Dave

It's probably best to explain with some examples. Say user 1 has friends 2, 3, 7, 18 and 30. Then you'd have a user_friends table that contained the following entries: userid | friendid -------+--------- 1 | 2 1 | 3 1 | 7 1 | 18 1 | 30 Then, to get a list of the friends that that user has, we use the SQL query: SELECT u.name FROM users AS u, user_friends AS uf WHERE uf.userid = u.user Or similar. To get a list of the users and how many friends they have, try: SELECT u.name, COUNT(*) AS count FROM users AS u, user_friends AS uf WHERE uf.userid = u.userid GROUP BY u.userid There's lots of variations on the theme.

Finish him! [/mortalkombat]

I misread the original my post. My mistake.

This isn't an inequalities concept. And the above post isn't really appropriate, since we're looking for a specific value of S. What you want to be looking at is the method of Lagrange multipliers, which allows you to find extrema of a function f(x,y,z) subject to a constraint g(x,y,z) = 0. In this case, [math]f(x,y,z) = S = x^3y^2z[/math] and [math]g(x,y,z) = x+y+z-1[/math]. You can find out more about it by looking at the Wikipedia article.

If you have Linux, then I highly recommend mencoder, which should be capable for the job. I think there's also win32 and OSX builds.

You can also connect to cube.xyloid.org if you have further problems.

For the record, I have PDFCreator on my machine, and it's rather good. I think it also requires GhostScript and possibly something else. It emulates a printer, and when you print to it from an application, you get a nice shiny PDF.

Those types of equations are called transcendental, in that the solutions cannot be derived algebraically. The only way to find the roots is by some form of root-finding estimation (e.g. interval bisection, Newton-Raphson, etc).

I don't think there's going to be a very good way of reading out base-16 notation aloud, other than to read out digits individually, for the reason you state. When you start to get letters as a part of the numbers, it becomes a little hard to find a way of pronouncing them properly. Of course, one doesn't have this problem with, say, octal.

Just realized I haven't really answered your question about exchanging linear approximations and derivatives. Ignoring matrices for a moment, we say that a function [math]f:\mathbb{R}^n \to \mathbb{R}^m[/math] is differentiable at a point x0, if there exists a linear map [math]d_{x_0} f: \mathbb{R}^n \to \mathbb{R}^m[/math] (called the differential) satisfying: [math]\lim_{||h||\to 0} \frac{||f(x+h) - f(x) - d_{x_0}f(h)||}{||h||} = 0[/math] With a little effort, one can prove that [imath]d_{x_0}f[/imath] can be chosen to be the Jacobian matrix of f, evaluated at x0. It should be clear to see from the definition that the differential is a linear approximation to f around x0, so I suppose you can interchange derivative with linear approximation as long as you're careful about the phrasiology.

I think the problem is that without a certain degree of formality, these things can appear to be very fudged. Certainly intuition can play a part, but I think you need to be a little more precise. Are we talking about a function, [math]f:M(n,n) \to M(n,n)[/math] defined by [math]f(A) = (AA^t + A^t)^{-1}[/math] and then taking the derivative? (M(n,m) is the space of real n by m matrices). I don't know an awful lot about matrix derivatives (other than the fact that since M(n,m) is isomorphic to Rnm we can use some results from that), but to answer the question it'd be useful to know what he regards as the derivative.

I imagine a lot of this stuff will be covered. You probably won't be able to get a hold of a copy online, so you'll need to find a big library (or at least one that's likely to stock it).

I haven't quite decided myself yet. Currently, it's looking like: Hyperbolic Geometry Calculus of Variations Dynamical Systems Homogenization Theory of PDEs (maybe) Advanced PDE's (maybe) Lie Groups Population Dynamics: Ecology and Epidemiology 4th Year Project: applications of wavelets to signal processing, implementation of the Wiener filter using wavelets - maybe. History of Mathematics Some random scientific computing modules A lot of good modules on offer to choose from this year, so I'm quite looking forward to it really.

Equations like that aren't necessarily hard, it's just the notation can sometimes confuse matters an awful lot. For example, the equation above simply involves a summation and a complex exponential, both of which are extremely easy to code. I'd try to find a book that covers a course teaching mathematics for computer scientists (there's a lot of those courses around). For example, the one at Warwick is pretty good and has a recommended book, although I can't comment on it having never read it.

I can't see mathematics education changing drastically any time soon, since it seems to work fairly well. I spent the first two years learning general mathematics (analysis, linear algebra, and the like) in order to specialize more in my third and fourth years. As it happens, I took a more general variety of modules in my third year and now I know that I'm going to specialize in computation mathematics for my MMath. One of the major problems that the mathematics institute faces at Warwick is the growing gap between A-level and university mathematics. In fact, the first year course has had to be completely re-written to accommodate a lacking of knowledge in areas such as basic complex analysis. Right now, I really think this is the more pertinant problem.

I find Mathematica vastly superior to Matlab/Maple, but the latter are probably better for programming. Mainly I use Mathematica for calculations so programming isn't a major concern.

There's so many different schools of argument that I won't attempt to list them. Usually in real analysis, choosing 0^0 = 1 is the most sensible option for a lot of reasons. You can find a more complete list of reasons here.

Just for the record; if you have concerns about your health or health-related matters, then you should always see your doctor before anybody else. Nobody online will ever be able to give you a good check-up based on written descriptions of symptoms, and no doctor would ever suggest you do such a thing. So please, see your doctor, and let us know how it turns out.

Sorry guys, it should all be working again now.

It does sound like a Java problem. X-Chat as mentioned above is a viable alternative; barring that just some simple IRC client like mIRC will do the trick.

As ajb said, it's the extension of the factorial function to the complex plane. There's a number of useful identities that you can find at the MathWorld page to do with dilogarithms and the like. I suggest you look at related functions as well, as there's really a whole bunch of them and it can be more interesting to look at the group of them rather than single out the gamma function.

Google is definately your friend in this instance. Look for something that you'd like to make (for example, a simple PHP image gallery) and have a search on Google for some examples. It's the best way to get to know any language. There's also the PHP tutorial which you can find at http://php.net/.

Good to know - I was just pointing it out for future reference

Unfortunately GNU/Hurd is in rather a bad position at the moment. Firstly, the monolithic Linux kernel is proving to be exceptionally popular at the moment for desktop machines, making it rather a trendy thing for developers to work on. This, in turn, drives them away from other projects (such as GNU/Hurd) and hence the already slow development cycle becomes extremely slow indeed. For example, I seem to remember a Gentoo GNU/Hurd development team. Unfortunately it suffered from the aforementioned problem, and is now rotting in a heap as I understand.