Introducing Dynamical Systems andChaos Early in Computer Science andSoftware Engineering Education Can Help Advance Theory and Practice ofSoftware Development and Computing

Dynamical systems, i.e., systems that progress along time according to fixed rules, exhibit many special phenomena like the emergence of interesting patterns, bifurcation of behavior, the appearance of chaos despite determinism and boundedness, and sensitive dependence on initial conditions. Such phenomena are encountered in diverse fields, such as fluid dynamics, biological population analysis and economic and financial operations. The study of dynamical systems, their properties, and the mathematical and computerized tools for dealing with them, are often designated as part of advanced curricula in physics or mathematics. Consequently, many computer science students, perhaps the majority thereof, graduate without ever being exposed to such concepts. We argue that with the pervasiveness of dynamical systems and manifestation of their properties in the real world, these concepts should be introduced early on; in undergraduate studies in computer science and related fields, and perhaps even in high school. Available introductory courses demonstrate that only a minimal foundation of knowledge in mathematics is needed for the basic understanding of the key ideas. Such an introduction would deepen one’s understanding of the world and highlight important capabilities and limitations of mathematical and software tools for analysis, simulation, testing and verification of complex systems. In turn, this can lead to enhancement and enrichment of languages, tools and methodologies for dealing with dynamical systems, and of research in computer science and software engineering in general.