As part of my preparation for M208 I've been trying to grapple with the epsilon - delta definition of continuity. Open up any Old style textbook on analysis and you will find a definition which is almost incomprehensible anyway things have improved greatly. At the risk of boring those people I know from the OU forums I've been using a book by Brannan called A first course in mathematical Analysis published by Cambridge University Press. This covers the analysis part of M208 and I would recommend anyone who is contemplating doing M208 to invest in it.
http://www.amazon.co.uk/First-Course-Mathematical-Analysis/dp/0521684242/ref=sr_1_1?ie=UTF8&s=books&qid=1289762572&sr=8-1
I think I finally understand (after 30 years) how to use the definition of continuity at least for simple cases. I've enclosed a basic summary on Mathbin
http://mathbin.net/55459
Duncan introduced me to Mathbin as a consequence of some work we are doing on the Cambridge Maths departments example sheets for rotational motion of which more later.
Mathbin is great for exchanging posts which require mathematics. Its based on Latex which Nilo has kindly given me some hints how to use. However it has it's own idiosyncracies in that for Internet explorer the previewer doesn't work and Latex copy doesn't copy across as mathematical text is bracketed with [EQN] [/EQN] instead of $ $ and it is a real pain to adjust LATEX files so that they work first time on Mathbin. It took me about 10 iterations before I got it correct. Fairly soon following the hints that Nilo gave me I hope to incorporate Latex on this blog. For now as I'm just getting used to the whole Latex thing then this hash will have to do. Eventually for my large projects I will use something like ScribTEX.
hello Chris,
ReplyDeleteScribTex ?! - Have you seen this: http://www.scribtex.com/site/plans ? Combine TeXnicCenter with Dropbox and you can store 2GB for free.
With a 'tool' like mathbin you can probably utilize less than 5% of the possibilities of LaTeX. And yes of course it is a pain in the ass. TeXnicCenter is the real deal, power + simplicity. Open Source and free as it should be.
ScribTex / Mathbin it hurts me in the eyes. Sorry, Chris. In Dutch we say: "Jump in the adult pool and try not to drown.' I am sure you won't by the way.
Just my 0,02c opinion.
Kind regards,
nilo
P.S.
You made an excellent start on M208 btw, that's exactly the topic to start with. M208 Real Analysis is hard. ( I am revising GTB at the moment. The instructional videos, especially the one on counting, 57 varieties is excellent. )
I'll take your advice and look at the sites you recomend. Thanks for the complements on M208. As I'm doing M337 at the same time thought it best to get analysis under my belt. Group theory seems more fun though !!
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