Research Group on Natural Computing

Prof. Dr. Joerg Flum

University of Freiburg

Resumen:

En 1948 John Von Neumann escribe:

There exists today a very elaborate system of formal logic, and specifically, of logic as
applied to mathematics. This is a discipline with many good sides, but also serious
weaknesses,,, The reason for this is that is deals with rigid, all-or-none concepts,
and has very little contact with the continous concept of the real or of the complex
number, that is, with mathematical analysis.

Partiendo de esta crítica Blum, Shub y Smale han desarrollado una teoría de la computación
para los números reales. En la introducción a su libro Complexity and Real Computation, Blum,
Cucker, Shub y Smale afirman:

The goal of our work is to develop a formal theory of computation that integrates major
themes of the classical theory and builds on the classical foundations, yet at the
same time is more mathematical, perhaps less dependent on logic, and more directly
aplicable to problems in mathematics, numerical analysis, and scientific computing.

En este curso se presentan partes de esta teoría eligiendo el enfoque que le da Bruno Poizat en
su libro Les Petits Cailloux.

• Fechas: 24, 25, 31 de marzo y 1, 7, 8, 14 y 15 de abril del 2008.
• Hora: de 10 a 12 h.
• Lugar: Seminario del Departamento de CCIA (ETSII, Módulo H, Primera Planta)