/sqt/ - Stupid Question Thread

Retard question.
How the fuck do I figure out which way the vector is supposed to be pointing? It's possible to draw different triangles with its components, which then gives different angles.

Thanks faggots. Would suck you off. N-n-no homo.

Does it have a known solution? Looks super non-linear for me to make some sense of. My guess was some type of fancy substitution

is Veeky Forums the least off-topic board for questions on recreational drugs

Your horizontal component is +4 and your vertical component is -3. That means your vector should be pointing at the spot 4 units to the right and 3 units down, which is what your diagram is showing.

>It's possible to draw different triangles with its components
It's not. When you have two components you have two legs of a right triangle; you can use Pythagoras to find the last side, so the triangle is unique.

Does the substitution [math]y_1 = 3y^2+2[/math] work?

Okay, I get it now.
Thanks man.

I believe there is and many great scientists have too. It depends on your personal interpretation of what God is and what the universe and its properties imply.

pic related

I understand how it follows from ZFC that a set can't contain itself, however, I fail to find a reason to show that sets can't cyclically refer to one another, which seems paradoxical to me.
You see,
[eqn]
x_1 = \{ x_2\}
x_2 = \{x_0\}
x_0 = \{x_1\}
[/eqn]
assuming none of the three are equal, they seemingly satisfy all axioms, or do they?

oh nvm I get it. the unity of all 3 (which must exist) clearly is inconsistent with regularity.

Whats the difference between software engineering and computer science?

How do you learn/study math?
Doing computer engineering and i struggle with math. Failed my "midterm" exam.
My brain just wont remember anything about math, but does fine with any other subject.
Any methods or techniques Veeky Forums got that could help me?

Should I research medical imaging or cryptography?
Which seems the more interesting for you?

Repetition is vital.
Im talking worksheets of 50 problems minimum, in varying difficulty of course.

Cryptography. I just borrowed Applied Cryptography from my University's library, and I'm loving it

How does one integrate pic related? Getting back into maths

The integral of that is inverse tangent. Just something you remember.

It's arctan(x). It's best to memorize this, but here's the proof (d/dx)(arctan(x))=1/(1+x^2):

y=arctan(x)
tan(y)=x
(y')*1/cos^2(y)=1
y'=cos^2(y)
y'=cos^2(arctan(x))
So now we have a triangle with angle arctan(x), adjacent side of 1, and opposite side of x. So we want the hypothenuse, which is sqrt(1+x^2). So cos^2(arctan(x))=1/(1+x^2) as desired.

Let [math]\displaystyle x = \tan \theta[/math], then [math]\displaystyle \frac{dx}{d\theta } = \sec^2 \theta[/math]
[eqn]
\begin{aligned}
\int \frac{dx}{1 + x^2} &= \int \frac{\sec^2 \theta \; d\theta}{1 + \tan^2 \theta} \nonumber \\
&= \int \frac{\sec^2 \theta \; d\theta}{\sec^2 \theta} \nonumber \\
&= \int d\theta \nonumber \\
&= \theta + C \nonumber \\
&= \arctan{x} + C
\end{aligned}
[/eqn]

who would win: 100 8 year olds with wooden spears vs 3 Bears?

Bears, but not all the children would die

The 'analysis' that CPAs like myself actually do is pretty simple, and I won't be surprised if some of that can be automated anyway.

You really don't want to be a CPA. It's just as much a turnoff to women as STEM, but without the high salary or transferable math and technical skills.

What type of bears? Kodiaks?

How feasible would 1984's techniques of torture and brain washing be for -- say -- prisoner rehabilitation?

How feasible would they actually be in a world as described in the book, and would they actually be worth the effort in order to eradicate any form of martyrdom and unorthodox thought?

>no

yes 3 medium sized

Is there any way I could experiment with genetic engineering without a big expensive lab?

How much progress can we achieve if we allowed unethical experiments in all fields of science?

Is this true or just a meme?

What about other business majors like logistics and finance?

Do you reckon that Field's medalist had all A's in their studies?

Do you ask this because you didn't have all A's but want to be a Field's medalist?

yes

but actually I'm just interested in "natural talent". like if a person got gold in the IMO then he is more likley to be a great mathematician.
Is it actually true? I don't believe in talent that's why I am just looking for other's opinions on whether mathematical "talent" exists. I am a strong believer of hard work

There's a nice discussion of that and more in this thread:

Knowing about the lives of accomplished mathematicians throughout history will also be helpful:

www-history.mcs.st-and.ac.uk/BiogIndex.html

I strongly recommend Weierstrass' biography. The dude had a pretty tough life. Another one is Cauchy, who doesn't seem to be of the "I can do all kinds of complex maths in my head and remember fucking everything" kind, it's just that he had really good mentors when he was young (Laplace and Legendre).

"If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries." - Gauss

"... through systematic, palpable experimentation.
[asked how he came upon his theorems]" - Gauss

"If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent" - Newton

"I keep the subject constantly before me, and wait 'till the first dawnings open slowly, by little and little, into a full and clear light. (Reply upon being asked how he made his discoveries)" - Newton

"I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." - Newton

Interpret all of this as you may.

Didn't expect such a detailed answer.
Thank you for the suggestion!

How much anecdotal evidence is required for it to be no longer anecdotal?

Will there ever be a eugenics paper not deemed racist?

Need help solving this meanie.

not all of them
en.wikipedia.org/wiki/Stephen_Smale

Initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself A's. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. However, with some luck, Smale was accepted as a graduate student at the University of Michigan's mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a graduate student. It was only when the department chair, Hildebrandt, threatened to kick Smale out that he began to work hard.[5] Smale finally earned his Ph.D. in 1957, under Raoul Bott.

Smale began his career as an instructor at the college at the University of Chicago. In 1958, he astounded the mathematical world with a proof of a sphere eversion. He then cemented his reputation with a proof of the Poincaré conjecture for all dimensions greater than or equal to 5, published in 1961; in 1962 he generalized the ideas in a 107-page paper that established the h-cobordism theorem.

This is literally high school physics.

I'd like to characterize maps [math] (a,b,c) \mapsto M(x,y)z [/math], that are linear in z, with
[math] M(x,y)x=y [/math]

More concretely:
Let a,b be vectors in a vector space like R^n.
I'd like to characterize matrices, with arbitrary dependency on a and b, so that
[math] Ma=b [/math]

----

Background/Example:
I came across this situation with the angular velocity tensor
en.wikipedia.org/wiki/Angular_velocity#Angular_velocity_tensor
There you have a curve r (a map from [math] \mathbb R [/math] to [math] \mathbb R^3 [/math]) and if its such that it rotates around the origin, then
[math] \frac{d}{dt} r = \omega \times r [/math]
where the vector [math] \omega [/math] is a function of [math] r [/math] and [math] \frac{d}{dt} r [/math] and the map [math] b \mapsto \omega \times b [/math] is linear.

What I go so far:
Why this works here, algebraically speaking, can be traced back to the vector triple product
en.wikipedia.org/wiki/Triple_product#Vector_triple_product
You have
[math] a\times(b\times c) = (a\cdot c)\,b - (a\cdot b)\,c [/math]
so
[math] a\times(a\times b) = (a\cdot b)\,a - (a\cdot a)\,b [/math]
so
[math] M(a,b)\,a = b [/math]
with
[math] M(a,b) = \frac {1 } { ||a|| } \left[ ( \frac{a} {||a||} \times b) \times + ( \frac {a} {||a||} \cdot b)\, 1_3 \right] [/math]

This map [math] (a,b) \mapsto M(a,b) [/math] actually is linear in b and "|a|^{-1}-linear" in a.

Can all matrices with all those properties be written like that?
Can all matrices with [math] Ma=b [/math] be composed with a cross product and a unity matrix?

I just want money so I wanna compare which majors out of mechanical engineering, aerospace engineering, computer science, computer engineering, and electrical engineering are better in terms of pay.

Which ones are better in terms of finding employment and which ones lead to higher paying salaries?
Is it impossible to find work as an EE or an AE? Are CS and CE the best in terms of employment and high paying salaries?

(a,b,c) ↦ M(a,b) c, linear in c

Study any engineering field while knowing learn C/C++/Java or even Python and do an internship of 1 month or a 20 hours job each year or each second year. Then you will always find a job, independent of why you studied.
If you study computer science and do code monkey stuff, you'll also always find a job and it'll be enough to live off.
To actually get to a high pay position, you'd be a person liking to work towards a managing job, which means eventually getting off the duty work you do at the start. The can work at a car company with aerospace engineering (think engines) just as with a computer science job at a tech company, or electrical engineering at a semiconductor firm. I can't give you the details which of those works better, and I doubt anybody can because times change.
In any case, going into a degree because of money is fucking retarded imho

>In any case, going into a degree because of money is fucking retarded imho

I agree but when you're poor money is all that matters.

AE/CS are my preferred majors but I wasn't confident I could find work in AE so I was leaning towards CS. It never occurred to me you could work in car companies with an AE degree which in hindsight should be quite obvious because of engines.

Anyway, thanks for the reply, very informative.

is protein folding a field of study i can pursue? how do i go in that direction?

biophysics maybe?

I did my PhD among aerospace engineers and then they all go to Bosch or Daimler (south of Germany, duh) and by now I did "freelance programming" a bunch of times and it appears to me you can't run out of jobs with some basic programming knowledge. That's where my perspective is coming from.

In fact my cross product problem is related to a freelancing job on something like GPS navigation (I always use those work-from-home jobs to write a sort of encyclopedic notebook for when I have to come back to it).

So reporting back on this, I'm somewhat surprised by this finding:

We have
[math] b = M(a,b)\,a [/math]
with
[math] M(a,b) = \frac{1}{||a||}\left[(\frac{a}{||a||}\times b)\times + (\frac{a}{||a||}\cdot b)\, 1_3\right] [/math]
and here, basically, [math] M = W(a,b) + h(a,b)\, 1_3 [/math] and what this does it factoring b into a part [math] h(a,b)\,a [/math] that points into direction a but has length |b|, and some other term [math] W(a,b)\,a [/math].

But this means that given ANY function
[math] f: {\mathbb R}^n \to {\mathbb R}^n [/math]
you can always "factor out" the argument by writing

[math] f(a) = M(a,f(a))\,a [/math]

In one dimension (in a ring), this can only be done via
[math] M(a,f(a)) := \frac{f(a)}{a} [/math]
and this decomposition matrix M above is one generalization of that, one that keeps the linearity.

Well anyway, back to the question if all such maps have to look like that. Well in any case I reminded myself that only in n=3 can we represent rotation generators (skew-symmetric linear maps, for which dim=n(n-1)/2) with a (rotation) vector and the cross product, so I'll fix n=3.

So am I never going to be successful because I haven't found a research lab and I'm going into my senior year of undergrad?

I have a summer job in the government in my field that will hire me back for this summer.

Eugenics is the scientific choosing of a type of person over another. Racism is the preference of a type of person over another. No

Did you try 4?

Depends. Are the eight year olds trained on the spear, or did they just acquire them now at the start of the fight with no prior training?

what's a good book/online course to learn math needed for digital signal processing? i need to brush up complex algebra. stuff from cal 2 probably. thx

Since nobody is answering my thread, maybe it's stupid.
So, I'm trying to understand a 4D Hyper cube, but no matter how hard I tried, couldn't figure it out.
I figured mapping it out might make it easier, but all that did was make me hit a brick wall once I decided to try mapping up and down (For reference, scribbles say what's on each side, scribbles inside the cube meant to say what's above and below.)
I mapped it out like a square, but I can't help but feel like that wasn't the way to go about it.
I know this'll probably be ignored, but is there any body who could tell me where I got it wrong, or maybe could show a diagram similar to this one, since the only one I could find was of a 5th dimensional one, and I don't think I wanna go that far yet.

Play around with the 4D Rubik's Cube.

superliminal.com/cube/cube.htm

Why does it look like there's only 7 "cubes", when wikipedia says there should be 8?
I'm still confused.
But also having fun with a weird shape.

What do you try to accomplish in this image?

In 1D, a "cube" is a line with 2^1=2 points and at each there is 1 edge going out.

In 2D, a "cube" is a square with 2^2=4 points and at each there are 2 edges going out
You can think of the edges as orthogonal lines in Euclidean space.

In 3D, a cube is a line with 2*^3=8 points and at each there are 3 edges going out.
You can think of the edges as orthogonal lines in Euclidean space. Imagine a dice.

In 4D, a cube is a line with 2^4=16 points and at each there are 4 edges going out.
You can think of the edges as orthogonal lines in Euclidean space. Pic related, except the diagonal lines are really going away orthogonaly, which we can't draw as a 3D picture anymore.

A map of a hypercube.
Basically, the idea is, let's say your in black.
You go right one, you're now in blue.
Go right again, you're in grey, what would be your opposite side of the hyper cube.
Go right again, you're now in green.
But go right once more, and you're now in black again.
The idea was to have a 3d map of what travelling from cube to cube in a hypercube would be like, because I thought it would help simplify things.
I think I might know what I did wrong, as this image helped, but it would mean redoing it a lot to get it right.

The corners of the cube are the 8 tuples with 0's and 1's. For example (0,0,0) or (1,0,1).
If you fix one component to 0 and/or 1, then moving with the others each in the interval [0,1] moves you around on the surface.
For example fix the second component to 1, then (0.3, 1, 0.9) is some point on one of the surfaces.
If you fix another of the components, then you move along an edge.
For example fix the second component to 1 and the third to 0, then (0.7, 1, 0) is some point on one of the edges.

Same for the hypercube.
The corners of the cube are the 16 tuples with 0's and 1's. For example (0,0,0,0) or (0,1,0,1).
If you fix one component to 0 and/or 1, then moving with the others each in the interval [0,1] moves you around on the surface.

What more do you need?
You can use the picture and () and label the edges and surfaces if it helps you?

Nah, Nah, I think I'm (sorta) figuring it out.
This has just been annoying me for a while, in more ways than one.

Trying to draw 2D diagrams of 4D objects is the road to madness. Much easier to try to deal with it algebraically.

A 3D cube is contains 2^3=8 vertices. You can use the Cartesian product of {0,1}^3 = {(0,0,0),(0,0,1),...,{1,1,1)}.

The cube has six faces, each containing the four vertices where one of the three coordinates has a common value. E.g. the vertices {(0,0,0},(0,0,1),(0,1,0),(0,1,1)} where the first coordinate is zero form one face. Each face has an opposite face where the "common" coordinate is flipped.

The cube has 12 edges, each containing the two vertices where two of the three coordinates have a common value. E.g. {0,0,0} and {0,0,1} form an edge. Each axis has four edges aligned with it, connecting the two opposing faces for that axis.

Now you just need to generalise this to four dimensions (a tesseract). This contains 2^4=16 vertices, C(1,4)*2^3=4*8=32 edges, C(2,4)*2^2 6*4=24 faces, and C(3,4)*2^1=4*2=8 cells.

It should be clear that it can be generalised to N dimensions, with C(N-n,N)*2^n of each n-dimensional group. The way in which n-dimensional groups relate to the n+1 and n-1 dimensional groups (e.g. faces connected by edges to form cells, etc) is reasonably intuitive (two combinations of axes which differ by a single element) but this is getting close to the post limit.

Jokes on you, I think I (Maybe) figured it out.

Robots are only good at highly specific tasks. Yes, they will take some jobs, but not everything. At the very least, robot maintenance will be open.

Because you're looking at a 3d shadow and one hyperface happens to be obscured (think of a 2d shadow of a regular cube for analogy)

In case the diagram isn't clear:
Blue cube = "Center", I.E. the cube that would be surrounded by 6 cubes in an "unfolded" hypercube.
Dots/ Scribbles of color indicate which cube is on that side.
On the interior, it indicates which cubes are above and below it.
As far as I can tell, it's not wrong.

Veeky Forums, I just had my mind blown by pic related. My trig class never bothered to define sec, csc and cot geometrically; it was all strictly symbolic (and always felt a little arbitrary). I made it to calc 3 without being aware that a geometrical definition existed.

Did anyone else get let down by their trig class in this way? Or have similar after-the-fact revelations about something that really should have been mentioned in a class, but wasn't?

My math teacher in HS actually defined secant this way before proving its symbolic equivalent

thats pretty satisfying

i still dont understand this trigonometry class thing, is it a meme or a real thing? i.e. separate to maths class

Doesn't this image combined with the Pythagorean Theorem imply that [math]\sqrt{\cot^2(x)+1} = \csc(x)[/math] and [math]\sqrt{1+\tan^2(x)} = \sec(x)?[/math] Or am I reading the image wrong?

take sin^2 + cos^2 = 1

now try dividing both sides of this equation by
i) sin^2
ii)cos^2

i never bothered learning the cosec and sec identities

Wait, I found some more. Assuming I'm reading the image correctly, using the Pythagorean Theorem and the fact that [math]x^2-y^2 = (x-y)(x+y),[/math] I can also find the following: [math](\csc(x)-\cot(x))(\csc(x)+\cot(x)) = 1,[/math] [math](\sec(x)-1)(\sec(x)+1)=\tan(x).[/math]

I was never taught these. All I was taught was sin, cos and tan. It was only until university that I came across cot.

how can one find all homomorphisms between two groups ?

Not asking for an answers, but a laymans explanation of pic related, just maybe the steps I need to follow in order to solve this.

Do you know about the Binomial Theorem? It states that

[math](ax+by)^n = \sum_{k=0}^{n} {n \choose k}(ax)^{n}(by)^{n-k}.[/math]

So what you do is you plug in [math](a,b,n) = (3,-2,13).[/math] Now you can find the coefficient of [math]x^6y^7[/math] by plugging in [math]k=7[/math] in the expression above, if that makes sense.

Wait, I fucked up the formula. It's supposed to be

[math](ax+by)^n=\sum_{k=0}^{n}{n \choose k}(ax)^{n-k}(by)^{k}.[/math]

The value of [math]k[/math] is still correct, though.

Yeah, that's more than enough, sorry I asked.

Just figure out the fundamental properties of the two groups you're working with. When you've done that, figure out if there's something you can do with these fundamental properties, like generators and the like. Also think about the orders of each element in the groups and the order of the group in general. Your question is rather general, so my answer is also rather general.

served well i guess, thank

Anyone ever done a physics co-op program? What was it like?

considering
[eqn]
a + ax + ax^2 + ... = \frac{a}{1-x}
[/eqn]
this means we can write
[eqn]
\frac{1}{1+x^2} = 1 - x^2 + x^4 - \cdots
[/eqn]
and, integrating, we have
[eqn]
\int \frac{1}{1+x^2} \text{d}x = x - \frac{x^3}{3} + \frac{x^5}{5} - \cdots
[/eqn]
i.e.
[eqn]
\int \frac{1}{1+x^2} \text{d}x = \sum_{i=1}^{\infty} (-1)^{i-1}\frac{x^{2i-1}}{2i - 1}
[/eqn]
which is exactly the taylor series for [math]\arctan(x)[/math]
lol @ all of the calc II kiddies and their trig subs

two questions because I'm extra stupid today

>would physics still work the same way if d=x+y+z-t instead of d^2=x^2+y^2+z^2-t^2
>how do I write equations here

No idea about your first question because I'm a mathsfag, but to your second question use [ math ] [equation here using TeX or LaTeX [ / math ], without the spaces in the "math" tags.

>would physics still work the same way if d=x+y+z-t instead of d^2=x^2+y^2+z^2-t^2
not even physics, but that's the taxicab metric. you can look up the impact of the taxicab metric on physics yourself i guess

I've asked at least 5 biology questions across different threads and never been answered and now I've forgotten my old questions so I'll never know that shit

1. When is it necessary to save the 5' information of mRNA during the synthesis of cDNA for cDNA libraries? There a bunch of methods on how to do this that take much longer than hairpin-primed synthesis/Gubler and Hoffman procedure, but they ensure that no information is lost and you end up with sticky ends ready for cloning. Why doesn't everyone do this? Is there any situation in which you can afford to just lose a chunk of the 5'-most sequence?

2. At uni we only ever learned about the use of lambda phage in molecular cloning? What are the benefits of using M13 phage libraries over lambda phage? Is it better in certain situations?

3. How are phage libraries good? Phages can't hold as much information as phagemids, cosmids, BACs etc. so why would you use a phage library? Someone told me they're easier to screen but I don't understand how that works/

I want this answer too

As much as money and science budgets could buy us, which is to say still very little.

consider where we'd be at if we had not done unethical experiments or those experiments that many people think are unethical.
we wouldn't have embryonic stem cell research, we wouldn't have the results of all of those holocaust experiments or japanese ones
i think that information has ended up being very useful to humankind, although the methods used to obtain that info may not be humane

I know that's the taxicab metric. I haven't been able to find how newtonian or modern physics would be affected by this change.

What exactly does "topology" mean? On one hand it seems to be concerned with properties of geometric objects preserved during continuous deformations, and on the other hand I see it mentioned as an abstract property related to sets.

Both metrics are things you can look at for vectors in Euclidean space.
To get an answer, you'll first have to take some physical law, write it down in a way that uses the norm, and then ask how things change if you adopt the modified law.
E.g. you might take the gravitational force F, which goes as 1/||r||^2from the center of gravity. You can write down the force law F and make all instancaes of ||r|| explicit and ask what the differential equation F=mx'' with this modified force brings about. Well firstly you wouldn't have a spherically symetrical law anymore, you'd lose isotropy of physics

Think "overlapping patches".
This is what connects the two.

The topologies possible for a set can be abstractly defined for any set X. If P(X) is the power set, a topology is a subset of this big set P(X) that fulfills certain properties (e.g. that the union of two element (patches) of this topology are again in it)

Now if you think of a geometric object as a collection of points, then a topology (of this set of points) tells you how these points hang together. It thus captures some (but not necessarily all) aspects of the geometric object.

The idea of a topology of a space as info about the patching can also be formulated without set theory in that sense, but that's a rather advanced notion.
On the flipside, you can take sets that are not associated with some geometric intuition and formally ask what the topologies on it are.

It would mean that reality had defined axes. Unlike the Euclidean metric, the taxicab metric isn't rotationally invariant.