/sqt/ /qtddtot/

[Anonymous No.10573543]

Stupid questions thread. Previously >>10554321
Dedicated to the faggot who makes /sqt/s on /g/.

[Anonymous No.10573555]

If I have all the pentagonal numbers from 0 to 40,000, is there a quick way I find out what numbers are not a sum of any combination of 3 of those numbers ?

[Anonymous No.10573560]

>>10573543
Those are cute Touhous.

[Anonymous No.10573928]

I have very, very bad test anxiety.
I've noticed that I also have a hard time seeing the way forward in a problem, and I think that contributes a lot. It's as if I have no confidence in my math skills whatsoever. I frequently get lost in the algebra when working through my calculus problems.

How do I build confidence in my mathematical ability and stop relying on crutches like a solutions manual to come to the right conclusions? It's severely fucking up my ability to perform in tests and my grades are nosediving because of it.

[Anonymous No.10573944]

>>10573928
I find this problem is less mechanical (ability) and more mental (emotional) in nature.

Freshman year of HS I had a bad experience at a math competition and similar stuff happened to me. The key is to not care about grades but care about the material itself, the grades will come.

For example: for hw you could use whatever book your school gives you, but for your own personal study of calculus make sure you have a high quality textbook to help you through the subject. Study because you want to learn the material rather than for the grade.

Once the grasp on the material is firm, then you recalibrate and try to get good at taking tests. The order is important here.

[Anonymous No.10573976]

What material should I use to store HCl gas? Will it corrode metals or does it only do that when it gets wet?

[Anonymous No.10573991]

>>10573543
Okay, /diy/ohm redirected me here.
How do I make a reflector for this contraption on cheap, so I can use it on e-bike, without risking being beaten to death by ongoing traffic.

[Anonymous No.10573992]

>>10573991
Forgot pic

[Anonymous No.10574108]

How to simplify pls

[Anonymous No.10574153]

>>10574108
[math]1 + \frac{2}{1 \pm \sqrt 3}[/math], and it can't be simplified futher unless you want more dumb [math]\pm[/math] and [math]\mp[/math] appearing in the expression.

[Anonymous No.10574156]

>>10574153
wait, I suck dicks. [math]\displaystyle 1+\frac{2(1 \mp \sqrt 3)}{1-3^2} = 1+\frac{2(1 \mp \sqrt 3)}{-8} = 1-\frac 1 4 (1 \mp \sqrt 3)[/math] works as well.

[Anonymous No.10574158]

>>10574108
Conjugates of irrational expressions
[math]\begin{align*}
1+\frac{1}{\frac{1+\sqrt3}{2}} &= 1+\frac{2}{1+\sqrt3}\\
&= 1+\frac{2(1-\sqrt3)}{(1+\sqrt3)(1-\sqrt3)}\\
&= 1+\frac{2-2\sqrt3}{1^2-(\sqrt3)^2}\\
&=1+\frac{2\sqrt3-2}{2}\\
&= \frac{2\sqrt3}{2}\\
&= \sqrt3
\end{align*}
[/math]

The other case (where the starting denominator is [math]\frac{1}{2}-\frac{\sqrt3}{2}[/math]) is left as an exercise for the reader.

[Anonymous No.10574668]

>>10573991
Are you sure they didn't direct you to >>>/diy/sqt ?

[Anonymous No.10574680]

What force do I poses to lift my hand up in the air and defy a force strong enough to bring down a plane?

[Anonymous No.10574683]

>>10573992
Uhm, take a reflector and some hot glue?

[Anonymous No.10574696]

>>10574668
Sure 100%.
>>10574683
How can I design a reflector?

[Anonymous No.10574705]

>>10574680
Are you talking about gravity? The force is proportional to mass. Your hand has tiny mass compared to a plane, by several orders of magnitude.

[Anonymous No.10574757]

Does that than mean I of smaller proportion of mass, my hand produce a gravitational force stronger than the gravitational force earth produces?

[Anonymous No.10574763]

>>10574757
It means the force of gravity on your hand is less than the force your skeletal muscles exert on your hand.

[Anonymous No.10574808]

>>10574763
Yes, however I am curious how is it that in relation to earth's gravity force which is so much stronger I am able to overcome it, merely by raising my hand up!

[Anonymous No.10574899]

[eqn]
\ln(x+1)=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}x^n
[/eqn]

How do I prove this converges for -1 < x <= 1?

[Anonymous No.10574903]

>>10574808
Mass of yer hand ~= 0.575% of body mass
(sauce: exrx.net/Kinesiology/Segments)
Mass of airplane = fuckhuge
Force of gravity on hand = 0.575% * body mass * 9.8 N/kg
Force of gravity on plane = fuckhuge * 9.8 N/kg

[Anonymous No.10574922]

>>10574899
When |x| < 1, it converges absolutely (by comparison with the geometric series, for example)
When x = 1, you can use the alternating series test, or compare it with the sum of 1/n^2 by considering partial exams

[Anonymous No.10574924]

>>10573543
>/qtddtot/

What is it ?

[Anonymous No.10574925]

>>10574808
Because gravity is weak. You hand weighs half a kilogram (very approximately). So there is only about 5 newtons of force acting on your hand (very very roughly). 5 newtons is tiny.

[Anonymous No.10574933]

>>10574924
questions that don't deserve their own thread
lurk moar, newfriend

[Anonymous No.10574935]

>>10574924
Questions
that
don't
deserve
their
own
thread

[Anonymous No.10574944]

>>10574903
Thank you.
I see what you mean.

So essentially mass produces gravity, gravity that is mass attracts mass proportinaly , or as close to.

I think I view gravity differently, I see how it works and for some reason which I must take some time to define I believe it works differently!

Silly stuff, given you explained it very well! Thanks.

[Anonymous No.10574967]

If time slows the fuck down while approaching the event horizon of a black hole does that mean all the mass the blackhole has accumulated is concentrated near the event horizon from our perspective?

[Anonymous No.10574982]

>>10573543
how do I prove that playing touhou is an NP hard problem?

[Anonymous No.10575470]

does everything alive shit? not plants obviously but if i let a dirty dish sit and it smells is that microscopic turd smell?

[Anonymous No.10575552]

Why does my brain compose much better music in my dreams as opposed to being awake? Whenever I make up music while awake, it's shit and boring. In my dreams, though, I get some sick original soundtracks.

[Anonymous No.10575553]

>>10574158
Thanks for the help
I’m pretty sure you can simplify both cases at once; the conjugate of 1 +/- root 3 would be 1 +/- root 3

[Anonymous No.10575592]

>>10575552
Do you actually write those things down or do you just think that? I used to have amazing revelations in dreams and started writing them down in the morning. Turned out, they suck.

[Anonymous No.10575610]

>>10574696
You buy it. Usually it's an array of mirrors in pyramidal patterns so that light gets reflected under 180°

[Anonymous No.10575615]

>>10575592
What kind of revelations?

[Anonymous No.10575620]

>>10574944
Gravitational force between two masses is always a product of those two masses. In this case it's the mass of the earth and the mass of your Hand. Since the mass of the earth is pretty much constant, it IS proportional to the thing you look at. At the surface the proportionality factor is roughly 9.81 m/s^2

[Anonymous No.10575634]

>>10575615
Mostly philosophical or about psychology

[Anonymous No.10575692]

How do I recover from a devastating hit to my career? I was in grad school for a master's, but I failed a single class due to a miscommunication and while I still got my master's, no grad school seems interested in picking me up for a PHD program.

[Anonymous No.10575700]

>>10575692
Of they didn't take anyone with a single failed course, they'd take virtually no one.

[Anonymous No.10575749]

>>10575692
It might have been because the graduate program you were applying to was underfunded and they have to make some cuts.

[Anonymous No.10575866]

I'm doing a review question where it asks to test the null hypothesis that a coefficient ß=1 at the 5% level, so I just did a t-test. I failed to reject the null, but then I thought afterwards that I'd also fail to reject the null if it was H0: ß=0. So I'm a little confused about what even to think. How can I fail to reject it equaling two different numbers?

[Anonymous No.10575905]

This might be better for /an/, but did dinosaurs behave more like birds or more like lizards and crocodiles. I get that they are all in the class reptilia at the end of the day, but am still looking for any solid facts (or believable opinions) that you can give.

[Anonymous No.10575990]

>>10575692
apply for the lower tier grad school

[Anonymous No.10575996]

Can a 3x3 matrix represent 3 different points in 3-dimensional space? With each column being a different point, and each row being a different component? Does this extend to higher dimensions? Does this apply to genomics where each column is an individual and each row is the genotype value at a specific SNP? Is PCA just finding the two (or three) rows that have the highest variance and projecting them onto two or three axes?

[Anonymous No.10576257]

>>10575996
>Can a 3x3 matrix represent 3 different points in 3-dimensional space?
YES

With each column being a different point, and each row being a different component?
YES.

Does this extend to higher dimensions?
Only for matrices 4 x n or higher. For example a 4 x 5 matrix can represent five points in the 4th dimension.

> Does this apply to genomics where each column is an individual and each row is the genotype value at a specific SNP?
Not sure

> Is PCA just finding the two (or three) rows that have the highest variance and projecting them onto two or three axes?
I don't know

[Anonymous No.10576265]

>>10574967
Just because time slows to a halt at the event horizon (from the perspective of a far-away observer), is not sufficient at mean that all the mass is condensed at the surface of the event horizon.

Schwarchild's solution to Einstein's field equations models the black hole with an infinitesimal singularity at the center. This theory predicts that an observer's proper time will halt compared to a time elapsed from a far-way observer.

[Anonymous No.10576320]

>>10575990
why bother with a low tier grad school?
Honestly at this point, he should just consider becoming a garbage man

[Anonymous No.10577194]

should i get a brilliantorg account? is it worth it? its only 100/y and thats not a lot for me. or should i just keep to khan academy or pirate books

[Anonymous No.10577247]

>>10577194
No, the problems they post are elementary and don't stimulate. Keep to khan academy. Read books and wikipedia.

[Anonymous No.10577252]

>>10575905
>did dinosaurs behave
You do know that all we have is some bones and fossil shit, right? We don't know much.

[Anonymous No.10577254]

Two questions about the Chebyshev's inequality:

1) For a random variable [math]X[/math], [math]EX = \mu[/math] and [math]DX = \sigma^2[/math]. Use the Chebyshev's inequality to find the upper bound to the probability [math]P(|X - \mu | \geq 7.6 \cdot \sigma)[/math].

2) Let [math]X[/math] a random variable which shows the number of hours between two cars passing a building. Use the Chebyshev's inequality to find the lower bound to the probability that after the first car passes the building, the time it takes for the second car to pass the building is within the interval [math](1.5h; 4.5h)[/math] if is known that [math]EX = 3[/math] and [math]DX = 0.5625[/math].

[Anonymous No.10577265]

>>10577254
For # 1):
https://en.wikipedia.org/wiki/Chebyshev%27s_inequality#Probabilistic_statement

The upper bound of the probability [math] P(|X - \mu | \geq 7.6 \cdot \sigma) [/math] is [math] \frac{1}{7.6^2}[/math].

[Anonymous No.10577287]

>>10577254
For # 2):
https://en.wikipedia.org/wiki/Chebyshev%27s_inequality#Inequalities_for_bounded_variables

Lower bound = [math] \frac{\operatorname{E}(|X|^r ) - k^r }{M^r} = [/math]

[Anonymous No.10577310]

>>10577287
Thought about it a bit and approached the solution like this:
[math]P(1.5 < X < 4.5) = P(-1.5 < X - 3 < 1.5) = P(|X - EX| < 1.5) = 1 - P(|X - EX| \geq 1.5)[/math]. Using the Chebyshev's inequality, [math]P(|X - EX| \geq 1.5) \leq \frac{0.5625}{2.25} = \frac{1}{4}[/math]. From this [math]P(1.5 < X < 4.5) = 1 - P(|X - EX| \geq 1.5) \geq 1 - \frac{1}{4} = \frac{3}{4}[/math].

Does it seem correct?

[Anonymous No.10577350]

How many elements will S3 have? Please help

[Anonymous No.10577417]

>>10573543
If lim x 3 f (x) = 2 and epsilon=3, how would I go about finding delta?

I know that 0<x-3<delta and that |f(x)-2|<epsilon=3 so we can rewrite this as -3<f(x)-2<3 and then we'd add 2 to the inequality to get -1<f(x)<5 but I'm really not sure where to go from here, there is a graph provided but I want to find delta algebraically and don't really know how we can do this when there is just f(x) without anything we can use to isolate x with.

[Anonymous No.10577426]

What are the production rules for this language? I don't see a way to produce a^k b^m and b^m c^n with only one variable.
Am I missing or misunderstanding something?

[Anonymous No.10577443]

>>10577417
You can't find delta numerically unless you're given an expression for f(x)

[Anonymous No.10577450]

>>10573928
Force yourself to work/study in test environments (timed with nothing but the problems) to get comfortable with it. Doing this makes testing feel normal and manageable, and it should show you what it's like to test without having the added stress.
If you're not willing to do this, you're not willing to improve.

[Anonymous No.10577559]

>>10577350
Show me first: how many terms are in S_2, and why?

[Anonymous No.10577569]

>>10577426
What do you mean, "one variable"? By production rules you mean a context free grammar, right?
Here's one way:
[math] S \rightarrow aS \\
S \rightarrow aT \\
T \rightarrow bT \\
T \rightarrow bU \\
U \rightarrow cU \\
U \rightarrow c [/math]

[Anonymous No.10577592]

Anyone know how to answer this?

[Anonymous No.10577608]

>>10577559
| S2 | = | S1 | + 3|S1| + 3

I got 15 terms - it's probably incorrect.

[Anonymous No.10577670]

>>10577569
Yea constructing the grammars productions rules and by the one variable I mean the S it represents the possible values that can be produced from a rule. What do the T and U represent, are they variables as well?

[Anonymous No.10577685]

>>10577608
Okay, take a look at the "if t1 then t2 else t3" part when you construct S_2.
S_1 has three elements, how many permutations are there?

>>10577670
S is just the start symbol, all uppercase terms are variables, all lowercase symbols are terminal symbols in usual notation.

[Anonymous No.10577700]

>>10577685
I get it now thank you. This makes its so much easier to understand and do.

[Anonymous No.10578027]

>>10577569
That requires k,m,n all >0.
This lacks that restriction:
S->aS
S->T
T->bT
T->U
U->cU
U->ε
An alternative formulation which follows the rules for a right-linear grammar is:
S->aS
S->bT
S->cU
S->ε
T->bT
T->cU
T->ε
U->cU
U->ε
The latter is more straightforward to convert to a DFA.

[Anonymous No.10578036]

>>10578027
Sure, it depends on what their definition of [math]\mathbb N[/math] is.

[Anonymous No.10578114]

I have a line in parameter form and a plane in cartesian form.
How do I find the point of intersection?

[Anonymous No.10578124]

>>10578114
by inserting the parameterized point into the plane equation and solving for the parameter.

[Anonymous No.10578138]

I’ve probably lost right? My queen is absolutely fucked solely because I took a pawn without spending any time contemplating the turn. I’d still play the match out without a queen but I’m sleep deprived with a headache and it would make my headache worse.

[Anonymous No.10578145]

>>10578036
N is the set of all natural numbers. I didn't think it was important so didn't specify .

[Anonymous No.10578156]

>>10578145
Yeah, don't worry about it. I've sat in some courses where [math]\mathbb N[/math] didn't include zero.
But you got the gist anyway, yes? Was this >>10577700 you?

[Anonymous No.10578159]

>>10578138
Maybe that's your problem. You acquiesce to defeat before you even begin!

[Anonymous No.10578168]

Electrical Engineering student here.
Where the fuck do I find internships not related to energy?
Through my school's website, almost everything is student assistants for my states energy division. I've had a few interviews there, but I'm pretty sure the reason I'm not getting accepted is because I keep telling them my main interests are in signal processing when they ask about my classes.
Do I just need to wait until I graduate to look for a job in my main field? Energy is so fucking boring

[Anonymous No.10578177]

>>10578138
Sacrifice knight? Gives you a rook or a revealed check

[Anonymous No.10578185]

>>10578159
Only after I yield a queen with no advantage gained

>>10578177
Moving the knight up means his best option is to take it with his rook - in which case my queen is still completely trapped because his queen is there.

[Anonymous No.10578216]

>>10578156
I understand >>10577569 answer, but I don't understand yours.
S->aS
S->bT
S->cU
Couldn't this produce a string like "acb" ?

[Anonymous No.10578219]

>>10578124
Righty.
If I put all that stuff into the cartesian equation and t cancels out, what does that mean?

[Anonymous No.10578230]

>>10578219
What do you think it could mean? Maybe take a look at whether the plane normal is perpendicular to the line direction vector.

>>10578216
> Couldn't this produce a string like "acb" ?
No, because you can't get a b from a U.
Try to attempt deriving acb. You'll need to start with S -> aS to get the first character. Then you want a c, so aS -> acU -- now you cannot expand your variables to create a b.

[Anonymous No.10578232]

>>10578168
Particle physicist here. We always need guys like you. Basically every physics institute has an EE lab, the bigger the institute, the better the lab obviously. If you're into building hardware that's going to be used at CERN and that kinda stuff.

[Anonymous No.10578236]

>>10575996
>Is PCA just finding the two (or three) rows that have the highest variance and projecting them onto two or three axes?

Kind of, it's about finding the two (or three, or whatever) *linear combinations* of the rows that have the most variance, and projecting onto the corresponding subspace.

[Anonymous No.10578245]

>>10578230
So they don't cross, righty.
So if one of the parameters was a+15t.
Then the line only crosses for a values except for the one that I can get by solving the equation. Because that one is parallel to the plane.
Right?

[Anonymous No.10578252]

>>10578245
Your post is too confusing to understand. Please show your example.

> So they don't cross, righty
Not exactly. There are three possible cases for a line/plane intersection: If the line does not intersect the plane at one point, it is parallel to the plane: in the parallel case, the line could be outside the plane or be a part of it.

[Anonymous No.10578256]

All memes asides is a PhD in Physics actually worth it?

I'm actually considering going for it.

[Anonymous No.10578257]

>>10578252
Line is
x=2+t
y=-1+2t
z=a+t
Plane is 2x-4y+6z=3

[Anonymous No.10578264]

>>10578257
>>10578252
I just realized that I had misunderstood the question completely.
It's not asking for an intersection point, it's asking for the a value where it's inside the plane.
Your first explanation still helped though.
Thanks.

[Anonymous No.10578298]

>>10578256
Depends on your background and what you want to do in life. Here's a few things you won't get:
>money
>free time
>girls

[Anonymous No.10578342]

>>10578230
Oh I see now. But what if there was a string a^2 b^0 c^2. Would b be 1 and if it is 1 does the string become aa1cc ?

[Anonymous No.10578397]

Am I shadow-banned? When does DC flows "backwards"? "current will flow from high potential to low potential.". So it will always go from higher voltage device to lover voltage one, yes? Wouldn't using high voltage/amperage batteries (with step-up DC power source(solar again)) be more cost-efficient than using high voltage AC main grid for level 3 electric vehicle charging stations?

[Anonymous No.10578427]

I have a chance to take a class in existentialism or on justice.
Which is more intellectually stimulating?

[Anonymous No.10578438]

>>10578427
A fleshlight

[Anonymous No.10578477]

>>10578438
While you are indeed right I just want to know which topic is more fun.
I can get the fleshlight after :^)

[Anonymous No.10578487]

>>10578427
Almost every individual is absolutely lurid when it comes to justice. You will probably be subjected to insanity if around justice discussion. At least with existentialism you might get some new ideas in your head. Just my perception/two cents on how I’d anticipate it to be.

[Anonymous No.10578498]

>>10578138
Ne5 allows the possibility of Qxf3+

[Anonymous No.10578562]

>>10578487
Thanks bud.

[Anonymous No.10578651]

>>10578487
>Almost every individual is absolutely lurid when it comes to justice
So, just read one piece instead?

[Anonymous No.10578813]

Any YouTube videos you guys can recommend to learn Microsoft Excel?

[Anonymous No.10579284]

>>10578498
Oh wow good eye, that was without a doubt the best move to have made. I still won anyways because it was against my friend the stoner retard.

[Anonymous No.10579530]

>>10576320
you think it's easy to become a garbage man these days? STEM is so oversaturated that you need a Masters from a good place to run a route, but I think the failed class would hold him back there

[Anonymous No.10579548]

What does "are said to be" mean in the following context? I see it often but am not exactly sure. I think it is used when giving a definition of a term or phrase, is that right? Why not just say "are"?

>The chemical species HA, A−, and H+ "are said to" be in equilibrium when their concentrations

[Anonymous No.10579585]

>>10578397
>Am I shadow-banned?
No
>When does DC flows "backwards"?
What?
>"current will flow from high potential to low potential.". So it will always go from higher voltage device to lover voltage one, yes?
Yes
> Wouldn't using high voltage/amperage batteries (with step-up DC power source(solar again)) be more cost-efficient than using high voltage AC main grid for level 3 electric vehicle charging stations?
Probably. I'm not sure I understand your question, but our grid is AC because power plants deliver AC and it's much simpler to transform to HV/LV. Also because of heavy lobbying.

[Anonymous No.10579654]

>>10578342
Exponent zero means "no occurrence of this character". You're not doing math.

[Anonymous No.10580054]

>>10579548
> I think it is used when giving a definition of a term or phrase, is that right?
Yes.
> Why not just say "are"?
Because that just says that the situation meets the definition, not that it *is* the definition.

[Anonymous No.10580141]

>>10579585
>> Wouldn't using high voltage/amperage batteries (with step-up DC power source(solar again)) be more cost-efficient than using high voltage AC main grid for level 3 electric vehicle charging stations?
Tesla owners confirm that around 80% of the power from a wall reaches their battery (https://teslamotorsclub.com/tmc/threads/home-charging-efficiency.73181/)(https://forums.tesla.com/forum/forums/charging-efficiency-0) Isn't this caused by all this power converting? Can't we go simply from PV panels through DC step-up converter to car battery?

[Anonymous No.10580257]

Okay.
Does anyone have a quick visual guide to vectors, planes, and how to calculate relations?
It's the one thing I have the worst understanding of.

[Anonymous No.10580294]

>>10580257
Are you studying vector calculus or linear algebra?

[Anonymous No.10580295]

>>10580257
People keep recommending a youtube series on this topic by a channel called, I think, 3blue1brown. They have good animations I think.

Here, I looked up the link for you
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

[Anonymous No.10580296]

>>10580294
Linear algebra
>>10580295
Thanks. I'll check it out

[Anonymous No.10580396]

What's the best field of mathematics to get into as an undergrad?

[Anonymous No.10580440]

>>10573928
Learning math takes time but a lot of is just memory, on a lower level if it's just applying a formula, or on a higher level by understanding fundamentally the concepts. Your reasoning will develop if you practice more. It seems like you're just doing math for the sake of doing it and not enjoying actually finding patterns in the problems understanding deeply the topics.
Just don't take it seriously but ignore any responsibilities and stress

[Anonymous No.10580449]

>>10579530
How difficult is it to get into a masters program at a good school?

[Anonymous No.10580600]

>>10580396
What do you plan on studying (majoring in)?

[Anonymous No.10580696]

>>10580600
Math and comp sci double major. I've been pretty into combinatorics and linear algebra as of late, but I know I'm capable of going much further with my studies.

[Anonymous No.10580737]

>>10580696
I would recommend taking:

- Probability theory.
- Group theory
- Graph theory

They are useful for computer algorithms, sorting, machine learning, and search engines.

[Anonymous No.10580745]

Can anyone give me a quick rundown on this notation? Is it just a series?

[Anonymous No.10580757]

>>10580745
Yeah.

[Anonymous No.10580769]

just what the FUCK is enthalpy? What's the actual physical significance?

[Anonymous No.10580779]

>>10580757
thanks

[Anonymous No.10580797]

>>10580779
ok

[Anonymous No.10580799]

>>10580797
Thanks for accepting his thanks for me.

[Anonymous No.10580802]

>>10580799
ok

[Anonymous No.10580818]

chat does it mean for transformation to be [math]\mathbb{Q}[\math]-linear or [math]\mathbb{Z}[\math]-linear?

[Anonymous No.10580824]

>>10580818
https://en.m.wikipedia.org/wiki/Module_homomorphism

[Anonymous No.10580826]

>>10580818
f is K-linear if [math] f( \lambda a+b)= \lambda f(a)+f(b) [/math] for any [math]\lambda \in K[/math].

[Anonymous No.10580852]

>>10580824
>>10580826
thanks!

[Anonymous No.10580982]

Assume you have x number of tables, each with y rows.
Would the overall average of some values of a column in them be:

>sum of values in column over all tables / x
or
>(sum of values in column over all tables/ y for that table) / x
?

e.g. each table has a "price" column.
would the average price over all tables be the sum of the prices per table / x or sum of prices per table / y (rows in that specific table) / x?

[Anonymous No.10581049]

>>10580982
Generally, the average of something is the sum of the somethings divided by the count of them.
If you have x*y prices, you'll want to divide the sum of everything by (x*y).

[Anonymous No.10581132]

i have the standard deviation of 10 sets of data (tournament results).
what can i do with these? can i average the total standard deviation over all the sets (stdDev/10) or is that not usable data?

[Anonymous No.10581254]

Now this may come off as undignified – but physiologically speaking can the heat of a woman’s womb cause her to overheat to some extent such that she might keep her stomach out to stay cool?

[Anonymous No.10581505]

Isn't it strange/too much of a coincidence, as to how many things top out at "the speed of light"? Like electricity, light, gravity, etc. Wouldn't it make more sense that our ability to measure is fundamentally flawed/wrong or our perception is somehow limited? Maybe many usual/mundane things move even several times faster than light, but we're simply unable to detect it, and the closest result we perceive/measure ends up being the c. Maybe one could compare how we can't see certain light spectrum or comprehend/interact with higher dimension, like 4th-nth.
Not sure how to really put this to words, hopefully it makes sense as to what I'm trying to describe.
t. a brainlet.

[Anonymous No.10581778]

Do precious gems have any value to a natural ecosystem? Like if humans cut down a tree for wood it has an impact on the ecosystem.
Assuming youre not mining upsetting the soil, like if you go into a cave and theres a gem on the wall, if you take it, does that have any impact?

I guess what Im asking is what do precious gems do, if anything, in the non human world?

[Anonymous No.10581791]

>>10573555
list=([ist of pentagonal numbers]
for i in range bignum,
answers.append(i)
for j,k,l in list
if i=j+k+l
answers.remove(i)
print(answers)
something like that

[Anonymous No.10581797]

>>10573543
i believe that science is just rationality so scientism is the most reasonable ideology
its true even with positivism and absence of evidence etc
do you dare oppose me?

[Anonymous No.10581888]

any hints on how to do pic related? so far ive got:

-suppose P is a longest path in G and |G|<2k+1.
-since |G|>2k, there exists a vertex v that is not on P.
-as G is connected, there is a path from v to P
-say x is the vertex that this path meets on P.
-then x cannot be the endvertices of P (this would contradict the maximality of P)

i havent really used anything to do with the minimum degree yet so im guessing its to do with that.

[Anonymous No.10581914]

absolute brainlet here, but what type of simulation should i be using to find the weight bearing capacity of something in abaqus?

My initial plan was to use riks since it can increase load at sensible levels, but its doing shit like having a negative timestep, and not applying enough load to squash what im working with. should I just use a dynamic
explicit simulation with an applied velocity? thats what some indian on youtube did

[Anonymous No.10582098]

Can I have some help figuring what I'm doing wrong?

[math]x(t) = \frac{1}{1-i2\pi t}[/math]

Find F(x(t))

[math]x(t) = \frac{1}{1-i2\pi t} = - \frac{1}{-1+i2\pi t}[/math]

[math]F(x(t)) = F({\frac{1}{1-i2\pi t}}) = -F(\frac{1}{-1+i2 \pi t})[/math]
through linearity property
Using fourier pair
[math]e^{-at}u(t)\Leftrightarrow \frac{1}{a+i2 \pi f}[/math]

and duality property

[math]y(t) \Leftrightarrow Y(f)[/math]
[math]Y(t) \Leftrightarrow y(-f)[/math]

new fourier pair
[math]\frac{1}{a+i2 \pi t} \Leftrightarrow e^{-a(-f)} u(-f) = e^{af}u(-f)[/math]

therefore

[math] F(x(t)) = -F(\frac{1}{-1+i2 \pi t}) = -e^{(-1)f}u(-f) = -e^{-f}u(-f) [/math]

Yet wolfram and matlab don't give me the same answer. I have included what wolfram give's me as a picture

[Anonymous No.10582161]

This came to me while I was trying to fall asleep and I can't get it out of my head. How does a gas bubble in a liquid always rise to the surface? Why doesn't it take off in a random direction trying to satisfy its buoyancy?

[Anonymous No.10582168]

>>10582161
Isn't it just because it has a lower density?

[Anonymous No.10582177]

>>10582168

Yea it I get why it is pushed out by the heavier surrounding material. But why is it always pushed directly up and not in a random direction?

[Anonymous No.10582194]

can someone explain how this simplification works

[Anonymous No.10582229]

Is the percentage of natural numbers that are below a googolplex literally equal to 0%?

[Anonymous No.10582231]

>>10582177
because the fluid above the fluid compresses the fluid below the fluid, so the lightest fluid is always above the heavier fluid. to satisfy its bouyancy the gas bubble moves through the heavy fluid to the light fluid. also bubbles don't go straight up in turbluent fluid

[Anonymous No.10582235]

>>10582194
googling suggests this is nontrivial so now i dont feel nearly as dumb

[Anonymous No.10582237]

>>10582229
Yes.

[Anonymous No.10582240]

>>10582231

Hmm, yea that makes a lot of sense. Thanks anon. I will sleep easy tonight.

[Anonymous No.10582289]

Now that Crispr is on the market does Jack Horner secretly have a bunch of dinochickens hidden somewhere? Can any asshole with a bunch of chickens and access to the various articles that describe dinosaur-like development (which are available freely online) and Crispr make a dinochicken?

[Anonymous No.10582438]

point set topology brainlet here. how in the sweet fuck do i do 9a) and 9b).

i tried rationalizing a simple example using O(2), but am still dumbfounded and at a loss for words

also important note: R^n^2 is not R^n x R^n, its R^n crossed n times. which is fucked

[Anonymous No.10582511]

>>10581797
science isn't rationality though, it's derived from it

[Anonymous No.10582524]

bump

[Anonymous No.10582647]

>>10581778
bump

thought /sci/ was a science board, not a math and physics board

[Anonymous No.10582671]

What is the (is there a) name for the physics subfield that deals with space as a thing in itself. That is, I want to know about what /makes/ something "distant" from some other thing. I don't like resorting to treating space as a given because the idea seems to break down in a late universe heat death scenario. How can you justify extent or direction if everywhere is energetically flat?

Really I just want to know what to google.

[Anonymous No.10582718]

Is there a way to speed up the process at which your brain comprehends things? There will be times where I am looking at a passage/part of a proof where I understand the individual words but the whole does not come together in a coherent way that really “sinks in”. Been having this experience a lot since studying PDEs.

Are there any specific things you guys do? Right now I just give it more time/go for a walk and hope it makes sense. Really doesn’t feel like I control how quickly I understand things. Does writing out the part word-for-word make a difference? Would be grateful for ideas.

[Anonymous No.10582725]

>>10582647
I don't believe any environmental use have ever been detected, though it would be cool and fantasy-novel like if they were. The minerals involved in making them are usually available elsewhere as well in lower concentrations and are more accessible to macro life forms.

[Anonymous No.10582729]

>>10580769
also want an answer

[Anonymous No.10582734]

>>10580449
I wouldn't know, I'm only Assistant to the Garbageman where I work. But bump for an answer for you

[Anonymous No.10582746]

>>10580054
thank you very much

[Anonymous No.10582946]

>>10582671
You could look into manifolds and general relativity

[Anonymous No.10583428]

>>10582438
[math] O(n) [/math] is the set of all matrices A such that [math] A A^T - I = 0 [/math]. If you identify the set of all n by n real matrices with the Euclidean space R^{n^2} and define the map [math] f: \mathbb{R}^{n^2} \rightarrow \mathbb{R}, A \mapsto \| AA^T - I \| [/math], where [math] \| \| [/math] is the Euclidean norm (i.e. the sum of the squares of all entries of the matrix), then [math] O(n) = f^{-1}(0) [/math]. As f is continuous (why?), the inverse image of a closed set is closed and so O(n) is closed. The norm of each column of an orthogonal matrix is 1 and so the Euclidean norm of an orthogonal matrix is n. This shows that O(n) is also bounded and hence compact.

[Anonymous No.10583438]

>>10583428
>(i.e. the sum of the squares of all entries of the matrix)
should be the square root of the sum
and
>Euclidean norm of an orthogonal matrix is n
should be sqrt(n)

[Anonymous No.10583613]

If I have two frequencies from two different data sets but about the same attribute (x = 15, y = 24), does this represent a 60% increase from x to y? Or can that not be applied to frequencies?

[Anonymous No.10583759]

>>10582718
Rewrite the definitions and proofs in your own words. Then try to explain them to someone else in conversation.

[Anonymous No.10583823]

>>10573543
Hey /sqt/, I guess this may be more of an /r/equest, but I looked in the sticky and couldn't find a good reference for a statistical mechanics book. I'm looking at applying to materials science graduate programs and would like to brush up on it (unfortunately I loaned my PChem text to a friend that has yet to return it, I'm about to give up hope on that returning).

Furthermore, if anyone has any recommendations on chemical/material engineering, or modern physics texts, primarily focusing on QM (mostly from electron and optic perspectives) I'd appreciate it.

[Anonymous No.10583834]

>>10573543
How do I reach the next level? You guys are smart that's why i'm asking you.

[Anonymous No.10583896]

>>10583834
Feed your pets rare candies?

What do you mean "next level"? Continuing education, increasing your earning potential in your career, learning more about science and math in general?

[Anonymous No.10584078]

>>10583428
This is very helpful thank you, but why do you want to define the map from A to the Euclidean norm of ||AA^T - I|| ? If that equation = 0

[Anonymous No.10584117]

>>10584078
It's not 0 for all matrices. It's 0 if and only if the matrix is orthogonal. This is done so that O(n) is expressed as the zero set of a continuous function, which is then used to conclude that O(n) is closed

[Anonymous No.10584120]

>>10584117
*orthonormal

[Anonymous No.10584360]

i think im missing something obvious, but why should k divide s?

[Anonymous No.10584480]

What is the probability of picking a black or face card out of a deck?
p(black or face)
I thought it is 26/52 + 6/12 but it is not.

[Anonymous No.10584494]

>>10584480
I dunno, how many red pip cards does a deck have?

[Anonymous No.10584499]

>>10584494
> red pip cards
sorry idk what that means im a brainlet

[Anonymous No.10584507]

>>10584499
Red non-face cards.

[Anonymous No.10584520]

>>10584507
There are 26 red cards. 12 face cards, 6 of them are red. so 26-6 = 20 non face cards.

52 cards in total so 1 - (20/52)? I entered that and it still says wrong unless I did it wrong again

[Anonymous No.10584527]

>>10584520
Did you try writing it as 32/52 or 8/13?

[Anonymous No.10584534]

>>10584527
Wait fuck im retarded. the question says to count Ace as a face card.
Thank you the answer was 1 - (18/52)

[Anonymous No.10584580]

Let [math]S_n[/math] be a series of real positive numbers. If [eqn]\lim_{n \to \infty} S_n = S[/eqn] can the following be said as well?: [eqn]\lim_{n \to \infty} log(S_n) = log(S)[/eqn]

[Anonymous No.10584609]

>>10584580
Yeah, because log is a continuous function.

[Anonymous No.10585121]

what explains the similarities between information theory and physics?

[Anonymous No.10585286]

can someone help a brainlet out?

[Anonymous No.10585295]

>>10585286
like I don't even know how to begin this one

[Anonymous No.10585307]

>>10582194
https://en.wikipedia.org/wiki/Bessel%27s_correction

[Anonymous No.10585374]

Are there any molecules that are referred to as a “salt” that are just as stable as sodium chloride?

[Anonymous No.10585383]

Assume you've connected a square wave to an oscilloscope but saw a signal that was differentiated, what could account for this effect?

[Anonymous No.10585571]

>>10585383
What are you talking about? There's OP-Amp circuits that do differentiation and integration.

>saw a signal
But _what are you measuring_? Give some details if you want a real answer.

[Anonymous No.10585668]

>>10574982
Well obviously the first step is to generalize what it meant to be "playing touhou games"

[Anonymous No.10585753]

"Show that if [math] A \in \mathbb{R}^{n \times n} [/math] doesn't have purely imaginary eigenvalues, then [math]x' = Ax [/math] doesn't have periodic solutions." We already know that the solution of such a linear ODE system is given by [math]e^{At}x = \varphi_{A}(t,x)[/math], where in this case x would just be the initial condition vector. Also, we say a solution is periodic iff [math]\exists t_{0} > 0 \text{ s.t. } \varphi_{A}(t,x) \neq x, \forall 0<t<t_{0} \text{ and } \varphi_A(t_{0},x) = x[/math] (I'm working mainly with a phase curve notation here).

I'm trying to work with the contrapositive statement here, so my hypothesis is that the ODE has periodic solutions. The case for n=2 is very easy because then I can just reduce the matrix to it's Jordan normal form, and since there are so few cases I can just manually go through each one of them. But how do I work in the general case? From the definition of periodic solution I think that [math] e^{A t_{0}}x = x[/math] would imply that the matrix [math]e^{A t_{0}}[/math] has an eigenvalue 1 and also x (and thus the whole orbit generated by [math]\varphi_{A}[/math]) are eigenvectors of said eigenvalue. But even if I'm not messing up I'm not sure that's helpful at all, I don't know where to find the purely imaginary eigenvalues from there.

[Anonymous No.10585775]

>>10585295
Start with the equation for the EMF

[Anonymous No.10585779]

>>10585383
A blown out capacitor

[Anonymous No.10585793]

>>10574982
Any game exhibiting both location traversal (with or without astarting location or an exit location) and single-use paths is NP-hard.

[Anonymous No.10585800]

>>10582647
You don't just find these lying there. It takes manpower (usually exploited locals) to dig and stuff, that has environmental impacts

[Anonymous No.10585849]

In all honesty, is there any point in pursuing science when you need competence in multiple disciplines, each requiring comprehension of several books of whcih requires looking up and evaluating the studies referred to therein (as well as contrarian studies) to gain even fundamental competence?

[Anonymous No.10585926]

>>10585849
Oh noes, your career requires you to read not one, but SEVERAL books!
Yes, there is a point for people with an attention span of more than 7 minutes.

[Anonymous No.10585944]

>>10582438
Recall that a matrix is orthogonal iff its columns v1,..., vn form an orthonormal basis. This is exactly saying that, for each i,j, [math]\langle v_i , v_j \rangle = \delta_{ij}[/math]. Each of these equations defines a closed subset of R^{n^2}, hence O(n) is the intersection of the n(n-1)/2 closed subsets defined by these conditions.
This proves closedness.
To prove compactness, you need, in addition, to establish boundedness. That is, you need to prove that each coefficient is bounded.
But again, you know that each column has norm 1, hence the sum of the squares of the coefficients along each column is 1. Hence, each coefficient is bounded (in absolute value) by 1.

[Anonymous No.10586007]

Could somebody point me to good materials to learn about truth trees in predicate logic? Google seems to be really lacking in that regard.

[Anonymous No.10586345]

What are some math books suitable for a high schooler interested in getting a math degree?
I'm 18 and a senior so not underage

[Anonymous No.10586750]

please help.
do i literally just use a table? what is the significance of a different system?

[Anonymous No.10586836]

Have any of you ever seen a theorem that looks like this:
>we give two "functors" F and G from a category C to D. If F is well defined for some object in C, G is also well defined for it
>>10586345
Spivak's Calculus, whatever Linear Algebra text, any Abstract Algebra text, Introduction to Axiomatic Set Theory (the "Graduate texts in Mathematics" is there to spook you, it's easy), Euclid's elements, any projective geometry text(i.e. this one: http://booksdescr.org/item/index.php?md5=45D4FD6144EEB4BE01D1366DF131CD8C ), Lovasz's complete works, How to prove it meme books, etc.

[Anonymous No.10587053]

>>10585849
Not gonna make it

[Anonymous No.10587155]

>>10585571
it's the question in my lab manual dude, that's all it says >>10585779 inside the signal generator?

[Anonymous No.10587165]

Does anyone know all the math one would need to solve all the problems on Project Euler? I know basic number theory/combinatorics are needed, but is there anything higher? I'd like to have resources so I'm not scouring constantly for good books to learn a math concept I need to solve a problem.

[Anonymous No.10587179]

What’s that word used to describe an organism that still has larval traits even after entering adulthood?

[Anonymous No.10587204]

>>10587179
an incel

[Anonymous No.10587218]

>>10586750
Bump.
My initial thought is that it would be 6e^-6t - 4e^-3t - 2e^-5t
but that "different system" is throwing me off.

[Anonymous No.10587219]

>>10586750
>do i literally just use a table?
Yes.
>what is the significance of a different system?
That it differs from the one in part 1)

[Anonymous No.10587222]

Ok what theorem is being used here?
He goes from a volume integral to an integral on an area. Is using something from the divergence theorem?

[Anonymous No.10587228]

>>10587165
I don't think there is a good answer to that question. The next puzzle could use an idea not seen before. I'd recommend you approach it in a different way, instead of "learning everything I need" -> "solving everything", do problem by problem and read up. That's what happens all the time on the job, so it's good practice.

[Anonymous No.10587230]

>>10587219
So would this >>10587218 be correct?

[Anonymous No.10587237]

>>10587230
Where did you get the e^(-6t) from?

[Anonymous No.10587240]

>>10587237
typo, should've been 6e^(-2t)

[Anonymous No.10587246]

>>10587222
That seems like Einstein summation notation and Stokes.

[Anonymous No.10587263]

>>10587240
Then yes, sure. What did you expect?
Don't put too much weight on the verbal frills on these exercise sheets. They're often either put together a couple of minutes before publishing, or edited every semester for the past 10 years.

[Anonymous No.10587283]

>>10587204
Hilarious

[Anonymous No.10587290]

>>10587246
isn't stokes theorem the one with the curl?

[Anonymous No.10587482]

>>10585753
Bump

[Anonymous No.10587551]

I have a degree in English and Philosophy and a masters in Education. I don't want to teach kids anymore and my Humanities degree is next to worthless. I learned python and then C which lead me to embedded systems and computer architecture. Should I go back to school for EE? I need to learn/ relearn a bunch of precalc but I'm extremely motivated and I'm a pretty fast learner. I also have a decent amount of free time. Is EE at a uni worth it, or should I take a college program? I'm not entirely familiar with my options yet but I'm neither afraid of rigor nor time commitment. Just looking for some general insight here...

[Anonymous No.10587603]

>>10587551
My first degree was a uni degree in kinesiology, went back to school for EE last year. Surprisingly a lot of my courses transferred, I took precalc I and II for physics I and II, as well as chemistry, which all have been more helpful to me as an EE major than they were as a Kin major. The math is very basic, mostly algebra, some trig and phasers, not much to relearn if you've learned it before. My bachelor's program hasn't required me to learn any additional math. It is basically applied physics, and understanding how that let's components function. The hands on stuff has been a lot of fun for me, especially the digital logic application of mapping and building circuits on breadboard as well as through simulations. My program starts as an associate's at my local community college which then transfers into the bachelor's program at the state college (but I'm already working on those courses as I finish my last semester of the AAS). There's some upper division EE classes but a lot of the bachelor's is typical college credits, and even management/accounting courses. Much of it is available online, and I've enjoyed the experience far more than my uni experience. I've already had internship offers, and the instructors are far more experienced than in university where there's usually either a grad student teaching for a stipend and tuition assistance, or a tenured academic who's less interested in working with students than getting home or publishing a paper.

[Anonymous No.10587614]

>>10587603
Thanks boss. This was nice to read. Wish you the best. Seems entirely crushable.

[Anonymous No.10587618]

Trying to understand computational complexity. Here's a naive multiplication algorithm:

inputs: a, b
counter = 1
ans = b
while counter < a
ans = ans + b
counter = counter + 1
endwhile
return ans

Whether I take the significant operation to be assignment or addition, I get that the algorithm executes in O(|a|) time. But that can't be right as the best algorithms (which I'm still struggling to understand the paper behind) are in O(n log(n)) time, and naive algorithms are in O(n^2) time. What am I missing?

[Anonymous No.10587630]

>>10573928
Try to proof everything that’s not written between the equations and steps, and of course do the proofs. This should give you enough mathematical confidence in parallel to learning the subject.

[Anonymous No.10587634]

>>10587614
And if you need more incentive:
>The top-paying bachelor’s degree, by the numbers, is electrical engineering. Though the starting annual salary average is $62,428, a job seeker coming out of school may see a variety of offers when scoping out the jobs market as the salary range for such a degree is between $25,000 and $130,000
https://www.forbes.com/sites/karstenstrauss/2017/06/28/college-degrees-with-the-highest-and-lowest-starting-salaries-in-2017/

[Anonymous No.10587636]

>>10587618
O(|a|) == O(n) here, which is best case

[Anonymous No.10587683]

>>10587618
Lad, how long does it take to sum?

[Anonymous No.10587685]

I'm a neet that want's to go to university. I finished high school but all my marks were around 50%, where are some places that I could get my credits?

[Anonymous No.10587692]

Thinking about pursuing a future career in auto engineering. Which is generally worth more a doctorate in electrical engineering with a masters in mechanical engineering, or vice-versa? And would tagging another masters as aerospace or nuclear (these are easy bait for GI bill to stay in the military and easily transition to a guaranteed job) be worth it in case of a never-meet-your-heroes phenomenon?

[Anonymous No.10587716]

>>10587165
However much you learn, PE will occasionally require something you a) don't already know and b) can't easily learn because there's no way of knowing where to start looking.

Apart from the fundamentals (modular arithmetic, combinatorics), either you recognise the concept that's central to the problem or you wait until googling "project euler problem XX" throws up something.

[Anonymous No.10587732]

>>10587618
> What am I missing?
When someone describes a multiplication algorithm as O(n.log(n)) or O(n^2), n is the number of digits, not the numerical value. So repeated addition is O(2^n).

[Anonymous No.10587744]

>>10585571
>>10585383
bumping for help

[Anonymous No.10587829]

>>10587732
you only need to iterate through a set of n integers once to sum them

[Anonymous No.10587847]

Not sure were else to ask for help so ill try here. Long story short I need to write a proposal for a new scholarly journal. I have no real idea were to even start on this. Are there any books or webpages that might help. Thanks in advanced if anyone here actually has experience in this kinda niche thing.

[Anonymous No.10587932]

Intuitively speaking, what does it mean for the Moore-Penrose pseudoinverse to provide an a matrix that minimizes the euclidean norm of x for [math]x=A^{+}b[/math] and how does this property pertain to applications?

[Anonymous No.10587941]

>>10587692
off topic but do your research on quality of life as an auto engineer. my impression is that its similar to game developers. (i.e. employers feel they can treat you poorly because it's something that lots of people eagerly want to do. ymmv)

[Anonymous No.10587977]

can someone help me out? I solved a similar question a few weeks ago but I dont remember how
this is an extra credit question so yeah I guess its a homework question

"At point A, 4.40 m from a small source of sound that is emitting uniformly in all directions, the intensity level is 56.0 dB ."

"What is the intensity of the sound at A?"

First I used:
decibels = 10*log(I / I_0)
56 = 10log(I / 10^-12)
this got me 3.98*10^-7 W/m^2

now I'm trying to use I1/I2 = (r_2^2)/(r_1^2)
but the radius at A would be zero and its killing me
help me escape limbo lads

[Anonymous No.10588029]

>>10587977
nevermind I cant even fucking read fuck me its been a long day
sorry for wasting your bump limit

[Anonymous No.10588237]

why did mods delete this thread (pic related)?

[Anonymous No.10588256]

>>10588237
because of trannies

[Anonymous No.10588262]

stupid question here, not sure how to do the second part.

[Anonymous No.10588281]

>>10588262
Integrate |v(t)| from 0 to 3.

[Anonymous No.10588286]

>>10588281
so 7.5? it said it was the wrong answer

[Anonymous No.10588325]

>>10588237
They’re trannies unironically

[Anonymous No.10588409]

Can someone explain this please? It's from the answer from https://math.stackexchange.com/questions/2128920/calculating-generalized-eigenvectors

The first generalized eigenvector he finds is
[math]
\begin{bmatrix}
x \\ -1 \\ -1-t \\ t
\end{bmatrix} [/math]
Do generalized eigenvectors not need to generate vector subspaces as their eigenspaces? Because from the fixed -1 in the 2nd component it doesn't seem that that particular vector would be able to generate a subspace.

[Anonymous No.10588447]

>>10588409
i dont know about generalized eigenvectors but
the eigenspace of an eigenvector is the span
so it contains the scalar multiples as well

[Anonymous No.10589052]

>>10585753
First we notice that the space [math]D(n)[/math] of diagonalizable matrices are dense in [math]\mathbb{R}^{n\times n}[/math], hence let [math]\{A_i\}\subset D(n)[/math] be a sequence of diagonalizable matrices that converges to [math]A[/math]; put [math]x_i[/math] as the solution to the ODE [math]\dot{x}_i = A_i x_i[/math], then by diagonalizing [math]A_i = P_i^{-1}D_iP_i[/math] for orthogonal [math]P_i \in O(n)[/math] and put [math]y_i = P_ix_i[/math], whence [math]\dot{y}_i = D_iy_i[/math] implies [math]y_i = \exp(D_i t)y_n(0)[/math]. If [math]A[/math] has no imaginary eigenvalues then [math]D_i = \operatorname{diag}(\lambda^1_i,\dots,\lambda^n_i)[/math] has [math]\lambda^m_i \in \mathbb{R}[/math] for all [math]1\leq m \leq n[/math], hence [math]y_n[/math] is not periodic, and indeed determine [math]n[/math] stability manifolds (may be degenerate) near each hyperbolic fixed point.Since [math]O(n)[/math] is compact, we have [math]P = \lim_i P_i \in O(n)[/math] and hence [math]A = \lim_i A_i[/math] uniformly in the operator norm such that the Grobman-Hartman theorem implies that the stability manifolds remain homeomorphic in the limit. This proves the result.
>>10587222
Integration by parts.

[Anonymous No.10589220]

>>10587941
That's why I was considering putting some of my own money forward to do aerospace or nuclear. The latter only because I initially tested to be an engineer on nuclear subs, but I'm claustrophobic and opted out of anything sub-related.

[Anonymous No.10589270]

hi /sci/, what books do you guys recommend for learning basic abstract algebra? Is herstein still a good choice or should go with something less archaic? thanks

[Anonymous No.10589357]

Hey lads, I am deciding between going to study Informatics or rather a bioinformatics. I have an intermediate knowledge of informatics, but am also passionate about biology in general, regardless the last time I got into a contact with biology was on high school.
Have you got any experience with bioinformatics or is it just a made up meme field and I should rather go to study Informatics? Thanks for help

[Anonymous No.10589379]

>>10587932
The intuition I use for that statement comes from linear regression. X and B are columns, A is a matrix whose columns represent the functions (basis functions or basis vectors) you're trying to represent X (your data) with, and B are the coefficients associated with each function (y intercept and slope of your line for instance). If you had a perfectly consistent square system, the true inverse and pseudo inverse give you the same thing, values in B that exactly represent X at those data points. If your system is overdefined, the inverse of A doesn't exist, but the pseudo inverse of A will solve the values of B that represent X using your basis functions that minimizes the mean squared error (Euclidean norm or Distance) between the data in X and the regressed representation of the data AB.

[Anonymous No.10589418]

>>10585753
>From the definition of periodic solution I think that [math]e^{At_0}x=x[/math] would imply that the matrix [math]e^{At_0}[/math] has an eigenvalue 1
Yes, and do you know of any connection between the eigenvalues of [math]A[/math] and those of [math]e^{At_0}[/math] ?

>>10589052
absolute nonsense

[Anonymous No.10589460]

>>10587618
You've got the wrong measure of size. For multiplication of integers, n is taken to be the number of digits, not the absolute value. For input x, working in base b,

[math]n = \log_b(x)[/math]

[math]x = b^n[/math]

So your algorithm is O(|a|) = O(b^n).

[Anonymous No.10589511]

>>10587179
I just remembered the word it’s neoteny

[Anonymous No.10589623]

>>10588286
No, [math] \frac{53}{6} [/math].
In general [math] \int |f|\neq |\int f| [/math]

[Anonymous No.10589658]

prove that a graph if a graph is not cyclic and has a hamiltonian circuit that at least two vertices have degree 3?

Is this a contradiction or something, how can a graph have a hamiltonian circuit and not be cyclic?

[Anonymous No.10589691]

If I have some integral
[math]I = \int f(x) dx[/math]
what happens when I apply functions/operators to the whole expression, can I do this with the natural log:
[math]Ln[I] = Ln[\int f(x)dx]=\int Ln[f(x)]dx[/math]

[Anonymous No.10589742]

>>10589658
Lemme correct that for you, *above three
Gee lad, I dunno.
Maybe every vertex in a graph with a Hamiltonian Cycle needs to have degree above two, but if every graph has degree two it's a cycle. I dunno, it's a dilemma.

[Anonymous No.10589813]

>>10589691
The first equality is true for (convergent) integrals, the second is not (in general).

[Anonymous No.10589883]

>>10589691
Nah.
>>10589418
>absolute nonsense
Brainlet.

[Anonymous No.10589888]

big think incoming

[Anonymous No.10589904]

>>10589888
Grams are properly a unit of mass, not weight. However, many scales will report in units of mass, as the scale makers assume the scales won't be taken off the Earth or used in freefall.
Assuming the scale was calibrated to read 600g for the test weight while on Earth, it would read about 100g on the Moon.

[Anonymous No.10589905]

>>10589691
No you can't but you can get inequalities if the function is convex/concave. Refer to Jensen's inequality.

[Anonymous No.10589912]

>>10589888
The obvious answer is 100g, so it won't be that.
This gunna use some trickery shit like the mass of the plate on which you place the weight is also less so that also contributes a shift towards less than 100g?

[Anonymous No.10589913]

>>10589904
To be accurate, it should weigh a tiny bit less than 100 g.

[Anonymous No.10589925]

>>10587551

[Anonymous No.10589926]

Look at the first step. It is a fact that subtracting H from x will result in shift to the right if H > 0 and shift to the left if H < 0.
What I am missing here?

[Anonymous No.10590015]

>>10589926
>no capacity to visualize in space
>>10589912
Stop hallucinating, it's 100g.

[Anonymous No.10590044]

>>10589926
Yeah they should be flipped

[Anonymous No.10590056]

>>10589926
>>10590044
Never mind I misread
Think about it like this: if you’re adding H to the input of a function, you’ll need that much less to get to the same value of x, meaning that it’s shifted to the left.

[Anonymous No.10590061]

>>10590015
>>10590044
I did visualize it but I don't get what the authors meant by this. I don't think authors and me have the same thing in mind.

[Anonymous No.10590073]

>>10590061
You’re probably thinking of the same concept just expressing it differently. Try doing some problems with it and it’ll be clear if you understand it or not.

[Anonymous No.10590128]

>>10587744
bump

[Anonymous No.10590147]

>>10587744
>>10585383
No one? What would make a signal that's meant to be square appear differentiated? >>10585779 anon suggests a blown capacitor, would that be in the generator?

[Anonymous No.10590158]

>>10590056
Yeah, if H is positive x + H will shift the graph to the left and if H is negative x + H will shift the graph to the right. I get that. But what step one is saying is
>If H is positive x + H will shift the graph to the right and if H is negative x + H will shift the graph to the left.
How do I reconcile these two things? It is obvious that authors are viewing this from a different angle than I do.
>>10590073
I did. I don't have a problem with other steps but this one baffles me.

[Anonymous No.10590207]

>>10590147
Jesus Christ anon, will you stop simply repeating the question and fucking show some of your own thoughts? We're not here to do your homework.

Also, can you explain to me what a high-pass filter is, and what its characteristics are?

[Anonymous No.10590217]

>>10589418
If [math] \lambda_{i} [/math] is an eigenvalue of A then [math] e^{ \lambda_{i} } [math] must be an eigenvalue of the exponential of A, right? I wanted to do something with that but wouldn't that just mean that the corresponding eigenvalue in [math] A t_{0} [/math] would be 0? The way Jordan normal blocks for conjugate complex eigenvalues are represented, having 0 in the main diagonal seems appropriate, but I don't know how to show that it's actually meant to be a pair of complex eigenvalues with 0 as their real part, instead of a real eigenvalue that is simply 0.

[Anonymous No.10590273]

>>10589658
>how can a graph have a hamiltonian circuit and not be cyclic?
there could be edges that you dont need to walk on to make a hamiltonian circuit, like any complete graph larger than K3
or for that matter, any cyclic graph with more than 3 vertices and extra edges connecting non adjacent vertices

[Anonymous No.10590399]

If I have a normed vector space V, and its dual V* with the usual norm, is there a name for the isometry f such that [f(x)](x)=||x||^2?

[Anonymous No.10590416]

in a planar graph is it possible to have a length/degree of a face as 1?

[Anonymous No.10590427]

>>10590207
it's a stand-alone question with >>10585383 as the referenced figure. I don't know the answer so I'm asking for help. You don't know the answer either, so you can't help.

[Anonymous No.10590442]

>>10590416
do you mean like K1?

[Anonymous No.10590444]

>>10590399
are you sure this is well defined when there's no inner product ?

[Anonymous No.10590451]

>>10590444
I'm not saying that it always exists, I'm just asking if it has a name when it does.

[Anonymous No.10590455]

>>10590451
musical isomorphism

[Anonymous No.10590466]

>>10590455
Thanks lad.

[Anonymous No.10590617]

What's a good book as an introduction to differential geometry?

[Anonymous No.10590659]

>>10590617
>>10588440

[Anonymous No.10590719]

>>10589883
>claims that matrices diagonalizable in an orthonormal basis (ie. symmetric matrices) are dense in M_n(R)
>claims that complex numbers are either real or imaginary
>invokes a graduate level theorem for a problem that can be solved in two lines with linear algebra 101
>at no point explains how it relates to the original problem
>calls me a brainlet

[Anonymous No.10590749]

What material exists that would prevent any liquid passing through it but also allows for the full extent of sun rays to pass through it?

[Anonymous No.10590807]

>>10590217
>If [math] \lambda_{i} [/math] is an eigenvalue of A then [math] e^{ \lambda_{i} } [/math] must be an eigenvalue of the exponential of A, right?
It's better than that. The eigenvalues of exp(A) are exactly the exponentials of the eigenvalues of A.
>I wanted to do something with that but wouldn't that just mean that the corresponding eigenvalue in [math] A t_{0} [/math] would be 0?
Well no, it would be a multiple of [math]2\pi i[/math], ie. imaginary

[Anonymous No.10591132]

>>10590749
my sperm lel

[Anonymous No.10591155]

>>10590807
Oh shit I forgot about the complex logarithm it seems. In that case it's almost over. But the contrapositive statement would be proving that if there's a periodic solution, then there MUST be purely imaginary eigenvalues. Even though it's not the only solution, the (real) 0 eigenvalue is still a solution of the logarithm, so there is still a matrix that doesn't require purely imaginary eigenvalues. How do I discard that option? Or does it really suffice to say that the eigenvalue is z=0+0i and it counts as purely imaginary because Re(z) = 0?

[Anonymous No.10591185]

>>10591155
>>10590807
Wait I think I have an idea, I know that the orbit of a point x is the singleton containing x iff [math] x \in Ker(A) [/math]. In the case A had a 0 eigenvalue, then Ax = 0x = 0 which by definition is the kernel, and then the orbit of x would be {x}, which would break the definition of periodic solution I'm using. Does that seem correct?

[Anonymous No.10591268]

>>10591132

[Anonymous No.10591360]

>>10589379
thanks

[Anonymous No.10591696]

Can someone help me with this? No idea how to do it.

[Anonymous No.10591854]

>>10591696
take L and subtract f(2)/2^s
then you show that forms (1 - f(2)/2^s) L = f(1) + f(3)/3^s + f(5)/5^s + ...
and then kill all the other primes too

[Anonymous No.10591970]

>>10590427
[ ] you understood why the question on high pass filters was included in the response

[Anonymous No.10592016]

>>10591185
>Does that seem correct?
Yup

[Anonymous No.10592155]

>>10590719
>claims that matrices diagonalizable in an orthonormal basis (ie. symmetric matrices) are dense in M_n(R)
https://ferngaston.wordpress.com/2016/04/16/density-of-diagonalizable-matrices/
>claims that complex numbers are either real or imaginary
Huh?
>invokes a graduate level theorem for a problem that can be solved in two lines with linear algebra 101
Huh? Hartman-Grobman is hardly grad level.
>at no point explains how it relates to the original problem
Huh? I provided a solution.
>calls me a brainlet
Huh? That wasn't me.

[Anonymous No.10592179]

>Have absolutely no idea what the heck I'm doing
>Have to comment the shit out of my work so that I don't forget what I've done and lose myself
>Also helps me find where I inevitably miss something after I check the solution and find it wrong
>Get an A on the course because my assignments were so nice and clear
Anyways I just wanted to say that the linear algebra went well and thank you for your help.
Thanks.

[Anonymous No.10592185]

>>10590158
Nvm I get it.

[Anonymous No.10592218]

>>10592155
>https://ferngaston.wordpress.com/2016/04/16/density-of-diagonalizable-matrices/
I know that, but you implicitly assumed all along that diagonalizable matrices are diagonalizable with a base change in O(n), which is incorrect. Your argument ends up showing that all matrices are diagonalizable.
>Huh?
Quote: "If [math]A[/math] has no imaginary eigenvalues then [math]D_i = \mathrm{diag}(\lambda_i^1,\dots,\lambda_i^n) [/math] has [math]\lambda_i^m \in \mathbb R[/math] for all [math]1 \le m \le n[/math]"
>Huh? I provided a solution.
Putting words back to back does not always count as an argument.
>we have [math]P = \lim P_i \in O(n)[/math]
what purpose does this serve ?
>uniformly in the operator norm
What does uniformly mean in this context ?
You have assumed that A_i converges to A from the beginning and norms are equivalent so what is the purpose of this ?
> Grobman-Hartman theorem implies
How ?

[Anonymous No.10592325]

How do you prove by induction when the subproblems depend on the larger subproblems?

Take this function for example (probably not the best example) which gives a rolling sum of contiguous subsequences:

f(n, k) = k + f(n-1, k+1 if num[n] = num[n-1], otherwise 0)
Sample input: num=1 1 3 4 5 5 5, f(7,1)=1+2+1+1+1+2+3=11

Is it valid to do the typical "assume correct for f(n-1,k) and show for f(n,k)? How do you assume f(n-1,k) is correct without first assuming f(n,k) is correct?

[Anonymous No.10592373]

How do you prove by induction when the subproblems depend on the larger subproblems?

Take this function for example (probably not the best example) which gives a rolling sum of contiguous subsequences:

f(n, k) = k + f(n-1, k+1 if num[n] = num[n-1], otherwise 1)
Sample input: num=1 1 3 4 5 5 5, f(7,1)=1+2+1+1+1+2+3=11

Is it valid to do the typical "assume correct for f(n-1,k) and show for f(n,k)? How do you assume f(n-1,k) is correct without first assuming f(n,k) is correct?

[Anonymous No.10592390]

>>10592179
damn, good work. you earned that bump like a muhfucka

[Anonymous No.10592404]

>>10591854
How does that help us to find the Euler product?

[Anonymous No.10592535]

>>10592179
Good job anon

[Anonymous No.10592789]

>>10592404
L ( 1 - f(2)/2^s )(1 - f(3)/3^s )... = f(1)

[Anonymous No.10592825]

>>10592789
You're such a babe

[Anonymous No.10592834]

>>10592373
> Is it valid to do the typical "assume correct for f(n-1,k) and show for f(n,k)?
Provided that you can first show that f(1,k) is correct.
> How do you assume f(n-1,k) is correct without first assuming f(n,k) is correct?
f(n,k) depends upon f(n-1,k), not the other way around.

[Anonymous No.10593093]

>>10592016
Great, thanks a lot

[Anonymous No.10593214]

>>10580696
Seconding this >>10580737
Also, if you have already taken linear algebra and combinatorics, i'd recommend trying to get into algebraic combinatorics (yes its a thing). It focuses on the uses of (both linear and abstract) algebra in combinatorics and graph theory. Pic related is a book i found and started reading on the topic.

[Anonymous No.10593378]

I'm a brainlet and forgot how to do pic related using contour integration

[Anonymous No.10593500]

>>10593378
If z=g(t) (where t is a real variable), f(z)dz is equivalent to f(g(t))dg=f(g(t))g'(t)dt. C(i,2) is z=g(t)=i+2e^it for t in [0,2π].
So:
[math]\int_0^{2\pi} {\vert i+2e^{i t} \vert}^2 2ie^{i t}\,dt[/math]

[Anonymous No.10593646]

Does anyone have any good pictures for the next thread? I'll just go find something from d@i otherwise.

[Anonymous No.10593706]

I think I just failed out of grad school. First semester after finishing my computer science BS. How do I go about finding a job now? In interviews do i tell them i failed or avoid it? If i avoid it what do i say ive been doing since i graduated

[Anonymous No.10593713]

>>10593706
Don't mention it. Say you were helping family with work or freelancing, if you can reasonably lie about either.

[Anonymous No.10593778]

>>10593706
don't say you failed just say you didn't complete the program

[Anonymous No.10593842]

I'm trying to prove that [math]d(x,y) = |x_1 - y_1| + |x_2-y_2| [/math] but I can't prove the triangle inequality part. I want to show that [math]|x-z| \leq |x-y|+|y-z|[/math] but I can't figure it out.

[Anonymous No.10593849]

>>10593842
nvm I'm fucking retarded. setting [math] a = x-y, b = x+y [/math] in [math]|a+b| \leq |a| + |b|[/math] does the trick

[Anonymous No.10593860]

NEW THREAD
>>10593857
NEW THREAD
>>10593857
NEW THREAD
>>10593857
NEW THREAD
>>10593857
NEW THREAD
>>10593857

[Anonymous No.10593862]

>>10591970
As an AC coupling setting filtering the DC component? I hadn't used the function yet but glad to have learned about it, and I can see how it basically utilizes a high pass filter to pass only the transitions.