Mathematics

I challenge the student of mathematics It appears to me that most people look on math as something with supernatural qualities. I challenge the student of math to develop and post short essays on Internet discussion forums about those fundamental aspects of math that you think people can and should comprehend. What follows is something that I have posted regarding my idea of what ordinary citizens should know abut this very fundamental domain of knowledge. Arithmetic is object collection It is a hypothesis of SGCS (Second Generation Cognitive Science) that the sensorimotor activity of collecting objects by a child constitute a conceptual metaphor at the …

The dot product of two i-sized vectors [math]\vec{A}[/math], [math]\vec{B}[/math] is defined as [math]\sum_i A_iB_i[/math], What if the vectors aren't equal in dimension? What is the scalar product of [math]\vec{A} = (1, 3, 5)[/math] and [math]\vec{B} = (2, 4)[/math]?

Does anyone have any recommendations for book on modern abstract algebra? They should include rings, fields, algebras, groups and their homomorphisms. I am looking for an accessible account of all the basics we should all know. Cheers.

Hello I'm an artist working on an illustrative project which revolves around the theme of a paradox. Using the Mobius Loop as its central iconic symbol, the message I'm trying to convey will be that of "the beginning is also the end " In this illustration I'd like to incorporate symbols/formulas of both religion and science. The snake eating it's own tail is a terrific spiritual symbol. However, is there such a scientific problem / formula in mathematics, physics or biology etc. which deals with this theme of a paradox. ie: that the beginning of the equation is also the same as the end?.. or perhaps a problem which turns back onto itself, creating a…

It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 20,000 km2 in 20 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r of the contamination as a function of t. Apparently Area = constant * t. As 20,000 km2 = constant * 20 days, the constant equals 1,000 km2/day Therefore Area = 1,000 km^2/day * t On the other hand Area = pi r^2. So pi r^2 = 1,000 km^2/day * t, meaning that radius r = sqrt (1000/pi km^2/day) * t^(1/2) I got this far but I don't think the answer …

it's not really homework or anything, just something that came into my head. for a regular shape with n sides of length m inscribed in a circle of radius r, write a formula of m in terms of r and n.

Hi all. I cant seem to get my head around this one. I will try and write it as it was explained to me. Is it possible to work out the Probability of e.g Who will win a race based on an individals odds measured against each others, in decimal. i.e 1. 9.9% 2. 32% 3. 19% Their odds are as above. Looking at that, to me the probability of 2 winning is high. But his odds are based on previous form, and the one we expect to win, doesn't always win. Is it possible to work out the probability based on their previous form and that of those on the field around them.

there are two hamburgers. one is poisoned. there are two guards in front of them. they both know which had been poisoned, but one of the guards (you don't know which) is a liar and always lies, the other always tells the truth. you can ask only one of the guards a single question. what question can you ask to know for certain which hamburger is poisoned?

Anyone suggest a book that deals with (the sheaf of) distributions over a smooth manifold? I want to find out how this ties in with the n-point functions in QFT. Cheers in advance

... and explain any implied wisdom (or possibly duhr-duhr-duuhrhrhr) regarding... Pi = n[sin(180/n)], lim n approaches infinity

I've have the following formulae to convert latitude and longitude to UTM: lon_utm = lon * 20037508.34 / 180 lat_utm = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180) * 20037508.34 / 180 I need the equivalent formulae to reverse this. Longitude I can do: lon = lon_utm / 20037508.34 * 180 but I'm completely stuck on latitude (I'm a programmer not a mathematician!) Can anybody give me some help or point me in the right direction please?

Are you smart enough to prove that for every natural number n, (x[math]^{n}[/math] - y[math]^{n}[/math]) is divisible by (x - y), where x and y are two nonidentical real numbers? I already solved its just it took me forever to get lol. If nobody solves it by the next time I visit, I'll post the solution.

matlab? Easy matrix calculator?

Hi, all! Google's turned up nothing relevant (except my post of the same thing on another non-SFN forum) to help me with this problem. I'm at a bit of a loss as to how to do the following elegantly—I've had some success with a slow, "nested" optimisation for what I'm trying to do, but I'm not happy with the results. I have a trajectory described by: [math]\frac{{dx}}{{d\tau}} = f(x,y,a,b,c)[/math] [math]\frac{{dy}}{{d\tau}} = g(x,y,a,b,c)[/math] where [math]a[/math], [math]b[/math], and [math]c[/math] are parameters. The functions [math]f[/math] and [math]g[/math] cannot be calculated analytically (iteration is required), but what happens internall…

Hello! I have recently ran into a productivity wall with my Pentium M 1,7 GHz Sony laptop, that I bought 3 years ago. I am working on a model of one process in Excel and the current version of the file is 200 Mbs comprised of 10 sheets filled to the brim with interrelated formulas (the final version is going to be close to 500 Mbs). Understandably my laptop is refusing to show any speed at all and takes minutes – and sometimes tens of minutes – to recalculate the workbook. I wonder if someone here is a power user of the Excel and can recommend to me a work station that can handle such files with ease? I am working in Excel 2003. Here are the specs of one PC that the loc…

Hello, In Wasserman & Faust's "Social Network Analysis" I read about the following problem with the n-clique concept: They give some references (Alba & Moore 1978, Mokken 1979) which I can't access. I've been drawing lots of graphs to find an example of the above but can't find any. Anyone knows? Thanks! For those not in the know: a geodesic is the shortest path between two nodes; an n-clique is "a maximal subgraph in which the largest geodesic distance between any two nodes is no greater than n".

I'm learning College Algebra. I'm wondering how to solve Exponential Equations, such as 8^(X^2 - 2X) = 1/2 8 to the [X squared minus 2X]th power = 1/2 and other equations of that nature.

Hello, I am studying for examinations and encountered a problem I do not know how to solve: Let w (omega) be a solution of the equation x^2 + x + 1 = 0 Then w^10 + w^5 + 3 = ? I first replaced x with w (omega) which yields w^2 + w + 1 = 0 What I actually tried to do is solve the actual value of "w" using the quadratic equation. However, when I plug this into the 2nd equation, this yields "3", when the answer is 2. Also, no calculators are allowed on the exam, so I can't be using the quadratic equation. Any help is appreciated. Thanks.

Is it true that if something is possible mathmatically it also possible in reality? If so what is this concept called?

I have a funny problem here... Solve for X: (sinX)/X = 0.5

As in the subject Pre-Algebra Pre-Calculus Calculus I Geometry etc. I will order them as a part of the Demystified series (with quizzes and tests) I really wanna get good at Maths Thanks

May algebra isn't that good, but I have a problem I would like to solve. If Mars' tectonics lasted only 800 million years and Venus' plate tectonics lasted for about three billion years and Earth's plate tectonics should shut down in about 2 billion years from now, then, I should be able to estimate when plate tectonics ceases on worlds, given their mass to Earth. 0.3 = 0.8 0.4 = A 0.5 = B 0.6 = C 0.7 = D 0.8 = E 0.9 = 3 1.0 = 6 1.1 = F 1.2 = G 1.3 = H Etc. How can I find the values of A though H and beyond? If I know that 0.3 is 0.8 and 1.0 is 6, then I should be able to solve this, but I can't figure it out.

Hi, I would like to know whether there exist two shapes A and B (in 2D plane) that are equal (ie. equal transformation between A and B exists) but A is proper subset of B. The definition of "being equal" (equal transformation preseves lengths - eg. rotation, traslation etc.) and "proper subset" (the sets are not equal) are I think commonly known. For infinite shapes these shapes A and B exist: eg. half-line, half-plane and so on but what about shapes that are bounded by say circle with the radius of 1? Does some examples exist (maybe some fractals) or can be proven that it is not possible? Thank you in any thoughts. Honzik

I am interested in the ontological status of mathematical entities and statements, and the place for mathematics in a reductive, materialistic universe. The mathematician Kronecker is supposed to have said 'God gave us the integers, all else is the work of man.' Translated into a secular form, this statement is the claim that the integers are somehow part of the 'ultimate furniture' of the universe. However, when we see two chairs, we will find on closer inspection that they are in fact not the same. I think that however natural it may seem to do so, and however ubiquitously it is done amongst many animal species, grouping objects with 'family resemblances' into cate…

Lorentz Contraction of a Moving Parabola http://mypeoplepc.com/members/jon8338/math/id42.html