At its heart, mathematics is a process of discovery. In this course, you will be introduced to the joys and challenges of mathematical discovery in a setting of accessible and engaging topics. Students will learn how to approach mathematical questions in a logical and precise way, and how to formulate and explore questions of their own. The choice of topics varies, but includes elementary material from such areas as graph theory, Euclidean and non-Euclidean geometry, number theory, combinatorial games, knot theory, infinite sets, probability, and the theory of fair division.