/sci/ - Science & Math

2/2

7. Write a worthwhile pseudo algorithm to numerically solve y(t) = ax(t) + bx'(t) + cx''(t) + d, where a,b,c,d are constants and y and x are vectors with 1000 elements each, and assume you have enough initial conditions given to do this.

8. Give an algorithm right now to invert a binary tree and work out its complexity.

9. Give descriptions and the difference between the world wide web and the internet. Explain in clear language what HTTP and HTTPS are and their differences. Where would a binary tree be used in the real world (outside academia)? Same question but for the binary tree inversion operation? Give three types of list sort, their complexities, and where they would be used outside of academia.

10. Write (on a computer) a program in any real programming language(s) that will take basic stock information (both from now and in the past), based on a selected stock input by the user, and to store it for use in later calculations defined by the user. Write a program that would display the user's selected information (i.e. stock price / P/E for the past 2 years) graphically and to compare it with the same information from other stocks. (You'd be given internet access to assist you but with a time limit of 45 minutes and it has to be original code.)

Frankly, I can't do any of this shit.

I can do some of these.
I think we should split the work between a few of us.
where are these questions coming from?

>>7627853

It's just stuff I made up right now. Familiar enough for us to recognise all the stuff, but hard enough that nobody can get a lot of it. In short, bait.

I think the first one may be an accidentally easier version of a question. I can't remember. I should've said 51:49 instead of 70:30

I'm gonna post some fun problems.

>>7627860

>>7627842
I can do all except 8 because I know jack shit about computer science, only some software design

>>7627861

>>7627865

>>7627868

>>7627870

>>7627874

>>7627876

>>7627877

>>7627878

>>7627880

>>7627842
ay yo stumbled on here from /b/, the fuck is this shit.

Im dumb as fuck.

peace! im outtie

Can you post solutions to the problems between posts >>7627860 and >>7627882?

>>7627860

a) Let's start with:

Ax = Lx (L is lambda)
By definition of idempotent matrix. We get:
A^2x = Lx
A(Ax) = Lx
A(Lx) = Lx
L(Ax) = Lx
L(Lx) = Lx
L^2x = Lx
L^2x - Lx = 0
x(L^2 - L) = 0.

x is an eigenvector therefore is nonzero by definition.

therefore L the only solutions for L are: 1 and 0.

b) The matrix [1,0;0,0]

Shit nigga I don't even fucking know what derive means. I had to google that shit.

>>7628023
Do you even LaTeX mate?

>>7627842
Why? sure its nice to study the proofs and derivations, but why should I just know that? I can just look it up if I need to.

>>7628268
Obvious bait is obvious

>>7627969
The solution to the matrix problem is basically >>7628023.

Here are the solutions I have on hand for >>7627880, >>7627882. They're not exactly complete, because the professor for the class is lazy, but you can piece the problems together from it. They're both Bessel equations.

>>7628511

>>7628512
I was just going to try [eqn]\phi=-\int_{\ 0}^{\phi_0}\mathbf{v}\cdot d\mathbf{S}[/eqn] for the first part to get phi.

And is that all Bessel functions are? I thought I was going to learn about them years, or whenever, down the line.

Anyone want to try an analysis problem I had last year? Shouldn't be too hard if you did chapter 7 of Rudin.

On topic, it seems like a lot of these are fairly solvable with the amount of math/computer science a physics major should know. Do you have any upper level math questions (algebra, analysis, topology etc.)?

I can do a few of these, but frankly I've forgotten a lot of thermodynamics (I'm no longer a physics major; I get bored of experiments so it wasn't right for me), and haven't bothered with differential equations in years either. I could definitely do 1, 2, 3, and 8 though.

>>7629979
Thats the generalized Arzela-Ascoli´s theorem, right? I had to do this once for an differential equations class and as far as i can recall you have to use the usal Arzela-Ascoli and the fact that precompactness is equivalent to totally bounded in Banach (or just complete) spaces. I dont want to work it out here right now but thats the idea, isnt it?

>>7629929
You can go into a lot of depth with Bessel functions, but simply obtaining a solution to a Bessel-type differential equation is fairly straightforward.

Bessel basically found a general solution to all functions of a certain type, so finding a solution is just a matter of comparing terms.

From an engineering standpoint, you don't often need to deal with Bessel functions beyond the solving point, although you do need to solve them a lot for transport type problems.

http://mathworld.wolfram.com/BesselDifferentialEquation.html

>Describe three or more counter examples to Descartes' "Cogito ergo sum" statement.

what?

>>7627843
1,2,3,8,9

10 is ill defined

>>7630587
translates to "I think, therefore I am. "
Some counterexamples:
-Alzheimer's. If you think you are only to forget (and your forgetfulness) then in this case the mind is deceived.
-Retardation. If you cannot think, then how can you be?
-Willful Ignorance. Welcome to [his] world, the reality does not make much sense. In [his] world, if logic doesn't exist then you must be deceived or mistaken.

>>7631060
A counterexample would be of the form "I think and I am not" ie "I think and I do not exist." None of those fit that form. In fact I would claim that the statement is rather trivial as it presumes the existence of the self by saying that that self thinks.

>>7627860
man eigen values were the only fun part of my diff eq/linear algebra class i took sophomore year. too bad that was when i had my mental breakdown and just barely made it out of that year

>>7631060
man you fail so hard at both logic and philosophy.

welcome to /sci/!

>>7627842
9

>>7627842
>the quadratic theorem
wat

>>7631690
I assume he's talking about the quadratic formula (that gives you the roots of a polynomial Ax^2 +Bx + C).

It's arguably the easiest thing in his list.

>>7627860
a- minimal polynomial is X2-X=X(X+1).
b- any projection is idempotent.

>>7627861
a- det(A-XId) =X(X-2) -1 = X2-2X-1= (X-(1-Sqrt(2))(X-(1+Sqrt(2)). I don't want to search eigenvectors.
b- see class notes
c- Compute D^n where D is the diagonal form of A. Use U matrix to get back A^n.
d- p_n = A^n (1 0).
e- Pell equation describes a union of conics. If the field has even characteristic, the equation becomes x^2=1 which has only solution x=1. Has someone investigated Pell Equation in all generality ?

>>7627878
is (d) true even for non continuous functions ?

>>7630137
it is Arzela-Ascoli's theorem.

>>7631747
The "class notes" part is just forming the diagonal matrix. He's just guiding people to part c.

As for the Legendre functions, I believe they can be used to model non continuous functions on the interval [-1, 1]. I know it can be used to model the sign function (f(x) = -1 for x < 0, f(x) = 1 for x > 0) which is discontinuous at x = 0.

If anything it could be done in a piecewise fashion along continuous intervals.