Exact real arithmetic
Exact real arithmetic is an interesting area: it is a deep connection between
- numeric methods
- and deep theoretic fondations of algorithms (and mathematics).
Its topic: computable real numbers raise a lot of interesting questions rooted in mathematical analysis, arithmetic, but also computability theory (see numbers-as-programs approaches).
Computable reals can be achieved by many approaches -- it is not one single theory.
Jean Vuillemin's Exact real computer arithmetic with continued fractions is very good article on the topic itself. It can serve also as a good introductory article, too, because it presents the connections to both mathematical analysis and computability theory. It discusses several methods, and it describes some of them in more details.
3 Portal-like homepages
There are functional programming materials too, even with downloadable Haskell source.