Mathematics

I have got a quadratic form as following: F(w) = g^T * w + (1/2)* w^T * B * w Here T is the matrix transpose. Someone said the if p is a solution to this quadratic form then p is a solution to an equation of the form: (B + aI) * p = -g Here I is the identity matrix. May I ask why please? Thanks a lot!

hi all, can anyone please help. Im stuck on calculating the volume - If you had a mass of 1.028 x 10^26 kg and density of 1.61 x 10^3 kg m-3. I have come up with what i think is the answer that is 0.63850931677m^3 If this is correct, then how do i write this answer to the appropriate number of significant figures. Many thanks Carl1

Is it true what people say to me that maths s easy and all it is a logical puzzle because i am so bad at it?

Hi, does anyone have an "order" of maths? I know it sounds strange, but I need a list of different types of maths, and in which order they should be explored. I hope to be a mathematician or a physicist someday, but I'm still struggling with the 10th grade math that I'm doing now >.< so I'd like some type of list, so that I can first perfect the current math that I'm doing with online guides, then know where to move next. Also, this would help me ace a lot of my math tests. If anyone has any advice, or a link or anything of the sort, it'd be greatly appreciated. Thanks.

I was reading about the Arecibo message thingy, with the message being transmitted in 1679 bits because there's only two ways to lay out 1679 in a grid, one of which would make "sense" and one that wouldn't. Then I thought, this would only work if aliens used a square grid system (where information can have x & y co-ordinates) for their layouts, which there's no guarantee they would... What if alien visual representations or data were laid out on a hex grid? Maybe they would arrange them from the center spiraling outwards either clockwise or counter-clockwise. Maybe they would be arranged in rows and zigzag columns, or columns and zigzag rows, or maybe …

I am dealing with tomography inverse problem by using trust-region optimization now. I compared my result with other optimization algorithms found that trust-region results are much better. May I ask if the trust-region optimization subproblem contains a regularization already itself please? If it contains regularization itself and how does this related to Tikhonov regularization please? By the way, I am using Matlab fminunc to implement the large scale trust-region Newton algorithm. Thanks a lot and I am looking forward to your reply!

Hi, everyone. Hey, so I have a statistics project to do. I'm just trying to balance some ideas. I need to make a research question and eventually a hypothesis and alternative hypothesis that I will prove or disprove. I was thinking of doing something related to the NBA such as Home vs Away game success or something about the business world. We learned annova tables, two samples, one samples to prove or disprove hypothesis. Anyone got any ideas or recommendations on something that wouldn't be too tough to do?

Hey all, I was browsing through our math book the other day, and I came upon an interesting question. Say you have a table with a diameter of 0.6m, and on that table a square meter-by-meter tablecloth. One corner of the tablecloth is hanging over by half a meter, and another by 0.3 meters. By how much are the other corners hanging over? I came up with 0.5 and 0.3 meters, but I'm not sure I'm right. Can anyone verify? Thanks in advance, Gabe

Posted below is a link to an attempted proof of FLT that I haven't been able to find a flaw in: http://groups.google.com/group/fermats-last-theorem-flt-2008

So today I was bored in class so I started to think about polynomials, specifically parabolas. I know that it is possible to find imaginary roots of a parabola. My question is when you graph this parabola that has two imaginary roots the curve never hits the x-axis then were are the imaginary roots at? When I asked my instructor he said he had no idea. My only guess was that there was a z-axis there the appeared somewhere but I really have no ideas. So where are the imaginary roots on the graph?

Is the fact that a Minus x Minus = Positive an axiom or is there a [simple] mathematical proof?

When I read " We work out this example as if it were 3(x - y) - 5(2y - x). We begin by multiplying out using the distributive property" Does "multiplying out using the distributive property" just mean multiplying everything inside the bracket by what's outside it, in this case 3 & 5?

What is the fastest proof of the Pythagorean theorem in the world? Thank you J5

Is the equation: (T/T)a^x=T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)) true or false? If true, then can we "cross out" the T's and make them "disappear" the way we were taught in school? Don.

I hope this question isn't to general but i feel like learning something new, so... I'm wondering what anyone can tell me about matrices/Matrixs? My teacher only spent one lesson on them and didn't really elaborate on anything... first i'm wondering if matrices and matrixs are the same thing?? Basicly i know what they look like, i can add two together and i've learned how to times them together also. So what else is there? What can we use them for? Remembering that i'm 15, i'm in the highest classes but if if it is something that shouldn't really be attempted for a while i'll understand, but any information would be greatly appreciated... Thanks!!

Hi I was just wondering if you can help me out on this. Note: this isn't a homework question ok! How you convert the wavenumber in cm^-1 into nm. I know if it said that you had to convert that wavenumber into nm^-1 it would be X 10^10. You people think that I might have to multiply it by 10^-10? Any help appreciated.

this maybe a little silly...but i have here a debate... Is algebra and calculus necessary for a comman man to live in the society??? That is, are they used in the pratical life?? I vote that they are not necessary for a common man.. What about you...

this is quite simple, if you divide 10 by 3 on any calculator or ask any professior, it/they will say that it is 3.3 to the inf yet this is fundimentaly wrong you do not get an infitite number when dividing 2 finite numbers so there fore 10 /3 = a number yet the reason we define it as inf is due to our lack of a word to describe said event the same applies to dividing by square roots, there is no need to multiply by resipricals as there is to reformulate the equation all that needs to be done is invent a new numeric language that accounts for all of the fallacies of the current one

In my presentation of my progress in my project on Topology, I mentioned something about how Non-Euclidean surfaces have curvatures [math]\neq 0[/math]. My math teacher pulled me aside afterward and proposed to me the following: Around a point on a Euclidean surface is 360º. You said that in order for this value to change, the surface must have some curvature. However, [at this point he took a piece of paper and pointed to a point lying directly on on edge] about this point there is 180º. I interjected at this point, claiming that I was talking about an edgeless plane, and he continued: [Making a crease at the point and then joining the two halves of the edge on w…

Or the they can be called "order of precedence"? I'd like to know why this is necessary -- how was it established. I'm making it a point to understand the necessity behind these things so I'm not just blindly following rules. You know...so my math skills are more intuitive. I'm asking for a relative, so Please Excuse My Dear Aunt Sally. ...I couldn't resist throwing a corny joke in there.

Is it?

Hey all, I just wanted to ask, I was thinking the other day and a though struck me. Given a number [math]x \in N[/math], then [math]x[/math] will be prime if [math]GCD(x\#,[/math] [math]x) = 1[/math], where [math] GCD(a,b)[/math] is the greatest common divisor of [math]a,[/math] [math]b[/math], and [math]x\#[/math] is the Primorial. In other words, [math]x[/math] is prime if [math]x[/math] and the product of all primes smaller than x are coprime, or relatively prime. While this could be used to prove a numbers primality, I think it'd be inefficient, if only because one would have to know all the primes smaller than x. It is possible to use a normal…

I am doing this 3D app that has some annoying trig in it, that is kind of messing with my head, as I am not the best trig guy on the planet...so please help! I start with 4 equilateral triangles, to make a tetrahedron, and all I want is to really have each point in the triangle touch a radius of a sphere. I map everything in horiz/vert degrees, to get the base down... I start with the "top down" and draw out on graph paper, an equilateral triangle and put a dot in the center, and draw a circle around it. I make isosceles triangles by drawing lines from the dots to the points, so you have three of those inside it, and it looks like the center point out of each…

Framework of the idea (1 phrase) In the equality A^n – (C^n – B^n) = AA^(n – 1) – (C – B)R = 0 the number u = A + B – C has k zeros at the end, but the last k + 1 digits in the numbers A^(n – 1) and R one can transform into 00…001, but then the number u = A + B – C has k + 1 zeros at the end. In any case the proof merits of careful analysis. ============ Short PROOF of FLT: If a + b – c = 0 mod(n^k) and a=/ 0 mod(n), then (c – b)^(n – 1) = [(c – b)^n]/(c – b) = a^(n – 1) mod(n^(k+1)) and therefore a + b – c = 0 mod(n^(k+1)) – cf. my Forum: http://www.ivlim.ru/fox/forum/FORUM.asp?FORUM_ID=20&CAT_ID=1&Forum_Title=%C2%E5%EB%E8%EA%E0%FF+%D2%…

So for a Senior project, my partner and I were assigned the topic "Mathematical Curiosities", which is quite a broad scope. We have, however, since narrowed it down (with some work on the properties of Möbius Strips) to the field of Topology, specifically manifolds and their properties. We can't, however, think of any good actual project ideas. I want to actually do something as opposed to simply exploring. I was wondering if you guys might have any suggestions? For instance, the string theories are starting to tie topology into physics and we were curious as to whether or not we could work that angle (since I'm going to major in physics in college). Anything would be wel…