/sci/ - Science & Math

is structural bio really just the chemistry of getting a peptide to crystallize in xtalography and the chemistry of getting a "gud ice" in cEM? Or am i misunderstanding this fields?

that sounds boring as fuck

>>10593857
>put sqt and qtddtot in the title
>listed the previous thread
>good spacing
>not a touhou image
I give it an 8/10.

Where can I learn about Andrew wiles proof of flt.

Suppose [math]R[/math] is a commutative integral domain and [math]I[/math] a projective ideal. Show that it is finitely generated as a module over [math]R[/math].

I don't know what to try here - I tried arguing using projective dimension but only get that [math]R/I[/math] is of dimension 1

>>10593891
Read Hida's book (Modular Forms and Galois Cohomology)

what's the difference between an axiom and a law? is axiom reserved for mathematics and law reserved for physical sciences?

>>10593857
I'm trying to derive second order perturbation theory in QM. First order was easy enough, but I've hit a block with second order. So far I've got [eqn] \langle \varphi^0 | H^0| \varphi^2 \rangle +\langle \varphi^0 | H' |\varphi^1 \rangle = \langle \varphi^0 |E^0 | \varphi^2 \rangle + \langle \varphi^0 |E^1 | \varphi^1 \rangle + \langle \varphi^0 |E^2 | \varphi^0 \rangle [/eqn]
So the first term on the left and the first term on the right cancel, we can remove the second term on the right by expanding [math] \varphi^1 [/math] in terms of [math] \varphi^0 [/math], ie [eqn] | \varphi^1 \rangle = \sum_{m\neq n} \lambda_n | \varphi^0_n \rangle [/eqn] So now we should be left with [eqn] E^2 = \langle \varphi^0 | H' | \varphi^1 \rangle [/eqn] Now repeat the same expansion procedure with the right hand side [eqn] \langle \varphi^0 | H' | \varphi^1 \rangle = \sum_{m\neq n} \lambda_n \langle \varphi^0_m |H' | \varphi^0_n \rangle [/eqn] So the only thing that remains now is to find [math] \lambda_n [/math]But I'm not sure how to go about this. It [math] looks [/math] like I'm on the right lines, and I was able to find the first order correction. Anyone got any ideas?

>inb4 mathjax fail

What is a question that deserves its own thread?

can i go straight from BS in comp sci into graduate math? i want to learn graph theory and comparability theory, i havent ever taken a formal linear algebra but ive done the calculus's etc

hi /sci/, what books do you guys recommend for learning basic abstract algebra? should i read herstein or go with something less archaic?

>>10593989
My favorite book in the world is Aluffi's algebra chapter 0. But it's not great for a first course. I think the best thing you can do is look up a set of lecture notes that have problem sets attached from any good university's website. Reading such a basic subject from an encyclopedic book is terrible. You don't want to cover too many things - that comes later. You want something designed to be quick and get to the point.

Find yourself some lecture notes that cover basic group theory that covers the Sylow theorems and perhaps glances at the fundamental theorem of finitely generated abelian groups. Then perhaps another set of lecture notes that covers ring theory and basic module theory. They usually are second or first year courses at UK universities - you could look at Cambridge or Oxford's website - they usually have lecture notes, problem sets and perhaps even solutions available for all to see.

>>10594147
>>10593989
eg:
Group theory
https://courses.maths.ox.ac.uk/node/37471
Ring theory
https://courses.maths.ox.ac.uk/node/37651

>>10593857
simple question for you guys:
i've read many definitions and examples, but i still don't understand completely whats the difference between deduction, induction and abduction.
any trick, definition or example i should check out?

>"F is applied to an object at some angle x below the horizon"

Pic is what the diagram looks like on the book. I'm supposed to find N. The answer on the back of the book says N = mg - F cosx
Is this a fucking misprint? Why wouldn't it be mg + F cosx ??

>>10594532
>below the horizon
>>10593944
An axiom is essentially a definition or a component of a definition, but the structure is a bit wonky sometimes. For example, Euclid's axioms don't immediately resemble definitions, but what's essentially happening is that he's defining an Euclidean plane as a space that satisfies those conditions.
A law is empirical.
>>10593962
>haven't taken formal linear algebra
Would not recommend, you'll be skinned alive depending on the uni. Try reading through Lax's Linear Algebra.

Why do undergrads make such a big fuss about needing to go to top tier colleges? It really doesnt matter

>>10594532
Assume F is below horizontal
The diagram is just generalized/autistic.

>>10594578
grad schools and fortune 500’s make it a big deal. many undergrad educations are just inadequate, the number of classes too limited, equipment subpar, peers not making you more competitive or sharper, and the quality of faculty not high enough to have any sort of skill transfer that’s worth something going into grad school.

Hello, can someone explain what the "Dubs" meme that I've been seeing lately in here?

It is always accompanied with the Batman guy like in the pic.

Thanks in advance guys.

>>10594532
Normal force has to equal the force opposite to it, newtons 3rd law... There is a vertical component added to the mg force assuming the diagram is correct.

my main circuit breaker is a double pole, but the store only has single pole unless I ship and kinda want electricity before two weeks. The single pole still has two spaces for my 220v wires coming into the box, so it should be fine correct?

What's it like doing an undergrad in Electrical Engineering? Given that you're interested in the subject, how rewarding is it and how difficult do you find it? I'm thinking about spending the next year preparing to enter into a STEM degree and EE is currently at the top of my list. I'm already brushing up on my precalc and know a few programming languages (for whatever that's worth). I'm a fast learner and highly motivated -- I also already have BA and MA in the humanities (again, obviously not worth much, but I'm familiar with university life and have a strong work/ research ethic). Any insight appreciated, thanks.

>>10594707
I would say do EE or CS/Math
You seem like you will do fine
Good luck anon

>>10594707
>Given that you're interested in the subject
piss easy otherwise hard

>>10594740
>>10594755

Thank you. Any additional insight of course appreciated

>>10594770
If you're willing to read ahead, show up to class knowing what to expect, and practice with simulations in your own time, EE is very easy to understand. It's basically applied physics, trouble shooting takes some practice but you'll literally be ahead of the curve just by taking the time to read. The math is plug and chug with a calculator online for almost everything, and a simulator for everything else. However, it's different than humanities in that it's much harder to show up and bluff your way through. In that sense, you really need to be interested and self motivated, but there's no exceptional requirements regarding mathematics or any other aptitude.

>>10594147
>>10594155
thanks anon

is brilliantorg any good? someone previously told me that its very basic and doesnt teach you enough

>>10594681
This is nonsensical to me. why is adding the vertical component end up being a subtraction? It’s in the same direction as mg, so if it’s equal and opposite of N it should be the sum of the vertical component and mg, not the difference.

>>10594532
Take a photo from the book. I’m pretty sure that the angle X has a negative cosine

i need help with this general chem hw. where the fuck am i supposed to start. am i supposed to use beers law or something else. please help me im a massive brainlet and i really hate this class

>>10594532
it's actually
N=mg+Fsin x without directional fuckery

>>10594532
What is x? I.e. which direction is x=0?
N = mg - F cosx is correct if x=0 when F is upward (in the same direction as N).

Hey, not sure if I'll get an answer but why not;
I'm working on blackbody radiation, and we use a a mercury and tungsten lamp. When you seperate the consituent wavlengths you get spectral lines from the mercury source, which just represent the energy states of the mercury atoms in the lamp when excited. But when using tungsten it emits a continuous spectrum. Whats happening on the surface here thats different from mercury excitation? It doesnt make sense if tungsten would have so many energy states. Thanks

In a million years Earth stays identical or almost identical to how it is right now.

Would it be possible for a species to develop language and culture that rivaled ours? Or will we always be the best species on Earth?

>>10595707
A Tungsten-filament lamp is an incandescent lamp, which emits thermal (black body) radiation. A mercury lamp is a gas discharge lamp. The spectrum of the former is continuous, the latter consists of discrete wavelengths corresponding to the available energy states for the atom.

A gas discharge lamp will also emit thermal radiation, but it's much weaker than the emission due to energy-state transitions, and much weaker than an incandescent lamp using the same power (all of the power consumed by an incandescent lamp is emitted as thermal radiation; for a gas discharge lamp, it's a small fraction of the power).

I made a thread and 4chanX notifies me (ie the thread watcher becomes red) every time someone posts, even if it's not replying to the OP. What feature do I need to turn off ?

Why does the cold make me tired?

>>10596132
Was this the thread?

>>10596199
yes

>>10593857
how fucked am I. I will be taking a 3 quarter sequence in undegrad analysis and algebra at the same time, I do not work, I will only be taking two classes, and I got a B+ in my intro to proofs class that would have been an A- if I had turned in one more homework.
keep in mind I want to get the best grades possible to go to grad school, preferrable A's in both classes

>>10596200
Damn I'm good.

If slope is 2/1, that means that for each x function increases by 2, so we have y = 2x. But then why do we have (6, 24) instead of (6, 12)?

>>10594639
it means you get at least 2 identical last digits of your post ID
it's rare and the more same digits you got it gets more and more rare

>>10596249
>implying y=2x is the only function with constant slope two
>implying we can't change the function by adding or subtracting a constant while preserving the slope
>implying y=2x even passes through either of those points

>>10596249
because y=2x+12 and not 2x

>>10596258
sorry bro im a beginner
i see it could be y = 2x+12, but is this the only one or there are more?

>>10596263
For any two points there's only one line.

>>10596259
oh k then
silly questions

>>10594964
answer me pls some1

>>10596351
from what i've heard, it's alright but you don't really learn much. Just tricks and stuff. It's much more worth to spend your time reading a textbook and doing exercises

Satistical mechanics question. Why does the density of phase space has to depend on the phase space coordinates (p,q) only implicitly through the Hamiltonian in equilibrium conditions?

Pic related: it says so in the book I'm studying from.

Is this kino?

I have to learn point set topology in a week to pass this class, we're using munkres but half the "proofs" take a lot of imagination to even start so I'm unsure how to apply them to the problems without also taking hours trying random shit until something works. Like 53 #2 the online solutions require rotating 180, but the book does nothing like that.
Is that me being bad at proofs or me being bad at topology?

when evaluating an integral, you by nature get terms that look like [math]2\pi \left(\left(...\right)-\left(\frac{64}{5}-16\right)\right)[/math]

I've been taught PEMDAS. Why is it that I have to distribute the negative first, rather than evaluate the parentheses and then negate the result? If I don't, I invariably get the wrong answer but it contradicts the order of operations I've been taught.

>>10596603
You have to add 116/5 either way you do it.

>>10595942
>Would it be possible for a species to develop language and culture that rivaled ours? Or will we always be the best species on Earth?
Sounds unlikely; humans already used fire, tools and had ritual burials, etc. a million years ago. We'd see that same kind of behavior in some other species at the very least.
>>10596208
>a 3 quarter sequence in undegrad analysis and algebra at the same time,
>I will only be taking two classes
Isn't this normal in just about any major involving mathematics? You don't sound fucked at all. I'd be comfy as fuck (and perhaps even bored) if I could take just two courses
>>10596603
It should work out fine; you're probably doing something horribly wrong. Note that if you distribute the minus sign first you'll get something positive; this is why in this particular case it's easier to distribute first. Generally, you should work on a by-case basis

whats the answer to this lads

>>10596518
It looks like bs desu. How is it clear that p^2/q^2 mod 4 = ...?

>>10596711
That’s proved elsewhere. It’s correct, isn’t it?

>>10596711
Suppose the integer z
z
is even. Write it as z=2n
z
=
2
n
, where n∈a
n
∈
Z
. Then z2=4n2
z
2
=
4
n
2
; z
z
is divisible by 4. Suppose the integer z
z
is odd. Write it as z=2n+1
z
=
2
n
+
1
where n∈a
n
∈
Z
; then z2=4n2+4n+1=4n(n+1)+1.
z
2
=
4
n
2
+
4
n
+
1
=
4
n
(
n
+
1
)
+
1.

We have just shown that for any integer z
z
, the square of z
z
, when divided by 4 gives remainder 1 or 0.

Is there some literature on the theory of axioms? Suppose you're setting up an axiomatic system, what is the most elegant way to do this? How to classify equivalent axiomatic systems? Perhaps a quantitative way to measure the "strength" of an axiom (how much can be proven by assuming it)? Stuff like that - I'm just curious because I have (as a physics student) never seen axioms properly discussed as a topic per se.

>>10596724
Yes >>10596711 is assuming you have to prove that again.

>>10596740
Steal Reverse Mathematics online somewhere.

>>10596724
What if q^2 = 0 mod 4?

>>10596753
Then isn’t r undefined? This is the part I was unsure of.

>>10596744
This is exactly what I'm looking for. Thanks for the recommendation.

>>10596758
Why should r be undefined? r = sqrt(2)

>>10596763

Because r is defined as p/q Z\0

>>10596767
So? q^2 = 0 mod 4 doesn't imply q = 0

>>10596518
this is probably one of the ugliest proofs i've seen, and the shitty notation doesn't help. Stop using | to signify "such that". Also 2 mod4 = 2 is meaningless. You either put mod 4 after every quantity or at the end of the sequence of equalities. Then again you have "it is clear" p^2/q^2 mod 4 = {0,1,-1}. This is again meaningless, and wrong. You are confusing integers with equivalence classes of integers.

How hard is this? Let [math]r^2=2=\frac{p^2}{q^2}[/math] with [math]p,q[/math] coprime. Then [math]2q^2=p^2[/math], hence [math]2|p^2[/math], hence [math]2|p[/math] (since prime), hence [math]4|p^2[/math], hence [math]2|q^2[/math], hence [math]2|q[/math], in contradiction to [math]p,q[/math] coprime.

>>10596771
>>10596518
For reference, [math]a|b[/math] is taken to mean a divides b, ie there is some c with ac=b.

If you want to frame it in the language of modulo, you just replace the "[math]a|b[/math]" symbol and replace by [math]b\equiv 0\pmod a[/math].

>>10596781
Thanks. This makes sense.
>>10596771
>Stop using | to signify "such that".
Why?
If I redefine r is the equivalence class, it is true that the mod of any numerator squared will be -1,0,or 1... same with the denominator?

>>10596724
>proved elsewhere.
Can you post the proof of that?

>>10596771
Also, isn't all of this still true if I don't reduce to equivalence classes because of the modulo?

>>10596801
>Why?
because I say so
It's not standard, it's ugly, and it stands for a million different things. It makes your writing unparseable because everything get's clumped together. It doesn't flow, it's jagged and confusing.

If you want to save space and avoid a lot of unnecesary writing, just write the universal "s.t." standing for such that. It's readable and cannot possible be confused with other notation. Especially in the topic you're doing, | stands for divides by almost universally. Sometimes a colon is acceptable when it flows nicely and it does not form part of a sentence. For example, [math]r\in\mathbb Q : r^2=2[/math] in your case. It wouldn't work with [math]p/q:p\in\mathbb Z[/math] because the sentence continues, and again q:p means either a ratio or a quotient in many fields.

>If I redefine r is the equivalence class, it is true that the mod of any numerator squared will be -1,0,or 1... same with the denominator?
i have no clue what you're saying here, but you have to note: once you pass to "modulo", you lose all the information about your number other than its residue.

If p^2/q^2 can only have residues 0,1,-1 as per your proof, then you are indeed correct it that it cannot be 2. But this sort of argument is rather weak, in the sense that it wouldn't tell you much if you were dealing with larger numbers (especially ones that are larger than the modulo you are taking)

>chem 1A lab with unknowns
>found one unknown easily (Beer's law)
>the other unknown seems incorrect, but can't find any errors in my calculations
Do I just call it human error? I've been screwing with it for 4 hours at this point.

How can I get started with finite elements?

Okay help would be greatly appreciated, how do I set this up?

>>10597201
>set up
The volume of a cylinder is given by the area of the base times the height. The area of the base is 25pi. For a volume of 3m^3, we need a height of 3/(25pi).
So 3/(25pi) per minute.

>>10593857
I'm doing a work right now about heat simulation. The professor asked for convergence tests about mesh sensitivity. The thing is, the whole thing is practically isothermic (I don't know why he did this). There's nothing I can put there that will show any convergence with respect to mesh refinement. I tried average temperature on borders, max(T)-min(T) on borders, heat flow on borders, heat in-heat out, a bunch of other stuff.

Is there any test that is suited to this kind of problem?

this is what I absolutely fucking hate about physics...

how the shit did they get [math]T=\frac{F}{2sin\left(\theta \right)}[/math] from [math]sin\left(\theta \right)+Tsin\left(\theta \right)=F[/math]

I can see algebraically manipulating it to [math]T=\frac{F-sin\left(\theta \right)}{sin\left(\theta \right)}[/math] but how they got their result? Fuck if I know

>>10597311
how did you get 3 from 3m^3?

>>10597744
it works if they just made a typo and sin is supposed to be T sin

Is it possible to go to grad school for solid state physics straight from an EE background?

>>10597790
What do you mean lad?
If the cylinder had a height of 3/(25 pi)m, it would have a volume of 3m^3, since it has a base of 25 pi m^2.
It fills one of those per minute, thus it changes the height by 3/(25 pi) meters per minute.

>>10597790
Even though you replied to something with a reply that didn't make sense, I'll answer your question nonetheless.
m=1 solves 3=3m^3

>>10598683
but how can that be a solution when 31^3 is 29791?

Here's my sq: can you refer me to a good primer on number theory? I have never spent enough time on it and would like to become more proficient at it.

>>10598909
Well for one, 3 times 1 is not 31.
And sorry but I don't have anything to refer to

What's the general form of a circumference with center (a,b) in polar coordinates?

>>10598683
>>10598570
>>10597311
okay, I must be retarded, because I still can't picture this for some reason.

>>10598998
polar coordinates are not really well suited for that. You're most likely going to get some elliptical function

>>10599129
here, I always wanted to try this 4chanX drawing tool.
it's crap, but it was fun.

>>10599163
wut
how do you use it?

i just got rejected from electrical engineering and computer engineering. i was wonder if it was still possible to pursue a career in those subjects without the degree in them?

Alternatively, what are some good resources online to teach myself the subjects for the upper courses for the major?

>>10593857
Where should I set my sights for grad school in ECE? I have 3.7 GPA, 98/94 percentile on GRE, but no research experience. I went into the Navy immediately after undergrad

What is the typical paper size for an academic journal?
I'm looking to buy a tablet for marking up PDFs of academic papers and I'd like to buy one that is the same size or even larger than the actual paper would be in real life.

>>10599274
A4, obviously.

>>10599174
You click the little drawing symbol between "No selected file" and "Submit"

This changes everything >>10599292

>>10599278
Huh I thought they were a little smaller. I guess it depends on the actual journal. Thanks for the help.

what to study in college to remove the limits of the brain in learning? computational neuroscience?

>>10599476
gender studies

would I have to use U substitution to find this?

>>10599534
Yes.

>>10599544
>>10599534
okay, I got this far, what do I do next?

>>10599617
replace that last sqrt(x) term with u and then solve with integration by parts

When working with ODEs/PDEs, what exactly determines the difference between a Boundary Condition/Initial Condition? When we're working with physical phenomenons, it's usually that the IC describes the state of the system at the beginning of the time line (so t=0), and BCs usually describe the state at a physical boundary of the system. But when there is no physical context to the equation, what happens? Is any known value at the boundary of the set the equation is defined on considered a Boundary Condition? Can the definitions of Boundary Conditions and Initial Conditions overlap?

I've got two tricky E&M problems that are of particular interest (and that I can't solve), mainly the first:
This one was on an exam. When there was only one infinity of infinite wires I made a harmonic series out of the sum of Biot-Savart equations (which diverges) to prove the fields were infinite in magnitude except at x=0, that doesn't seem to work for this part though. A different method is definitely expected because we don't have to know series for this intro E&M class

>>10600235
This one is Gauss's law but has some peculiarity to it I can't make sense of, thanks in advance for any insight /sci/

Please someone help. I'm tasked with showing that the cocycle φ in pic related is not a coboundary, but I keep getting that it is. I don't see a contradiction

>>10600357
can't help you but just wanna say - nice handwriting

Inspired by this thread: >>10598301

Can anyone explain what I'm doing wrong here? I'm trying to find the complex cube roots of 27, under the assumption they're at 120 degree rotations around a point circle. Every time I try to re-cube the complex solutions, however, I end up with a complex number times 1/2. Where is the 1/2 coming from? Why is there a residual rotation of -60 degrees?
>inb4 just use de Moivre's theorem
Did I mistake, or are complex cubes incompatible with polynomials?

>e^i5pi/6 in the answer
I meant 5pi/3

>>10600357
If that's supposed to be the torus, then all of those vertices are the same.

>>10600456
you are forgetting the coefficients in the binomial expansion, the middle terms should both have coefficients of 3

>>10600698
Fuck, thank you. It's been a while

could somebody give me examples of graphs that satisfy all the following conditions:
a) non-isomorphic
b) contains eulerian cycle
c) isn't an eulerian graph

>>10601206
Why don't you go ahead and show what the difficulty is, captain homework? Give us your examples for a-c, individually, and I might be tempted to help.

>>10600559
i wasted like 3 hours on that fuck my life

The age of a woman when conception occurs is a factor in the chances the child will develop certain birth defects of genetic origin.
I think the age of a man also affects negatively, although maybe not exactly in the same manner.

My questions are:
1) Does this only affect "on/off syndromes" such as Down's, or is it possible the genetic deterioration also affects variables that we consider can be on a spectrum, such as general IQ?
2) Could those defects not only affect the child, but also be passed down on his or her offspring?

That is: if we had two separate populations and one had kids around 20yo and the other population when they are in their forties, and this went generation after generation, and we checked 1,000 years later: would the population that exclusively reproduces in their forties have not only a larger Down's syndrome subpopulation, but also worse health in general?
I guess what I'm really worried about is: would I be condemning my offspring, and the offspring of my offspring, and so on if I wait too much?

>>10601335
I forgot the pic, sorry.

>>10593872
1. Yes, it is.
2. Yes, it is. Friend was realy good at it (as an undergrad) but left it.

>>10594639
I recognise that spaghetti

>>10602079
i literally only posted it one other time on /tv/ like 10 minutes prior and I made it myself

When designing a heat sink how are the boundary temperature and fin surface temperatures related?

Say I worked out a fin design based on the desired surface/boundary temp. How does this relate to the starting boundary temp?

>>10601206
>b) contains eulerian cycle
>c) isn't an eulerian graph
hahaha funny i get it kys

Can someone give me a hint on how to solve this PDE? Thanks in advance!

I need a blanket on some kind to sleep. It doesn't need to be an actual blanket, any covering works, but it does need to be touching my neck/face. Is there any literature on similar psychological hangups?

Im reading a basic geometry exercise. They say an isosceles triangle has x+7 and x+9 as sides. It task you with finding area, perimeter, and all 3 angles. Is that doable? Isnt there info missing?

how do i read this

>>10603785
Where is your trouble exactly? P(n) is the set of those polynomials of order n, whose sum of absolute values of coefficients is between 1 and n.

>>10603807
What does Z[x] mean?

>>10603859
I only know that notation as the ring of a residue class.

Theta is a function that gives the number of significant operations when you use the Karatsuba algorithm to multiply two 2-digit numbers. Or at least, I hope it is. How do I find a closed form for any n? I get that it's a recurrence relation, but none of the standard formulas in my notes fit. You can solve easily when n is a power of 2, but otherwise I'm stumped.

>>10603877
>when you use the Karatsuba algorithm to multiply two 2-digit numbers

Should be "two n-digit numbers".

>>10596263
Im an studying engineering and even im not that rarted

>>10603877
Okay, new question. I plotted the recurrence equation versus n^log2(3) and got pic related. Does this mean there's no closed form? I mean, it kinda looks like the blancmange function.

>>10603764
Don't know of any literature, but I need a pillow (or other weighty object) to lay vertically over my eyes for me to sleep comfortably

Been trying to figure out this. Please help a brainlet understand the solution, and how to get it:
What logical operation (denoted by "op") allows getting on the factors (X and Y) knowing the result (Z), and one of the other factors (X=Y op Z -> Y=X op Z)?

>>10604670
The result of what?

>>10604677
Good question. This is the original question, which I've translated. I can't even understand the question, much less answer it. But some anon here managed to solve it, without giving me the process of how.

>>10604708
Is the answer XOR? Because X = Y XOR Z implies X XOR Z = (Y XOR Z) XOR Z = Y XOR (Z XOR Z) = Y XOR 0 = Y

>>10604725
Yes, the answer is XOR. Could you explain that, but to a complete fucking brainlet? Cheers, mate

>>10593857
How do I calculate how much mass can pull an electromagnet at a certain distance, I have the following data:

Sorry to ask, but I have no idea and just want to know the limitations of this soft magnet.

>>10604733
Well I still don't understand the question I just "solved" the implication given in the brackets.

Suppose that the operation is XOR
Then we are give that
X = Y XOR Z
Apply XOR to both sides to get
X XOR Z = (Y XOR Z) XOR Z
Use associativity of XOR on the RHS to change the positions of the brackets
X XOR Z = Y XOR (Z XOR Z)
Now use the fact that anything xor with itself is 0 to get
X XOR Z = Y XOR 0
Finally, use the fact that anything XOR with 0 is itself to get
X XOR Z = Y

Intuitively, XOR makes sense because it's basically just addition modulo 2

>>10604767
Cheers, lad. I'm self-studying this, and have no idea what I'm doing. Any tips or resources to enlighten myself in this topic?

>>10604813
This seems to be related to digital logic design or something. I'm not an engineering guy though so I can't really give any tips. Maybe look at the sci wiki

>>10604007
If you remove the "odd" case from the equation (removing the constraint that n must be an integer), you'll see that Θ(n)=3^log2(n) satisfies the even case and the base case.

Karatsuba's algorithm is divide-and-conquer; given a pair of n-digit numbers, you need to perform 3 multiplications of n/2-digit numbers. But if e.g. n is 9 you can't multiply 4.5-digit numbers.

The asymptotic complexity is O(n^log2(3)) = O(3^log2(n)). If n is a power of two, then log2(n) and 3^log2(n) are integers. That's where the recurrence relation and 3^log2(n) are equal, as the odd case never occurs.

If you plot the ratio Θ(n)/3^log2(n) (ideally with logarithmic X axis) you'll see a repeating pattern. Note that the ratio peaks at ~1.38; the peaks correspond to values of n whose binary representation looks like 10010101010... . This corresponds to numbers where the odd case happens most often (if the expansion ever ends in a run of 1s then n+1 will end in a run of zeros, resulting in several iterations of the even case, while (n-1)/2 will end in a slightly-shorter run of 1s). IOW, the ratio depends upon the rough "shape" of the digit sequence. Shifting the digits (multiplication or division by 2) has negligible effect.

I just started relearning math from the ground up. You people suggested Gelfand and Lang so I got both and I'm working my way through Lang's Basic Mathematics. I find that he moves quite fast and I've gotten stuck pretty early. Yes, I know I'm fucking stupid. But I'm trying, so give me a break. Tell me the steps to solving these bitches and I can move on. I can't practice this shit if the instructions aren't clear. Anyway, thanks in advance.

mukade

>>10605044
you shouldn't be looking at me telling you the steps to solve them. In that case you'd be learning nothing but the algorithm, which defeats the point. You should understand what the symbols mean and what the theory tells you.

The only thing that you need to know is that multiplication is commutative, that is, ab = ba for any two numbers a,b, you also need to know how exponents work (at least for positive integers), and the fundamental theorem of arithmetic, that any integer is a product of primes.

Why is the field of computer science big pile of gay, boring, monotonous drudgery?

>>10605112
unironically thank you

what's a good way of seeing if an integral will need U-substitution used for it?

>>10605319
if the derivative of the function in the integrand is inside the integrand

Why do affine combinations sum to 1--what's special about this property? Also, how does an affine combination relate to an affine space? Seems to me like the only thing in common is the word affine.

So the Fibonacci sequence is where you start with two 1's and for every next number in the sequence you sum the two previous numbers.

1,1, 2, 3, 5, 8 ...

But is there a name for sequences where you start with N 1's and for every next number in the sequence you sum the N previous numbers?

For example, N = 3

1, 1, 1, 3, 5, 9, 17 ...

>>10605693
> Why do affine combinations sum to 1--what's special about this property?
Any affine combination of vectors lies in the same subspace as the vectors. E.g. if a set of vectors all lie in a plane, any affine combination of them lies in the same plane.

>>10605782
That particular sequence doesn't have a name, but for similar sequences see
https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers

There is a long bar with length A+B which has 4 moving bars: Q,A,B,C. And 3 static bars: 0, (A+B)/2 and A+B.
The bars A and B move away/closer from/to the center the same distance at the same time.
The bars Q and C move away/closer from/to the center the same distance at the same time but never further than half the remaining space between their respective surrounding bars ( Q > A/2 for any A and C < B+A/2 for any B ).
The bars cant overlap or past each other (distances A+B > C > B and Q < A).
The position of the Q and C bars is random within the previously stated boundaries and conditions(the couple of bars A and B have different speed than the Q and C couple).

Which range of values holds true for Y > A?
Which range of values holds true for Y < A?

I have no idea what to do. Is this even algebra?
please help

>>10605816
So does that mean that I get to name it? I'm shit at

>>10606072
*I'm shit at that.

>>10606072
>https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers
its called the n-fibonacci sequence

>>10593857
Where am I going wrong with my attempt for problem 1?

>>10606076
Is my assumption that r=1, correct? I think I’m messing up with the “real” part. Any suggestions?

>>10606075
They dont seem to work like how I described. N-fibonacci numbers are made by adding the previous number to N times the number previously. Unless I'm mistaken?

>>10605159
Trade school degree

>>10606091
sorry, i meant a Fibonacci sequence of order n
The wiki page states that they were already investigated by Mark Barr, if they were going to be named it would be after him

>>10606154
> sorry, i meant a Fibonacci sequence of order n
Right; but that's a category rather than a specific sequence. The specific sequence depends upon the initial values as well as the recurrence relation.

The Tribonacci numbers are a Fibonacci sequence of order of order 3 but the initial values are 0,0,1, resulting in a sequence starting 0,0,1,1,2,4,7,13,24,... An order-3 sequence starting with 1,1,1 would give 1,1,1,3,4,8,15,27,...

AFAIK there's no name for the order-3 sequence starting with 1,1,1 (ignoring any initial zeroes). That page defines the classical Fibonacci numbers as starting with 0,1 (so 1,1 are the 2nd and 3rd numbers), so the Tribonacci numbers are a logical extension of that.

>>10606256
>A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous n elements (with the exception of the first n elements in the sequence).
the starting digits are irrelevant

>>10606256
I guess that's close enough to the sequence I proposed. Regardless of the initial values, I've noticed that the ratio of successive numbers of this Tribonacci sequence tends towards a number (something like ~1.838...) . Does anyone know the exact definition of this number?

>>10606285
Search for "tribonacci constant" in the linked page.

The limit of the ratio between successive numbers depends only upon the recurrence relation, not the initial elements, so the value is the same for any Fibonacci sequence of a given order.

>>10605693
write an arbitrary affine combination, say with coefficients a_0 to a_n, with the "sum to 1" condition. then you can write a_0 = 1 - a_1 - .. - a_n, and you can substitute for a_0 in the affine combinations. manipulate a bit and you will get that affine combinations is actually "a point + linear combination of vectors fixed in that point" which is what you understand by affine subspace intuitively - it's a vector subspace shifted to some point other than the origin.

Let's say I have N cups and M marbles. All of the marbles are put into cups randomly, with repetitions. How do I find the expected value of the number of cups with at least one marble?

let [math]S_n[/math] be the permutations of [math]\left \{ 1,2, \dots n \right \}[/math].
for each [math]a \in S_n\ L(a)[/math] is the length of the largest increasing sub-sequence of [math]\left (a(1), a(2), \dots a(n) \right )[/math]

prove: [math]\sum_{a\in S_n} L(a) = \Omega \left ( \frac{n^{n+1}}{e^{-n}} \right ))[/math]

So i've figured that if i can prove that [math]\sum_{a\in S_n} L(a) \geq \sum_{a\in S_n} \sqrt {n}[/math] then the rest will come from stirling's formula, but how can I prove this?

Why is the ISS not very bright when it's low in the sky? I realize seeing is poor when viewing objects at low elevations because you're peering through much more of the Earth's atmosphere, but I'm wondering if this explains the low magnitude of the ISS when it's near the horizon or if it might have something to do with the angle of the solar panels relative to the observer.

>>10607829
Probably light reflection angles. I don't think you could possibly see its actual cross-section with the naked eye; only its bright glare is visible so if you don't have a favorable angle you won't see it at all.

>>10607824
Maybe try induction on n.

Math brainlet undergrad here in Calc 2. For integration by parts why so some questions only include 1 function within the integral? Example: Integral of arccos(x) is an integration by parts problem I'm getting. Do I set u = arccos(x) and dv = 1 here?

>>10607786
Consider the problem of putting M marbles into N cups with every cup having at least one marble. It's obviously the same as the problem of distributing M-N marbles among N cups, since we can just consider every cup as already having a marble.
Now consider the problem of putting M marbles into N-i cups, and apply the technique from earlier, while taking into account the possible selections of N-i cups.
There you go lad.

>>10593857
What is the minimum grade needed in calculus 1 to be a non-brainlet? What should I expect in calculus 2 in terms of relative challenge?
t. 99% average in calc 1

>>10609153
getting 100% in calc 1 is not indicative of being smart, just saying.

>>10609222
What would the minimum grade for non-brainlet status for calc 2 be, then? If not calc 2, what is the lowest level math course needed to properly screen for brainlet status?

lads for an assignment I'm supposed to put a line of best fit for some data in the form of y= a +b*x^(c). Excel has a "power" LOBF but it doesn't include the "a" term. Any help?

>>10609668
excel fitting is absolute dogshit, save yourself the trouble.

Try a grid search

>>10609668
scipy.optimize.curve_fit

>>10609324
>what is the lowest level math course needed to properly screen for brainlet status
real analysis (equivalently, any course on metric spaces) and abstract algebra

>>10609723
Thanks so much lad, have fat assed azn grill

If x+y=n , how can I prove x*y is maximized when x=y=n/2?

>>10610305
do you know calculus

>>10610310
I took 4 semesters of it, I know I have to set the derivative to 0 but I dont know what to derive.

>>10610310
Oh shit, f = xy =x(n-x)
Then setting f' to 0 will give me x = n / 2.
I'm a fucking idiot. Thank you anon.

Is there any trick to knowing trigonometric integrals other than rote memorization of trig identities and their derivatives?
Jesus Christ it's so fucking convoluted when it comes to trigonometric integrals.

Why do I sleep better with the tv on? (without sound)
I've tried sleeping in the dark for a couple motnhs but went back to sleeping with the tv on, it turns off after a couple hours but when I fall asleep with it on I feel more refreshed, get to sleep quicker and wake up easier does it have something to do with my autism?

The solution to this shit is [math]60.625[/math], but I don't know how to come up with the formula [math]p(x)=\frac{9}{4000}x^2+10[/math], where x is length (here 50) and p is height of the cable. How to come up with that formula?

I feel like this is more of a numerical analysis question than a programming one. I'm trying to perform bicubic interpolation on a set of points (this 256*256 image was generated from a data set with <200 points) and I get weird artefacts at the boundaries of grid cells.

Is this likely due to some silly error in programming or a simple limitation of bicubic interpolation?

>>10610498
You can derive them all quite quickly using Euler's identity. Or, when applicable, simply do the integration in the complex domain.

>>10610315
No need for calculus.
f=xy
=x(n-x)
=nx-x^2
=n^2/4-(x-n/2)^2
This is maximised when (x-n/2)^2 is minimised, which is when x-n/2=0 => x=n/2.

>>10610783
Gut feeling says programming error. How are you choosing the derivatives?

>>10610913
https://en.wikipedia.org/wiki/Bicubic_interpolation

Following that. It could be that I've miscalculated one of the partial derivatives since the error is with the rate at which the colour is changing across cell boundaries, not discontinuities in colour values themselves.

serious question
what causes me to be a pedophile? why do I find young girls with no sexual maturity or ability to reproduce so sexually appealing? I'm not exclusively a pedophile btw, I just like young girls more than others.

Bey guys how the fuck do I find an integral curve of a vector field? I'm in calc III and we didn't learn it in lectures and it's extra credit if we figure it out on our own but my textbook is really not helpful and I can't find any useful videos on the topic.

>>10610931
you might find it simpler to separate it into x,y than to do the whole thing as one step:
float cubic(float u, float p[4]) {
return (u * (u * (u * (p[3] - 3 * p[2] + 3 * p[1] - p[0]) + (-p[3] + 4 * p[2] - 5 * p[1] + 2 * p[0])) + (p[2] - p[0])) + 2 * p[1]) / 2;
}
float bicubic(float u, float v, float p[4][4]) {
float q[4];
for (int i=0; i<4; i++) q[i]=cubic(u,p[i]);
return cubic(v,q);
}

>>10603071
its directly seperable

>>10611090
Nvm I figured it out

Negative area over/under a curve? Does it make sense? I was asked to find the area between the X axis and a function using definite integrals. Looking on a chart the function has more area underneath the X axis than above. Should I express the total area as a negative or positive value?

there's no such thing as negative area you nonce
take the absolute value of the interval beneath the curve

Has bitching and moaning to professors for a better grade ever worked for anyone?
All of my profs tell the class that they won't change any grades, even if it's rounding up from an 89.9 to a 90.

>>10611181
offer coitus

how's my resume? I'm mainly trying to get my first full time job in the space industry (antenna, satellites, telescopes, rockets, etc), both of my "experience" section jobs are summer internships for a well known aerospace company.

>>10610901
The elegant answer

>>10596258
ask me how i know you're a teenager

>>10611222
Why did you write it in Latex, nerd

>>10611271
partially for the fact that you knew it was written in latex just by looking at it, and partially because I used latex for all my formal documentation in school and it just sort of feels more 'proper' to me for something like this

>>10611282
it's a really nice resume

https://www.youtube.com/watch?v=cISYzA36-ZY

>>10610698
Probably mostly just because you grew up with some such sounds as you slept

>>10611222
In your objective, change "...gathering and design of software and implementation..." to "...gathering, design of software, and implementation..."

In your first work experience, say "...time consuming tasks for a client." if you can. Plurality implies a larger project of higher value.

In your second job experience, you say you worked with a team. Maybe consider adding in some leadership BS, additionally, changing the the EXPERIENCE title to WORK AND LEADERSHIP EXPERIENCE. Boomers dig it

Include a references line, you don't even need them on there, just say references available upon request. It makes the recruiter reach out to you if they're actually interested.

Put a period on the end of your last line (ending in "...storage software").

>>10611341
okay. my boss did actually say I could use him as a reference, and told me I took on the roll of leader for that team project and was pleasantly surprised with that / said I did a good job guiding them. That being said I excluded it because it was conditional on the fact that I was the most experienced member on the team and I was already intimate with the process

>>10611355
Never exclude something like that especially if your boss thought you did a good job. It prompts the recruiter to ask about that experience, at which point your boss makes you out to be the second coming of christ.

I've been trying to solve this home assignment exercise for way too long, i just have to clear Z, but can't seem to make it (non native english speaker):

At what points does the equation x4 + y4 + z2 +2xz−2yz +5=0 define a function z = g(x,y) implicitly?

>>10611539
The equation i meant was x^4 + y^4 + z^2 +2xz−2yz +5=0

I still don't understand voltage division, past the basic series example. Why is Va = Vs(R2/(R2 + RQ2), here?

>>10611586
Since the branch with R2 and RQ2 is purely parallel to the branch with RQ1 and RQ3, the other two resistors won't show up in the determination of VA and VB. So, you have (effectively) one loop up VS, down R2, down RQ2, back to where you started. When you have this path, it forms a voltage divider, and you can prove the voltage Va will always be Vs * RQ2/(R2 + RQ2).

You can use this reasoning to remember the formula. If RQ2 were massive, then no current would flow and Va ~= Vs. If R2 = 0 then Va = Vs. if RQ2 = 0 then Va = GND. The simplest formula for Va/Vs that matches all of those properties is RQ2 / (R2 + RQ2)

>>10611608
Thank you very much for the explanation, I'll try and apply this to other problems.

>>10611222
The italics as a heading looks disgustingly bad. Please reconsider putting it bold instead, or some sort of underlining. It's a mess

>>10611539
use the implicit function theorem

>>10610765
The general equation for a parabola is y = ax^2 + bx + c.

The parabola has to go through the point (0,10). So plug in x=0 and y=10:
c = 10

The parabola also has to go through the point (200,100). So plug in x=200 and y=100:
100 = 40000a + 200b + 10
And it also has to go through the point (-200,100). So plug in x=-200 and y=100:
100 = 40000a - 200b + 10

Subtract the second equation from the first to get:
0 = 400b
b = 0
And now we can get a from b:
100 = 40000a + 10
a = 90/40000 = 9/4000

So we have a=9/4000, b=0 and c=10, which results in the parabola:
y = 9/4000*x^2 + 10

>>10609019
I should specify that N > M

>>10593857
How dangerous is liquid nitrogen really? I've heard it is the most dangerous lab chemical. Is this true. Like can nitrogen really kill you in a couple of minutes if you take a deep breath of it? Does it really smell like wine?

>>10608908
Yes

>>10611828
> Like can nitrogen really kill you in a couple of minutes if you take a deep breath of it?
Not breathing enough oxygen will result in suffocation. Nitrogen is particularly problematic because it makes up most of the air, so the body doesn't complain about it. Whereas breathing anything containing a noticeable proportion of CO2 will trigger a panic reflex and gasping for breath (because too much CO2 in your lungs is a symptom of the most common modes of suffocation), breathing pure nitrogen doesn't; you just lose consciousness and die.

>>10611828
Liquid Argon is the real scary shit

Physicsfags answer me these two

Einstein based his theories on the invariance of c, that it is constant and does not change. Later calculations show that light can slow down due to gravity up to not being able to escape the gravitational pull of a black hole. It seems to me that these results violate the second postulate and make the theory inconsistent?

The cosmological model says that space is expanding, which means there is more space between objects or that extra space is being created. According to quantum field theory all space has quantum fields and these or at least the higgs field has some nonzero energy value. If more space is being created and it has an energy value how does this not violate the first law of thermodynamics? Or does the Higgs field energy value go down over time? It seems space and energy are being created out of nothing.

>>10611170
Negative

>>10611978
how fast though? What are the chances of getting revived should you have an accident? I hear that it forms a layer close to ground because cold, so that when someone else comes to pick you up, they go down too resulting in double damage.
>>10611983
how scary?

>>10612033
Light never slows down. The geometry of space around it bends so that it takes longer to pass through that area relative to an outside observer. At the event horizon of a black hole the spacetime is curved enough so that the only possible outward trajectories require superluminous speeds.

Space doesn't "have" quantum fields, the quantum fields reside throughout space. The space is expanding 'under' it, if you will.

>>10611753
Oh thanks, it was simpler than I thought.

Can anyone help me understand Holliday Junctions and branch migration?
This is a graphic from a paper about entropic DNA machines and shows a basic circulatory process whereby the two units of RNA strand on the topside of the substrate are released as a signal and an output using fuel and recycleable catalyst to speed it up.
I understand the first step, where the [math]5[/math] from the catalyst bonds to the [math]\bar{5}[/math] since they are both free. But then why does the [math]4[/math] from the catalyst replace the one from the signal? Apparently they form a holliday junction at the contact line between catalyst and signal, but a) according to everything I managed to find out, holliday junctions always seem to involve two full DNA strands whereas here I only have three RNA strands and b) what forces the junction to move leftwards and why doesnt the signal randomly capture back parts of the 4? Do the junctions always move away from the part added last and only in one direction? That would explain how the reaction behaves, but I dont understand the chemical motivation for that to be the case...

Link to the paper in case anyone is interested: https://www.ncbi.nlm.nih.gov/pubmed/18006742/

The human brain on average weights 3 pounds. What would happen if it started to weight 10-15 pounds?
Does the increase of the weight make us even smarter, or just make us eat more calories?

Brainlet here. How would you define, strictly in set-theoretic notation and using only quantifiers (i.e. no verbal descriptions), the following set:

Given a fixed natural number N, and a fixed natural number K, define the set of all possible products made up of K multiplicands, such that each multiplicand is a prime number (ANY prime number), none of these K prime multiplicands are identical, and each multiplicand is raised to some power, and that power can be any natural number that is strictly less than N.

In other words: Given fixed natural N and K, I'd like to choose any possible combination of K distinct prime numbers, raise each of them to any possible natural power that is strictly less than N, and then take their product. My set should contain all those products.

For example, if N=7 and K=3, then the set should contain all possible products of any 3 distinct prime numbers, such that each of these primes can be raised to any natural power that is strictly less than 7.

How does one define this set rigorously? I feel like a complete retard for not being able to tackle this properly

The threshold for product safety is 1% degradation. At 295 K the time taken for 1% of the
antibiotic to degrade is found to be close to 0.01/ k. Comment on the shelf-life of the drug

How do I answer this?

Is B[i] just equal to the sum of A[1.. n], minus A[i]?

>>10613380
just break it up
P is a set of K distinct primes
take the set of products of elements of P
{ a^k1 * b^k2 * ... | ki < N , a,b,c.. in P}

>>10613380
I'm not incredibly familiar with set notation, but I'd imagine something like this:
[eqn] \{\prod_{i=1}^{K} a_i^{b_i}: a_1...a_K \in \mathbb{N}_P ,\ a_i \neq a_j,\ b_1...b_K \in \mathbb{N},\ b_i < N \} [/eqn]

>>10613599
product, not sum

>>10613638
thanks whoops

if I have two fixed points A and B and a third point C which I move to every possible place, did I cover all possible angles and ratios of sides of triangle ABC and how do I prove it?

>>10613664
>did I cover all possible angles and ratios of sides
this is the same as covering all congruence classes which you clearly did

If I have a population of roughly 8.8 million and want to do a study, say about how informed people are about something. How many people do I need to ask to somewhat accurately have that be representative of the entire population of 8.8mil?
What would be a good sample size for that?

Is it true that engineers graduate on average of 5+ years instead of 4 years?

>>10613746
the program usually is 4 years, but there are some mix programs like engineering management which are 5. Also there is an increasing trend to do a coop year/work term where usually after your 3rd year you work for 16 months which obviously adds an additional year. The goal of this is to make you more hire-able as companies always want experience and they tend to offer special internship programs for those still enrolled so it's a win-win.

(I've taken up to calc II as my background)
Is there any significance/reason/deeper meaning as to why the derivative of a function may be defined where its parent function isn't?
For example, ln(x) is only defined for numbers greater than 0, but 1/x is only undefined at x=0

>>10613961
ln(x) is defined for all non zero complex numbers
if x is positive then for any negative -x
ln(-x) = ln(-1) + ln(x)
take the derivative of the right, ln(-1) is a constant, its i*pi
so
(d/dx ln(-x)) (d/dx -x) = 1/x
d/dx ln(-x) = -1/x

>>10613983
I figured it had to do with complex numbers

I guess I'll have to wait until I get to complex analysis to really understand

>>10613935
>>10613746
there's also the study abroad, community college transfers, double majors, dual BS/MS or BS/MBA, and science/arts to engineering school transfers that typically take 5 years too.

>>10613983
>ln(x) is defined for all non zero complex numbers

No, you need to make a cut say (0,-i*infinity) or enter into multi-valued/set-valued functions or Riemann surfaces

Am confused. Solution says 12 ohms, but isn't it 29 ohms? What am I missing?

>>10611181
Imagine begging to have your score increased by .1 points. Lmao

Can /sci/ find infinitely many *maximal* anti-chains on the poset (ℕ, |)? (That is, the set of natural numbers (excluding 0) equipped with the relation of divisibility)

All my attempts led to failure - either the set I constructed was not actually an anti-chain, or it was not maximal. Would appreciate any tips

ESL here. I need guidance over learning english the academic way.
I'm having a though time writng academic articles in english, things such abstracts or the entire text.
Right now I'm planning to use vocabulary.com to learn new words and textbooks for technical stuff. But I don't know what to do over grammar. What do you guys recommend? Is this plan (vocabulary + grammar) good enough for writing technical texts?
pls respond, everyone ignored me on /adv/

>>10614720
>>10613935
Holy fuck, you're both right. I'm so shortsighted, seriously, thank you two!

I asked this on the textbook thread but got no replies.
Dumb question but seriously, why do people only do odd questions? Like I've seen some solution manuals where they ONLY do odd questions, is there something special about it? What about the even ones?

>>10616127
that's only the case in freshman tier textbooks (most high level textbooks dont even have solutions)

as to why only odd questions in solutions books, simply because it's easier and faster and cheaper. Also because most of those books have hundreds of questions, and they all look and are pretty similar, so there is not much opportunity cost in just doing one half of them. also allows you to do exercises without the allure of cheating by looking at solutions.

>>10616154
oh shit, so that's how it is. thanks bro!

How the heck do they do the circled part? I feel like they're forgetting to include the arclength of the derivative of the parametrisation they're using.

I'd like to write:
[math]\int_a^b L(x,g_1(x))||(1,f'(x)||dx[\math]
as it seems to me they're evaluating a line integral over a scalar function. Please send help.

How the heck do they do the circled part? I feel like they're forgetting to include the arclength of the derivative of the parametrisation they're using.

I'd like to write:
[eqn]\int_a^b L(x,g_1(x))||(1,f'(x)||dx[/eqn]
as it seems to me they're evaluating a line integral over a scalar function. Please send help.

>>10616161
You can make that factor equal to 1. (see https://math.stackexchange.com/questions/751781/how-to-parametrize-a-curve-by-its-arc-length )
Good on you for actually noticing that!

>>10616180
OK, so we're using an arclength parametrisation but still using x as our variable? I'm not used to working with arclength parametrisations (especially with regards to line integrals) since we're so often independent of parametrisation.

>>10613195
It would require vastly more calories and an evolution of the spinal cord, motility and human digestive system that isn't plausible. There's also no evidence that strictly increasing absolute brain mass is what correlates with intelligence, its more a ratio of the brain to the rest of the body mass. If somehow humans grew to be 3-5x bigger its possible that this could happen but I don't see any reason why that would be the case especially since natural selection on humans is so difficult to detect and divorced from the typical paths of evolution that most other intelligent mammals are driven down due to not being able to modify their environment or engage in agriculture.

How do I prove that the circle is the closed curve with least perimeter without calculus? So far I only managed to prove that this curve is convex

>>10616404
Show that it has a ridiculously large group of isometries.

>>10616404
false: consider the curve x^2+y^2 = 0 over the reals. No perimeter.

Also, do you mean least perimeter with fixed area? otherwise i can just pick smaller and smaller circles

Now, with that out of the way, try showing that a minimizing curve must be rotationally symmetric. Then a method of exhaustion-type argument.

However, the circle is intrinsically an analytic object, so you can't really escape calculus, so any proof you give will be either with calculus or a roundabout calculus method.

So maybe I'm just not looking in the right places, but is an uncountable space - an uncountable subspace path connected? It's true if the subspace is countable, but I feel it's not true with uncountable but not sure what the contradiction would be other than "because I said so".

>>10616973
why would it be? What topological space are we speaking about?
How is the interval [math][0,1] \setminus [\frac13,\frac23][/math] not a counterexample to what you're saying?
And the latter is not even true, [math]\mathbb R \setminus \mathbb Q[/math] is clearly not path connected but it's a difference of an uncountable space and a countable one

>>10616973
Do you mean "If a space is locally path connected, does removing an uncountable subspace necessarily keep it locally path connected?"
If so, no, not at all. It's not even true if we're removing a countable set, since we can take the rationals from the reals.

>>10617003
>>10617053
The space is [math]\mathbb R^2 \setminus A[/math] with [math]A[/math] being a countable subset of [math]\mathbb R^2[/math] and with the standard topology, which is path connected, but I'm struggling with if [math]A[/math] is uncountable, is [math]\mathbb R^2 \setminus A[/math] path connected. I was thinking like [math]\mathbb R^2 \setminus [0,1][/math], as not being path connected?

>>10617058
jesus dude, have you thought about, i dont know, actually picturing the spaces?

If you have [math]\mathbb R^2[/math] and you take off, say, the x axis, then you have a path disconnected space with two path components. If you take off, say, the positive x axis, then the space is still going to be path connected (even simply connected, if you know what that is)

Can someone fetch me an Algebra problem? I'm bored.

>>10617074
For any group [math]G[/math], find a Galois extension realizing it

>>10617068
Isn't the "positive x axis" still uncountable though?

>>10617083
you were asking about the uncountable case.

Consider [math]\mathbb R^2\setminus \mathbb Q^2[/math]

>>10617085
That's path connected.

>>10617098
hmm you're right, i learnt something valuable today

>>10617100
I'll add proof of the impossibility of disconnecting with a countable number of points since it's a nice and comfy one.
Assume A contains a point in every line. It can't, since R^2 contains an uncountable number of lines. Then, we have a full line B outside A.
Assume we can't connect a point (a, b) to the line. Then, for every line we trace that goes through (a, b) and a point in the line, it touches a point in A. This gives an explicit injection of the reals into A, which contradicts the countability of A.

Which subfields in physics should one stay away from when entering a phd program?

>>10617079
I've never heard of Galois extension before, so I'm trying to fathom what this means and decipher it.

>>10617119
the ones you don't like, allegedly

Guys, could you help me? I'm probably just too retarded to get it, but I just can't understand what my professor mean in our Calc III book. In a theorem he says something like "we are going to refer to the hessian ([math]Hf_{P}[/math]) and its associated quadratic form ([math]Q_{P}(V)=\frac{1}{2}\langleHf_{P}V,V\rangle[/math]) indistinctly.".
As far as I know, in a quadratic form ([math]Q(X)=\langleXA,X\rangle[/math]), where [math]A=a_{ii}[/math] is given by [math]a_{ij}=a_{ii}[/math] if [math]i\eq j[/math] and [math]a_{ij}=\frac{a_{ij}+a_{ji}}{2}[/math] if [math]i\neq j[/math]. So I don't get how he can refer to them indistictly.

Does this thread accept really basic questions? I would like to ask if someone can explain certain basic chemistry to me, but in simple terms because I'm a brainlet. It's not homework, just things I'm curious about.

What is "information" in the context of the physical sciences. I hear it all the time in pop-sci shit but I have no idea what it's supposed to correspond to. I remember my philosophy of science lecturer had a hot take on it but I can't remember what it was.

>>10617516
Perhaps you should review the theory of quadratic forms. The associated quadratic form of a symmetrix matrix (ie the Hessian) also defines the Hessian itself. That is, if you're given a symmetric quadratic form, then through the so-called polar identity, you can recreate the Hessian. So in essence, you are dealing with the same object.

during esterification, is water formed with the -OH group from the acid (red) or from the alcohol (blue)?

>>10617825
Thingies are made of itsy bitsy thingies called atoms. Two atoms of the same type are mostly indistinguishable except for the number of neutrons it has. A molecule is made up of atoms connected to each other. Chemists take molecules of different types and, by introducing or removing heat from the system force the atoms to rearrange into new molecules.

Software question.
Which are the best free graphing programs?

>>10618557
desmos

>>10618557
Phython/matplotlib
Gnuplot is easy to use but not so pretty

>>10612068
An area can't be negative; it's an absolute unit dummy

ML question (do people know ML here..?):

What's the point in splitting the training up in mini-batches if you're going to train using the entire dataset before completing an epoch? If I'm not thinking wrong, doesn't it become the same amount of calculations anyway?

Pic related from source: http://neuralnetworksanddeeplearning.com/chap1.html

>>10618703
Now, I have no idea about ml or statistics, but wouldn't it be because there might be a bias in the data collection?

>>10618488
First of all, thanks. I didn't ask about what is chemistry specifically, but it was helpful nonetheless

What I want to know is, can anyone give a quick rundown on carbon, nitrogen and hydrogen (uses, properties, the simple relevant stuff)? I know a quick Wikipedia red would give me pretty much all I need, but the language is too technical for me.

>>10618714
No, mini-batches is meant to boost training efficiency, but I don't see how if an epoch is training through the entire set.

For your interest: the bias in the data is dealt with with different forms of regularization methods such as differentiating learning rate.

Is LLN enough to say that [math]g(X_n) \rightarrow g(\mu)[/math] as [math]n \rightarrow \infty[/math]?

>>10618743
Carbon is important because it can catenate, which means that it can form fuckhuge chains of C-C bonds. That's why organic chemistry is such a big sub-discipline of chemistry, because there is a giant diversity of compounds with carbon backbones.

>>10618743
Hydrogen is the smallest element, so it's the one used for fusion.

>>10614748
still confused btw.

>>10618782
>>10618791

Thank you so much!

Help, I am a brainlet

Can someone please help be figure this out

f(x)=x^2-6

Where do I begin and how do I work it out? It wants to know the vertex and axis of symmetry

>>10618946
Vertex is average of roots. It's symmetric around the vertex.

>>10618959
Dude, I seriously have no idea where to even start on this problem. Can you explain how to go about solving it?

I have a question regarding manipulating Taylor polynomials and I have a final tomorrow. Are there series of polynomials that are known/established, and would I have to work from there? Or do they vary, as in sin(x) can have different series across multiple questions? pic related

>>10618946
treat it as an equation, not a graph, look through other problems to find a pattern.

>>10619050
What is the first thing you'd do when you see f(x)=x^2-6? What do you do?

>>10619060
>What is the first thing you'd do when you see f(x)=x^2-6?
If you were to ask me what its axis of symmetry is, the first thing I would do is realize that f(x) = f(-x), because x^2-6 = (-x)^2-6, and therefore it's obviously symmetric around the y-axis.
If you were to ask me what its vertex is, the first thing I would do is realize that f(x) is the lowest when x=0. And the corresponding y-coordinate is 0^2-6 = -6. So the vertex is at (0,-6).
And I might even graph the function to double check: https://www.desmos.com/calculator/81zc3yatig

>>10619060
well, first off it might be easier to treat f(x) as y, so the equation is y=x^2-6. the graph will look kind of like a U shape, right in the center of the x axis

y=ax^2+bx+c is the standard form of quadratic functions, so a=1,b=0, c=(-6)

axis of symmetry is very simple to find in this equation because it obviously isnt moving on the x axis, but for harder problems the formula for axis of symmetry is x = -[b/(2a)]. seeing as b =0, x has to equal 0, x = 0.
I'll do the vertex in another reply

>>10619060
as for the vertex, in this problem it's (0,-6). x=0 because of the axis of symetry, and y= -6 because of the -6 in -6 in the original equation

>>10619045
What do you mean sin(x) having different series across multiple questions? Yeah you can write its Taylor series in a variety of ways if you change where the center is but usually when it comes to expanding out functions in terms of Taylor series of other functions you stick with ones you know. Like in the picture you posted we know what $\frac{1}{1 - x}$ Taylor series is centered at 0, we also know what $e^x$'s Taylor series is and sine and cosines. Most problems I see like this that pop all you end up doing is just manipulating the Maclaurin series of functions.

Redpill me on climate change

>>10619639
When's the last time you saw butterflies, bees, songbirds?
Remember when it used to snow on Christmas, now we get ice rain in the spring.
Remember when it snowed, the snow was almost knee deep and lasted for weeks and months, now it's barely a few inches and melts away in a few days(with the exception of blizzards, but even those are rare).
In the fall the leaves turn into many shades of brown, gold and orange and stay like that for at least a month, now they quickly turn and fall within a week before you can even notice their beauty.
Remember the wildflowers that used to spring on your lawn, now you only have dandelions and weeds.
Climate change may or may not destroy the world, but it sure as shit destroys the beauty of it.