Computer science

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Introduction

Wikipedia's Computer science.

Martín Escardó maintains a Computer science page, being both detailed and comprehensive.

Structure and Interpretation of Computer Programs (by Harold Abelson and Gerald Jay Sussman with Julie Sussman, foreword by Alan J. Perlis).

Computability theory

Wikipedia's Computability theory.

An interesting area related to computabilty theory: Exact real arithmetic. For me, it was surprising, how it connected problems in mathematical analysis, arithmetic and computability theory.

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