Dave

Yeah, it's all pretty interesting stuff. We've just moved onto Fourier series, so expect the same kind of thing.

I have to say, I'm finding this all rather tedious. Granted, I don't know a lot about set theory, but I do know how a piece of mathematics should read, and this just isn't maths tbh. Please either post something using some strict mathematical notation or just don't post. I'm fed up of reading the same old thing time after time, quite frankly.

I have to say, I'm finding this all rather tedious. Granted, I don't know a lot about set theory, but I do know how a piece of mathematics should read, and this just isn't maths tbh. Please either post something using some strict mathematical notation or just don't post. I'm fed up of reading the same old thing time after time, quite frankly.

That's the one. It's quite a nice proof, or so I thought The advantage of regulated functions is that you can define their integral as follows: If f is regulated on [a,b], with a sequence of step functions [math](\psi_n)[/math] converging uniformly to f (i.e. [math]d(f, \psi_n) \to 0[/math] as [math]n\to\infty[/math]), then define [math]\int_a^b f = \lim_{n\to\infty} \int_a^b \psi_n[/math]. I'm not sure how this relates to Riemann sums (mainly because I haven't done them yet) so I'll leave that to someone else.

That's the one. It's quite a nice proof, or so I thought The advantage of regulated functions is that you can define their integral as follows: If f is regulated on [a,b], with a sequence of step functions [math](\psi_n)[/math] converging uniformly to f (i.e. [math]d(f, \psi_n) \to 0[/math] as [math]n\to\infty[/math]), then define [math]\int_a^b f = \lim_{n\to\infty} \int_a^b \psi_n[/math]. I'm not sure how this relates to Riemann sums (mainly because I haven't done them yet) so I'll leave that to someone else.

I know, but video/image codecs interest me for some peculiar reason. My favourite topic of the moment is fractals and their applications, but I feel I have to research this a bit more. Hypergeometric series also look quite interesting.

I've been looking into using maths for video codec compression, but it's a little beyond me. There are various things I've been looking into (fractals being one) but I don't know yet. I shall ponder for a while.

Well, more or less none of the maths we've been doing is "fun" really. We're only just starting to touch on new stuff because we went back to the beginning and started over properly with sequences, series, etc. I'm looking at doing something about curl/divergence of a vector field, so I'll get some books out tomorrow and start reading. Joy of joys

Thanks for all the suggestions I'm in my second year, and have done a fair bit of analysis (just starting to formally define Fourier Series), just done Sylow's Theorem in Algebra and have just finished line integrals/curl/divergence/Stokes's theorem/etc in Vector Analysis. The essay itself is just to write about a particular topic - as long as it involves a fair amount of maths, it's fine. I suppose therein lies the difficulty - there's just too much to choose from. Some of the suggested topics are things along the lines of "Sylow's theorem and it's applications", "Matrices in Robotics" and "Construction of the reals using ... " (can't remember what exactly). All kinds of stuff. Thanks again.

I'm coming up to a stage where I need to write an essay about some topic in Mathematics. Now, before you ask, the purpose of this thread is not to say "omg he's trying to get us to write his essay n00b fs". I'm trying to look at particularly interesting topics in mathematics to formulate some kind of essay title - and no, I don't want you to give me titles. Contrary to some common misconceptions about students, I want (and need) to do this by myself. I've had a fair amount of mathematical experience now, but I'm struggling to find some topic I find interesting enough to write an essay on. If anyone has any suggestions, then that would be much appreciated.

Gaussian elimination is definately the best method.

Kerry decided to pull out, which I think is rather sensible. However, I am really not looking forward to the next 4 years. I had rather hoped Kerry would make it, but, of course, he didn't. Great.

phpBB 2.2.x looks pretty damn nice, on a par with vBulletin. Just gotta wait a bit longer to get it

I can't really run very fast at all. Too much beer, I'm afraid.

Quite. Kids want McDonalds' every day, but if they got it, they'd suffer a heart attack (or 6) by the time they were 20.

Sure. What exactly do you define the "concept of length" to be? A cursory glance doesn't give much in terms of a mathematical definition.

MathWorld is a great resource: http://mathworld.wolfram.com/

I don't think anyone can now argue this any other way Thanks slacker. (somehow that thanks seemed quite amusing )

In engineering you usually have particularly complex analytical problems to model, and these often have no (or at least a particularly complex) solution. Using numerical methods to give a very good approximation for the solution of these models is all the engineer requires.

A Cauchy sequence is defined as follows: A sequence [math](a_n)[/math] is Cauchy if [math]\forall \epsilon > 0 \,\,\, \exists N \in \mathbb{N}[/math] such that [math]\forall n, m > N, \,\,\, | a_n - a_m | < \epsilon[/math]. A function [math]f : [a,b] \to \mathbb{R}[/math] is regulated if [math]\forall \epsilon > 0\,\,\, \exists \varphi[/math] where [math]\varphi[/math] is a step function such that [math]| \varphi(x) - f(x) | < \epsilon[/math].

It just struck me that for some reason, when I looked up regulated functions the other day, nobody seemed to know about them so maybe they're known under a different name; if anyone doesn't know what the hell I'm on about, please let me know

Since everyone's posting questions here, I thought I'd post a nice question I got on my Analysis III assignment last week. It's a bit involved (and somewhat pointless) but I thought it was pretty nice for some reason: Let [math]f : [a,b] \to \mathbb{R}[/math] be a regulated function, and let [math](x_n)_{n=1}^{\infty}[/math] be a sequence in [math](a,b)[/math] such that [math](x_n) \to a[/math] as [math]n \to \infty[/math]. Show that [math]( f(x_n) )_{n=1}^{\infty}[/math] is a Cauchy sequence.

It's not something you'll find outside university level (normally). I've only just started it properly at the end of last year (in the 1st year of my maths degree), and that was nothing but a cursory glance. If you do a degree that involves quite a lot of maths (Physics, Computer Science, etc) you'll get a maths course in the first year that will probably have some kind of introduction to modular arithmetic.

Any good? Looks pretty damn nice.