Tutorial on
Computable Analysis
A compact course on computable analysis will be offered
at Hagen, Germany, during
February 2125, 2000,
by the theoretical computer science group:
Prof. Dr. Klaus Weihrauch
Theoretische Informatik I
FernUniversität Hagen
D58084 Hagen
Germany
About computable analysis
All over the world numerous computers are used for real
number computation. They evaluate real functions, find
zeroes of functions, determine eigenvalues and integrals
and solve differential equations, and so they perform
or at least are expected to perform computations on sets
like the set of real numbers, the set of open subsets of
real numbers or the set of differentiable real functions.
The increasing demand for reliable as well as fast
software in scientific computation and engineering requires
a sound and broad foundation. Computable analysis is the
mathematical theory of those functions on the real numbers
and other sets from analysis, which can be computed by
machines. It connects the two classical disciplines
analysis/numerical analysis and computability/complexity
theory combining in particular the central concepts of
limit and approximation on the one hand and of machine
models and computation on the other hand.
Computable analysis may serve as an additional framework
for numerical analysis and all other disciplines which
need an exact concept of computation for real functions.
Though computable analysis started in the early years of
computability theory, the field is still in its infancy.
It has a great potential for further development, since
there are numerous challenging open problems, many basic
questions have not yet been studied systematically and
only occasionally its concepts have been applied to
advanced problems.
At present computable analysis appears as a juxtaposition
of several approaches producing a number of very
interesting results but developing more or less
independently. Therefore, for the interested newcomer
the situation is bewildering and learning the state of
the art is a laborious undertaking.
About the tutorial
This tutorial will give a selfcontained introduction
which will focus on the representation based approach to
computable analysis. In this approach computability is
defined explicitly on infinite strings and transferred
to other sets like the real numbers by means of
representations, where infinite strings are used as names
of abstract objects.
The following topics will be treated, among others:
computability on infinite strings, representations of
objects via infinite strings and relative computability
via representations, computability over the real
numbers, computability on closed or open sets,
computability on spaces of continuous functions,
computational complexity.
In order to make the workshop as efficient as possible,
lectures will alternate with exercises and discussions.
It is aimed at graduate students and researchers in
computer science or mathematics who are interested in
an introduction to computable analysis.
Only basic knowledge in analysis, computability theory
and complexity theory will be assumed.
Time table

Morning Session 8:30 to 12:00 
Afternoon Session 14:00 to 17:30 
Monday February 21 
Introduction 
Computability on Cantor Space 
Tuesday February 22 
Naming Systems 
Computability on the Real Numbers 
Wednesday February 23 
Computability on Closed, Open and Compact Sets 
Excursion 
Thursday February 24 
Spaces of Continuous Functions 
Analytic Functions and Power Series 
Friday February 25 
Computational Complexity 
Extensions and other Approaches 
All lectures take place in room number F 09,
Informatikzentrum, Feithstraße 142, FernUniversität Hagen,
D58097 Hagen
Participants
This picture shows some participants of the tutorial
Contact
by letter:
Tutorial
Prof. Dr. Klaus Weihrauch
Theoretische Informatik I
FernUniversität Hagen
D58084 Hagen
Germany
by email:
[Email remove]
or one of the lecturers:
Klaus Weihrauch
Vasco Brattka
Peter Hertling
Registration
There will be only a small fee of DM 30,.
For registration please send an email or a letter
to the contact address given above.
Accommodation
Here you can find a
List of hotels in Hagen
The hotels in "HagenNord" are quite close to the university; e.g.
Birkenhof (20 min. by feet)
and
Zum Bauernhaus (3 min. by feet).
Please ask us in time if you need help with finding
accommodation. (For students a limited number of
reasonably priced accommodations is available.)
Further Information
