublock to selectively eliminate the ads, so that you don't get ads while still being able to read the latex

>>10147838
a=b since arcsin is injective in its domain of definition

>>10147774
@@||4chan.org^$csp

I have a 4.0 and am a first semester junior.
I've been pretty depressed and unmotivated lately so I will probably get an even 3 gpa or loke a 3.2 this semester.
How bad will this look to grad schools?

>>10147947
I don't think this is the case when you consider the periodicity, and looking at the graphs it's obvious that solutions exist. Numerically I get for example that with a=2 and b=3 x=pi/5 is a solution

>>10147990
You're thinking of it wrong, or the questioner asked it wrong. The equation sin(ax)=sin(bx) means for all x, we have that, then as I said, the only solution is a=b. If you're looking at fixed values of a and b and want to find solutions of x to those a and b, then yes, there are going to be solutions, in fact, infinitely many, since sin is periodic, and you can easily use the identity

[eqn]\sin(ax)-\sin(bx)=2\cos\left(\frac{a+b}2x \right)\sin\left(\frac{a-b}2x \right)[/eqn]
To find when each side is 0, which is obviously at all the zeroes of the cos and sin function on that side.>>10147838

>>10147838
A trigonometric equation?

>>10147838
>>10147990
The criterion is
[math]ax = bx + 2k\pi \lor ax = \pi - bx + 2k\pi[/math]
Which leads to
[math]x = (2k\pi)/(a-b) \or (\pi + 2k\pi)/(a+b)[/math]
Which leads to the same solutions you'd get if you were to use >>10148042's method.

CHEMICAL ENGINEERING QUESTION

If I have an isentropic turbine with known mass flow, input temp, and input pressure, but I'm only given the output pressure, not temperature, how do I solve for work?

I know entropy is the same before and after in these situations. I know the entropy before in this situation, however the output seems to be a mixture and I don't know the quality so I can't figure out how to solve for the final temperature, to then solve for work.

I'm trying to find the distance from the focus to the co-vertex. Using the Pythagorean theorem, I keep getting that the distance is equal to the semi-major axis, but that seems impossible. Am I right or did I fuck up somewhere?

I've been asked to prove that every inner product is differentiable, but I literally have no information. I've seen proofs showing that, but under specific assumptions. Is it possible to show differentiability just using the definition of inner product?

>>10148834
Seems right to me, if I remember my ellipse properties.

>>10148834
no, that's the correct answer
you can take a ruler or a straightedge and measure the two lines if you don't trust the result

>>10148839
Just exploit linearity to show that <x+tv, y>/t has a limit as t approaches zero for any v. I doubt your teacher expects anything too different.

>>10148867
My bad, [<x+tv, y>-<x, y>]/t as t approaches zero.

if i need to burn down a room with thermite, the size of 20x20x8 (yard), how much do i need?

>>10148841
>>10148844
Cool, thanks. Now I need to find the distance (call it r) from the focus to any arbitrary point on the ellipse, in terms of a, b, c, and the angle between a and r.
All I have so far is:
>angle = 0: r = a-c
>angle = pi: r = 2a

>>10148867
>>10148876
I hope that's it, then. I was expecting something along the lines of proving <f(t),g(t)> is differentiable, but that would require information of f and g, right?
Thanks

>>10138165
Why can't you use two curves to generate random values in elliptical curve cryptography?

>>10148924
> <f(t), g(t)> is differentiable for differentiable for differentiable f and g
It's annoying but it's easy.

Can I pull out this X(t)? It's a 2x2 matrix with t the independent variable of the equation. I know matrices aren't commutative, but it's such a pain to have the X(t) there.

>>10149152
No.

How can I show that if a curve intersects all lines tangent to the unit circle, then its convex hull must contain the unit circle? This seems like a pretty intuitive result but I'm having trouble translating it into rigorous math.

>>10149272
If I have a point a, there's at least one secant trough it which touches two points of the curve. Force this result through continuity, and the rest follows.
Tip: consider the points (1, 0), (0, 1), (-1, 0) and (0, -1) of the circle. Their respective tangents are (1, x), (x, 1), (-1, x) and (x, -1).

>>10149272
By contradiction? If the tangent at some point doesn't intersect the convex hull, then the entire convex hull lies on one side of that tangent, and so the tangent point lies outside of the convex hull.

>>10149152
Yeah you can, obviously, since it's constant and just a linear transformation, which is just sums and rescalings, both of which commute with integration. If you had a more complicated thing, like a squaring operator or something, you wouldnt be able to

What are your general ways of studying STEM subjects through exercises ? Like, is the textbook>exercises>exercises you couldnt do>answers/resolution>repeat order any good ? Im a little insecure about my study habits.

Does P imply not not P in intuitionistic logic?

>>10149272
how do you define the convex hull of a curve?

I'm reading Discrete Mathematics and Its Applications (Kenneth Rosen) and half the explanations and proofs go right over my head. Am I a brainlet or is the book bad? Reviews on amazon seem bad too but this is what my university uses and others seem to recommend it.

At this point I'm just memorizing theorems/formulas without knowing why they work because I don't understand the explanations. Here's a prime example. I just googled the inclusion/exclusion principle for a much simpler explanation: just sum the lengths of the sets, then alternate between subtracting and adding the sets of the (2..n)-ary disjoint pairs between the sets.

>>10149418
>At this point I'm just memorizing theorems/formulas without knowing why they work because I don't understand the explanations
If you've gotten to this point, you are doing something wrong. Try reading HOW TO PROVE IT: A Structured Approach, Second Edition

>>10145257
Since the curves invert their placement halfway through the interval at 0, then by default half the integral is negative already, but since part of it is negative like you said, the lower part in the III quadrant becomes a double negative

Picture it like this: whenever you do an integral over a line you're always taking one line over the other. if you chose arbitrarily to integrate the green line over the black one, you'd get a positive result in the first half and a negative result in the other, since the green line ends up below the black one

likewise if you're integrating the black line over the green one, you'd get a negative result in the first half of the interval, positive in the second

since the first half of the interval happens to be negative due to its location in the Cartesian space however, you're essentially getting a double negative (positive) in the first half and a straight positive in the second half

This may seem strange, but you already have the intuition that if a line is integrated above y=0 the result is positive and if it's integrated below y=0 it's negative. just extend that to include the areas between lines, so that if an integral is evaluated over an equation it's positive, and if it's done below an equation it's negative.

>>10149429
too late, exam is tomorrow :^)

>>10149418
im pretty tired so cba reading the explanation, but it really is "obvious" just by looking at the formula:

You have finite sets with possible intersection, and you want to find the amount of distinct elements in total. So you find this by:
>add all the elements |A_i| (with repetitions included)
>fix an i, then remove all the elements in the intersection between A_i and A_j for i<j, so you remove all the repetitions between i and j. You dont count those for i>j because otherwise you would double count. Do this for all elements 1<=i<=n and add them
>But whoops, in this sweeping motion, you accidentally removed too many elements, notably you want to keep those that you removed in the intersections of (A_i and A_j) and (A_i and A_k) that were the same, in particular those in the intersection (A_i and A_j and A_k), so you add all those back
>But whoops, you accidentally added too many elements, in particular, those that were in ...
>repeat until you run out of elements

>>10149442
It's not that I don't understand it after reading a different explanation, I just wonder if I'm a brainlet for thinking this explanation was overcomplicated. It was much easier to understand using a venn diagram for example.

>>10149465
venn diagrams don't constitute a proof

>>10149475
>>10149465
to add to that, Venn diagrams can only accurately represent at most 3 sets. For 4 sets, there are missing intersections, so for arbitrary ones, you can imagine it's not gonna be accurate at all

I tried everything , I gave up

>>10149500
[math]\frac{\partial f}{\partial x}= 4e^x-e^y[/math]
[math]\frac{\partial f}{\partial y}=-xe^y[/math]
[math]\frac{\partial^2 f}{\partial x^2}=4e^x[/math]
[math]\frac{\partial^2 f}{\partial y^2}=-xe^y[/math]
[math]\frac{\partial^2 f}{\partial xy}=-e^y[/math]

So the critical point is when the first 2 equations are 0. Note the [math]e^y[/math] cannot be 0, so we get [math]x=0[/math] from the second. Substituting this into the first equation, we get [math]4e^0-e^y=0\iff y=\log 4[/math]. Now the Hessian at the point [math](0,\log 4)[/math] is the product of the third and fourth equation minus the fifth squared, all evaluated at that point, notably, [math]4\cdot (-4e^{\log4})-(e^{\log 4})^2=-64-16<0[/math] so it is a saddle point.

I think you made the mistake to think that [math]e^y=0 \iff y=0[/math]

>>10149513
Thanks a fuckton

So, when I typically find solutions, there are scalar variables, but when I do the problem again (using pic), there are no variables just a very particular solution. What am I doing wrong?

I did it on x'' + 3x' + 2x = e^(-5t).
My intended solution is like: Ae^(-t) + Be^(-2t) + (1/12)e^-5t. The solution looks the same, but there aren't any A and B using pic related.

physics person explain

I have baked a new bread. The new bread is for sale at >>10149752

>>10149481

>this fucking idiot doesn't set up 3D Venn diagrams in CAD

>>10149769
>limiting oneself to 5-6 sets
ishy...

>>10149539
each hump on a line is a tiny little FEDEX package filled with energy

when the packages get to your ear the little deliveryman either rings the doorbell (aaaaa) or knocks (ooooo) depending on the urgency of the rate of packages coming in

>>10149365
Textbook concepts > examples > exercises

I like seeing it done first