Set Theory

Set Theory is a math course in the CTY program. It requires previous enrollment outside of CTY in Geometry. Its course code is SETM, and it is offered at Lancaster both sessions and Los Angeles second session only.

Course Description

From the CTY course catalog:

In the town of Seville, there is a male barber who shaves all men, and only those men, who do not shave themselves. Does the barber shave himself? This is an applied form of Russell's paradox, which served as a crucial turning point in the development of set theory.

Just as atoms are fundamental to the study of matter, sets may be viewed as the building blocks of mathematics. A set is a collection of objects, and set theory studies the properties of sets and their relationships. Despite this seemingly simple subject matter, set theory is a vibrant branch of mathematics, as well as its most common foundation.

In this course, students move beyond the use of formulas and equations and into the realm of proof as they examine the essential components of set theory, such as functions, relations, and orderings. They explore cardinality, learning how one infinite set can be larger than another. By the end of the class, students consider complex topics in set theory, such as the axiom of choice, transfinite arithmetic, and the continuum hypothesis.

Students leave the course with not only a razor-sharp understanding of the central concepts of set theory and an enriched mathematical vocabulary, but also a firm foundation for advanced exploration in all branches of mathematics.

Class History

Set Theory is a new class for 2009; as such, no history is currently in existence. Details should surface after this summer's sessions.