Mathematics

Recently I've been reading up on QM and came upon the lovely little thing known as the fourier transformation. I was able to tell that it involved calc, and my physics teacher explained what it did, but does anyone know exactly what level of mathmatics is involved in it? or the specific subjects needed to understand it?

umm here is the question "Here V is a nonzero finite-dimensional vector space: If dim V = p and if S is a linearly dependent subset of V, then S contains more than p vectors. True or False?" Now i am not sure , i could argue either way, although the answers says that it is false. i think it is false because it doesnt say that S is a basis, and so S can have less than p vectors and still be a subset of V. on another note, can a z-dimensional vector space V have a basis with less than z vectors in it? (or is this a related note? )

would anyone be able to give me a hint to get me going with this problem, i am unsure as what i should start by doing... small hint? Cheers Sarah

Hello... I am currently doing my U.G in electronics... However I am suffering with a networking course which has a tinge of graph theory in it. I feel my graph theory skills should be optimised, but i fail to find a good book which deals with the subject and its networking applications with sufficient rigour. Could anyone direct me to one?

I figured since I don't want to clutter up this board with a bunch of newly created threads, that I'd post whatever math problems I'm having in here. I suck at math, sadly. The most recent problem I've come across is this: factor each expression completely x^3 - 8y^3 So I tried doing this since: (x-y)(x^2 + xy + y^2) factored: x^3 + 2x^2y + 4xy^2 - 2x^2y - 4xy^2 - 8y^3 Which turns out to be: (x -2y)(x + 2xy + 4y) what I don't understand from this problem is how 4 gets there.

I am sure this is very simple, but could someone work through this question for me? This is not homework, I just want to learn the steps to do it. x = (4-i)/(1-3i) I am supposed to put it into the form x = a + bi The answer is: x = 7/10 - 11/10 i Thanks for any help you can give me.

hey i was just wondering how you show this... or well if i am doing or done it right? thanks -Sarah ...i'll post my answer in a min, just let me type it up...

i can't quite work this one out... i think the first step is to say that we want to find complex root of this: z^{n} = a but yeah...i dunno...can someone give me a few pointers please Sarah

Right, Aparantly the chance of England not winning the test today is approx 2-1 Now, in theory that means in say 3 matches England would not win 2 and win 1. But what are the chances of the afformentioned situation occuring. In theory they are certain, but evidently that is not the case.

yay! i might have actually got this one right hopefully, how'd i go... i reckon R = 2 , where R is the radius of convergence of the power series....

hi, yet another one of my questions i can't quite figure out how to prove this....i can see its true, but i just don't know how to write it out formally :S -Sez

Ok, i got a couple of probs. how do i prove if a series is divergent or convergent? and what is the nth term test? can someone please explain it to me?

I don't know the latex symbol to get long division symbols but hopefully someone can figure this out for me. I've been doing pretty good until I came across this problem: (x^3 + 1 + 2x) / (x^5 + 3x + 2) Answer is: [hide]x^2 - 2 + [(-x^2 + 7x + 4) / (x^3 + 2x + 1)][/hide] I was going to go in depth about this, however, I don't see the latex symbol that closely looks like the square root symbol for division.... It's very obvious to me that I need long division. I just didn't know how to solve the problem, that's all. I don't understand the long division processes used in this. Long division in plain numbers is somewhat easy, however, this p…

Here's a maths question I have found in a maths test. Solve for x. Give me some hints please...I am clueless. Anyway ignore those green squares.

hi all , i can't figure out how i am ment to use the stated fact about tan x. the way i'd do it is dividing the series expansion for cos(x) into that for sin(x)... but yeah i dunno any advice would be greatly appreciated __sarah__

i am new to this forum and not exactly sure if this post belongs here. i need a concrete idea for a determinant. i understand the determinant as the volume of the parallelopiped in the n dimensions corresponding to the order of the determinant. but is there an alternate idea? while working with polygonal numbers and determinants i found that the 3*3 order determinant of any 9 consecutive n-polygonal numbers is -(3*(n-2))^3. i was trying to understand what this result could mean but since my idea of the determinant is vague i was trying to go backwards and understand the determinant. anyway does this result have anysignificance? i proved this by obtaining a general form…

This is the problems on the 46th International Mathematical Olympiad. My friends got excellent result from it, some of them are still very young, the youngest is 2 years smaller than me. That could depress me much. [as I even could not get the qualification to join the competition] http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/1dayenglish.pdf http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/2dayenglish.pdf

hey guys could i get a hint at how to do this problem please? i just can't quite work out what my first step should be,.... Thanks -Sarah

Hi all! i can't work out the method to solving this problem or proving it i suppose i guess induction doesnt work but i am stumped for ideas, if anyone has any hints they could give that would be great! i don't to be told exactly how to do it at the moment, but i do need a few hints to get me started. Cheers Sarah

can someone please explain to me how it goes from the first line to the second? (from a normal equation to an infinite series)?? Thanks Sarah

e^(i*pi)+1=0. What is it used for? Why is it special? Ok, it relates pi,e, i, 1, and 0, but does it have a practical application?

hey everyone this is a physics/maths ish question. to do with the michelson-moreley experiment. about light travelling up the arm to the mirror kind of thing anyway, i don't know how to get the approimation part (i gather it is a first order appoximation?) can i do this using linerisation (taylor series stuff) or what? (i don't know how to do binomial expansion at the moment ) Thanks Sarah

hey i have another question if someone is willining to help i can't work out how to use the c and v in this diagram ?? Thanks guys Sarah

What's the convention nowdays? The reference book I am using (which is pretty old btw) goes [math]a_1+\cfrac{b_1}{a_2+\cfrac{b_2}{a_3+\cfrac{b_3}{a_4+\ldots}}}[/math] While the online resources goes a_0,b_1,a_1,b_2... Also which one is more conventional [math][a_1;a_2,a_3][/math] or [math][a_1,a_2,a_3][/math] I know it doesnt matter, but I just wanna stick to the standards.

can someone cleverer than me point out how this problem goes from the second last line to the last? Cheers Sarah