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)

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