Learning Theoretical Computing from the Mathematical Impossibility Results of the CS Curriculum

Abstract

In this paper, we present a novel technique to systematically introduce questions of computability and algorithmic complexity in the curricula of the early years of Computer Science degrees. We propose to start from those results of impossibility that are already included in the curriculum of CS-geared mathematics courses, and around these classical impossibility theorems, we identify motivating and interesting theoretical computing questions. We provide a helpful list of impossibility results and motivating problems, and we analyze how and where they could be introduced in the CS mathematics curriculum. We also provide a preliminary evaluation of the effectiveness of the proposed technique to demonstrate that the introduction of theoretical computing questions from impossibility results could increase students' academic results in theoretical computing subjects and mathematics subjects of the CS curriculum.