/sqt/ - Stupid Questions Thread : Ask the Math Oracle

[Anonymous No.8894488]

Tips for good questions:
>provide context
>show partial work
>check stackexchange.com and wolframalpha.com

Previous thread: >>8871108

[Anonymous No.8894570]

hopefully fast and easy question, google is being shit

how do you find fixed points for higher order ODEs? do you have to convert to a system of 1st order and mess about with jacobians? or is there another way

[Anonymous No.8894579]

>>8894570
If you mean a way to have a qualitative analysis of a n order autonomous ODE, yes you need to transform it to an autonomous system and then take the derivative of your field F(X) and put it as the jacobian matrix. Then you apply what you know about linear planar systems.

[Anonymous No.8894608]

Suppose that you have that [math]x^3 + y^3[/math] is a power of 2. I am almost sure that that implies that both x and y are a power of two.

More than that, it implies that x and y are the exact same power of two.

Any idea of how to rigorously prove this?

[Anonymous No.8894637]

>>8894608
for powers x^3+y^3=2^n with n=4,5,7,11,13 and 17<=n<=10^9 your claim is true by work on the beal conjecture:

https://en.wikipedia.org/wiki/Beal_conjecture#Partial_results

[Anonymous No.8894638]

The correct answer is 1.5% right?

.35 ^ 4 = .015, 1.5%?

[Anonymous No.8894645]

what is the antiderivative of position with respect to time

[Anonymous No.8894657]

>>8894637
What the fuck? This is an unsolved conjecture? This shit came up in a number theory homework. The fucking fuck.

The problem is this:
Find all the pairs of positive integers (x,y) such that if [math] \alpha , \beta [/math] are coprime and positive divisors of the number [math] x^3 + y^3 [/math] then [math] \alpha + \beta - 1 [/math] is also a positive divisor of [math] x^3 + y^3 [/math]

I proved that the pairs asked for are equivalent to the pairs (x,y) such that [math] x^3 + y^3 [/math] is a prime power.

Then I proved that it can be narrowed down to just pairs (x,y) such that [math] x^3 + y^3 [/math] is a power of 2.

And now I am trying to characterize those integers (x,y) and the natural characterization is that x=y= some power of 2.

But I guess now I'm fucked.

[Anonymous No.8894780]

What's the fastest way to review math? I was doing some kind of integral calculus in college, but I haven't had to manually do any math in like 8 years so I've just about forgotten everything I used to know.

[Anonymous No.8894808]

>>8894780
take a test

[Anonymous No.8894876]

fa/tg/uy here

Having never taken statistics I assume this is a stupid question, but how do I calculate how often one function is going to end up greater than another function?

For context, I've got two opposing rolls in a game that I'm playing in, and I want to know if I should even bother with some checks and what have you.

The problem is they're not really "functions" so much as just fucking dice. So they have a probability curve but I'm not really aware of any function that would give me that curve. Which is probably where the stupid part comes in.

So really I could use any help at all but my searching has left me more confused than anything on how to do a probability curve based on results and then presumably use calculus to compare them?

[Anonymous No.8894880]

Hello,
Any ideas for b,c, and d?

[Anonymous No.8894901]

Hey /sci/ I have a College Mathematics examination in the morning at 9:15 AM
On the examination there is 4 questions each a different topic. I know the first 3 but the fourth not too well.
My question is should I stay up and study for the fourth question?
For context its currently 1:30 AM at the moment.
Or should I get some sleep?
Also of note is that I will pass this Module either way.

[Anonymous No.8894996]

What's the fastest method for checking if something is a prime number?

I think I found a fast way (albeit overly complicated) that doesn't rely on super computers checking every possible solution, but it requires a huge integral I have no idea how to do. I'm wondering if it's worth it to try to figure it out.

[Anonymous No.8895027]

>>8894880
For b just take an arbitrary number r and asign a polinomial whose only non 0 coefficient is r. For c use rank nullity theorem, because it's surjective Dim(Im)=1 ans the dimension of the polinomial of powers at most n is n+1 so the dimension of the kernel must be n. For d, just prove then, that all those polinomials are in fact in the kernel by direct substitution and then show its linearly independent.

[Anonymous No.8895057]

>>8895027
Thanks mate that helped a lot

[Anonymous No.8895060]

Can someone explain why the second way of solving the problem is wrong? 1/2 is the correct answer and I don't understand why I'm getting 1/4 the second way.

[Anonymous No.8895074]

if the integral of f(x)dx is g(x), how would I go about finding the integral of f(h(x))dx?

[Anonymous No.8895094]

>>8895060
What's the square root of 1/4 m8? Your taking the limit of the product of the original with itself which obviously changes the limit to square of the the limit i.e. 1/2^2

[Anonymous No.8895101]

Is an into to discrete math hard
is an intro to algorithms hard

is taking both at the same time along with two other classes hard?

Want to get Computer Science stuff out of the way and getting into the algorithms class is fucky so if im able to do it early as i can (next semester) itd relieve a lot

sorry, not really a homework question but you know

[Anonymous No.8895117]

>>8895074
You need f(h(x)) h'(x) dx instead

[Anonymous No.8895120]

why are the limits T1 and -T1 when they explicitly say that the limits are T/2 and -T/2? It looks like T is greater than the length of T1. mildly confused.

[Anonymous No.8895127]

Is blue light exposure something I should genuinely be concerned about?

[Anonymous No.8895142]

>>8895117
So there's no way to do f(h(x))dx?
I thought there'd at least be a complicated way

[Anonymous No.8895165]

>>8894876
You can modelize it by a probability tree.

[Anonymous No.8895182]

>>8895165

Okay. Any advice on how to do that?
I'm willing to do the groundwork, I just don't have any idea how. I'm a grognard playing dice games, not an actual STEM guy.

[Anonymous No.8895187]

>>8894645
https://en.wikipedia.org/wiki/Absement

[Anonymous No.8895265]

>>8895165

[Anonymous No.8895269]

>>8895182
You can modelize it by two random outputs : the attack value and the defense value. For each "leaf" of the tree, you have a probability (pic related). For example, the probability of the "leaf" (attack=20 ; defense=14) is 11.57 % × 9.72 % which is approximately 1.12 %.

[Anonymous No.8895274]

>>8895182
Since each "leaf" is exclusive, you can just add the probabilties. For example p(attack<defense) = p(a=15 ; d=16) + p(a=15 ; d=17) + p(a=15 ; d=18) + ... + p(a=19 ; d=20)

[Anonymous No.8895292]

I know this is baby math, but can I get a hand here?

[Anonymous No.8895300]

>>8895292
You have
[eqn]\frac{7}{x-1}+\frac{8}{x+1}-\frac{4}{x^2-1}=0[/eqn]
Put in on a common denominator and then find the roots of the numerator

[Anonymous No.8895313]

>>8895300
Thanks anon. This make sense.

[Anonymous No.8895315]

What kind of skills and tools would you need to be able to effectively analyze and find meaningful patterns in market data for commodities futures? Would working through a regular Statistics textbook be enough or anything else?

[Anonymous No.8895332]

>>8895274

Full disclosure, anon, I have no idea what a probability table is. I'll look it up, but is it more complicated than what it sounds like?

[Anonymous No.8895336]

>>8895292
remember that [math](x+y)(x-y)=x^{2}-y^{2}[/math]

[math]\frac{7(x+1)}{x^{2}-1}+\frac{8(x-1)}{x^{2}-1}=\frac{4}{x^{2}-1}[/math]

[math]7(x+1)+8(x-1)=4[/math]

[math]x=\frac{1}{3}[/math]

[Anonymous No.8895352]

Any botanists here?
I've never seen these before, they're sprouting all over my grandmas "garden"

[Anonymous No.8895409]

How do I get a Newton polynomial from this?

[Anonymous No.8895452]

If I have a function that oscillates between 0 and 1 (not periodically), how can I take the integral of it?

[Anonymous No.8895462]

>>8895452
monte carlo

[Anonymous No.8895467]

>>8895462
Is there no way to find the indefinite integral?

Sorry I didn't specify that I wanted the indefinite integral at first

[Anonymous No.8895479]

>>8895467
Well, post the function you twat.

[Anonymous No.8895485]

What is the best way to ask professors for an opportunity to do undergraduate research with them during the school year? Email? In person? And should I only try to ask professors that I have classes with our any professors in the department?

Please help I dont want to make a thread for this

[Anonymous No.8895551]

>>8894996
Probably Fermat test
There are some tests which can determine primality for certain forms of numbers, ie potential Mersenne primes

[Anonymous No.8895620]

what is the equation of this line:

(0,100) (.75,200) (1.5,400) (3,800) (4.5,1600)

[Anonymous No.8895623]

>>8895485
in person is probably best

i had good luck asking professors i didn't even know by email though (for a summer research project)

[Anonymous No.8895626]

>>8895485
If you have a class with them, just go to their office hours and ask.

If you don't, email them and say you are interested in their research and ask if you can come to their office and discuss research opportunities.

[Anonymous No.8895632]

>>8895620
That's not linear.

[Anonymous No.8895645]

>>8894645
>antiderivative
jesus, man, they're called integrals

[Anonymous No.8895648]

>>8895645
brainlet

[Anonymous No.8895657]

say i have a bus in verilog like so

output reg [11:0] bus

and i want to assign 4 bits each to 3 parts. would this be the correct syntax?

bus[11:8] = 4'b0000;

etc
bus[7:4] = 4'b0000;

[Anonymous No.8895660]

>>8895632
how would I find it then?

[Anonymous No.8895665]

>>8895660
Look up polynomial interpolation.

[Anonymous No.8895669]

>>8894488
In what space is the riemann zeta function with -1 as an input defined? What is the value in that space and why isn't it the same in Hilbert space?

Describe the intricacies behind why this is a weird as fuck thing.

[Anonymous No.8895684]

>>8895669
>In what space is the riemann zeta function with -1 as an input defined?
in the complex plane... you just use analytic continuation

[Anonymous No.8895718]

>>8894638
No. You need the sum of the probabilities of getting 4 fakes, 5 fakes, 6 fakes, ... 11 fakes
It's easier to calculate 1 - the sum of the probabilities to get 3 fakes, 2 fakes, 1 fake, 0 fakes

And your formula to get exactly 4 fakes is wrong

[Anonymous No.8895720]

>>8895413
Repost from prev thread in case you are still lurking

Your vector has 3 variables, and you have 3 equations:

0 v_11 + 2 v_12 + 2 v_13 = 0
2 v_11 + 1 v_12 + 0 v_13 = 0
2 v_11 + 0 v_12 + -1 v_13 = 0

Solve them and you get an eigen vector

[Dumbass No.8895754]

a friend of mine recently got cancer. People around him say that his exposure to the sun made the cancer worse. Are they right?
When you have cancer, does the sun make it worse?
Personally I think that logically it shouldn't, but my friends keep insisting that the trip he took to turkey made it worse.

[Dumbass No.8895758]

>>8895754
oh by the way it's lung cancer

[Anonymous No.8895820]

>>8895332
It really is not.

[Anonymous No.8895976]

>>8895820

Alright, I've looked it up, thanks, anon. I don't suppose there's an easier way than brute forcing it?

[Anonymous No.8896017]

>>8895976
There is probably a clever way to do it if you know the formula that gave you the curves (>>8894876), but
with just the raw datas I don't think there is an easier way.
In that case, bruteforcing it is not very difficult since there is only a handful of possibilities (225) and you won't need to compute most of them.

[Anonymous No.8896043]

>>8896017

Alright this is what I came up with after several formula errors.
Looks like if I'm rolling against that in that specific circumstance I'm pretty well screwed.

[Anonymous No.8896090]

>>8896043
Kek, the odds don't look good for you.
A good way to check that your model is correct is to sum all the odds in your table. You should get 100 %.

[Anonymous No.8896101]

whats 1+1? Asking for a friend.

[Anonymous No.8896102]

>>8896090
They do! I'm fucked!
Time to go do some more quests before we fight this guy, holy shit.

[Anonymous No.8896104]

>>8895409
There are many ways:
[eqn] p(x) = f(x_0) + A (x - x_0) + C (x - x_0)(x - x_1) \\
= f(x_1) + A (x - x_1) + C (x - x_1)(x - x_0) \\
= f(x_1) + B (x - x_1) + C (x - x_1)(x - x_2) \\
= f(x_2) + B (x - x_2) + C (x - x_2)(x - x_1)
[/eqn]

[Anonymous No.8896121]

>>8895754
Unless it's skin cancer sun isn't really a factor, though the trip to Turkey may well be

[Anonymous No.8896137]

>>8895754
>a friend of mine recently got cancer.
is he scared of the cancer?

[Anonymous No.8896142]

>>8896101
We can only guess.

[Anonymous No.8896151]

>>8895120

What book is this? Lathi? Also the limits might be just a typo. It should be T1/2 and -T2/2. Maybe they just wrote the general formula?

[Anonymous No.8896358]

Could someone give me a quick rundown on ampholytes/polyprotic acids and how to work them? Does a standard ICE table using both the Ka and Kb and then subtracting the smaller value (either [H+] or [OH-]) from the larger and then finding pH work?

[Anonymous No.8896382]

>>8896101
>>8896142
>wolframalpha uses the common core number-line approach
Common-core haters BTFO

[Anonymous No.8896416]

>>8896358
HELP! I have a final in 30 mins and this is the only thing i didnt understand from the course

[Anonymous No.8896445]

>>8894657
>Then I proved that it can be narrowed down to just pairs (x,y) such that x3+y3 is a power of 2.

I don't know much about number theory but it seems that if this is true then [math] \alpha[/math] and [math]\beta [/math] must both be even an therefore [math] \alpha+ \beta -1[/math] is odd and can't be a divisor of the power of 2.

[Anonymous No.8896461]

>>8894657
>>8896445
If alpha and beta are coprime, they only one of them can be even, otherwise both would have the same factor 2.

[Anonymous No.8896481]

Is there a book on abstract algebra that really holds me hand. I'm having a hard time building intuition.

[Anonymous No.8896483]

>>8896461
Yeah, I forgot what coprime meant, but again that's impossible because if they both divide 2^n ,or any prime number p^n for that matter, they both must share a factor of p, right?

[Anonymous No.8896505]

>>8896481

Visual group theory by nick whatever is fantastic if you are really having trouble understanding what is going on. The color coded matrixes really really helped me to understand what was really going on. Pic related.

Also the Pinter book is a classic, really readable. I read it in like a week.

[Anonymous No.8896517]

>>8896505
I'm somewhat okay with group theory but having some difficulties with rings and fields

I'll check out Pinter book. Thanks

[Anonymous No.8896519]

Are there a lot of jobs in population biology? It's something I have been wanting to study and was wondering if I could find a job in it.

[Anonymous No.8896539]

>>8896481
I'm currently using hungerford.
It seems rather easily digestivable and alot of the sections are only 1-3 pages.

[Anonymous No.8896546]

How do I stop playing Stardew Valley and write my goddamn lab report?

[Anonymous No.8896584]

WHY IS MATHEMATICA SO FUCKING SHIT

WHY IS THIS ALLOWED

FOR FUCK'S SAKE HOW DO I PLOT A CONTINUOUS FUNCTION WITH DECIBEL Y SCALE

PIC RELATED; IF I HAVE A PLOT LIKE ON THE LEFT HOW DO I TURN IT INTO A PLOT LIKE ON THE RIGHT

[Anonymous No.8896585]

>>8896539
>>8896481
can second hungerford

[Anonymous No.8896586]

[Anonymous No.8896685]

>>8896483
That would mean that the pairs you are supposed to find are (x,y) for all integers x,y

[Anonymous No.8897032]

I'm trying to understand these problems but I'm just not.

Question: http://imgur.com/a/wt0vA

I'm trying to get down the step by step process but I'm currently at a loss in direction. Can someone give me a bit of guidance? Any bit helps.

[Anonymous No.8897063]

>>8897032
Set x = y and restrict t?

[Anonymous No.8897067]

>>8896481
i've heard good things about Algebra by M. Artin, although I haven't read it myself

[Anonymous No.8897072]

>>8897032
>>8897063
If you want to know verify your answers, enter the following into wolframalpha:

2- pi cos t = 2t - pi sin t, -pi <= t < pi

If you want to know how the functions look, enter

x= 2- pi cos t, y = 2t - pi sin t, -pi < t < pi

[Anonymous No.8897079]

Anyone know any place that has comprehensive practice tests (with solutions) for junior/senior level math courses?

[Anonymous No.8897090]

>>8897072
>>8897063
I should have mentioned. These are parametric equations. They're not 2 different functions entirely.

[Anonymous No.8897163]

What is it called when three(or more) things are equal to each other, as opposed to the usual case where two things are equal?

[Anonymous No.8897171]

>>8897163
equivalent modulo 3

[Anonymous No.8897173]

What is your top advice on approaching math classes in college ?

[Anonymous No.8897180]

>>8897173
Go to the lectures and stay focused during them

[Anonymous No.8897184]

>>8897180
lectures are for gaylords. just skip class and go to youtube and watch patrickjmt

[Anonymous No.8897187]

>>8897173
start homework as soon as you get it, just spend ~5 minutes on each problem getting used to the questions and figuring out where the obvious difficulties are

[Anonymous No.8897213]

>>8897032
I can't fucking solve this shit. No one in any medium online has been able to help me. No response from Reddit. Inaccurate responses on here. No one on Discord. What the fuck is going on.

[Anonymous No.8897214]

>>8897173
don't be retarded

[Anonymous No.8897222]

>>8897173
It's all about doing practice problems.

[Anonymous No.8897228]

>>8897213
it's easy as shit if you know what cos and sin look like

[Anonymous No.8897241]

>>8897228
shit i forgot everyone on here was a genius.

[Anonymous No.8897271]

>>8897213
Evaluate [math]\frac{\mathrm{d}y}{\mathrm{d}x} [/math] at t=-π/2 & π/2

[Anonymous No.8897301]

Why can't there exist an onto homomorphism between (Z mod 4) cross (Z mod 4) and Z mod 8?

[Anonymous No.8897342]

>>8894645
>position
velocity

[Anonymous No.8897346]

>>8894638
If you have a TI 83 just do

1 - binomial cumulative density function(11,4,.35)

[Anonymous No.8897424]

What's the number of ways to partition n unique objects? I can't seem to google this question without just getting "number of ways to partition n identical objects".

Also, why is counting partitions so complicated?

[Anonymous No.8897460]

WHAT THE FUCK DOES IT MEAN TO FIND A MEDIAN OF THE FIRST 9 WHOLE (NEGATIVE 0 AND POSITIVE) NUMBERS OF THE RANGE OF VALUES OF THIS FUNCTION?

It should be zero but IT FUCKING ISN'T FFS.

[Anonymous No.8897463]

>>8897424
https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

[Anonymous No.8897472]

>>8897424
There are 2^n subsets if thats what you mean. What the fuck do you mean by partition? How many partitions?

[Anonymous No.8897478]

>>8897301
Since no one could answer it, there does not exist an element in the domain of order 8

[Anonymous No.8897494]

>>8895300
I dont really know math very well but say you find a common denominator, and its a polynomial with x^n asthe highest power term. If n is greater than 1 doesn't that mean its non-linear? This way you dont even have to solve the roots?

[Anonymous No.8897501]

I know the meme about reimann zeta function that:
[math] \zeta(-1) = 1 + 2 + 3 +4... [/math] and that through analytical continuation [math] \zeta(-1) = -1/12[/math] so people meme [math] -1/12 = 1 + 2 + 3 +4... [/math] but is this actually true outside of the context of the reimann zeta function? If so isn't it better to just explain this equivalence as sort of a "id" that corresponds to this particular divergent infinite series rather than actually equivalent?

[Anonymous No.8897513]

>>8897501
Just think of it like a piecewise defined function. It's defined as the infinite sum where it converges and as the value of the continuation where it does not.

[Anonymous No.8897516]

>>8897460
Show the full question because Im kind of confused.

[Anonymous No.8897518]

>>8897513
Yeah thats what I was thinking, thats why asked in the context of the reimann zeta function I guess [math] -1/12 = 1 + 2 + 3 +4... [/math] because both of those are equal to [math] \zeta(-1)[/math], but they aren't REALLY equivalent outside of the scope of the function are they.

[Anonymous No.8897528]

>>8897518
I'm unsure what you're asking.

zeta(-1) is not 1 + 2 + 3 + ...

[Anonymous No.8897543]

>>8897528
Oh so the [math] \zeta(s) = \sum_{n=0}^{\infty} = 1/n^s [/math] definition of the zeta function is only valid for convergent series. Ok I understand. If thats the case though, shouldnt on wikipedia for example state that the series definition of the zeta function only refers to s<0, and s>1?

[Anonymous No.8897553]

Nonhomework question here guys.

Im putting a lithium based densifier on a concrete slab. This densifier reacts with the concrete and creates a crystaline structure that strengthens the concrete surface. I would like to add uv resistance to this, is this as easy as mixing in uv stable polymers/solution into the densifier?

[Anonymous No.8897558]

>>8897543
Read the wiki again

[Anonymous No.8897566]

>>8897543
s=1 is a harmonic series, which is a classical example of a divergent series. 0<s<1 follows from harmonic series. And s<0 is just obviously divergent.

[Anonymous No.8897609]

Dumb question

If [math]V[/math] is the volume, then what's [math]\Delta V[/math], the infinitesimal volume?

[Anonymous No.8897628]

>>8897501
Ramanujan found another way to get to 1+2+3+4+...=-1/12. Is what you're looking for an example of a divergent series being evaluated as one value in the context of one function, and evaluated as another value in the context of another function i.e. an example of divergent sums being inconsistent?

[Anonymous No.8897630]

>>8897609
delta V = V1 - V2

[Anonymous No.8897631]

>>8897609
Delta Volume, so change in volume. When you study integrals the idea is you divide the container into equal intervals of x for example, and the volume on that range is delta V. Integrals are as those intervals of x approach infitesimaly small. So Delta V doesn't have to necessarily mean infinitesimal volume, but likely in this context it is.

[Anonymous No.8897635]

>>8897609
[math]\Delta V[/math] is a change in volume, [math] \mathrm{d}V [/math] is an infinitesimal change in volume

[Anonymous No.8897643]

>>8897630
>>8897631
Thanks,

I'm guessing in this case it means the volume between the points [math]\mathbf{x}[/math] and [math]\mathbf{x}[/math]
<-context

[Anonymous No.8897645]

help

[Anonymous No.8897650]

>>8897032
>http://imgur.com/a/wt0vA
Well when you graph that parametric you will have some <x,y> that will satisfy 2 t-values

the slope of the tangent line will be dy/dt divided by dx/dt

[Anonymous No.8897684]

How much does somebody need to learn about math before they stop being strictly worse at math than a computer?

[Anonymous No.8897747]

I some how got an A in Calc II despite having a rocky foundation in math. This summer I would like to strengthen my foundation, what's the best way to relearn the things I would have learned in high school If I had paid attention? Should I just go on Khan Academy and review basic Trig and Algebra?

[Anonymous No.8897760]

>>8897747
Yes, his videos are pretty godlike for HS and first/second year stuff.

[Anonymous No.8897800]

>>8897643
Well when you deal with 3rd integrals you can linearly go from one point to another, there are infinite amount of ways to go from one point to another, so all [math] \deltaV [/math] means here is if the Volume you are integrating over contains X, it will evaluate to 1, otherwise 0.

[Anonymous No.8897805]

>>8897800
You can't* linearly go from point to point, not can, so no, in this context delta V is necessarily infinitesmal, its just an arbitrary volume to explain the properties of the Delta function.

[Anonymous No.8897806]

>>8897805
You can if you integrate over a convex domain.

[Anonymous No.8897813]

>>8894488
do any of you whiz's have a black/dry erase board in your apartment/house?

Is it worth it?

[Anonymous No.8897814]

>>8897813
im talking large honey

[Anonymous No.8897842]

>>8897494
Well, you'll have to find the roots of the numerator even if it's non linear, since the roots are the solutions

[Anonymous No.8897844]

>>8897813
No. I really only find board useful for collaboration. Great when working as a team on some system and drawing diagrams. However, when working out problems, I'd rather the old pencil and paper. I really value having my train of thoughts written down (not having to erase)

[Anonymous No.8897868]

>>8897842
Wait nevermind, I thought the question was just whether to determine if the function was linear or not.

[Anonymous No.8897888]

So was the forbidden fruit an Apple?

[Anonymous No.8897890]

>>8897844
i like your input.

Do you keep neat copies of your work?

[Anonymous No.8897900]

>>8897760
Okay thanks.

[Anonymous No.8897907]

>>8897888
Pomegranate possibly. Based on the region.

[Anonymous No.8897964]

Can someone explain unitary matrices. like an example of a path for it

[Anonymous No.8897972]

>>8897964
>a path for it
Wut

[Anonymous No.8898070]

>>8897964
fucking google it

[Anonymous No.8898083]

>>8897645
with what?
also that N should be cap
fag

[Anonymous No.8898099]

Can somebody explain how to do 192 - 293?

I can subtract just fine when the top number is greater than the bottom but this kind of shit requires an additional step that I forgot how to do.

[Anonymous No.8898109]

Using residues.

Should I expand, or just plug in my substitution and go from there? I mess up both ways, apparently.

[Anonymous No.8898160]

>>8898099
/sci/ - Science & Math, ladies and gentlemen

[Anonymous No.8898179]

>>8898099
It's the same thing as -(293 - 192)

[Anonymous No.8898187]

>>8898109
https://en.m.wikipedia.org/wiki/Tangent_half-angle_substitution

[Anonymous No.8898191]

>>8898187
not that anon but the whole point is that it's an exercise in using residues
i haven't calculated a residue in over a year and despite acing complex analysis (at least the version offered by the physics department) can't help lol

[Anonymous No.8898257]

>>8898099
subtract 192 from 192 to get to 0
subtract (293 - 192) from 0 to get to -101

[Anonymous No.8898280]

>>8895292
i mean if you're trying to find the roots the other guy has you done, but if you're just solving for x it's 1/3

[Anonymous No.8898285]

>>8895127
No but if you're concerned just get f.lux

[Anonymous No.8898291]

>>8895127
no it's a meme. the companies that are involved in this type of business don't even claim any health benefits just that the colder color temperatures of pc monitors and smartphones match daylight but they don't match typical night-time indoor lighting like incandescent light bulbs and candles and such

[Anonymous No.8898296]

Sit down anon. Mother of all brainlet questions inbound. Steady yourself.
With nothing but:
>Pen(cil)
>Paper
>Calculator
>Infrequent use of the SciPy library
What research could be done? Other than pure maths obviously. Would there be much of an opening for applied maths in biology? Basically looking for something that can be done anywhere with little to no equipment (ie. theoretical) without being pure maths or theoretical physics.

[Anonymous No.8898300]

>>8898296
data analysis?

[Anonymous No.8898588]

how do i prove that this is equal to the set of the positive rationals? induction or counter example?

can someone show me an example proof?

[Anonymous No.8898604]

>>8898588
That's not equal to the set of positive rationals due to the density of the irrationals in the real numbers.

[Anonymous No.8898610]

>>8898604
but it's not the set of all reals from [1, infinity) is it? i'm lost. what does it represent?

[Anonymous No.8898627]

>>8898588
>prove that [math]R^+ \subset S[/math]
>prove that [math]S \subset R^+[/math]
there, you're done

[Anonymous No.8898641]

>>8898627
>>8898588


how can that interval contain pi? i don't think it can because pi is not a ratio of 1/x

[Anonymous No.8898652]

>>8898641
pi is in (1/4, 4) so yes it can contain pi.
Also, I misread your question. It's not the set of positive rationals, it's the set of positive reals

[Anonymous No.8898700]

>>8898610
It's the set of reals from (0, infinity)

[Anonymous No.8898778]

>>8894488
An object is measured in the air and its weight was W1 = 11.4 g . When the object is completely immersed in water ( ρ = 1.0 g/cm 3) the weight was W2 = 9.9 g . The density of the object is (in kg/ m3 )

I need this

[Anonymous No.8898819]

>>8898778
[math]\rho _{objet} = \rho_{eau}\frac{W_1}{W_1-W_2}[/math]

[Anonymous No.8898824]

Is (x)->(x,1) a homeomorphism. Stupid question I know but does each element of the function have to be continuous.

[Anonymous No.8898889]

>>8898778
ρ_water = 1.0 g / cm3 = 1000 kg / m3
V_object = (W1 - W2) / ρ_water = (0.0114 kg - 0.0099 kg) / (1000 kg / m3) = 1.5 * 10^-6 m3
ρ_object = W1 / V_object = 0.0114 kg / (1.5 * 10^-6 m3) = 7600 kg / m3

[Anonymous No.8898899]

Can someone help me understand this? I have a pretty solid foundation in non-multivariable calculus but I can't figure out what this is saying. Is H the matrix equivalent of dx?

[Anonymous No.8898916]

>>8898899
the derivative is a linear transformation
if you take the function f: x -> x^2 in the reals, then the derivative f'(x) is the linear transformation that sends y to 2xy, written f'(x) : y -> 2xy.

the identification of R with the space of linear functions from R to R allows us to just write it as a number, as 1x1 matrix, so you just say it's 2x

[Anonymous No.8898930]

>>8898824
>Is (x)->(x,1) a homeomorphism
No Idea. And there is no way to check unless you provide image and preimage.
> does each element of the function have to be continuous.
That is not a question. A function has no element.
If you are asking whether the function is continuous (at every point), then yes, a homeomorphism is a bijective continuous function with a continuous inverse.

[Anonymous No.8898940]

>>8898824
assuming you mean a function in X -> X x {1} with the product topology, yeah.

not in R -> R^2 though

[Anonymous No.8898951]

>>8898588
If you mean the real numbers then start by taking an element x from the reals and show that it is included in one of these intervals (round down to a lessser rational or greater integer (maybe have cases for x<=1 or x>=1) ).

The other direction is obvious because any number in that set is certainly a real number greater then 0.

[Anonymous No.8898960]

>>8898940
Yeah, can you give an example of a function thats not continuous then. Does it mean that the function cant take x in X. Or something like (x)->((x/x),1)

[Anonymous No.8898966]

>>8897684
About 5 hours into something about (uncountably-)infinite sets (so literally everything about mathematics that is commonly used) and you are far beyond what a computer could do.

If you want to solve integrals, then bad luck. The computer is always better then you.

Automated theorem solver already exist, but even with them anyone who is taking some college math is better then a computer in terms of serious mathematics.

[Anonymous No.8899014]

>>8898899
What text is that?

[Anonymous No.8899028]

Beginner Ochem, shitty 'bonus' question on a test: Which of Oxirane/Oxirene follows the pattern: Ozone, Trioxidane, Methyl Peroxide, Dioxirane?
I'm not sure if this even has much to do with Ochem.

[Anonymous No.8899060]

>>8894488
Help a guy out? This seemed more clear last night

[Anonymous No.8899067]

>>8899014
Linear algebra, vector calculus, and differential forms: a unified approach
http://libgen.me/view.php?id=405404

[Anonymous No.8899106]

I hit my head pretty hard yesterday, am I doomed to be a brainlet now?

[Anonymous No.8899136]

>>8898966
>Automated theorem solver already exist, but even with them anyone who is taking some college math is better then a computer in terms of serious mathematics.
Sure.

[eqn]H_0 = 0\\H_{n+1} = H_n + \frac1 {n+1}[/eqn] or equivalently
[eqn]H_n = \sum_{k=1}^n\frac1 k[/eqn]

Go ahead and try to solve for an arbitrary n (so that the solution does not contain a sum, except H_k) without a computer

[eqn] \sum_{k=0}^n H_k^2 = ?[/eqn]

A computer can do it.

[Anonymous No.8899159]

>>8899136
[eqn] \sum_{k=0}^n H_k^2 = (n+1) H_n^2 - (2n + 1) H_n + 2 n [/eqn]

You don't need a computer for that.

[Anonymous No.8899173]

why is a "square" frequency response considered to be the "perfect" filter? what are the drawbacks of a smooth transition in the frequency domain?

[Anonymous No.8899192]

>>8899159
Ok, you got me

I have actually no idea how to solve it "by hand", what did you do?

[Anonymous No.8899201]

>>8899192
Summation by parts

[Anonymous No.8899251]

>>8899060
Please help

[Anonymous No.8899256]

Precalculus with the unit circle or Stewart's Precalculus?

[Anonymous No.8899258]

>>8899256
I'm doing the latter

[Anonymous No.8899275]

How do i deal with binary operations on random variables in probability?

For example, say X ~ uniform (0,1) and Y ~ uniform (0,1)

How would i go about solving something like:

P(|X - Y| < .01)

What if X ~ a different distribution?

[Anonymous No.8899343]

>>8899275
>How would i go about solving something like: P(|X - Y| < .01)


You can't. You also need to know the joint distribution to solve this.

[Anonymous No.8899389]

>>8898588

[eqn]\bigcup_{i=1}^{\infty}\ (\frac{1}{i}, i) \equiv \{x:\frac{1}{1}< x < 1 \} \cup \{x:\frac{1}{2}< x < 2 \}\cup\{x:\frac{1}{3}< x < 3 \} ... [/eqn]

[Anonymous No.8899390]

How does set derivation work?
For example when proving that (X ∪ Y ) ∩ X = X, it uses algebraic laws that don't exactly match the structure.
e.g.
[math]
(X ∪ Y ) ∩ X =
(X ∪ Y ) ∩ (X ∪ O)
= X ∪ (Y ∩ O)
= X ∪ O
= X
[/math]

The third part of that, X ∪ (Y ∩ O), uses an algebraic law which is of the form:
(A ∪ B) ∪ C = A ∪ (B ∪ C)

But the two don't match. None of the laws match the second part of that.
How does it work?

[Anonymous No.8899393]

>>8899251
Can't see the whole qn mate

[Anonymous No.8899399]

>>8899390
Second equality is wrong.

[Anonymous No.8899401]

What is it called when each output of a function matches only one input? Does every function of this nature have a corresponding function where the axes are switched? If so, does finding said function involve differentiating, reciprocating, then integrating?

[Anonymous No.8899406]

>>8899401
1) injective
2) yes if you restrict the domain of the inverse function to the range of the original function
3) usually it is possible to find the inverse without differentiation

[Anonymous No.8899412]

QUICK tell me a good book on ODEs or this lady gets it

[Anonymous No.8899419]

>>8899406
I ask this because I thought of the equation
[math]y=2x+sin(x)[/math]
and I wanted to isolate [math]x[/math] from it. Does this require differentiation?

[Anonymous No.8899420]

>>8899390
You prove it by set inclusions.
Note that any x in B := (X ∪ Y ) ∩ X satisfies the following: [math](x \in X \, \vee \, x \in Y) \, \wedge \, x \in X[/math], from which the following can be deduced:
[math]x \in B \Rightarrow x \in X[/math].
Further, [math]x \in X \Rightarrow x \in B[/math].
Hence, X is a subset of B and B is a subset of X, which implies they are the same set and equality holds.

[Anonymous No.8899421]

>>8899389
That's not a proof.
>>8898588
That set does not equal positive rationals, so you can't prove it.

[Anonymous No.8899447]

>>8899419
That equation isn't injective, unless we restrict it to say 0 to π/2.

It might be possible if we use the closed form for arcsin.

[Anonymous No.8899453]

>>8899447
It's not? No two inputs share the same output.

[Anonymous No.8899550]

very stupid question as im sure theres primary school pupils that know this. which line exactly is the "vector equation of a straight line passing through A" referring to on the graph? i thought it was what i circled, but that doesn't pass through A unless λ=0, right?

[Anonymous No.8899554]

probably shouldve posted this as well

[Anonymous No.8899569]

>>8899554

yea but lambda is a variable so its effectively _a right?

[Anonymous No.8899576]

>>8899393
i need to solve for n

[Anonymous No.8899588]

I bet /sci/ can't even prove this basic arithmetic law:

[math] y-(x-1) = (y-x) +1 [/math]
x and y are integers

[Anonymous No.8899595]

>>8899588
distributive law and associativity on the lhs

[Anonymous No.8899601]

>>8899595
too vague. show the actual equations and transformations

[Anonymous No.8899604]

>>8896481
Pinter, the one and only that does exactly what you are asking.

[Anonymous No.8899629]

>>8899588
too vague. show the actual meanings of those strange symbols

[Anonymous No.8899631]

>>8898951
i love you /sci/, your maths is strong

[Anonymous No.8899632]

>>8899412
thinking

[Anonymous No.8899641]

>>8899632

well i cant think because i swear ODEs are bullshit math, like what the fuck you can just move dy dx around

[Anonymous No.8899802]

when can i put my brain in a body that isn't susceptible to disease or trauma?

[Anonymous No.8899817]

where is the hump?

[Anonymous No.8899953]

How do I solve this for p?
4^(-1/p)*Г(1+1/p)/Г(1/2 + 1/p) = 0

[Anonymous No.8899961]

Why isn't the residue here -1?

[Anonymous No.8899966]

>>8899802
When you die

[Anonymous No.8900252]

How do PhDs work exactly? Like do you apply for a specific concentration or professor and then later determine your main research topic? Or are you supposed to have your main research topic determined when applying?

[Anonymous No.8900263]

I have 2 hours or so to learn Lorentz Force and the magnetic field, I have wasted 3 of them on it, my books simply are not clear enough for me, what should I use?

[Anonymous No.8900281]

Is a series being divergent a rigorous thing? The same method that says 1+1/2+1/4+1/8+...=2 also says that 2+4+8+16+...=-1. Is there a truly rigorous reason for why the former is true while the latter is false?

[Anonymous No.8900286]

>>8900281
no it doesn't. it's not the same method at all

you're probably thinking of S = ..., 2S = ..., S-2S = 2, but that's wrong because the tail terms don't tend to 0

[Anonymous No.8900316]

>>8900286
I don't know what you're trying to say, but both series follow the pattern of
1+aS=S
Where "S" is the series and "a" is the second term of the series.

[Anonymous No.8900326]

>>8900316
that's exactly what I'm saying. the plug and chug you're doing is wrong. it happens to work in the first case because the terms tend to 0, and more properties are fulfilled (so just dumb luck)

[Anonymous No.8900332]

>>8900326
Why should the terms tending to 0 matter?

[Anonymous No.8900340]

>>8900332
Yes, why would that matter? I don't understand why I can't just add these terms (who never approach zero) together an infinite number of times without them reaching infinity! XD XDXD!

https://www.youtube.com/watch?v=v5CHTVDiMkQ

[Anonymous No.8900346]

>>8900332
because something arbitrarily large minus something arbitrarily large is not a computation you can carry out (limits aren't preserved under arbitrary infinite sums)

[Anonymous No.8900366]

>>8900340
>what is an alternating series
Also, infinity isn't a number and intuition isn't an argument.

[Anonymous No.8900374]

>>8900366
shut the fuck up imbecile. he clearly knows his shit and posted a good resource on rigorous treatment. you're an autist nitpicking his sarcasm
>hurr infinity is not a number
projective spaces are really fucking natural. what's more natural than a polynomial? just fuck off

[Anonymous No.8900379]

>>8900366
The guy clearly doesn't understand what a series is, me misusing infinity doesn't really matter. If you're that guy, just watch the fucking video. You will learn to prove everything you need to prove.

[Anonymous No.8900380]

>>8900379
>doesn't understand what a series is

doesn't understand what it means for a series to converge*

And if he gives a shit about learning this stuff rigorously, and not just some intuition, he will watch the video.

[Anonymous No.8900396]

>>8900374
Somebody who clearly knows their shit doesn't make three obvious errors while typing like a retard then post an hour long video with no elaboration.

[Anonymous No.8900399]

>>8899961
it has a removable singularity at z=0. cos(z)=1-z^2/2 + ...

Subtract 1 from that, you can divide by z and get an analytic function.

[Anonymous No.8900407]

>>8900399
yeah, i did the expansion of cos z wrong, my bad

thank you

[Anonymous No.8900455]

Can someone teach me how to convert from rectangular equation to polar equation?

The equation I'm working with right now is y = 4.

[Anonymous No.8900458]

When evaluating something like Log(2e^(it)+3) (Log is the principal branch), how exactly do I get the absolute value of the meat inside into a nicer form after taking its modulus?

[Anonymous No.8900468]

>>8900455
tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx

You have y = rsin(a), x = rcos(a)

rsin(a) = y = 4 => r = 4(sin(a))

[Anonymous No.8900484]

Hey guys I see this sometimes where there's an integral but only one of the bounds is filled out. It looks like [math]\int_{\mathbb{R}}[/math] or sometimes instead of R it'll have an equation like 2x^2<1 on it. What does that mean?

[Anonymous No.8900491]

How do people find partial sum formulas for really strange sums like pic related? do they just think really hard about it and then prove by induction or is there a way to find them?

[Anonymous No.8900520]

>>8900468
That's not making much sense. I can see that you get the radius to equal 4 because y = 4 and that's the distance from the origin.

Pic related is the entire question. Maybe the graph will give you a better idea.

[Anonymous No.8900523]

>certainty has been superseded by probability

why is this happening?

[Anonymous No.8900530]

>>8900468
Oh nevermind. I got it. Thank you brotha

[Anonymous No.8900532]

>>8894901
personally I would sleep and do a little last minute studying in the morning. Lack of sleep can cause you to fuck up what you already know.

[Anonymous No.8900538]

What are some good books/resources for the math I'll need in Engineering courses? (Civil Engineering or Material Engineering). What type of math will I need in general? I wanna get a head start.

[Anonymous No.8900747]

[math]\exists{x}P(x) \rightarrow S \vdash \forall{x}(P(x) \rightarrow S)[/math]

Can I just use universal generalization to prove this?

[Anonymous No.8900801]

I'm trying to figure out what the volume of habitable space on Earth is. This space includes ~25 miles into the crust and ~3 into the atmosphere, and the surface area of land on Earth is ~57,268,900 square miles (I'm only counting land for this, no lakes or seas).

Simply going for cubic miles seems too easy and crude, but would that be a fair estimate? I'm not a math guy, just trying to figure this out for fun. I was also looking at the formula for the volume of a torus, but that would leave out a large part of the earth. I assume you'd have to use a combination of volumetric formulas, but I don't really know, I studied theatre in college.

It's like if you put two bowls together to make a sphere, and then wanted to find the volume of space the bowls' walls occupy. Anyone got any ideas?

[Anonymous No.8900820]

How the fuck do I integrate this? Brainlet here learning Fourier series for the first time.

[Anonymous No.8900822]

>>8900801
My guess would be using spherical coordinates and integrating.

[Anonymous No.8900826]

>>8900822
Shit. I only got to trigonometry.

[Anonymous No.8900854]

yo can anyone help with

[Anonymous No.8900856]

test

[Anonymous No.8900862]

>>8900801
just use volume formula for a sphere and modify the radius part to be an outer and inner radius

[math] V = \frac{4}{3} \pi (r_{outside}^3 - r_{inside}^3) [/math] (if you subtract the volumes of two spheres with different radii you get this formula)

where [math] r_{outside} [/math] is the radius of the outside sphere and [math] r_{inside} [/math] is the radius of the inside one

you said your radius change was -25 miles to +3 miles then you would need to add on the radius of the earth to both numbers before cubing

as for the approximation; if we can live there fine then it's fine as the earth is smoother than a billiard ball so i hear

>>8900854
you're a stupid nigger

[Anonymous No.8900864]

>>8900862
Can you keep the racism to /pol/

[Anonymous No.8900873]

if that integral is over some interval like [math] -\pi [/math] to [math] /pi [/math] then you can recognize that the integral is zero from integrating an odd function (flipped over y-axis) over it's interval

this is because an odd function multiplied by an even function (symmetric over y-axis) is an odd function and an odd function's areas cancel off over an interval across the axis

if you don't have bounds just use some trig identity

[Anonymous No.8900881]

>>8900820
> How the fuck do I integrate this? Brainlet here learning Fourier series for the first time.
Use
[math]cos(\alpha ) sin(\beta )=\frac{1}{2} [cos (\alpha +\beta ) +cos (\alpha -\beta )[/math]

[Anonymous No.8900884]

>>8900862
Nice.

[Anonymous No.8900906]

I might be doing this wrong, but when I use that formula, I get like 2.71 times 10 to the 27th or some shit, so then I just subtracted the volume of the inner sphere from the outer sphere and got 5,484,335,363.45, which seems much more reasonable. Then, since land is 29% of earth's surface, I got 1,590,457,255.4. Is that shit right?

[Anonymous No.8900910]

>>8900906
Fuck, which is only slightly less than just multiplying the square miles of the land on earth by 28 (1,603,529,200). I thought there'd be a greater disparity than that.

This is all assuming I'm right, of course, which I'm probably not.

[Anonymous No.8900987]

>>8894488
THICC

[Anonymous No.8901026]

>>8894488
Is everything a conductor given the right voltage? Obviously we know wood or something typically seen as a non-conductor can conduct electricity at high voltages, but is there any object in the world that has infinite resistance?

[Anonymous No.8901031]

>>8900906
>>8900910
i got comparable values for my calculation using 3959 miles for earth's radius so it looks like you did it right

as for if it makes sense
the volume region in that zone is just stacks of the surface area on top of eachother modified differently by radius (cubed instead of squared as you get further out) and multiplied by a different constant (4/3 instead of 4) so it's not going to be substantially different over a 28 (25 - -3) mile difference

btw the i got the volume formula from visualizing two spheres with one inside the other then removing (subtracting) the inner one and taking everything with it leaving only a shell

[Anonymous No.8901038]

>>8901031
i can't post my latex for the calculation but everything was on the same order of magnitude (same 10^number) and had the same first digit

[Anonymous No.8901043]

>>8900906
>>8901038
don't know how the fuck you get 10^27

http://www.wolframalpha.com/input/?i=volume+of+earth

[Anonymous No.8901045]

>>8901026
a conductor is defined as something that can conduct electricity (electrons can flow through it)

so technically everything except a vacuum is a conductor (no electrons to flow) because you can theoretically supply a voltage difference high enough to rip the electron into flowing

[Anonymous No.8901048]

>>8901043
yeah i assumed he had misread it as my difference between volumes was almost the same

[Anonymous No.8901051]

>>8901026
>Is everything a conductor given the right voltage?
Yes, and that value is called Dielectric strength.

[Anonymous No.8901081]

whats the best precalc book for self-study?

[Anonymous No.8901091]

I'm confused with how line 5 works in this proof.
Where has ¬A come from? How can ¬A be justified when it has not been assumed?

It uses classical contradiction which I still don't fully understand so I'm hoping someone here knows how it works.

[Anonymous No.8901120]

[math]g(f(g(n)) = g(f(n + 5)) = g((n + 5)2 + 7) =
(n + 5)2 + 12 = n2 + 10n + 37[/math]
Where has 10n come from?

[Anonymous No.8901128]

I'm about to sign up for biology for the next semester, what are the odds I will regret it?

[Anonymous No.8901184]

>>8901091
Might be clearer with works. We want to prove (A -> B) -> (~A or B). So for contradiction, assume A -> B is true and ~(~A or B) is true

We show that ~(~A or B) is false regardless of A. If A is true then, we have B is true which implies ~(~A or B is false. if A is false then ~(~A or B) is again false.

This is a contradiction.

[Anonymous No.8901210]

A` U B`
"The set of all elements that are not in A or are not in B"
So why are both A and B shaded if none of the elements can be in A or B?

I don't get set operations.

[Anonymous No.8901219]

>>8901210
The elements of A that are not also in B are in B'. So that part of A gets shaded.

[Anonymous No.8901226]

>>8901210
not in A OR

OR

OR not in B

[Anonymous No.8901227]

>>8900538
You will need a lot of trigonometry to convert force diagrams into equations.

[Anonymous No.8901351]

>>8894488
how 2 show the luzin property n for absolutely continuous functions?

[Anonymous No.8901396]

Are there languages that are recognized by a one-counter automaton that can test for zero, but not by any one-counter automaton that cannot test for zero?

[Anonymous No.8901427]

>>8901120
I'm guessing whoever wrote this wanted those 2's to be superscripts. It's probably supposed to be [math]f(n) = n^2 + 7[/math], not [math]f(n) = 2n + 7[/math].

[Anonymous No.8901455]

>>8900484
[math]\int_S[/math] - integrating over all elements in [math]S[/math].

[math]\int_{\varphi(x)}[/math] - integrating over all [math]x[/math] such that [math]\varphi(x)[/math] is true.

[Anonymous No.8901478]

>>8901427
Yeah, that's right. My bad.
I still don't know where 10n came from though.

[Anonymous No.8901495]

>>8901478
(a+b)^2=(a+b)(a+b)=a^2+ab+ba+b^2=a^2+2ab+b^2

[Anonymous No.8901625]

Does anyone know if this is a good book? I really want to get into mathematics but I don't know what to read.

[Anonymous No.8901629]

>>8901625
What kind of get into?

[Anonymous No.8901634]

>>8901629
I want to get into advanced mathematics but I don't know where to start.

[Anonymous No.8901635]

>>8901634
What is your background?

[Anonymous No.8901637]

>>8901635
Explain by background?

[Anonymous No.8901638]

>>8901637
Mathematics background. As in, what do you know? What classes have you have taken in the past?

[Anonymous No.8901644]

>>8901638
All up to Algebra 2 and Pre-Calc.

[Anonymous No.8901668]

How would you prove:
A ∩ (A ∩ B) = A ∩ B
Using the algebraic set of laws?

Could you apply Idempotent 1b to it?

[Anonymous No.8901675]

>>8901644
Pick up some book on calculus, and a book on elementary number theory. The former is a primer for analysis and the latter usually is a good introduction to proofs and some abstract algebra ideas.

[Anonymous No.8901679]

>>8901675
But what if I run into something I don't remember?

[Anonymous No.8901684]

>>8901679
You look it up. If you find you don't remember a lot pick up a precalc/algebra book

[Anonymous No.8901689]

>>8901684
How much are these books and where can I get them?

[Anonymous No.8901694]

>>8901689
For non-proof based math there are loads of decent resources if you look around

Or you can sail high seas

[Anonymous No.8901695]

>>8901668
>How would you prove:
Start with associativity.

>Could you apply Idempotent 1b to it?
I have no idea what rule that is in your textbook. (They are not standardized in any way.)

[Anonymous No.8901696]

>>8901694
>Or you can sail high seas
I'm sorry, what do you mean?

[Anonymous No.8901708]

How do i solve this?

[Anonymous No.8901724]

>>8901708
You can prove it converges pretty easily.

Also it is pretty common knowledge that [math]\sum_{n=0}^{\infty} \frac{1}{2^n} = 2 [/math] so you only have to really figure out what [math]\sum_{n=0}^{\infty} \frac{2n}{2^n} [/math] is.

Do you have any method that would allow you to directly know what that limit is?

[Anonymous No.8901726]

let a, b and c be integers with a!=0.
Prove that gcd(a,b) = gcd(a,c) = 1 iff gcd(a,bc) = 1

The solution starts with "as+bt=1 and ax+cy=1" but I don't understand how that's true?

[Anonymous No.8901727]

>>8901726
https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity

[Anonymous No.8901735]

>>8901726
>The solution starts with "as+bt=1 and ax+cy=1" but I don't understand how that's true?

That is a theorem that stems from an alternative characterization of the gcd. But also can be known as Bezout's identity.

Anyways, applying that identity most of the time is fucking useless. Argue by contradiction:

Suppose gcd(a,b) = gcd(a,c) = 1 but gcd(a,bc) > 1.

That implies a and bc share at least one prime factor. And whatever that prime factor it is, it must divide either b or c (or both). Suppose it divides b.
Then gcd(a,b) > 1 which contradicts the hypothesis
Now suppose it divides c. Then gcd(a,c) > 1 which contradicts the hypothesis.

etc. etc.

[Anonymous No.8901739]

>>8901708

[Anonymous No.8901741]

>>8901739
Where did the d/dx come from my main man

[Anonymous No.8901745]

>>8901739
Oh, and also how did it disappear?

[Anonymous No.8901746]

>>8901741
[eqn] \frac{d}{dx} x^n = n x^{n-1} [/eqn]
Multiply by x:
[eqn]x \frac{d}{dx} x^n = n x^n [/eqn]

[Anonymous No.8901750]

>>8895313
This is not all. Make sure that the solutions you find do not cause division by zero when substituted back into the original equation.

[Anonymous No.8901760]

>>8901746
Holy fucking fuck. I went to a whole calc 2 course and no one told me this what the hell. THIS IS GENIUS

[Anonymous No.8901766]

>>8899453
>>8899447
It is. He didn't check that the 2x term takes out the cyclic part of sine.

[Anonymous No.8901767]

>>8901739
>>8901724
Thank you so much.

[Anonymous No.8901769]

>>8901760
this: >>8901746 is the first thing you do in calc 1 but >>8901739 is some wizardry bullshit

[Anonymous No.8901778]

>>8901769
>this: >>8901746 is the first thing you do in calc 1

Yeah I know. But I never saw it applied like that before. It is so clever.

The sad thing is that I probably used the ratio test a billion time to prove those kinds of series converge but was never actually told how to find what value they converge to nor how to compute it. It is crazy.

[Anonymous No.8901780]

>>8901668
Assume an element exists that is in LHS but not RHS, lead this to a contradiction (with the definition of intersection)
Do the same the other direction

Done

[Anonymous No.8901783]

let k be a positive integer.
Prove that if 2^k-1 is a prime then k is a prime.

Solution from the book:
Assume k is not prime, then k=ab
2^k-1 = 2^(ab)-1
(2^a)^b-1 = (2^a-1) * ( (2^((b-1)a)+2^((b-2)a)+.....2^a+1)

So the second step looks kind of like difference of squares expansion which I've only seen for degree 2. Is this a generalization?

How would I prove this if I didn't know the said expansion?

Thanks anons

[Anonymous No.8901785]

>>8901780
>by contradiction
why?

[Anonymous No.8901789]

>>8901783
x^a-y^a
= (x-y)(x^(a-1)+x^(a-2)y+...+xy^(a-2)+y^(a-1))

its worth remembering

[Anonymous No.8901797]

>>8901785
Because I can

[Anonymous No.8901799]

>>8901668
Oh man, you give me memories of the good old days back in freshman days.

[math] x \in A \cap(A \cap B) \iff x \in A \land x \in(A \cap B) \iff x \in A \land( x \in A \land x\in B) \iff \\ x \in A \land x \in A \land x\in B \iff (x \in A \land x \in A) \land x\in B \iff x \in A \land x\in B \\ \iff x \in A \cap B [/math]

[Anonymous No.8901802]

>>8901799
Does it only get harder from here?

[Anonymous No.8901807]

>>8901802
Eh, I wouldn't say it gets harder.

I said what I said because it feels good to write proofs that go this smooth. You basically only need to take what you were given, slowly decompose it into a propositional statement, apply some tautologies, and then you take your new propositional statement and tie it up back into a set theoretical statement. Pretty direct. And also pretty short.

I am just in my sophomore year and I am already writing 4 page long proofs that all start with some contrived construction, then I prove a couple of minor lemmas, and then write a long conclusion about why everything proved before proves what was originally asked.

It isn't hard, but it is stressful.

[Anonymous No.8901809]

>>8901802
No. The proofs get harder but since you get better at proving things they also get easier

[Anonymous No.8901946]

Need to make a committee of 4 members.
1 must be from group a(total of 6)
1 must be from group b(total of 5)
1 must be from group c(total of 4)
The solution breaks this into 3 possible types:
(6c2)*(5c1)*(4c1)
(6c1)*(5c2)*(4c1)
(6c1)*(5c1)*(4c2)
=720
but I was thinking
(6c1)*(5c1)*(4c1) * (15-3c1)
How am I wrong? We picked 1 of each so we want to know ways to pick 1 member the remaining 12 guys?

[Anonymous No.8902000]

>>8901946
Notice that your formula gives the actual answer times 2. This is not a coincidence - you are counting each possible committee twice. In each committee you counted, there are two guys coming from the same group. One of them you first selected as a representative of the group, the other from the "remaining 12 guys," but it doesn't matter which one is which.

[Anonymous No.8902005]

>>8902000
so how would I adjust my approach without going into categories? Just divide by two and justify by using inclusion/exclusion?

Thanks anon

[Anonymous No.8902017]

>>8897424
>why is counting partitions so complicated

because you've been lied to your whole life about "discrete math" being easier than calculus so you underestimate the difficulty of counting problems and their associated functions.

>>8897501

the sum of natural numbers equals -1/12 really means that it intersects the y axis if you "smooth" the curve "pushing" its initial value down to y = -1/12. this smoothing technique allows you to assign values to other divergent series as well.

>>8899421
>that's not a proof

no kidding. he didn't seem to understand what the notation meant so I thought I would give him a hint.

[Anonymous No.8902039]

>>8902017
but intersecting the y axis is completely different to a sum

[Anonymous No.8902056]

>>8897424
Depends. If you're partitioning [math]n[/math] unique objects into [math]k[/math] identical bins, use Stirling numbers of the second kind. If the bins are also unique, it's just the number of functions from objects to bins, so [math]k^n[/math].

[Anonymous No.8902063]

>>8901766
How do I invert it then?

[Anonymous No.8902098]

>>8900747

it isn't true, but the converse is

>>8901091

If A leads to a contradiction you can introduce A's negation.

>>8901210

first remember what complement and intersection mean, then remember you could have just used de morgan's law the whole time.

[math]A^c \cup B^c = (A \cap B)^c[/math]

>>8901799

try writing well formed formulas if you're going to boast

>>8902039

Yes, that's why it is a joke, because it is not actually a sum, it's just a technique of assigning values to a divergent series.