Is there algorithmic mathematical analysis? There are algorithmic graph theory/number theory/combinatorics/information theory/game theory.


  Is there algorithmic mathematical analysis?


According to wiki, mathematical analysis includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions. It is OK to focus on real analysis (wiki) that deals with the real numbers and real-valued functions of a real variable.

"Algorithmic" means studying something from the perspectives of computability theory and complexity theory.



Googling of "algorithmic mathematical analysis" leads me to "mathematical analysis of algorithms" or "applications of analysis to algorithms", which is not what I mean.
Check out
the Computability and Complexity in Analysis network. Quote:

The topics of interest include foundational work on various models and approaches for describing computability and complexity over the real numbers. They also include complexity-theoretic investigations, both foundational and with respect to concrete problems, and new implementations of exact real arithmetic, as well as further developments of already existing software packages.