Reddit mentions of Godel, Escher, Bach: An Eternal Golden Braid, 20th Anniversary Edition

Gödel, Escher, Bach: an Eternal Golden Braid is a good book that introduces a lot of computer science topics.

Godel Escher Bach: An Eternal Golden Braid is pretty classic.

Zero: The Biography of a Dangerous Idea all about zero and infinity is pretty cool

Schild's Ladder by Greg Egan - SciFi - is pretty good. Though it's not so maths heavy, I find it to be more maths heavy than most sci-fi books I've read.

EDIT: Typo

A relevant book you may enjoy:

http://www.amazon.co.uk/Godel-Escher-Bach-Eternal-anniversary/dp/0140289208

I don't always contemplate reality up to the brink of insanity, but when I do I'm usually high as fuck.

One thing that usually gets me is contemplating the enormity, the complexity, and potential fragility of the myriads of systems that compose our body, and moreso the brain itself, and the strange loop of the brain contemplating itself, and this is the closest I've gotten to making myself faint just by thinking.

The idea of ending up insane at some point in my life is something I've genuinely contemplated. There seems to be a trend for people that think of reality too much to lose it, but I'd like to believe that what we see as insanity is simply the mind transcending the body and the concepts we think of normal. I'd be almost disappointed if I get to old age and still think like a normal person.

thanks for the link, anyone who liked this might like (more suggestions welcome)

http://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads

https://www.amazon.co.uk/Godel-Escher-Bach-Eternal-anniversary/dp/0140289208

https://www.amazon.co.uk/d/Books/Prime-Obsession-Bernhard-Greatest-Mathematics/0452285259

A few years ago I was in a similar situation to the students you describe and am now at one of the universities you mention, so these suggestions are bound on what I found useful, or would have liked in retrospect.

Do you know about nrich? They have some interesting puzzles, arranged by keystage. They used to have a forum 'Ask NRICH' which was great, but currently closed for renovation, so look out for its reopening.

If it doesn't already exist, encourage the students to set up a maths society, research into something they find interesting (you can give suggestions) and give a brief talk to their peers.

However, what most inspired me was my teachers talking about what they found interesting. At GCSE, my teacher told us about Cantor's infinities as a special treat one day; we had pictures of Escher drawings in the classroom. At A Level, my teacher used to come in with maths puzzles he'd been working on over the weekend, and programs he'd written to demonstrate them (in Processing & Mathematica). Encourage them to come to you with questions too!

You can recommend some books to get them hyped. Anything you've enjoyed. I'd recommend Gower's Introduction to Mathematics for an idea of what maths is really about (beyond crunching equations at GCSE & A Level). Singh's Fermat's Last Theorem and Hofstadter's Godel, Escher, Bach are classics (especially on uni application forms) - the former an easy read, the latter somewhat more challenging. I'm sure you can find some more ideas on /r/mathbooks.

For STEP preparation, Siklos has an unbelievably helpful booklet. For the older ones, this would be instructive to look through even if they're not planning to apply for Cambridge.

Also (topical), arrange a class trip to see The Imitation Game!

> That's not art.

Says you. I like explosive art, and records that break the record player they are played meant to be played on. Yolo.