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/sci/ - Science & Math


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9023428 No.9023428 [Reply] [Original]

>> No.9023445

Severe brainlet here.
https://www.youtube.com/watch?v=VmTZcNVzp7A
Watch this video. It's a simple experiment demonstrating how oxygen + hydrogen = water. I'm sort of confused - how does this experiment work? How is water being created here? What's the purpose of the fire - is that to make the chemical reaction happen?

>> No.9023481

any youtube channels on math/sci that people would like to suggest for interesting/basic learning?

>> No.9023517

what can i do so that i can get paid big bucks to learn new math all the time but not have to teach dumbass kids?

>> No.9023532

>>9023428
Epigentics would be favored by natural selection, right? It seems pretty advantageous to me to pass down the proper way to react to certain stimuli with just an interaction with said stimuli.

>> No.9023543

>>9023517
solve the remaining 6 millennium problems 4 years apart.

You will earn $250k/y for the next 24 years

>> No.9023560

What are some simple scientific experiments involving everyday chemical compounds? My intro chemistry course wants me to submit a problem or question that I need to structure an entire project around. I'm feeling uninspired and uncreative right now.

>> No.9023571
File: 29 KB, 800x400, 123.png [View same] [iqdb] [saucenao] [google]
9023571

where does 2/3 come from? in the 2nd to last line?

>> No.9023573

>>9023571
1-1^3/3=2/3

>> No.9023582

>>9023573
is that for the one in brackets? what about the positive 2/3?

>> No.9023587

>>9023582
>is that for the one in brackets?
no, the one in brackets is -2/3

>> No.9023591
File: 25 KB, 1128x400, notation.png [View same] [iqdb] [saucenao] [google]
9023591

>>9023571

>> No.9023598
File: 84 KB, 1191x670, ahkshajhak.jpg [View same] [iqdb] [saucenao] [google]
9023598

What is the simplest possible way to convert direct current into alternating current without ANY moving parts?

This question is really bothering me because all of modern civilization depends on the process but yet nowhere does it actually explain how its done. I am neither a physicist nor an electrical engineer, but I've been trying to teach myself and I think I have a good understanding of the basics.

>> No.9023608

>>9023587
i think im asking where we get the numbers to replace x

>>9023591
i got that part, im just unsure on how it goes from there to the next line

>> No.9023617

>>9023587
>>9023591
>>9023608
nvm i got it thanks. if i seem retarded its cause im teaching myself and it can be hard to grasp it all just by reading worksheets.

>> No.9023619

>>9023608
>unsure on how it goes from there to the next line
f(x) = x-(x^3)/3
b=1
a=-1

>> No.9023642

>>9023598
>convert direct current into alternating current without ANY moving parts
you can't do it, as far as I know

>> No.9023657

>>9023598
http://www.electroschematics.com/7032/12v-to-120v-voltage-inverter/
Depends if you want a specific waveform. That'll give a square wave.

>> No.9023664

>>9023445
Oxygen is produced from the bleach/peroxide reaction, hydrogen from the aluminum/acid reaction.
They mix together in the bottle. The fire triggers the reaction. Oxygen+hydrogen=water.

>> No.9023685

>>9023532
right
>>9023560
Bicarb soda + vinegar is always a hit.
idk, maybe make batteries? Work up from basic lemon batteries to electroplating and rare metal recovery.

>> No.9023725

>>9023617
Dude just fucking write it out next time. It's simple algebra at that point

>> No.9023738

>>9023560
Make an IED my dude

>> No.9023973

Can someone please explain the axiom of choice to me? As far as I know given sets A B and C it's possible to construct a set D that contains one element from each of them. Why wouldn't that be possible and why does AC imply you can somehow double objects?

>> No.9024373

Can you define a homomorphism from a group to another in this "cheaty" way?

Let [math]A,B[/math] sets and [math]A\coprod B[/math] their disjoint union. Let [math]F(Z)[/math] be the free group on the set [math]Z[/math]. Suppose there are homomorphisms [math]f_A: F(A)\to G[/math], and analogous for [math]B[/math], to a set [math]G[/math]. We have some natural injections [math]j_A:F(A)\to F(A\coprod B)[/math], analogous for [math]B[/math].

Can I define a homomorphism [math]\phi :F(A\coprod B)\to G[/math] by [eqn]\phi(x)=\phi\left(\prod_{g\;\mathrm{ a\;generator}} g^i\right):=\prod_{g\;\mathrm{ a\;generator}} \phi(g)^i[/eqn]

Define [eqn]\phi(g)=\begin{cases} f_A(g) & g\in A\\ f_B(g) & g\in B\end{cases}[/eqn]
Which obviously is a homomorphism by construction, and makes the diagram commute?

>> No.9024411
File: 258 KB, 876x1476, 1499418528543.png [View same] [iqdb] [saucenao] [google]
9024411

what's gonna happen on september 23rd

>> No.9024422

>>9024373
yes

>> No.9024584

Why do people tend to get worse hangovers as they get older? Something I hear from a lot of people: "I didn't get hangovers in college, but I started getting them in my mid 20s, and they kept getting worse". Why does this occur? I remember in college I would wake up after a night of heaving drinking feeling fresh as a daisy, but now, after a heavy night of drinking, I feel severely debilitated mentally and it takes me like a full 2-3 days to recover.

>> No.9024588

>>9023428
Is my this correct??

Use induction to show that n3-n+3 is divisible by 3 for all natural numbers n

P(1) —> 13-1=3 = 3 P(1) is divisible by 3

Assume P(k) is true

k3-k+3 is divisible by 3

Show P(k+1) is true

(k+1)3-(k+1)+3

= k3+3k3+2k+3

P(k+1) is true thus, for (n), all natural numbers are divisible by three

>> No.9024593

>>9024588
damn , messed yup the exponents

>> No.9024609

I dont' know anything about science so this question is very stupid: how would a scientist actually "see" my genetics, or DNA? Would they have to take a piece of my body (skin, hair or such), place it under a microscope? Can they actually see, with their own eyes, what my genes look like?

>> No.9024753

Hi guys I started learning linear algebra last week and I'm stuck on a part of a problem here.
Let T be in Hom V and nilpotent so that T^n=0, but T^(n-1) =/=0 and assume V has the property that any of its subspaces has a complement (in terms of direct sum to V). That is for any subspace M in V, there is a subspace N with M and N forming a direct sum for V.
Now let V_1 be the complement of the null space of T^(n-1) called N^(n-1) here. I have shown that the intersection of T[V_1] and N^(n-2), the nullspace of T^(n-2), only contains the 0 element. I have also shown that T[V_1] is a subset of N^(n-1).
The part I'm stuck on is asserting the existence of a subspace V_2 such that V_2 and N^(n-2) form a direct sum for N^(n-1) but T[V_1] is a subset of V_2.

>> No.9024932

>>9024373
>>9024422
No. [math] \phi [/math] can give different values for different presentations of the free groups. It is not well-defined.

>> No.9024950

>>9024932
what is the step that is incorrect then?

How else would you show that [math]F(A\amalg B)=F(A)\ast F(B)[/math]?

>> No.9024962

>>9024588
[eqn](n+1)^3-(n+1)+3=n^3+3n^2+3n+1-n-1=(n^3-n+3)+3(n^2+n)[/eqn] and it is divisible by [math]3[/math] by induction hyp.

>> No.9024990

Suppose that [math] gcd(m,n) = 1 [/math]

How do I prove that [math] gcd(m^2 - n^2,mn) = 1 [/math] and [math] gcd(m^2 + n^2,mn) = 1 [/math] ?

>> No.9025005

>>9024990
ill post the answer after this hint:

Let [math]d=gcd(m^2-n^2,mn)[/math]. Now show [math]d=1[/math]

>> No.9025019

How many hours a day would I have of classes (assuming 5 days with classes per week) if I had set myself the goal of a BA with a double minor in 4 years? What if it was a triple minor?

>> No.9025021

I'm an illustrator, and I need a little help understanding a positive control test for a comic I'm doing in which the script has some sciency jargon.

Is a positive control test basically just a way to compare something you expect to happen against whatever you're testing if a variable in the positive control is removed or nonexistent?

Say you were testing a bullet-proof vest against an older version of said bullet-proof vest. Is that considered a positive control experiment?

>> No.9025029

>>9024990
Let [math]d=gcd (m^2-n^2,mn)[/math]. Then in particular, [math]d|mn\implies d[/math] divides exactly one of [math]m[/math] or [math]n[/math] by the condition [math]gcd(m,n)=1[/math]. Then assume without loss of generality that [math]d|m[/math]. So we can write [math]m=kd[/math] for some integer [math]k[/math].

Now we also have [math]d|m^2-n^2=k^2d^2-n^2[/math]. So we have to have that [math]d|n^2\implies d|n[/math]. But since [math]gcd(m,n)=1[/math], then [math]d=1[/math]

>> No.9025042
File: 54 KB, 788x535, Screenshot - 07092017 - 05:05:36 PM.png [View same] [iqdb] [saucenao] [google]
9025042

How do you get from "Since ..." to "we see that ..."?

>> No.9025054

>>9024411
September was last year, my dude

>> No.9025074

Best way to find top professors in a given field? Just searching google scholars? Will top unis always have top professors aswell?

>> No.9025079

>>9025074
given its a finite field just look for the one with the highest characteristic

>> No.9025081

>>9025029
>. Then in particular, d|mn⟹dd|mn⟹d divides exactly one of m or n by the condition gcd(m,n)=1

What, why? What if d is equal to mn. Then d does not divide either.

>> No.9025089

>>9025081
Think of d,m and n in terms of their decomposition into prime numbers. If d divides a bit of m and a bit of n, then that means that gcd(m,n) is at least d>1. Contradiction

>> No.9025090

>>9025042
You use the given identity to get to an equivalent expression and then you use the triangle inequality.

>> No.9025096

>>9025029
>>9025081

Wait, I think I can formalize your idea. I can say [math] d = d_1 d_2 [/math] where [math]d_1 [/math] is the biggest divisor of d that also divides m (but not n), and [math]d_2[/math] is the biggest divisor of d that also divides n (and not m).

Then using your method I can prove [math]d_1 = 1 [/math] and [math] d_2 = 1 [/math] and therefore [math] d = 1 \times 1 = 1 [/math].

>>9025089
>. If d divides a bit of m and a bit of n
I am saying in the case that d does not divide either m or n, which is possible if you only know that d is a divisor of mn. Like in the case d=mn

>> No.9025111

>>9024950
>what is the step that is incorrect then?
Attempting to define the homomorphism by its action on the elements. Essentially, you're passing the construction through a functor [math] \textbf{Grp} \rightarrow \textbf{Set} [/math], which is forgetful, and pretending that this never happened. You no longer have the group structure, it went poof through the functor.
>How else would you show that...
You can't. They're isomorphic, not equal. Equality only holds if you define the free group by a universal property, i.e. by a functor [math] \textbf{Set} \rightarrow \textbf{Grp} [/math] (so you essentially don't care about the underlying set any more).

>> No.9025125

>>9025081
>>9025089
>>9025096

Of course, you should be able to produce a formal proof, but I'm assuming it's your first time with these arguments, because that is wrong.

Suppose the [math]d_i,m_i,n_i[/math] are primes, and that [eqn]d=d_1^{\alpha_1}\cdot d_2^{\alpha_2}\cdot...\cdot d_{k}^{\alpha_k},\; m=m_1^{\beta_1}\cdot m_2^{\beta_2}\cdot...\cdot m_{h}^{\beta_h},\;n=n_1^{\gamma_1}\cdot n_2^{\gamma_2}\cdot...\cdot n_{j}^{\gamma_j}[/eqn]
This is obviously very cluttered already, but what it means is that you can decompose [math]d,m,n[/math] in to products of prime powers.

You have that [math]d|mn[/math]. This means that there is some integer [math]a[/math] such that [math]da=mn[/math]. Now write out what this means:

[eqn]ad=mn\iff a\cdot d_1^{\alpha_1}\cdot d_2^{\alpha_2}\cdot...\cdot d_{k}^{\alpha_k}=m_1^{\beta_1}\cdot m_2^{\beta_2}\cdot...\cdot m_{h}^{\beta_h}\cdot n_1^{\gamma_1}\cdot n_2^{\gamma_2}\cdot...\cdot n_{j}^{\gamma_j}[/eqn]
Since you can decompose every integer into prime powers uniquely, this means that you can mix and match [math]a[/math] and the [math]d_i[/math] with [math]m_i,n_i[/math]. But [math]gcd(m,n)=1[/math] means that none of the primes are shared between m and n. But now you think, yes, but what if d has some primes that divide m, and some that divide n? Well, if that were the case, then those primes would divide both m and n. But this is not possible because their gcd is 1

>> No.9025130

>>9025111
well, how do you show they're isomorphic then? I'm assuming it's a typo in the book

>> No.9025157

>>9025130
I think you.re being trolled. The construction in your first post was fine. Also saying "equal" instead of "isomorphic" is common practice and not such a big deal

>> No.9025173
File: 420 KB, 444x363, amethyst-rough-zambia.png [View same] [iqdb] [saucenao] [google]
9025173

i'm curious about growing crystals or making synthetic stones. there are a bunch of "grow crystals at home" projects using alum and copper sulfate etc, but apparently the resulting crystals are quite fragile.

i want to make crystals/stones that are about as durable as decorative natural crystals/stones, such as amethyst or just a plain normal stone.

do you know what types of crystal/stone and the method of synthesizing them would be worth looking into? if it requires using equipment like a pressure cooker or an autoclave or exotic chemicals i'm still curious about it.

>> No.9025222

>>9025157
>saying "equal" instead of "isomorphic" is common practice
In category theory.
>The construction in your first post was fine.
Except it wasn't.

>> No.9025301

How do you guys maintain motivation and focus to study? I'm struggling right now to study mathematics :/.

>> No.9025331

>>9025021
I think you've got it. It just means that, if your experiment is set up correctly, you will see x result with y control since you already know that y control gives x result under the right conditions. Say if I were testing the pH of some substance, a positive control would be when I test a known acid or base to make sure I get that result. You probably could have just googled this though

>> No.9025350

Are blacks (on average - and that's an important word) genetically less intelligent?

I think they are.

>> No.9025353

>>9025350
yes

>> No.9025402

>>9023428

can I use binomial theorem in place of pagels triangle in any problem that calls for expansion?

>> No.9025418

hey i fucked up and need to learn stoichometry, termochemistry, kinetics, and daniel pill untill tuesday
is it possible or should i just give up and try general chemistry for the 3rd time?

>> No.9025534

>>9025353
I think that's right. Which is why we need to seriously reconsider "diversity" policies.

>> No.9025771

>>9025350
>genetically
Do you mean do they genetically have a lower capacity for intelligence? If so, there is no definitive proof. Yes they do have a lower average IQ, but whether that it is caused by a lower capacity for intelligence genetically or a lack of quality education is unknowable, because the only way to really know that is to give them quality education.

>> No.9026203

Can anyone help me understand how time spent in college works? I've never been to college before. From what I read, its way less time than school (18-20 hours a week as opposed to 30-40). Is there an option to go to college for 7 hours a day, but only 3 times a week? Or do you have to spread the hours over the five weekdays?

>> No.9026333

So it's been a while now

I don't want to make a thread about this

Has the discovery of the Higgs boson yielded any new shit that's interesting or useful to humans?

>> No.9026578

>>9026333
No. Most of these discoveries don't mean much to the average person, but at least it's still better than investing the same money in wars.

>> No.9026873

Gonna soon go through a government clearance for an internship which will probably lead to a job. I'm 23 and live in the state of California, when I was 20 I got my medical marijuana prescription, kinda on a whim with my buddy cause it took 30 mins. I plan on telling them this, but do you think there's a chance that it could give me problems with passing? Rest of my file is clean

>> No.9026998
File: 9 KB, 521x208, 2017-07-10-162505_521x208_scrot.png [View same] [iqdb] [saucenao] [google]
9026998

[math]13-.5w+6x; w=10, y=\frac{1}{2}[/math]
why is the answer not 5

>> No.9027008

>>9026998
fuck, I figured it out
[math]13-5+3[/math]
I keep on getting questions wrong on khan academy because I've always been taught Multiplication gets priority over Division, Addition gets priority over Subtraction a la PEMDAS

what the fuck is the truth?

>> No.9027016

>>9026998

13-5+3

Hmm rly makes me think

>> No.9027021

>>9027016
see
>>9027008
I was always taught that you always do addition before subtraction, not that they have equal priority and to go from left to right through the equation

>> No.9027023

>>9027008
It's more like PE(MD)(AS)

Multiplication/division and addition/subtraction have equal priority

>> No.9027035

>>9027008
>I keep on getting questions wrong on khan academy because I've always been taught Multiplication gets priority over Division, Addition gets priority over Subtraction a la PEMDAS
fucking burgersharts lmao

>> No.9027113

>>9027035
my math education was so poor that I'm now trying to re-teach myself basic algebra so I don't blow it when I start college

>> No.9027438

What are some good books or resources for learning notation?

>> No.9027624

Is there any simple way to prove that the diophantine equation [math] x^4 + 4y^4 = z^2 [/math] has no all-positive solutions?

>> No.9027668

Can anyone recommend a chemistry textbook for someone who failed high school chemistry, mostly for not doing any work, but who enjoyed it none the less?

>> No.9027797

How many hours of classes a week would I need to get the following in 4 years:
-1 major 1 minor
-1 major 2 minors
-1 major 3 minors
-2 majors 1 minor
-2 majors 2 minors

>> No.9027824

Have we found anything smaller than quarks yet?

>> No.9027830

Would it be a good idea to put little windmills on top of those really tall power lines? That way we don't have to build that whole big windmill thing and it saves money right?

>> No.9027833

>>9027824
Fields.

>> No.9027859

We have a deck of 25 cards with 2 jokers in there, we draw 10 cards, and we can shuffle 1 back 3 times, a card we've choose to shuffle back cant be re-drawn. What are our chances of having 1, or the 2 jokers amoung our 10 cards after the shuffling?

>> No.9028010
File: 982 KB, 320x287, 1498082149705.gif [View same] [iqdb] [saucenao] [google]
9028010

>>9023642
Nearly every electronic device you interact with every day relies on the creation of an alternating electric potential, in some way. Smartphones are powered by a DC battery and can generate signals at 5 billion hertz. How does THAT happen?

>>9023657
From my understanding, the voltage on the gate of each resistor will always be the same, even if the resistors are open, so both will be held open constantly. I can't see how this would alternate.

>> No.9028022

>>9028010
>Nearly every electronic device you interact with every day relies on the creation of an alternating electric potential, in some way.
And mechanical switches haven't been used in over 50 years.
>resistors
I meant transistors.

>> No.9028023

>>9027830
Shut it, brainlet, yeah? We power engineers don't need advice from you. If it was that easy we'd have done it already. Or maybe you think there's some conspiracy "keepin' duh white man down"?

>> No.9028153

is the derivative and integral of e^-x = e^-x like how e^x = e^x?

>> No.9028178

>>9028153
No, use the chain rule.

d/dx e^-x = -e^-x

>> No.9028184

>>9028178
cool thanks

>> No.9028474

I don't know if I should do EE or CS yet, fuck.
I also have the chance to study in a top 4 uni in Japan (I'm here right now preparing for entrance to uni but I still can't decide my major, I have 3 months left, can anyone give me some advice?(

>> No.9028715
File: 1.41 MB, 1080x1920, Screenshot_20170711-140147.png [View same] [iqdb] [saucenao] [google]
9028715

I only did basic calculus in school but I remember using the power rule and other formulas. I've opened Keisler Calculus and I'm being bombarded by infinitesimals and standard parts. I have no idea what these are.

>> No.9028727
File: 46 KB, 854x480, Screenshot_2017-07-11-20-08-49.png [View same] [iqdb] [saucenao] [google]
9028727

Why is the voltage across C1 is 0?

>> No.9028730

>>9023428
If I have a cube in a vacuum and there's gas inside the cube that produces a pressure of 10 Pa, will then the force that the pressure exerts on each side of the cube be 10/6N?

>> No.9028733

>>9028727
You have symmetry. C2 = C4 and C3 = C5, so the voltage across C1 must be symmetric: V1 = -V1 => V1 = 0.

>> No.9028769

>>9028733
What if the capacitors aren't symmetrical?

>> No.9028772

>>9028769
Then you have to calculate.

>> No.9028777

>>9028772
How do I do it? Make equation from each loop using V=Q/C?

>> No.9028802

Deck is 16 red, 16 black
"How many results are there to draw 3 cards with exactly 1 red card"

do i have to add or multiply the C ?

>> No.9028815

>>9028802
Multiply,since you are drawing 1 red AND 2 black.

>> No.9028861

>>9028815
thanks

>> No.9029020
File: 23 KB, 600x484, c4a.jpg [View same] [iqdb] [saucenao] [google]
9029020

How bad is direct skin contact with 95% ethanol?

Just spilled a bunch on my bench and some got on my arm.

>> No.9029044

>>9028777
Each loop and each junction. Kirchhoff's laws but with charge instead of current.

>> No.9029055

>>9029020

It's literally alcohol. You can literally drink it.

>> No.9029076

>>9024609

You can visualise DNA chains with certain microscopy methods like TEM or AFM.

>> No.9029256

Is homosexuality genetic?

I'm bi, my brother gay and my father in the closet

>> No.9029467
File: 13 KB, 640x400, lattice.png [View same] [iqdb] [saucenao] [google]
9029467

is there a mathematical way to determine the center of a N x N grid like pic related stored in an 2d array?

it just needs to be in the center, no clear boundaries. i just hardcoded it.

>> No.9029571

Trying to do some high school grade stuff to prepare for getting back into college. Having trouble with a particular type of problem in combinatorics.
For example, how many six-digit numbers are there that have at least a single (random number) or a single (another random number) in them? It's easy with one, but how do you make sure you're not repeating numbers that fit both conditions? Help me out, math di/sci/ples.

>> No.9029663

>>9029571
How many six-digit numbers are there in total?
How many six-digit numbers are there that do not have either of the given numbers?
You might see where this is going.

>> No.9029668

>>9029663
Knew I'd feel dumb. Fucking knew it.
Thanks, anon.

>> No.9029684

>>9023481

numberphile

>> No.9029723

>>9027008
This may seem counter-intuitive in the beginning anon, but to get away from that line of thinking, try substituting subtraction with addition of a negative number. Instead of it being 13 - 5 + 3, think of it as 13 + (-5) + 3, and try to use the number line as much as possible to navigate yourself during these early operations. I get your line of thinking and it's not as degenerate as people here might think. Just avoid associating them unnecessarily.

Your way of approaching the problem turns it into 13 - 5 - 3. KhanAcademy is a good place to start, just don't give up, take breaks if you're frustrated. Misconceptions this old take time to be replaced.

>> No.9029773
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9029773

How should I go about assessing maths courses at universities that cover topics I don't yet appreciate?
+
What UK unis should I be looking at if I want to go into research?

>> No.9030028
File: 65 KB, 500x464, IDONT.jpg [View same] [iqdb] [saucenao] [google]
9030028

What's the best the best/quickest way to refresh my algebra/geometry/algebra2/trig/precalc knowledge so that I'm ready for Calculus? Is there any decent test to find my holes? And what's the best way to drill the knowledge quickly?
Yes, I know I'm a brainlet who never took calculus in high school.

>> No.9030142

>>9029044
Alright I get it. Thanks anon.

>> No.9030190

>>9029773
>What UK unis should I be looking at if I want to go into research?

If you haven't even started your math career then the last thing you should be thinking about is doing research. Just focus on getting into the highest ranked uni you can get in and then start like every mathematician starts: by assesing how retarded you are. We are all retarded, but some more than others. See how retarded you are and then compare with your peers. If you are at the lower level of retardation compared to the other students then perhaps you should do research.

>> No.9030196
File: 10 KB, 170x250, 1495492820945.jpg [View same] [iqdb] [saucenao] [google]
9030196

>>9023428
ATTENTION GRABBER

>What is the world average IQ if you exclude Africa?

ATTENTION GRABBER

>> No.9030246
File: 100 KB, 1212x706, Untitled.jpg [View same] [iqdb] [saucenao] [google]
9030246

is this valid or did i fuck up on just choosing an arbitrary sequence?

>> No.9030253

>>9030246
The idea is right but the execution is flawed. Why do your choice of vectors have only the first two components be non-zero?

You should do the more general case in which they have an arbitrary but fixed number of non-zero components

Also, you start by saying [math] v_1, v_2 \in \mathbb{R}^{\infty} [/math] but actually you mean [math]v_1,v_2[/math] in the subspace, that you should first, for the sake of rigor, write explicitly in set notation.

So just do those things and then proceed in the exact way you already did.

>> No.9030269
File: 95 KB, 1212x706, Untitled.jpg [View same] [iqdb] [saucenao] [google]
9030269

>>9030253
like this?

>> No.9030280

>>9030269
No. See that you defined the set wrong. The way you defined it, it seems that all the vectors have the same "last point" when in reality some vectors could have the first 5 points be non-zero while others could have the first 2 quadrillion be non-zero.

I would say [math] W = \{ v \in \mathbb{R}^{\infty} : \exists n \in \mathbb{N} : \forall k > n, v_k = 0 \} [/math]

The rest is still okay, you just need to adapt it so that it encompasses all the actual possibilities. Note that what you are actually proving is that all the [math] \mathbb{R}^n [/math]s are subspaces of [math] \mathbb{R}^{\infty} [/math] and while that is true, the subspace you are being given is actually way broader than just a simple [math] \mathbb{R}^n [/math]

>> No.9030315

>>9030280
it makes sense but i struggle to rationalize how you can indicate an arbitrary n as being your components in the n-tuple by just saying "there exists an n". wouldn't you have to say for all n?

>> No.9030323

>>9030315
If that have that [math] \forall n, v_n = 0 [/math] then you just have the trivial 0 vector space because the ony vector that satisfies that is (0,0,0,0...).

You say there exists an n such for all k bigger than n, [math] v_k = 0 [/math] to indicate that each vector has an "end-point". You don't necessarily know the endpoint of each vector, you just specify that one exists because that is the vector space that was described to you in the problem.

It says "All sequences whose components are 0 from some point on". It says "some" point on. It could be any point, so you generalize by sayng that there exists an n such that... etc. etc.

>> No.9030333

>>9030323
wait so it's implied that n is k itself then? ok my bad, i was struggling to grasp how you included the endpoint.

>> No.9030339

>>9030333
No, n isn't k. And k isn't really an object you are counting on, as for k I am using the "for all" quantifier.

>> No.9030344

>>9030339
no i mean saying "for all K that are greater than n" you have basically saying that nk=0, but also that n<=k can be w/e. is that what you're doing?

>> No.9030349

>>9030344
>you have basically saying that nk=0

No, n and k are natural numbers so their product can be 0. I am just saying that given any choice of k, [math] v_k = 0 [/math].

> but also that n<=k can be w/e
I am saying this. n can be whatever. It is arbitrary.

>> No.9030351

>>9030344
>>9030349
>so their product can be 0

I meant can't.

>> No.9030353

if a sinusoidal displacement indicates insufficient damping, does a sinusoidal velocity indicate insufficient spring constant?

>> No.9030386
File: 33 KB, 739x134, Screenshot (9).png [View same] [iqdb] [saucenao] [google]
9030386

Can someone give me a more in-depth explanation of torsion coefficients? This is the first time the book mentioned them and I'm lost. Theorem 11.12 is the fundamental theorem of finitely generated abelian groups.

>> No.9030388

>>9030353
Sinusoidal displacement would directly imply sinusoidal velocity, so that shouldn't tell you anything new.

>> No.9030402

>>9030386
Okay, after a bit of googling, I think I understand this more. For a, since [math] \mathbb{Z}_4 [/math] and [math] \mathbb{Z}_9 [/math] can't be decomposed further, the torsion coefficient would just be 36, since [math] \mathbb{Z}_4\times\mathbb{Z}_9 \cong \mathbb{Z}_{36} [/math]. Then for b, we can decompose and recompose it as follows: [math] \mathbb{Z}_6\times\mathbb{Z}_{12}\times\mathbb{Z}_{20}\cong\mathbb{Z}_2\times\mathbb{Z}_3\times\mathbb{Z}_4\times\mathbb{Z}_3\times\mathbb{Z}_4\times\mathbb{Z}_5\cong\mathbb{Z}_2\times\mathbb{Z}_{12}\times\mathbb{Z}_{60}[/math] so it has torsion coefficients 2, 12, 60. Is this correct?

>> No.9030408

>>9030388
Ok, so it's just a lack of damping. I think I was trying to see more into this than was actually there. Thanks

>> No.9030432

>>9030402
I checked and this is correct. Thanks for nothing you worthless faggots

>> No.9030445
File: 209 KB, 1713x340, xharcoalwaves.png [View same] [iqdb] [saucenao] [google]
9030445

>>9023428
>Their experiments helped researchers verify the relationship between mass and potential force between objects as “a 10-fold reduction in size [which] should translate to a 100-fold increase in force relative to mass”.
>https://en.wikipedia.org/wiki/Claytronics

What does this mean? Give me a real life example.
Is it like ants being able to lift a lot of weight proportional to their small size? Or fleas being able to jump very high proportional to their small size?

>> No.9030447

Vector Calculus

Question 1:
Why does f=sqrt(x+y+z) have the same critical points as f=x+y+z? And in general every time i've encountered a sqrt function the solution is always to just treat it as if it didnt have sqrt.

Question 2:
Why can you remove e^x when finding critical points? Like when you set f(x) = x(x-1)e^x = 0 and get x =0, x = 1 as your critical values.

bless

>> No.9030478

what should I know to pass my calc 2 exam on Thursday? more specifically, what about series and sequences and it's more centered around that topic.

>> No.9030495
File: 32 KB, 789x358, Screenshot (12).png [View same] [iqdb] [saucenao] [google]
9030495

>>9030386
Is this a satisfactory answer for 3, or is there a more efficient method?

>> No.9030497

>>9030447
1) sqrt() is a bijection over non-negative reals. Let f be the function you're taking the root of and g be sqrt(f(x)). If you had a local minimum of g at a point y, the points around y must have a g value greater than g(y).
sqrt(a) > sqrt(b) => a > b.

2) I assume f(x) is your derivative in this case? exp(x) is always positive, and more specifically it never equals zero. Thus, you can just divide through without worrying about ending up with 0/0.

>> No.9030540

>>9030497
Can 1) be explained in another way?

I'm confused because y=sqrt(x) is completely different graph to y=x, so i dont see how they can be similar except that y=x is always bigger than y=sqrt(x).

>> No.9030562

>>9030540
[math] \sqrt{x} > \sqrt{y} \Rightarrow x>y [/math]
So if [math]f(x)[/math] has a local maximum at [math] x_0 [/math], all the other points around it on [math] f(x) [/math] are less that [math] f(x_0) [/math]. Since the square root function preserves this inequality, [math] g(x) [/math] also has a local maximum at [math] x_0 [/math]

>> No.9030812

>>9030445
can anybody help me with this?

>> No.9030900

>>9030812
>>9030445
please?

>> No.9031006

>>9023428
Why is the speed of light the speed it is, is it possible to derive the speed of light or is c just a constant that is?

>> No.9031054

If energy is mcsquared

Is the energy of an electron 0.0549 joules?

What does that mean, is that the potential of energy it has or what the fuck

>> No.9031087
File: 581 KB, 4032x2268, IMG-20170712-WA0002.jpg [View same] [iqdb] [saucenao] [google]
9031087

Could someone help me with question 11. I know it's 3/2 root x (using power rule). I'm trying to do it using the difference quotient fx+h -fx /h but I'm fucking up my algebra

>> No.9031213

I have a couple of questions.

1- Which would take longer, getting a Double Major or Double Minor? And by how many semesters? How many hours of classes a week to complete each in under 5 years?
2- How deep does a Minor go? For example, can I learn Topology I with a Math Minor, or Quantum Mechanics with a Physics Minor?

>> No.9031288
File: 19 KB, 1500x808, gorillion hours in paint.png [View same] [iqdb] [saucenao] [google]
9031288

How to get the surface area of the blue part?

>> No.9031331

How do I not fall asleep while trying to learn programming? Is it just code academy or what?

>> No.9031350

>>9031331
>learning programming with courses
>not just manually trying to edit code from scratch
Also:
>>>/g/

>> No.9031363

e1: 2x + z + w = 5
e2: y - w = - 1
e3: 3x - z - w = 0
e4: 4x + y + 2z + w = 9

This system, I believe, has infinite solutions, but how can I prove it? trial and error and not getting anywhere doesn't seem like proving anything.

>> No.9031391

>>9031288
Integrate

>> No.9031413 [DELETED] 
File: 7 KB, 519x581, Untitled.png [View same] [iqdb] [saucenao] [google]
9031413

>>9031288
do you see that yellow is one fourth of the area of a cicle of radius equal 2? so yellow equals pi.
and the red is equal to the total area of the square, minus the yellow part, which is 4 - pi.
Now S is surrounded by 4 areas which are identical to the red part.
S + 4 red = the total area of the square.
S + 4(4 - pi) = 4

S = 4pi - 12

>> No.9031417

>>9031363
2*e1 + e2 - e4 => 0 = 0
So clearly it doesn't have a unique solution.

You can use Gaussian elimination to reduce the system of equations to:
x=1
y-w=-1
z+w=3

=> x=1, y=w-1, z=3-w

IOW, the solution space is one-dimensional (the matrix has nullity equal to one).

>> No.9031439

How challenging is the math in intro computational science courses with matlab? I have to take an intro and the next level of that for my CS degree

>> No.9031480

>>9031054
If it annihilated, it would release that amount of energy.
If you calculated the mass in some excited state, some of that would release when the electron goes near positive things, and the electron would lose mass.

>> No.9031508

Lets say I have two subspaces X and Y in a finite dimensional vector space V. Can someone give me an example of a linear T on V, codomain irrelevant, such that the null space is exactly the intersection of X and Y

>> No.9031522

>>9031508

once you have a basis for [math] X \cap Y [/math], construct T with one of the basis vectors as an eigenvector, then take (T-I*lambda)

continue constructing T's this way and then multiply them all to get your matrix.

>> No.9031544

>>9031522
How about as well I extend the basis of the intersection to a basis for V, and then have the T that maps from V to a finite dimensional W with T(a_i) = b_i, where {a_i} is the basis for V and {b_i} is a basis in W with 0's added in to correspond for each basis element for the intsection of X and Y. I make the conditon that T(a_i)=0 for each a_i in the basis for the intersection of X and Y. Then clearly all elements in X intersected with Y are 0 under T, and elements outside will have a corresponding coefficient tuple with at least one nonzero coefficient for a basis element outside X intersected with Y, and so under T will be nonzero.

>> No.9031550

>>9031544

i think that would work too. my suggestion was just the first thing that came to mind.

>> No.9031555

>>9031550
Some of the terminology you have used hasnt been introduced in my book yet but I didnt consider the basis for X intersected with Y I think thats the clinch regardless of the strategy

>> No.9031613

>>9031555

the way you suggested is much better.

>> No.9031630

hi everyone. any mathematician here, please? i have a question about combinatorial game theory.

>> No.9031876

>>9030900
>>9030812
>>9030445
I'm not but a poor NEET brainlet. Please.

>> No.9031917

>>9023532
Epigenetics is NOT heritable

>> No.9031978
File: 60 KB, 384x269, 1498599636111.gif [View same] [iqdb] [saucenao] [google]
9031978

>>9031630
>hi everyone. any mathematician here, please? i have a question about combinatorial game theory.
don't ask to ask brainlet, just ask

>> No.9031984

How do I actually understand math? I have no issues with learning methods to solve problems, but I don't actually understand how or why they work. If I bump into a problem where I can't just apply the method, I'm lost.
Does it just click for you guys?

>> No.9031998

How do vaccines cause autism?

>> No.9032001

>>9031998
>How do vaccines cause autism?
Have you never met a vaccinated person before?

>> No.9032013

>>9032001

Well I'm vaccinated and I have autism, so the two must be related.

>> No.9032024
File: 62 KB, 578x325, car of the future.jpg [View same] [iqdb] [saucenao] [google]
9032024

Turbine-electric hypercar.

Best idea, or dumbest idea?

Pros:

>higher TWR than piston engine
>moderately better maintenance
>electric engines allow the turbine to operate at peak efficiency even at low speeds
>bragging rights for being the first one to the idea

Cons:

>engine has to spool up
>shifting from the electric motor to direct shaft power from the turbine might be jarring/mechanically difficult
>noise makes a formula one car sound like a hair dryer
>batteries may not charge quickly enough to absorb all of the power of the engine
>exhaust may fry pedestrians if you try to spool up the engine to charge the batteries
>who even drives a hypercar around long enough to care about fuel efficiency at low speeds

>> No.9032027

if you crush an object into extremely high density does the temperature of the object increase?

>> No.9032099

>>9031288
divide the shape into four 1x1cm pieces, take the area of the blue circular segment and add the area of the triangle that the circular segment doesn't cover, and multiply by four

>> No.9032102

>>9031998
the research on autism is far from complete. afaik the claim is that some vaccines cover too many diseases in one shot and that the dosages are way too high for an infant or a small child

>> No.9032131
File: 8 KB, 236x177, comfycat.jpg [View same] [iqdb] [saucenao] [google]
9032131

Scientifically speaking, what's so bad about net neutrality going away? Shouldn't companies be allowed to conduct business and provide services the way they want to?

>> No.9032170

>>9032131
it's a political thing, if you want more government regulations or less. there's lots of shilling from both sides and it's not a black and white thing, there are pros and cons.

>> No.9032205

>>9032131
There isn't a scientific argument for why net neutrality is good or bad. It's just that not having net neutrality allows ISPs to fuck you over way more than they already can.

>> No.9032211

>A problem arises when a number ends with zeros but contains no decimal point.
In such cases, it is normally assumed that the zeros are not significant.

So, what should happen here?

438/10

And what about this?

438/10^2

>>The exponential term (...) does not add to the number of significant
figures.

For both,does this not apply?

>For multiplication and division, the result contains the same number of significant
figures as the measurement with the fewest significant figures.

If so,do I just ignore those numbers? how many significant figures should the results for both cases contain then ? 3? ballpark?

Too retarded.Help would be appreciated.

>> No.9032212

I dabble in physics and philosphy for fun, but I really dont grasp alot of things concerning quantum mechanics. What is the general consensus of the scientific community regarding the double slit experiment? Is it really spooky observer stuff or is that a meme? Also what are the main elements in quantum studies that make the field un reconcilable with classical physics? And how exactly does something like string theory solve these problems?

>> No.9032226

>>9032102
This is typical anti-vaxxer drivel that misunderstands vaccines on a fundamental level. The "dosage" of a vaccine is irrelevant. Vaccines work by exposing your immune system to antigens in the local area of the vaccine, which then produce memory cells that are replicated throughout the body. Vaccines don't work on a blood concentration level.

tl;dr
>Antigen-presenting cell absorbs antigens from vaccine, displaying some antigens on the surface of the cell
>APC travels to areas like lymph nodes where immune cells cluster
>Naive T cells and B cells detect antigen and become activated
>Some B cells mature into plasma B cells which produce antibodies specific to the antigen detected from the vaccine
>If the vaccine includes an attenuated virus killer T cells are activated and kill cells displaying vaccine antigens
>Result of the process is production in your body of antibodies for the vaccine antigens and memory B cells, memory T cells and memory killer T cells that react quickly to the presence of the antigen if it is detected again

Antigens in the vaccine don't travel through your body and reach a certain blood concentration like a medication does. The antigens only activate an immune response in the local region of the injection, causing an immune response and the proliferation of memory cells and antibodies which are then distributed around the body.

>> No.9032228

>>9031917
It is. It's literally called epigenetic inheritance.

>> No.9032239

>>9032228
To clarify, most epigenetic tags get removed when reproductive cells are created. Some however do not get erased.

>> No.9032243

>>9031363
Put the equations in a matrix [x y z w val]

2 0 1 1 5
0 1 0 -1 -1
3 0 -1 -1 0
4 1 2 1 9

Use your calculator to reduce that to

1 0 0 0 1
0 1 0 -1 -1
0 0 1 1 3
0 0 0 0 0

Which means you have infinite solutions.

>> No.9032254

>>9032226
>implying
http://www.sciencemag.org/news/2015/07/why-pandemic-flu-shot-caused-narcolepsy

>> No.9032309
File: 113 KB, 866x1300, 14195241-Portrait-of-a-young-man-skeptical-Stock-Photo.jpg [View same] [iqdb] [saucenao] [google]
9032309

What will happen to humanity once we have a vaccine for gravity?

>> No.9032325

>>9032309

We gain the ability to fly, but we will also get autism and narcolepsy

>> No.9032327
File: 82 KB, 800x1000, koolbeaner.jpg [View same] [iqdb] [saucenao] [google]
9032327

>>9032325
>We gain the ability to fly, but we will also get autism and narcolepsy
worth it

>> No.9032342

>>9023445
Chem fag here
It's an endothermic reaction
Hydrogen + Oxygen +heat = water.
It's very dangerous. Be careful m8.

>> No.9032423

>>9032228
>>9032239
>>9031917
Wait hold on, when we talk about "heritable" do we mean to daughter cells or offspring organisms (for example plants or animals)?

I thought it was only heritable to daughter cells, not whole animals and the like.

>> No.9032431

>>9032423
To clarify, does it only affect somatic cells and therefore subsequent divisions of them in mitosis. Or does it affect somatic cells and gametes (and by extension offspring of sexual reproduction)?

>> No.9032515

>>9032131
You can't derive an ought from an is.

Science gives you the is.

>> No.9032568
File: 72 KB, 1284x424, halp.png [View same] [iqdb] [saucenao] [google]
9032568

Vector Calc finding absolute max/mins.

I don't understand how they get a maximum of 3 on the boundary. It says (1,+/-1) as the point on the boundary, but the boundary has been parameterized, so why did they say that?

(1,1) = 45deg = pi/4, right?

so i dont get how 2+sin^2(t) is supposed to equal 3 when t = pi/4.

>> No.9032659
File: 137 KB, 904x1169, 138-c36f9004e5.jpg [View same] [iqdb] [saucenao] [google]
9032659

>>9023428

Why does establishing a tensor equation in a local coordinate chart (eg. an approximate local freefall frame) establish it's validity in all charts throughout space-time?

Wouldn't the equations only hold good for arbitrary charts *over the specific subset* of space-time the chart was defined on? Are we just assuming that any and every region can be treated as locally free falling?

Pls halp

>> No.9032766

>>9032568
>It says (1,+/-1) as the point on the boundary, but the boundary has been parameterized, so why did they say that?
since sin(t)<=1, 2+sin^2(t)<=2+1=3

this happens when sin^2(t)=1, so either sin(t) = 1 or sin(t)=-1

this is when t=pi/2, 3pi/2

so (x,y)=(cost +1, sint) is equal to (1,1) at t=pi/2 and equal to (1,-1) at t=3pi/2

>> No.9032782

>>9032568
f(1,1) =2*1 - 4*1 + 3*1 + 2 = 3

>> No.9032804
File: 100 KB, 1288x504, halp2.png [View same] [iqdb] [saucenao] [google]
9032804

>>9032766
thanks i'll try and work through this :)

i think i just encountered it again though, i am on a similar problem and cant find where they get the point (1,-2) from.

>> No.9032811
File: 5 KB, 420x115, squaring a cube.png [View same] [iqdb] [saucenao] [google]
9032811

Im dont understand Q2. what the hell is squaring a cube?

what I can think of is
>construct a cube with volume equal to volume^2
>construct a square with area = volume
>construct a square with area = area of cube

But all of those are constructable.

>> No.9032820

>>9032804
cos^2(t)+1>=0+1=1

cos^2(t)=0 when t=pi/2, 3pi/2

(x,y)=(1+cost,-1+sint)
(1+cos pi/2, -1+sin pi/2) = (1,0)
(1+cos 3pi/2, -1+sin 3pi/2)=(1,-2)

>> No.9032842

>>9032782
>>9032766

sorry i'm actually still confused where the point (1,+/-1) is coming from.

i'm confused why it had me maximize f(t) = 2 + sin^2(t) by looking at it and seeing that sin^2(t) = 1 when t = pi/2, giving the highest value possible of 3.

i never had to do this with other problems. i thought it was always critical point and end points.

is this something special with sin and cos?

>> No.9032856

>>9032842
>i'm confused why it had me maximize f(t) = 2 + sin^2(t)
because in two dimensions to find maximums and minimums you have to look for critical points and look on the boundary as well, and that f(t) is just the function parametrized on the boundary of R

>> No.9032857

>>9032820
oh oops i see thanks

>> No.9032864

>>9032856
i'm confused what point on the parameterized boundary it is

its not a critical point and the endpoints are 0 to 2pi.

the critical point i get is sin2t = 0, giving t =0 and the endpoints also give 0.

>> No.9032868
File: 238 KB, 1024x768, 1484193851775.jpg [View same] [iqdb] [saucenao] [google]
9032868

I could study physics at the 2nd best uni in my country and be jobless or I could be a gay and make money.
What do?

>> No.9032882

>>9032327
FUCK bitbean

>> No.9032892
File: 39 KB, 640x633, l8e3m78m4uwx.jpg [View same] [iqdb] [saucenao] [google]
9032892

>>9029773
>We're going to find out if 35 goes into 16

>> No.9032905

>>9032864
>its not a critical point and the endpoints are 0 to 2pi.
but it is

f(t)=2+sin^2(t) has critical points when f'(t)=2sin(t)cos(t)=0, so when t=0, pi/2, pi, 3pi/2 or 2pi

t=0, pi and 2pi give minimums of f, t=pi/2 and 3pi/2 are maximums of f

>> No.9032938

>>9032905
ohhh thanks so much, i was doing the derivative as sin(2t)

does this still work when you do the derivative as sin(2t) rather than 2sin(t)cos(t)?

>> No.9032941

>>9032938
>does this still work when you do the derivative as sin(2t) rather than 2sin(t)cos(t)?
of course, sin(2t)=0 in the interval [0, 2pi] for t still has solutions t=0, pi/2, pi, 3pi/2, 2pi

>> No.9032946

>>9032941
oh shit i wasnt considering what the 2 was doing to the sine wave

thanks a lot!

>> No.9032987

>>9032882
agreed, but if you lost money on bitbean, you should have seen it coming from a mile away, and you shouldn't have put a lot of money into it anyway because of the high risk, let it be a learning lesson

>> No.9033099
File: 74 KB, 716x718, BandGap-Referencer.png [View same] [iqdb] [saucenao] [google]
9033099

Don't quite get the Bandgap-Referencer. I understand the NTAT Voltage, but why is UR3 PTAT?

>> No.9033166

I have mass anxiety. I can never tell if I'm wearing a shirt that is too tight that it's choking me, or if it's just anxiety - my anxiety tends to be centered in the throat area, so I always feel like it's so tight that it's harming my throat. Is there any way to objectively tell that a shirt is too tight that it's doing damage? "Tightness feeling" is not exactly a good threshold because agian, I always feel tightness in the throat due to anxiety.

>> No.9033171
File: 9 KB, 800x422, Capture.png [View same] [iqdb] [saucenao] [google]
9033171

How do I answer this question?

>> No.9033223

What are some good/recommended textbooks for somewhat rudimentary math?
I want to learn shit like vectors but not in an overly confusing way.

>> No.9033372
File: 201 KB, 1120x630, soylent.jpg [View same] [iqdb] [saucenao] [google]
9033372

Anybody regularly use this?

Being a student on a campus who works out and plays sports with nothing but fast food available sucks and im forced to wake up early to pack my own lunch.

I ordered a pack of these from amazon while they were on sale during prime and was wondering what people think of it.

I was concerned about the testosterone effects but after doing some research it seems to be negligible if any.

Not going full soylent of course, just something simple to take to uni during the long days.

>> No.9033385

Can anyone post the info graphic with math books where the last stage is to read Bourbaki?

>> No.9033392

>>9030196
140

>> No.9033675

I've been stuck on this one question all day yesterday I'm looking for some assistance.

Suppose dim(V/N_1) = dim(V/N_2). Prove that dim(N_1/N) = dim(N_2/N), where N is the intersection of N_1 and N_2, arbitrary subspaces of the vector space V. I know the inequality dim(V/N) =< dim(V/N_1) + dim(V/N_2) if it matters.
I realize that even if N_1 and N_2 arent finite dimensional that the quotient space being finite dimensional is like a more general property than being finite dimensional, but dont know how to proceed. I've tried alot of crazy stuff but havent gotten anywhere really

>> No.9033704
File: 53 KB, 600x670, 6436706c9b2528c55c9ff3f172bd76de.jpg [View same] [iqdb] [saucenao] [google]
9033704

Is it plausible that some big setup with a bunch of scientific equipment would actually produce top-tier coffee?

>> No.9033709

>>9033385
Second this.

>> No.9033717
File: 2.13 MB, 2784x2872, 1490454786394.png [View same] [iqdb] [saucenao] [google]
9033717

>>9033709
this one is optimal

>> No.9033732

>>9033717
Does one really need any prerequisites for Aluffi's book? Personally I was able to work through this book with knowing like 70% precalculus and 60% calculus I. I was 18 at that time

>> No.9033734

>>9023428

how do I calculate the energy needed to accelerate 0.1kg to 0.5c but that is including relativistic effects?

>> No.9033741

>>9033732
>Does one really need any prerequisites for Aluffi's book?
Strictly speaking no, just a non-zero level of 'mathematical maturity'

>> No.9033787

>>9033704
yeah you just need good fresh beans and get the brew right

>> No.9033911

How do I prove

[eqn] \sum_{i=1}^{n}a_{i}^{2} \sum_{i=1}^{n}b_{i}^{2} - \left(a_{i}b_{i} \right)^{2} = \sum_{1\leq i < j \leq n} \left(a_{i}b_{j}-a_{j}b_{i}\right)^2 [/eqn]

by induction?

for the basis I let n=1 and get

[eqn] 0 = a_{i}^2b_{j}^2 - 2a_{i}b_{j}a_{j}b_{i} + a_{j}^2b_{i}^{2} [/eqn]
or equivalently
[eqn] 2a_{i}b_{j}a_{j}b_{i} = a_{i}^2b_{j}^2 + a_{j}^2b_{i}^{2} [/eqn]

but I'm not sure what to do next.

>> No.9033912

>>9033911

shit, the LHS should read

[eqn]\sum_{i=1}^{n}a_{i}^{2} \sum_{i=1}^{n}b_{i}^{2} - \left(sum_{i=1}^{n}a_{i}b_{i} \right)^{2} [/eqn]

in the problem statement

>> No.9033917
File: 49 KB, 253x213, tfw.png [View same] [iqdb] [saucenao] [google]
9033917

>>9033912
>>9033911

oh wait, the indices are supposed to disappear aren't they

>> No.9033925

>>9033917

or...not disappear but rather be a_{i=1}, b_{i=1}, a_{j=1}, b_{j=1} and so the last line of my workings is thus equal...r-right?

>> No.9033942

>>9033925

a-and, the inductive step is just showing the k+1 terms 'cancel out', r-right. I'm the poster boy for brainlet of the year

>> No.9033943

Hi guys. I took an IQ test (in person over the course of several hours) recently and found out that my Spatial intelligence is within the top 0.01 percentile. I scored above average in all other areas as well but nothing special.

Are there any fields of Math or Physics that I might be able to truly excel at?

>> No.9033946

>>9033943
>>9033911

>> No.9033955

>>9032868
study both and reject family

>> No.9034001
File: 66 KB, 554x400, 1498243955848.png [View same] [iqdb] [saucenao] [google]
9034001

>>9023428
Hello sirs
What would happen if electronegativity didn't exist in the universe - as in all atoms share electrons equally?

>> No.9034041

How bad is it to have all of your degrees from the same school? I'm in a NE master's program right now and there's a chance for me to do a PhD on an experiment in France. I'll definitely be applying elsewhere but it sounds kinda nice.

>> No.9034074

Ok, I'm just having a little trouble approaching probability from a practical standpoint.

Lets say you had a data set, and someone tells you to give them probability of X event based off the data.

What is the proper way to answer? Couldn't I just use the relative frequency? Or do I have to identify the type of distribution and compute the PDF? And if its the former, then what exactly is the PDF actually used for?

They both yield an answer less than or equal to 1, after all

>> No.9034274

>>9034074
In a scientific/academic context, p=x where x is 1 or less.

In any other context, just use a percentage.

>> No.9034408

>>9024588
You forgot 0

>> No.9034429

>>9033171
tell them what they want to hear
look for some buzzwords in the job description or whatever it is and reword them into an answer

>> No.9034481

What's a good way to practice actually writing proofs? In my abstract algebra class or just some of the more advanced real analysis classes it always felt like I had the right ideas of how to prove things but on tests I'd get hammered for being 'too informal.' It seemed like I had a problem with actually communicating my proofs well, and I wanna fix this but i dunno where to start.

>> No.9034533
File: 15 KB, 536x184, exerciseimg.png [View same] [iqdb] [saucenao] [google]
9034533

Ultra brainlet here.

Having trouble with the second exercise. The data the exercise is referring to is the volume of Earth's oceans (1.36 x 10^9 cubic kilometers) and the answer is 1.2 x 10^4 ft.

What exactly am I supposed to do? I tried calculating the cubic root of the volume , the square root of the area (then dividing it by 6) , adding the respective results, dividing the sum by 2 and finally using the conversion factor feet-km to get the average depth. Needless to say, nowhere close to the answer.

Really struggling with this. Any help would be appreciated.

>> No.9034546

>>9034533
Divide the volume of Earth ocean by the 71% of the surface area of Earth.
With that you have the average depth and convert it to feet.

>> No.9034549

>>9034546
The volume is of earth is equal to the surface area multiplied by the height)

>> No.9034560

Imagine that Cambrian explosion would have happened not 600 millions years ago, but much earlier, about 3 billion years ago. That'd be awesome, the humanity would be 2.4 billions years ahead in technology, maybe we would already answered the question about extraterrestial life.

>> No.9034565

>>9034549
no

>> No.9034622 [DELETED] 

>>9034560
The big problem is that there wasn't enough oxygen for complex multicellular life.

The original atmosphere on earth (after things cooled down enough for the water vapor to rain down and create the oceans) was about a third carbon dioxide, a third nitrogen, and a third hydrogen.

Tiny little photosynthetic organisms had to work for about a billion years to turn most of the carbon dioxide into the atmosphere into carbon.

Also, iron rusts, and the earth had a lot of iron deposits exposed to the air, so the earth's crust soaked up most of the excess oxygen until the bacteria had produced enough oxygen to rust every iron deposit in the earth's crust.

>> No.9034626

How much does GRE really matter for EE grad school? My gpa and everything else is fine, just took GRE and got a 167Q, 161V, and a 4.5 writing. This should be fine for any top unis right?

>> No.9034628

>>9034560
The big problem is that there wasn't enough oxygen for complex multicellular life.

The original atmosphere on earth (after things cooled down enough for the water vapor to rain down and create the oceans) was about a third carbon dioxide, a third nitrogen, and a third hydrogen.

Tiny little photosynthetic organisms had to work for about a billion years to turn most of the carbon dioxide into the atmosphere into oxygen molecules.

Also, iron rusts, and the earth had a lot of iron deposits exposed to the air, so the earth's crust soaked up most of the excess oxygen until the bacteria had produced enough oxygen to rust every iron deposit in the earth's crust.

>> No.9034641
File: 99 KB, 640x640, confused looking anime girls with interrogation marks on their heads 2.jpg [View same] [iqdb] [saucenao] [google]
9034641

Could the reason that red is such an eye-catching color be because our eyes have evolved to make it easy to see blood?

>> No.9034654

>>9034565
>no
What did he mean by that?

>> No.9034670

>>9034654
>The volume is of earth is equal to the surface area multiplied by the height
this would be true if the earth was flat, but it is not

>> No.9034672

>>9030196
100, by definition. It may however correspond to a different overall ability (megaflops if you will)

>> No.9034681

>>9032027
Well, ideally it would as you apply work to the object. If it was gas, that "shrank" then no, unless P*V changed. But any work means heat

>> No.9034690

>>9034560
>the humanity would be 2.4 billions years ahead in technology

Probably not

>> No.9034694

>>9032882
>he invested in a meme

lol you're supposed to mine and dump

>> No.9034706

>>9034670
obviously not in the real case but for sake of simplicity in that exercise is implied like that. Read the context and don't be so dense

>> No.9034723

>>9034546
>>9034549
Thank you very much.

>> No.9035065

Hello, i've recently been learning about the Cardiovascular System and have come across the Endothelium - which is the inner lining of the blood vessel walls and heart chambers.
Its function is to act as a non-stick layer that prevents blood from sticking and clotting to the vessel wall...

I was wondering, is there a thing (a substance, pathogen, etc...) that is able to dissolve or remove this layer in a living organism specifically?

>> No.9035459

Assuming I had enough gear reduction, could I actually use a tiny DC motor to lift a bus, albeit at extremely slow speeds? Or am I missing something?

>> No.9035579

>>9035459
It would work, but the speed might be a millimetre per year.

>> No.9035592

Maybe not that stupid of a question but I have a choice to study either Computer Engineering or pure Software Development.

I've heard most people who study anything in the IT field will almost always later work as a software developer. Is there any point in studying CE then?

>> No.9035614
File: 8 KB, 222x188, inductionhandwave.gif [View same] [iqdb] [saucenao] [google]
9035614

I'm somewhat confused by the handwavy shit I've been fed in electromagnetism 1:

>In a uniformly increasing magnetic field as pictured, what does the induced electric field actually look like?

Consider the loop in a constantly increasing magnetic field as with pic related and assume the field extends beyond what is pictured. The electric field is counter clockwise around the loop, right? If I imagine another loop to the right that shares some single point with this loop(without interacting), I seem to get a contradiction in the direction of the electric field. What's really going on?

>> No.9035683
File: 29 KB, 489x366, mio-8.jpg [View same] [iqdb] [saucenao] [google]
9035683

>>9023428
Anyone does some drugs like ritalin, concerta etc to study? specifically for it and how did you get it from doctors? what do you pay /month to get it?

I have like absoulte zero focus i could not even write this sentence without switching tabs or spacing out like a dumbo. It's hard to get anywhere when you can't even listen to a teacher for half a lecture.

>> No.9035735

>>9035683
Dunno if this works for everybody, and it's not a pill but whenever I see I'm getting distracted easily while I'm studying I focus more and then I don't get distracted as much.

>> No.9035764
File: 393 KB, 696x717, 1499794838174.png [View same] [iqdb] [saucenao] [google]
9035764

>>9035735
this is one hell of a weird method, anything is worth trying tho thanks!

>> No.9036057

>>9035683
I tried adderall a few times and while my ability to get work done improved I always felt like shit afterwards. I used to get it from a friend who actually needed it, so I never had to pretend I had ADHD or anything to a doctor. I've heard that's very easy to do if you have to though.

What I do now is just go to the library without any technology (no laptop or phone) and study there. Seems to be more effective and I don't feel like shit once the adderall wears off.

>> No.9036561

>>9035579
That's what I thought but it still seems a bit counterintuitive. Could it be that in most cases, if I tried something similar, the additional losses introduced by adding larger and larger gears would result in friction torques that would basically negate any kind of mechanical advantage you'd get from said gears?

>> No.9036582

what causes the smell of coffee to linger in the air? especially if it's a dark roast. do i need to dehumidify the air in my room or what i can do?

>> No.9036617

>>9036582
>what i can do?

Why though? Do you live in Indonesia or something? Will you be put to death for the possession of stimulants?

>> No.9036645
File: 189 KB, 626x690, 1485139665684.png [View same] [iqdb] [saucenao] [google]
9036645

I need help, this could change my life for better.
When top universities look for students, they basically are looking for top grades and additional stuff (reccomendations letters of teachers, chess club, debate club, that kind of shit). I have tons of those "extra" things, but I have C average grades.
My question is, how hard or easy would it be to lie about my grades? What top universities would be best to "cheat" to get into? I swear I'm not a brainlet, I have been doing calculus since 13 but I had depression during high school and that fucked me real time. I am not from America so they are probably going to want me in for muh diversity.
Please help.

>> No.9036649

>>9036645
you're a fucking brainlet and also a dishonest fuck
you don't deserve shit
don't even go to any university, piece of shit

>> No.9036664

>>9036645
just take a GRE in a relevant subject (eg physics/math, or english)

>> No.9036667

>>9036645
Nigga, what do you think you do at a uni?

Spoilers: It's classwork, same as in high school.

>> No.9036677

How do I go from being addicted to weed to being addicted to math?

>> No.9036685

>>9036617
the stale coffee smell is fucking disgusting mate

>> No.9036687
File: 556 KB, 838x455, 1461471382257.png [View same] [iqdb] [saucenao] [google]
9036687

>>9036667
I know what uni is like. It's just that I had extreme depression in highschool. I would skip up to one whole month of classes, including test days. I would mostly go only on test days, and take only enough tests, answering only enough questions, so I can pass to the next grade with the minimum effort. Little did I know what consequences would this have. On the other hand I have tons of extra curricular things. Math Olympics, Astronomy Olympics, Astronautics Olympics, Homemade Rocket Contest, best entry at Science Fair, some 5 UN Model Simulations, chess championships, CEFR certificates, among [math]several[/math] other things. And also affluent parents that can afford paying for tuition and housing. If I had a 4.0+ GPA I could probably make it into any cawllege I wanted. I just need to do something about the GPA.

>> No.9036694

I'm building a small robotic vehicle. I need to figure out the power rating i need for my motor(s). Is there any way of doing that without knowing the exact friction forces and losses i'll have once the thing is built? No right? All I can do is eyeball it?

>> No.9036705

>>9036687
there's nothing you can do about your GPA now.
Things you can do:
>GRE in math and physics
>Letter of recommendation from supervisors of the activities you listed
>Cover/Motivational letter explaining who you are, what you can do, and why your GPA is the least relevant thing on your CV (ok not exactly like this but hopefully you get what i mean)

>> No.9036710

>>9036705
Isn't it just easier to lie? I praise honesty, integrity and honor a lot, but all the time I see undergrads on /sci/ saying they lied about their grades.

>> No.9036711

>>9036687

I know a big part of cawlij is being seen in the right place with the right people - but seriously, it's fucking undergrad. Go somewhere merely good, crush everything and extend your studies in your own time, then look to transfer/exchange/climb or whatever it is you think you need after you prove yourself.

If you're competent, you won't let your school get in the way of your education.

>> No.9036721

>>9036645

Take a gap year so you have time to retake your exams and apply again? Not sure if this is an option in your country but it certainly is in the UK. Universities in the UK don't view it negatively at all, just make sure you show you spent some time volunteering/working too to help justify your decision.

If you take a year out it could also be good for your mental health - and your emotional maturity. Higher education and living alone is actually a lot of pressure and stress, and a lot of people end up dropping out or failing.

>> No.9036724

>>9036710
ok anon let me put it this way: if you lie on your application I will be very disappointed in you and I might have to call your parents.

Also, what makes you think you're more deserving of a spot at a top college than someone who doesn't lie about their grades?

>> No.9036731

>>9036724
Weren't you listening? He has wealthy parents and was in model UN but also chess competitions!

>> No.9036745

>>9036710
Of course it's easier to lie. But then why stop at lying about your grades? You could just write a CV where you have a degree already and start applying for jobs. Then you save tuition money that you can use to buy a sweet car by going to the DMV and lying about having a driver's license. Just keep lying about everything until one day the FBI catches you and they make a movie about you starring Leonardo Di Caprio and Tom Hanks.

Lying is always the easier option but as it turns out sometimes it is more satisfying to have things knowing you earned them.

>> No.9036746

>>9036745
>Just keep lying about everything until one day the FBI catches you and they make a movie about you starring Leonardo Di Caprio and Tom Hanks.
That actually sounds cool.

>> No.9036755

>>9036746
except by the time you'll be done they'll be old as fuck and it'll be a movie about two grandpas chasing each other around the geriatric ward at sloth-like speeds while mumbling incomprehensibly at each other.

>> No.9036766
File: 65 KB, 800x562, 18mld7f74mocfjpg.jpg [View same] [iqdb] [saucenao] [google]
9036766

How do i find the area?
f(x,y) = 1 + x^2y^2, Region is bounded by x = y^2 and x=4.

Answer given is 2336/27.

>> No.9036812

>>9036766
>f(x,y) = 1 + x^2y^2
>area
Are you supposed to project it to z=0? I'm confused

>> No.9036817

>>9036687
Same tee bee aytch

I just went to community college for a while to get a better GPA and then transferred into a college.

>> No.9036891

>>9036766
You don't find the area, you find the volume.
1. Integrate 1+x^2*y^2 wrt x
=> x+y^2*x^3/3.
2. over the range [y^2,4]
=> (4+y^2*4^3/3) - (y^2+y^2*(y^2)^3/3)
= -y^8/3 + 61/3*y^2 + 4
3. Integrate wrt y
=> -y^9/27 + 61/9*y^3 + 4*y
4. over the range [-2,2]:
2*(-2^9/27 + 61/9*2^3 + 4*2) [f(-x)=-f(x) => f(x)-f(-x)=2*f(x)]
= 2*(-512/27 + 61*8/9 + 8)
= 2*(-512 + 3*61*8 + 8*27)/27
= 2*1168/27
= 2336/27

>> No.9036898
File: 647 KB, 2361x2358, FutureSoBrightIGottaWearShades.png [View same] [iqdb] [saucenao] [google]
9036898

Is there a theoretical way of having permanent night, given that the Earth has a way of sustaining itself without the sun?

>> No.9036984
File: 30 KB, 414x472, 1462355707381.jpg [View same] [iqdb] [saucenao] [google]
9036984

>>9036891
thank you glorious being

>> No.9036997

>>9036898
nuclear energy

>> No.9037016

>>9036891
wait why is y bounded from -2 to 2?

y= sqrt(x) so how can x be negative?

>> No.9037066

Are /sci/entists able to work under the influence? I don't want to imbibe ethyl alcohol. It numbs the nervous system and impairs my cognitive faculties. Maybe you have an IQ of 200 so you don't mind the temporary loss of intelligence under the influence of ethanol, but I'm not a genius and the world is difficult enough to grasp sober.

>> No.9037367

>>9037066
The IQ drop only starts to kick in after 2 or more drinks.

You're supposed to only have one to two servings.

>> No.9037373

>>9037367
>The IQ drop only starts to kick in after 2 or more drinks.
>You're supposed to only have one to two servings.
I just assume that people who drink alcohol must be geniuses. How else could they still process the world in that state?
I'm not a dummy, but my brain capacity is 100% utilized when unimpaired and I still discard the majority of all sensory inputs.
Good for you, if you're smart enough to function acceptably under alcohol. I'm not.

>> No.9037433

>>9037373
I can only play pool if I'm a little buzzed.

>> No.9037672

Looking for some reputable, free places I can go on the internet to keep up to date with things going on in Math, Sci, Tech, etc? I always hear people saying, "this week in the journal science" etc, etc. I'm assuming all of this is behind a paywall though.

Is their any sites that aren't behind a paywall, or are reasonable and offer a wide variety of topics across all research fields?

>> No.9037736

>>9037016
> why is y bounded from -2 to 2?
The integral is supposed to be finite. Given that it's over y^2<x<4 => y^2<4 => -2<y<2.

> how can x be negative?
Who said anything about x being negative?

>> No.9037738
File: 12 KB, 260x194, IMG_8257.jpg [View same] [iqdb] [saucenao] [google]
9037738

Why do caterpillars fall from trees? Are they trying to switch trees? Aren't they certainly dead walking on the ground aimlessly ?
I asked this before but I didn't make my question clear.

how can they tell where their next trees are?
I sometimes followed these caterpillars and they never reached another tree.

>> No.9038120

>>9037672
> I always hear people saying, "this week in the journal science" etc, etc. I'm assuming all of this is behind a paywall though.
You can use http://sci-hub.bz/ to get around the majority of paywalls

>Is their any sites that aren't behind a paywall, or are reasonable and offer a wide variety of topics across all research fields?
http://arxiv.org/

>> No.9038189

>>9037738
they can fall off because they are just stupid like you said but i would imagine that wind, rain and predators are more common reasons.
caterpillars dont need a tree that badly, they can and do survive on most plants. forests or overgrown open fields offer plenty of places to hide and food to eat even if you arent on a tree
>how do they know where the next tree is
they dont

>> No.9038224
File: 12 KB, 236x229, 2929e470710350b12d9b3a55d724d3d7.jpg [View same] [iqdb] [saucenao] [google]
9038224

In a Factory line the 2% of Laptop produced is defective.

What's the proability that in a batch of 100 laptops 2 will be defective? What about 3?

Pls help, I'm a severe brainlet and I hate statistics :(

>> No.9038338

Why does water from the tap feel cold on my hands but lukewarm in my mouth? Isn't the inside of my mouth much warmer than my hands, so shouldn't the water feel even colder by comparison? Obviously this isn't the case but I don't understand why not.

>> No.9038371

>>9038224
>What's the proability that in a batch of 100 laptops 2 will be defective? What about 3?

100% odds of two laptops being defective as you already said that 2% of the laptops that the factory produces are defective, and 2% of 100 laptops is exactly 2.

0% odds of there being 3 defective laptops for the same reason.

Now, if you weren't a complete fucking moron and stated the problem correctly by saying "each laptop produced has 2% chances of being defective" then there would be 0.04% chances of there being 2 defective laptops and 0.0008% chances of there being 3 defective laptops.

>> No.9038394

>>9038371
I think it's the question written in my book that is worded vaguely. I think it was a trick question and the solution is 0 of there being 3

>> No.9038397

>>9038394
Ah then the first solution is true.

>> No.9038428

>>9038397
how did you get the second solution though? What formula did you use? Binomial probability?

>> No.9038434

>>9038428
(2%)^2 = 0.04%
(2%)^3 = 0.0008%

>> No.9038439

>>9038434
Yes, but the question stated that there are 100 laptops in total

>> No.9038442

>>9038439
Yeah but for the second I stated a different problem. If each laptop has a 2 percent change of being defective then the total amount does not matter.

I assumed this was the actual problem to be solved, because the problem you gave is actually really dumb. I don't know why someone would ask something so trivial.

>> No.9038541
File: 283 KB, 416x416, shaking-dolphin.gif [View same] [iqdb] [saucenao] [google]
9038541

Does every set made up of countable members have measaure 0?

>> No.9038559
File: 28 KB, 463x513, 1475147848465.jpg [View same] [iqdb] [saucenao] [google]
9038559

>>9038541
If we are using the Lebesgue measure, then yes.

A funny consequence is that in a parking lot with only countably infinitely many white cars, almost no car is white.

>> No.9038571
File: 3 KB, 190x56, Screenshot_1.png [View same] [iqdb] [saucenao] [google]
9038571

>>9038224

>> No.9038582

>>9036766
do you mean the surface?

>> No.9038596

>>9038224
P(X=2) = 0.02^2 * 0.98^98* (2 choose 100)
P(X=3) is analogous

>>9038371
Bullshit, the description of the problem is fine

>Factory produces laptops, 2% of which defective
>For a sample of 100 laptops, how many are defective
What if the question asked about 110 laptops instead of 100? Would you say then that exactly 2.2 laptops are defective?

>> No.9038677

>>9023428
is math related to science - katy perry

>> No.9038861

Can someone explain a quick thing about Bell's theorem for me?

Everything I keep reading online about it, I understand it to the point that they say "if local variables existed, this is the % of the time the experience would get the same results."

But then the videos and articles always pull a "but real experiences don't come to the same conclusion" and then stop there. If its something about spin, it says instead of 5/9 of the time its the same, it comes out to 1/2 of the time. If its about polarization it sais instead of 1/3 of the time, experiments only stay above 1/4 of the time.

But they never explain why, or show any math as to how that would work would. Why, lets just say for spin, do the particles match 50% of the time?

>> No.9038871
File: 34 KB, 784x532, Capture.png [View same] [iqdb] [saucenao] [google]
9038871

>>9038596
doesn't seem right

>> No.9038877

>>9038861
It doesn't matter why it comes out how it does, the whole point of Bell's is to say that the local variables are wrong.

Since experiments show that it is less accurate than local variables would allow, local variables must not be used to decide something about a particle

>>9038871
it should be 100 c 2, but its otherwise right

>> No.9038885

>>9038189
i see. Thanks. And thank the guy who replied me in last thread

>> No.9038914

How much chemistry do I need to know to get into rocket fuels? I mostly want to know if my fuel will corrode my tank structure, if it will evaporate, how much energy density it has, how expensive it is, the temperatures involved etc. And please recommend some books on the subject.

>> No.9038924

>>9038914
Depends on what you want to do.

I'm pretty sure you can just buy APCP online.

If you want to deal with liquid fuels, the oxidizer is going to be a bitch. LOX hates you. High concentration H2O2 hates you. Hydrazine and other monopropellants really, really hate you.

>> No.9038932

>>9038924
Right now I only want to study it. Starting from the basics, chemical structure, reaction, energy, production, containment, etc. A book would be nice.

>> No.9039000

>>9038932
Do you have a CHM-101 level education?

Because the basics, like balancing equations, energy density, stoichiometry are all covered in an intro chem class.

You don't really even need to know them so much as

>specific impulse of the propellant
>correct fuel-oxidizer ratio
>engine efficiency
>Tsiolkovsky rocket equation for the desired level of delta V
>if it's a gaseous propellant, pressure levels

Also, solid rocket fuels are easier to deal with than liquid or gas, hypergolic fuels are really dangerous, and both liquid hydrogen and liquid oxygen have the potential transform you from a solid into a liquid if you fuck around with them.

>> No.9039046

>>9039000
>Do you have a CHM-101 level education?
Yes, but it's rusty. Also
B O O K
O
O
K

>> No.9039073

>>9039046
Did you keep your textbook?

If so, you're better than me, I didn't even bother to buy one for the class.