What is computation? This is the question that birthed Computer Science as a discipline, and serves as the focal point of this course. Our plan for answering it is twofold. First, we will introduce functional programming through Scheme (a dialect of Lisp). Second, we will use our understanding of functional programming to explore the nature of computation itself. This will involve reading parts of Alonzo Church’s revolutionary article, “An Unsolvable Problem of Elementary Number Theory.” We will see how the notion of computation emerges from his understanding of functions, and engage with the fundamental conjecture of Computer Science (the Church-Turing Thesis).

Embark on a deeper exploration of computer science, where the focus shifts from programming and foundations of computer science, to the intricacies of algorithms and their real-world applications. This course reinforces and builds upon the concepts introduced in Introduction to CS 1, and provides an introduction to algorithm design, data analysis, and the practical application of computational techniques.

This is not your typical class in computer science, or in formal logic; but you will learn a lot about both by taking it. Our subject will be one of the most important and influential papers that has ever been written—“On Computable Numbers, with an Application to the Entscheidungsproblem,” by Alan Turing. This is the paper that birthed computer science as a discipline. Understanding it requires that you be comfortable with some mathematical concepts (powers and roots) and with thinking abstractly; but the most important prerequisite for understanding this paper is determination. What is the best way to characterize Turing’s paper? Simple. It changed the world.