The references listed at <http://en.wikipedia.org/wiki/Computable_analysis> have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the current paths of research in computable analysis? (In case they are not, where can I find a good introduction to the current trends?)



Recent trends in effective analysis
(At François's request, my comment in now an answer.)


Yes, it is still an active research area. It however is spread out throughout a number of camps (traditions): The Weihrauch camp, the reverse math camp, the computability theory camp, the randomness camp, the proof theory camp, and a few different constructive math camps. (Also, see many of the quantitative results in classical analysis.) Most researchers span two or more camps, and I don't mean to imply there is a feud or anything. However, there isn't necessarily an organized central list of open problems or a central agenda. You may want to check out [cca-net.de](http://cca-net.de) as a starting point.


Edit: You may also want to check out [this survey](http://arxiv.org/pdf/1206.3431v2.pdf) by Brattka and Avigad. It does a good job of explaining many of the different traditions.


