/sci/ - Science & Math

>>6979302
When did you become a pretentious little shit?

Can you do triple integrals?

>>6979311
What the fuck did you just fucking say about me, you little bitch? I’ll have you know I graduated top of my class in Triple Integration Theory and I’ve been involved in numerous secret math classes on triple integrals and I have over 300 confirmed triple integrals computed I am trained in triple integration and I’m the top triple integrater in the entire US. You are nothing to me but just another target. I will wipe you out with precision the likes of which has never been seen before on this Earth, with barnett's identity. Mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting jacob barnett so we can kick your ass. The storm that wipes out the pathetic little thing you call your ego. I can be anywhere, anytime, and I out triple integral you in over seven hundred ways, and that’s just with my bare hands. Not only am I extensively trained in mathematics, but I have access to the entire arsenal of geniuses like jacob barnett and I will use it to its full extent to wipe your miserable ass off the face of any math competition. You’re fucking owned, kiddo. Consider yourself triple integrated.

Where did the jsMath button go that used to be in the bottom right corner of my browser when I'm on /sci/?

>>6979310
Consider this a crowd surfing thread. Everyone is fair game to ask/answer questions.

is calculus I hard? ive been doing trig and algebra practice all winter break cause im scared..

>>6979322
Calculus is much easier once you mastered algebra/trig. The basic ideas of Calculus isn't hard (e.g. limits, differentiation, integration, etc.), but the difficulty arises if you are on an integration problem and get stuck on something basic with algebra/trig. It comes down to practice too. Calculus isn't inherently difficult, but if you aren't good with the basics you'll struggle and that isn't due to how hard Calculus is, but because you lack the basics.

>>6979327
thanks! so Ill keep practicing alebra and trig stuff until my time comes. Im kinda looking forward to calc and want to do well

>>6979339
Yup! A lot of problems students have with Calculus isn't even Calculus. It's because of algebra/trigs problems.

What the fuck is linear algebra and differential geometry?
examples would help

How do I get started with proofs? I had an idea a couple of days ago that is completely trivial but realized that I can't even begin to prove it because I only know like two methods.

>>6979343
>be me
>find trig identities pieces of illogical shit
>find out about Euler identity of writing sine and cosine
>always simplify trig expressions with complex exponents now
>shits way easier and straight forward without having to remember a thing
Never again that highschool shit

I have a question,can't remember the answer (if I saw it):
Value of /sum_1^inf (-1)^n-1 / n ?
Thanks anon!

what is precalculus anyways? what are the prerequisites for learning calculus, either from something rigorous like spivak or something simpler like Stewart?

what is the difference between the direct sum of vector spaces and the cartesian product of vector spaces?

or for any kind of structure (obviously the direct sum of groups carries the operations somehow while the cartesian product has nothing to do with operations). but is that it?

Geometry for a change:
Why is it so difficult to find the sides of a known solid given its volume and surface area?

>>6979534

Because there's several possible solutions.

In your case though, where two of the sides are the same, it shouldn't be a problem because you have two variables and two known equations.

>>6979534
You have two unknowns (a and b) and two equations (V and A) which are functions of a and b. Simply find the expression for V and A and solve the system of equations by substitution. Its pretty easy once you see this.

>>6979534
It's not that difficult, but it's because you get a set of non-linear equations instead linear equations. Those are usually a little more difficult to solve (often it's even not possible).

<span class="math">V=a^2b\Longleftrightarrow b = \frac{V}{a^2}[/spoiler](1)
<span class="math">A=4ab+2a^2\Longleftrightarrow b = \frac{A-2a^2}{4a}[/spoiler](2)
Solve (1)=(2) for <span class="math">a[/spoiler], then use (1) to solve for <span class="math">b[/spoiler].

>>6979473
"How to Prove It" is a good book to start with.

What if the world suddenly started spinning in the opposite direction? INB4 the sun setting in the east.

What would really happen is a super villain blew up the moon?

What's a hypothenuse?

Is there a store of all the world's scientific knowledge somewhere that could survive a nuclear war?

>>6979560
>>6979561
>>6979567
Thanks guys.
I did all that and arrived at
2a^3-Aa+4V=0
which I can't solve without the help of walpha :(

>>6979302
How can I appear smarter than I actually am?

>>6979676
engineering degree

>>6979669
That is.... actually a pretty good question. How many Gigabytes/Terabytes of information would that be? What exactly would you decide to save? Who would be in charge of this? Does art go in there to?

>>6979567
I've been wondering for some time now. What are the tags to put the TeX in?

Function notation.
Do you just let it keep getting bigger and bigger?

x:(R×R→R+)→R
(θ,θ↦E)↦E−Cθ^2/2

Too lazy to redo the the latex: https://archive.moe/sci/thread/6972791/#6978275

>>6979659
If the world suddenly starting spinning in the other direction: At first, everything on the planet would fall, fly, tumble because of the crazy acceleration. The sun would indeed set in the east instead of the west. Perhaps the flow of magma inside the earth would get all messed up. Earthquakes and would ensue. This all assuming the Earth's magnetic field is still intact or else we'll able be blasted to death by the solar wind.

If the moon is blown up:
We would have dark nights. Oh, and probably most of the human population would die. Lots of countries will be flooded. A lot of humans live near an ocean btw. Others might perish due to drought. All in all not a good idea.

If you have more like these kinds of question, xkcd's Randall Munroe has a book "What If?" in which he does these kinds of things. He also posted a ton of them online, go have a look.

>>6979694
<span class="math">E^2=m^2 c^4+p^2 h^2[/spoiler]

>>6979684
IIRC all of humanity's written works is around 10 petabytes.

You can now buy My Books at $250 for 6 TB.
that's around 1700 drives for $420,000 at consumer prices.
Not much for a government.
Of course there's safer ways to get up that high in data centers.

>>6979482
Are you me? Trig identities and functions are retarded

>>6979742
What about >muh cinema and >muh music

>>6979749
http://www.imdb.com/stats
320000 movies
4 GB for 1080p a piece
1.2 PB.
https://www.apple.com/pr/library/2013/02/06iTunes-Store-Sets-New-Record-with-25-Billion-Songs-Sold.html
26 million songs at 30 MB flacs
only 780 TB.

Keep in mind Google uses 10 Exabytes of data.
https://what-if.xkcd.com/63/

>>6979521
bumping this

If there is an infinite number of universes, would there be universes where the laws of physics are different? And, if that is true, could there be universes where physics makes it impossible for there to be multiple universes?

>>6979302
have you ever counted to ω?

>>6979521
Not OP but if I were designing a curriculum for pre-calculus I would probably make the first month or two of the course advanced algebra concepts like basic combinatorics and summations, followed by a larger unit all about trig functions and trig identities (possibly including complex exponent definitions of those functions), then finish the course with calc fundamentals like limits, sign charts, and block summations.

The whole course would be algebraically rigorous and most of the focus would be on the trigonometry. Trig is really important to calc but I don't think it's worth a whole-year course in any secondary school worth its weight.

>>6979521
>>6979826

Generally, in the USA, remember that College Remedial math to Calculus III are made for people who give zero fucks about the inner workings, proofs ect. These courses are focused on getting the math that Scientists + Engineers will need without being burdened by having to prove a thing. Its entirely mechanical. Precaclulus essentially does the following three things when focused on these who large groups: 1. Review or Overview of the Trigonometric functions. Where I came from, Trig was its own course, but others tell me that they just took precalc 2. Synthetic division for finding roots which will be needed later at least in Diff Eq, if not, sooner. 3. Partial fraction decomposition for having to integrate dem really tough functions.

Generally speaking, if you were aiming to learn mechanical Calculus 1~3, you could just work a book of College Alg, A book of trig, and start immediately in calculus, picking up any stuff skipped by precalculus along the way.
-
For Math Majors, I personally rarely used any precalc (honestly I can't remember if used any) in either my Group/Fields/Galios course work or my Analysis course work, outside of the trigonometric functions.

They way it was presented to me, after calc 3, Math Departments have to rebuild you from the ground up in order to get you quickly on par with the real mathematics thats going on. There is a huge emphasis on "you're not a fucking calculator, thats the computer's job". That being said, if you want to shoot for spivak, I'd recommend learning some Set Theory first just so you can see how proofs are done and shit.

Hope it helps

How hard is it to transition from engineering undergrad to applied math grad?

>>6980253
Depends, did you ever do proofs and/or Analysis? If you did you should be just fine. If you did not, you might need to study those things before you start. That or your advisor will advise you take undergraduate courses.

Alot of Applied Mathematicians grad students freak out finding out they will need to learn Real Analysis. Its a staple of the field. Sooner you take it, the sooner it will be over.

>>6979702
>>6979524
>>6979311

>the real math gets skipped over

>>6980253
Not hard. You need proofs, analysis, & algebra. After that you are ready to specialize in your area of interest.

>>6979482
Holy shit this is 1000x easier than rote memorization.
Thanks anon, I completely forgot about that shit in high school.

what is a good text to learn statistics?

Why do black students make lower scores than their white and asian counterparts? Do they genetically have a lower IQ?

>>6979302
Why are chimps and bonobos different species when their Fst is only 0.103
But Europeans and Saharan have an Fst of .15 and are the same species?
Chimps and Bonobos can interbreed.

>>6980370
> Chimps and Bonobos can interbreed.
then they aren't different species

>>6980388
http://en.wikipedia.org/wiki/Chimpanzee
Says here different species.

So, are the science and math AP tests I'm taking/have taken actually a valid measure of my skills? And please give some tips and pointers? I'm taking AP Biology, Physics 1, and Statistics this year. I've taken AP BC Calculus (got a 5 and 5sub).

>>6980395
source on them being able to produce viable offspring?

>>6980388
this is the bullshit high school definition

in reality the definition is fuzzy, even animals of quite clearly different species who are usually incapable of breeding can sometimes produce viable offspring, mules are usually sterile but occasionally you get one that isnt

>>6980405
But eventually, some offspring down the line of the mule won't be able to reproduce, showing the hybrid ' s unsustainability.

>>6980400
http://www.uptheriverendeavors.org/pdf/bonobo_Parish_and_de_Waal.pdf
De waal

Side note, wolves coyotes and dogs are considered different species but can all produce viable offspring and mean fst of 0.2790–0.3379
http://wwww.idahoforwildlife.com/files/Cronin_et_al_2014_wolf_snp_JOH_online_jhered_esu075_full.pdf

>>6980405
But shouldn't Fst provide a better 'litmus test?'

>>6980410
Maybe, or you might breed a fertile mule with a donkey or horse and end up with an endless line of viable mule-horses or mule-donkeys, it doesn't really matter point is "two different kinds of animals that cannot produce viable offspring" isn't a proper definition and is not at all rigorous.

>>6980350
>>6980350
>>6980350
>>6980350
>>6980350
will someone please answer this?

>>6980435
/pol/ will if you go ask them, go on

>>6980435
If you just ask that, pic related happens.

>>6980434
what would constitute a rigorous definition?
or is it all fuzzy?

How does one begin to study higher-level mathematics?

I'm a chemical engineering undergraduate who has a solid understanding of calculus, differential equations, statistics and most things relevant to the discipline. I've always had an interest in pure mathematics.

Just doing some basic research on google doesn't leave me with much. There are a ton of mathematical structures and subfields to study, and I'm not sure where to start. I would be doing this in my free time, unfortunately I can't take any courses in this vein for electives.

What do, and where should I start? Help me /sci/entists.

>>6980446
Start with the book "How to Prove it".

Move into basic mathematical logic and branch from there.

>>6980446
Your math department should offer a proofs course. That with analysis/algebra is the gateway to math.

>>6980446
master basic linear algebra then learn abstract algebra, analysis, topology, diff geo. Then learn about how all that shit plays together.

(i'm not an expert, this is my experience)

>>6980444
plz?
It's my understanding there are certain species of birds (seagulls?) where one can breed with the next closest geographically along longitude and literally go up and down the earth but if you jump a few links they can't interbreed.

Obviously crocodiles aren't pigeons. "Species" is a useful scientific definition, it just seems that at the nitty gritty it's a bit arbitrary. Which is fine. As George Box said "all models are wrong, some are useful." I just want to know.

>>698044
its all fuzzy in bio

a rigorous definition would go something like 'a helium atom is an atom containing exactly two protons', i dunno im a mathfag not a physicist and in math you get to define your own terms but i think that is the definition of a helium atom, point is if it has more or less than 2 protons it is clearly not a helium atom, there is nothing fuzzy at all there, anything in bio is more of a gray area

basically, if you go so far as to give a rigorous definition for a species, you are either making it far too lax to be of any use at all referring to a close subset of genus, or you are doing the opposite and dividing extremely similar and almost indistinguishable animals who can interbreed (but are from different continents or something) into different species

>>6980530
>its all fuzzy in bio
So, to return to the root question.

Why are chimps and bonobos different species when their Fst is only 0.103
Chimps and Bonobos can interbreed, producing viable offspring.
http://www.uptheriverendeavors.org/pdf/bonobo_Parish_and_de_Waal.pdf

But Europeans and Yoruba have an Fst of .15 and are the same species?
Europeans and Yoruba can obviously interbreed.
http://en.wikipedia.org/wiki/Fixation_index

>>6979318
Do you have adblock installed? Check the blocked items
Do you have javascript enabled?
What happened/changed around when it disappeared?

>>6980564
because thats the way biologists have defined it.

>>6979347
Linear algebra very basically deals with vectors and matrices. Remember systems of equations? It covers that and a bunch of less trivial stuff that follows. Can't speak about the latter, or how the two might relate

>>6980667
yep. we don't really know what a species is. there are over a dozen species concepts, but the easiest and most applicable to animal life is the biological species concept (the idea that a species is a population of interbreeding individuals).

we rely on "species" because of ease, and the reality is that a species is simply a snapshot in time on a continuum of genetic differentiation. if you think the chimp example is tricky, try the entire plant kingdom. shit hybridizes like no other, and the biological species concept completely falls apart. what a species is and is not is rather unimportant, but we like to give it meaning because of our limited understanding/perception of evolutionary history and geologic time.

>>6979318
>Where did the jsMath button go..
Don't know where it went but you can always ALT-click on some Latex to open the panel.

What kind of jobs coukd an associates degree in math get? Ive been womdering if the high risk of gpa is worth the reward of actually completing a math degree up to calculus 3 and linear algebra. And afterwards what majors are in the same field but would expand career opportunities and are more valuable?

>>6980781
>associates degree in math
honestly I didn't know that even existed.

I've learned up to ODEs in college around a decade ago, but forgot most stuff. Want to start fresh.

What's a good concise book on trigonometry that's rigorous and to the point? Most books are written for children, apparently, not for someone with a (forgotten) math background.

PERIODIC TABLE
blocks are the width they are cause thats the number of electrons in each shell, I get it.

Shells are seperate cause you can only fit a certain number of electrons into a configuration before moving up due to paulis inclusion principle.

What is the quantum number or distinction that means the 1p orbital is different from the 2p orbital?

(ie explain the height of the blocks in the periodic table)

>>6980833
http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html
has a detailed explanation

>>6979347
You see surfaces and curves ? it's their study and their equivalent in higher dimension vector space (the relation to linear algebra) called Manifolds. The study is based essentially on the overview of tangent spaces (tangent for curves, tangent planes for surfaces) and resulted fibrations (here is the source of "differential" because of the relation with infinitesimal open limits).

This is the source of it, but you can do better with general topological manifolds where the structures are all replaced by general topological space and where a manifolds is defined by "set of points so that for all points it is homeomorph to a unique smooth topological space (ex : R^n) "
then the study revolves around doing geometry with those weird but pretty spaces.

TL;DR : differential geometry is study of higher dimensional curves and is way more technical than classical linear algebra

>>6979659
>>6979712
if the earth stopped spinning it would be nearly the end of all ground life . Because of the half liquid mantle the earth's crust would slidedue to the acceleration and as they haven't the same speed it would be apocalyptic. Of course sea life would be a bit better but still it means huge tidal waves all over the world. It's like you're spinning with something and then stop suddenly, all fluids get messed up bad and for the earth, it's similar :we'd be fucked up. On human scale you would be propulsed quite badly due to earth's speed.

As for the magnetic fields, it's produced by the earth's seed so it depends on how you want to change the spinning, if you allow the seed/liquid core to still move during the change, as one of those body will change it's moving sense, the magnetic field will weaken for a short period then be normal again, otherwise if there is a full stop, as >>6979712 said, it means solar windstorm : no more ground life except extremophile


TL;DR : we're fucked up.

>>6979702
I'm doubtfull, is this unknown beauty or an abomination ?

>>6980239
elementary set proof are hard dude, there is nothing to prove except zorn Lemma and well ordered things, and those are fucking mindblowing for one without proof knowledge.

if you want to start with proof, just read some little things about it and then go full algebra with groups or highschool arithmetic : existence of divisor, infinity of prime number set. Those are easry to grasp, not ZFC mindfucker proofs.

Where can I study modeling a fluid wave oscillating in 3 dimensions inside a tank?

>>6980700
So given that the genetic distance between Chimps and Bonobos is greater than the genetic distance between Yoruba and British which would you say is a more arbitrary distinction?
Just trying to make sure we're being consistent.

I'm a math major that doesn't know any programming. I'm wanting to learn java, but I don't know what resources to learn from. Can anyone give recommendations? The books I found all assume familiarity with programming, I have no such familiarity.

>>6981081
Download Eclipse or Net Beans for java.
Type "Hello world java" into google.
Do that.
Then do a program that takes input and decides an output based on if statements.
Then do something with a for-loop.
Then do a sorting problem.
Then do a magic square thing to learn double arrays.
That should be enough to get you started.

>>6980982
> Just trying to make sure we're being consistent.
> biology
> consistent
lol

>>6981081
Java is shit, stay away from it.
As a mathematician you would probably be interested in functional programming.

Read the following:
- Structure and Interpretation of Computer Programs (there are also video lectures on youtube)
- Learn You a Haskell for Great Good
- Real World Haskell
- The Art of Assembly Language (not functional programming, but just so you know how computers really work on a low level)
- Types and Programming Languages

>>6981089
Thanks. Just installed Eclipse. Do you always have to do packages -> projects -> classes to write source code?

I was playing around with some if statements, then saw how if else statements can make the program more efficient than simple if statements, eg:

if(x<y){
System.out.println("X is less than Y");
}else if(x == y){
System.out.println("X is equal to Y");
}else if(x>y){
System.out.println("X is greater than Y");
}

I'll work through the rest of your suggestions, i may be able to pick this up pretty quickly (least I hope!).

Thanks again.

>>6981094
I'm very interested in mathematical logic. Thanks for your suggestions. I'll look into Haskell very soon.

>>6981096
>Thanks. Just installed Eclipse. Do you always have to do packages -> projects -> classes to write source code?
I believe so. It's been a while since I used eclipse.

>I was playing around with some if statements, then saw how if else statements can make the program more efficient than simple if statements, eg: (etc)

you're going to make it my friend. But make the last one an else not an else if

>>6981094
>As a mathematician you would probably be interested in functional programming.
this guy might be right matlab or python might be better. But java is a really good "my first language."

>>6981098
Don't forget about Lambda Calculus

>>6979498
its not divergent but wouldn't it be zero?

>>6979524

Given a family sets (X_j) with j in J, the cartesian product is the set of all functions f from J to the union of X_j such that for every j, f(j) is an element of X_j. This object does not depend on the structure of the sets, however in the case that each X_j is a vectorial space, then the cartesian product is again a vectorial space.

Given a collection of sets with some structure (for example, vectorial spaces) (X_j) with j in J, the direct sum is usually defined as an object X satisfying an universal property (its really anoying to write it down here, look for the coproduct article in wikipedia). Contrasting the cartesian product, this object does not have an absolute definition, this will depend on the structure of the X_j. For example, if the X_j are topological spaces, then the direct sum is just the disjoint union of X_j and if X_j are vectorial spaces, then the direct sum is a proper vectorial subspace of the cartesian product: you only take those functions such that f(j) = 0 for all but finitely many j. For example, in the context of vectorial spaces, if J is a finite set, then the Cartesian product and the Direct sum are exactly the same object. On the other hand, if R is the set of real numbers, and N is the set of natural numbers, then the cartesian product of R_n, with n in N is a vectorial space of uncountable dimension and the direct sum of R_n, with n in N is a vectorial space of countable dimention.

>>6981094
Why Haskell?

Why not python?

Have any of you niggers played Batman: Arkham City?
I was wondering if the "dive bomb" would work in real life. As in, Batman enters free fall, then deploy his wings, and that lifts him up in the air a big, enough to gain height and stay in the air more than he would with just straight gliding.

>>6981135
No it'd waste energy.

>>6981131
because autism/superiority complex

Hey /sci/...
W-what is 2×2?

what is 4 + 1 - 7 / 2
85% of people answered wrong the answer may sur prize u

>>6981124
okay, so then the direct product is what you'd expect right; it takes the cartesian product of the structures (allowing up to uncountable dimension) and preserves the structure like the direct sum.

>>6981131
python slow, python no monads, python no semantically complete. There are really deep reason to prefer Haskell over python, but for the commoner, it's the same thing except maybe for the speed for which you can clearly see a difference (python interpreted and virtual machine, haskell compiled). That's not for nothing that functional languages (with integrated assembly) such as Caml are used for microtrading rather than python.

Is this a correct proof?
Prove that if |H|=a, |K|=b are coprime then the intersection is trivial.
let <span class="math">g\in H\cap K[/spoiler] then g is in H and in K. so we get that <span class="math">g^{a}=1[/spoiler] and <span class="math">g^{b}=1[/spoiler] . g generates H and g generates K, then this imples that H=K a contradiction. ( im not sure about the g generats H and K part i dont think it true)

>>6981269

I'm waiting for the day when functional languages like Haskell and LISPs outshine the retarded programming languages like JAVA. But it's "Object oriented " dewd111!!

why is the triangle rule
|a| + |b| >= |a + b| ??

Obviously it's easy to see that it's true if the vectors are collinear, like on a real number line, but for non-collinear vectors it should be
|a| + |b| >= |a - b|
as pictured

If we're talking about the sides of a triangle, the length of the third side of the triangle in terms of the vectors of the other two sides is obviously
|a - b|

and so stating how the sum of lengths of two sides of a triangle is always greater than or equal to the third length , is obviously given by the inequality
|a| + |b| >= |a - b|

not |a| + |b| >= |a+b|

>>6981291

>>6981269
one company uses caml
and if that company were founded today they certainly wouldn't be usinc caml, they'd be using f#

face it, ml languages are an academic curiosity whose only real world use is proof software.

>>6981291

Vectors "a" and "b" are always collinear when you're talking about obtaining a magnitude.

>>6981276
Let K be the intersection of H and G. Then an element in K has an order that must divide the order of H and it must divide the order of G.
Since H and G are coprime, that number is 1, which implies that the intersection is the identity.

All you need for this proof is Lagrange's theorem.
Assuming this is a group theory question.

>>6981299
that doesn't make sense.
here for example we can clearly see 3 non-collinear vectors forming a triangle.
>>6981294

>>6981291
Proof of the triangle inequality in R^n:
| a + b |^2 = (a +b ).(a + b) = a.a + 2a.b + b.b =< |a|^2 + 2|a||b| + |b|^2 ( because of the Schwarz inequality) = (|a| + |b|)^2 (binomial theorem).

Now, just take square roots.

>>6981294
the absolute value lines are because its physically impossible to have a negative length

>>6981311


A and B in the picture are collinear vectors.

>>6981304
yes it is but is this the only way to prove it? where is my proof flawed i thinki its at the generatingpart

>>6981304
also check this out:
https://crazyproject.wordpress.com/2010/03/25/bounds-on-the-index-of-an-intersection-of-two-subgroups/

for this question dont 3 lemmas seem a bit unnecesarry? cant you at least for the upper inequality argue that
because there are n coset and m cosets for the respective groups, then we that the intersection is definitely smaller (or equal) to the product mn and so we have that fpr <span class="math">|G:H\cap K|[/spoiler] there will be less cosets.

>>6981317
they don't lie on the same straight line so no.

>>6981314
thank you

Why did Grimm's Law take place?

>>6981319
Your way assumes g is a generator for H or G which isn't necessarily true.

>>6981334
When you say something in mathematics like this, when you use the phrase "can't we just", the first thing you should ask yourself after is " why?".

>>6981419
what i should ask why cant we just?

>>6981446
I mean it seems so artificial he s introducing this notion of maps between sets whereas the previous proofs were a bit more self contained, thats the problem i have with this!

>>6981297

Why would you lie like that on the internet?

https://ocaml.org/learn/companies.html

>>6981081
this thread may be a bit interesting https://archive.moe/sci/thread/6977703/

>>6981285
>I can blow glass with a hammer.
This is what you sound like.

Can you explain how the big bang happened?

>>6981612
Ronald Regan was fighting the evil Jews while reading Aryan Rand when Master Jew Sheklestein tricked him into thinking evolution is real, so god had to restart the universe with a big bang to fix it.

>>6981636
>Aryan Rand
/pol/ please stay.

>>6981101
I disagree that java is a good language for a math major just starting out. The syntax is very verbose and seemingly pointless/handwavey when you start out until you understand the purposes of classes, polymorphism, public and private flags, etc. It'll also teach you bad habits. Java has its time and place (great for large teams wanting modularity) but for starting out I'd recommend python then lisp or lisp then python. If you enjoy it, move onto c and assembly.

tl;dr: don't learn java first. also, read SICP.

Hey guys, I'm really bad at math (i don't even understand algebra) and I was reading about calculus the other day. I want to see if I got the concept behind it.

So basically, they take a number that when divided equals infinity, and then expoit the fact they can get closer and closer to the answer but never reach it to mke enough space for them calculate the rate anything changes over time? Sorry if my question doesn't make sense, I don't know how to explain it mathematically.

>>6981696
Yes, that's the intuitive definition of a limit.

If you wish to study calculus though, you should really have a solid foundation in algebra.

I've learned up to ODEs in college around a decade ago, but forgot most stuff. Want to start fresh.

What's a good concise book on trigonometry that's rigorous and to the point? Most books are written for children, apparently, not for someone with a (forgotten) math background.

>>6981698

Thanks. I am learning math on khan academy but I left school at the age of 18 without knowing anything past multiplication. I got impatient and read ahead to calculus and wanted to know if I got it right.

At what altitude is it possible to see the curvature of the Earth?

>>6981719

Any, provided your view is unobstructed. When you look at the horizon, you're seeing the curvature of the Earth.

>>6981719

Theoretically ground level should be enough if you're in an empty field, yeah?

>>6981719
graph shows apparent angle of the horizon from vertical, i.e. perpendicular at ground level

Mount Everest is 9km

>>6979302
I've got some stats exams coming up and I've been doing old papers and that sort of stuff.

What the fuck does "allow limits" mean in the context of a Confidence Interval? The exam board treat the limits as being wrong (allow limits if not already penalised) but I have no idea what they even are.

Like seriously, where does the term "limit" ever come up in confidence intervals?

>>6981891
*allow limits if already penalised (I shouldn't have said "not")

>>6979498
I'm of the impression like >>6981113 that the value is 0.
I don't remember the specific criterion or the result of a proposition but look up 'Alternating series test' basically if you have a sum like \sum_1^{\inf} a_n where the a_n switch signs for each adjacent term, or a_i * a_{i+1} < 0 for all i, then the series converges and, don't quote me, the limit is 0

>>6980435
>>6979498
Log(2)

>>6979849
No

>>6979302
Could someone break a dam if he flew over the barrier lake with a helicopter, lowered in a 10 meter (or however many are needed) long hose so that the tip just entered the lake and filled it with water causing the water pressure to rise dramatically?

>>6984537
Dams are designed with a huge margin for error, so that would have to be one fuckhuge helicopter to carry all that water.

what kind of function would give me y=n for every integer n? I.e. how to get y=1, y=2, y=3 and so on from a single function

Why is methione apolar while cysteine is considered polar ?

>>6984572
Well if you had a very thin hose you wouldn't need that much water right?
Since only height and not the diameter matters.

Well, on /g/ faggots say math's just self masturbation. True or false?

>>6984573

...you mean the function f(x) = x?

if you want it to ONLY give you integers, you would need to do something like f(x) = floor(x) or something. Look up the step function.

Do I have to rotate solutions to determine the correct answer after rotating a polynomial to eliminate an x*y components?

>>6979302
I just want clarification on something.

Light is just electromagnetism, right?
And it's propagated by the photon?
Does this mean every part of the EM spectrum is delivered by photons- radio, microwaves, etc.?

If so, how can electromagnetism be both a photon, a form of energy, AND a fundamental force?

>>6984792
technically light is electromagnetic radiation and not electromagnetism itself, though they are very related.
Yes
Yes, and all at the speed of light

A photon is just a particle, it acts as the force carrier for the electromagnetic force. Electromagnetism isn't a form of energy, it's a force. That force can do work, therefore there is energy associated with it.

>>6981285
Why do people hate Java?

>>6981719
>At what altitude is it possible to see the curvature of the Earth?
I've noticed it while bicycling in eastern North Carolina.
I was on a 3.5-4 mile stretch of flat, straight road, ans I saw that it looked like I was going up a small, gradual hill, because I couldn't quite see the base of the trees straight ahead (miles away).
The base of the trees were hidden by the "hill" ahead of me.
Then I noticed the ditch full of water along side the road stayed at the same level the entire length of the straight section of road.

Say I have the following equation:

h''(t) + PI * h'(t) + 100 * h(t) = 10 + f(t) / PI

with f(t) = PI for t between 0,1 and f(t) = 0 for other values of t.

Why do I need to use green's function on the f(t)? Why can't I just replace f(t) by PI when trying to find a solution in the 0,1 range?

>>6984584
>Well if you had a very thin hose you wouldn't need that much water right?
>Since only height and not the diameter matters.
Dude, what?
If you dangle a hose into a lake, and the hose is filled with water, do you think it will cause an increase in pressure of the water in the lake because it's now "deeper"?
Are you smoking the weed Anon?
If the upper end of the hose is plugged, no water will flow out, and the lake is completely unaffected.

If the upper end of the hose is open, the water will flow out, raising the level of the lake by a tiny, immeasurably small fraction of a millimeter.

In NO case is the water pressure against the dam increased any more than if you added this water to the lake by more conventional means.

>>6984851
Why not?
Doesnt this apply https://en.wikipedia.org/wiki/Vertical_pressure_variation#Hydrostatic_paradox
http://physics.kenyon.edu/EarlyApparatus/Fluids/Hydrostatic_Paradox/Hydrostatic_Paradox.html

>>6984851
>>6984863
I'm asking because I learned that shit once in school. It's the experiment described in the last paragraph here: http://www.cosmovisions.com/Williams020501.htm

Is the scenario I'm describing not suitable because the lake is closed off like a barrel or chamber would be?

>>6984875
*is not closed off

>>6984863
>Why not?
I thought I was perfectly clear:
If the upper end of the hose is plugged, no water will flow out and the lake is unaffected.
If the upper end isn't plugged, the water will flow out, raising the lake by an inconsequential amount.

Sure, sure, as the water flows out, a tiny volume of the lake is subject to a large pressure, but this disperses in all directions, and doesn't affect the dam because no more than one tiny part can be affected by the pressure.
The total force directed against the dam can't be any larger than the total weight of the water in your "thin" hose.

The "Hydrostatic Paradox" isn't a paradox at all, and doesn't have any impact on the issue.
I can put a piece of plain typing paper in my driveway, and drive my car over it. Is the car "supported" by the paper?

And do tell Anon, ARE you smoking "the reefer"?

>>6984889
Actually, if the upper end is not plugged, the water will NOT flow out. The water pressure below in the lake is higher than high above at the beginning of the hose. I tested it with a glass of water and a straw. The water in the straw stays at level I filled it in.

>>6984875
>Is the scenario I'm describing not suitable because the lake is closed off like a barrel or chamber would be?
I don't know.
Forget the lake, think about a sealed tank. If you get a long enough hose, full of water and open at the top attached to the tank, it should raise the pressure in the tank, possibly enough to damage the tank.
But then what?
If the tank is made of metal, it will stretch a little before anything bursts.
If the tank is large enough, and the hose thin enough, the tank may stretch enough to receive enough of the the water from the hose to lower the water level and reduce the pressure.
In any event, bursting the tank seems is "useful work" and would require your hose water to fall.
The thinner the hose, the further the water level would have to drop.

And seriously, are you smoking the dank?

>>6984909
>it should raise the pressure in the tank
Not unless the pressure in the tank is less than atmospheric.

>>6984906
>Actually, if the upper end is not plugged, the water will NOT flow out.
That's not correct.
https://en.wikipedia.org/wiki/Pressure#Liquid_pressure
"water seeks its own level"

By the way, I'm not trying to be an ass about the reefer thing, but your question reminds me of the shit stoners talk about while smoking weed.

>>6984931
>Not unless the pressure in the tank is less than atmospheric.
What?
I'm assuming the tank starts out full of water, and let's say the water at the top of the tank is at atmospheric pressure (about 14 psi).
If the attached hose is even a foot tall, the extra depth adds to the pressure in the tank because the hose is open at the top, and subject to the same 14psi as anything exposed to the atmosphere, PLUS the weight of the water.
For a foot long hose, the pressure in the tank will rise to about 14.5 psi (at the top of the tank).

is a one dimension vector a scalar ?
is a scalar a one dimension vector ?

>>6984934
Oh, yeah sorry I just saw it. There was a water drop in the straw and it looked like the water level but it actually flows into the glass of water. So the only possibility to keep the water level in the hose high is to plug it up.
So why shouldn't the plugged up hose, which holds its water level, increase the water pressure in the lake?

>>6984953
>So why shouldn't the plugged up hose, which holds its water level, increase the water pressure in the lake?
The same reason a wound up clock spring dropped in the lake wouldn't increase water pressure.
If water can't flow, it can't affect the water pressure in the lake.

>>6979302
The row vectors of a matrix at least /appear/ to be somewhat "disconnected" from its column vectors. Yet if I were to exclusively use elementary row transformations (is 'transformations' the correct term? English isn't my first language) to get the row rank of a matrix and then only elementary column transformations to get the column rank of a matrix, I'd get the exact same result.
I'm confused by the fact that for every matrix, the row rank of the matrix is always equal to the column rank of the matrix.
Does anyone have an intuitive (sorry, I know this word probably irritates you guys) explanation to this?

>>6984967
Ok. I though about it now. If I put my thumb on a water filled straw the water doesn't flow out because the air pressure from below pushes up but since there's no or barely no air pressure from above (vacuum).
If I lower this straw into the water then the water must exercise an upward pressure against the water in the straw so it doesn't get pulled down by gravity, right? Because the water in the straw now touches the water in the glass. Does this count as flowing? What's exactly the force keeping the water in the straw?

>>6984950
A one dimensional matrix is a one dimensional vector is a scalar. They are the same with different names.

>>6984950
A one-dimensional vector space (whose elements are "one-dimensional vectors") isn't the same thing as the underlying field (whose elements are "scalars"), because they have different operations. Suppose F is a field and V is a one-dimensional vector space over F. Then F has addition and multiplication operations <span class="math">+: F \times F \to F[/spoiler] and <span class="math">\cdot: F \times F \to F[/spoiler], while V has addition and *scalar* multiplication operations <span class="math">+: V \times V \to V[/spoiler] and <span class="math">\cdot: F \times V \to V[/spoiler].

The multiplication operation on F makes F into a one-dimensional F-vector space. However, while F and V are isomorphic as F-vector spaces, they aren't *naturally* isomorphic, since giving an isomorphism between them requires making an arbitrary choice of basis of V (i.e., choosing a nonzero element of V). This specifies an isomorphism: we send the multiplicative identity of F to the chosen element, and that determines the isomorphism.

Furthermore, while F is a field, V is not, because V doesn't have a multiplication operation. After choosing an isomorphism of F-vector spaces between F and V, we can transfer the field structure across this isomorphism and make V into a field; however, the resulting multiplication operation depends on the choice of isomorphism, so V isn't naturally a field.

>>6985086
>What's exactly the force keeping the water in the straw?
If it were to flow out, that would have to somehow create a lower pressure at the top of the straw.
Since nature abhors a vacuum", it would take more energy to create this vacuum that the potential kinetic energy of the water in the straw.

Self teaching here. Can someone please explain U-Substitution for integration. An example would be nice.

>>6985188
Do you even Khan Academy?

>>6985192

>do you even know u-sub

Can someone explain to me how to calculate the moment of inertia of a solid ?
First year of engineering here, I heard that at the exam we will have to do it ourselves if we have to use a moment of inertia, so I'm scared.

>>6985198
Of course, but why take the trouble to type out an explanation, and set up something decent looking?

I know Khan Academy has a video on it, and it's a solid resource. Someone will get far more from watching a video on there than they will from reading a post on 4chan.

>>6985188
<div class="math"> \int x^3 \, \mathrm{d} x </div>
<div class="math"> \int x^2 x \, d x </div>
<span class="math"> u = x^2 [/spoiler]
<span class="math"> du = 2x dx [/spoiler]
<span class="math"> du/2 = x dx [/spoiler]
<div class="math"> \int u\, du/2 </div>
<div class="math"> \frac{1}{2} \int u \, d u </div>
<div class="math"> \frac{1}{2} \frac{u^2}{2} + C </div>
<div class="math"> \frac{u^2}{4} + C </div>
<div class="math"> \frac{(x^2)^2}{4} + C </div>
<div class="math"> \frac{x^4}{4} + C </div>

>>6985220
Good example, but there's no explanation.

You also left out changing the upper and lower limits (which don't apply to this example), which is one of the benefits of u-sub.

>>6985216
Usually you use simple shapes, the parallel and perpendicular axis theorems and add them
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
http://en.wikipedia.org/wiki/Perpendicular_axis_theorem
http://en.wikipedia.org/wiki/Parallel_axis_theorem
But you can always calculate it.

http://en.wikipedia.org/wiki/Moment_of_inertia#Calculating_moment_of_inertia_about_an_axis

Just started learning about spacetime topology. Should I throw my notions of freewill out the window? It's not that it matters either way, which is why I'm posting it here instead of a new thread. I guess I'd just like to know if my life is a series of points whose causal relationships are predictable.

>>6979343
well i'm fucked

So this is the idiot thread? Alright, I'll ask my question then. I'm completing high school slightly late, so using ILC.

Which of these courses would you take? 10 credits left, so choose only 10. To best prepare for ANYTHING University throws at you.

http://www.ilc.org/school/courses/cred_courses_twelve.php

will everything sam/hitch related, even if its about philosophy or neuroscience, get immideately deleted?