My undergraduate degree (MSci/ARCS) at Imperial College was in maths — mainly pure maths, too. I have to confess that really what I do now is very different and my direct use of the skills I picked up there is pretty small; also I’ve forgotten a lot! So what’s here is pretty limited: some book recommendations, links to friends and colleagues and a few essays I came up with in the course of my undergraduate days. Hopefully it will be useful to someone. ;)
Essays
Some old coursework from the Imperial College days which might (might;) be fun for someone to read.
 An Exploration of Continued Fractions
 A small introduction to the ideas of continued fractions, a form of expression of numbers which allows for some interesting analytical insights. An interesting question which I’ve never bothered to find the answer to: what is the relationship between the form of a continued fraction given in Definition 1.1 with Euler’s definition (Example 3.2)?
People
 Brad Baxter
 Brad Baxter does fun work on numerical analysis and mathematical finance. He’s an excellent teacher and some really good notes on various numerical analysis methods are to be found on his website.
 Kevin Buzzard
 Kevin Buzzard teaches number theory at Imperial College and is frighteningly smart.
 Rupert Ford
 Rupert Ford taught the scientific computing course where I learned to program in C, and tragically died the next year. His kindness and support helped me gain the computational skills that form a major part of the research I do now.
Books

Richard Courant and Herbert Robbins (revised by Ian Stewart)
What is Mathematics?  amazon.com amazon.co.uk amazon.de
 This is a wonderfully written, extremely readable and enjoyable introduction to the field of mathematics. I keep returning to it just for pure pleasure, never mind scholarship; it’s definitely a ‘musthave’ book.

G. Stephenson
Mathematical Methods for Science Students  amazon.com amazon.co.uk amazon.de
 This is a good (though very dry) introduction to a whole load of mathematical methods that are useful for scientists and engineers. For some of the subjects it may well be useful to get out some library books to go into more detail on specifics and examples. There are a few passages where things are casually demonstrated, not proven; it’s sometimes worth trying to figure out the genuine proof yourself in these cases.