Title of the course: Counting past infinity: Ordinals and how to use them
Instructor’s Name: Asst. Prof. Burak Kaya
Institution: Middle East Technical University
Dates: 24-28 August 2020
Prerequisites: None
Level: Advanced undergraduate, beginning undergraduate
Abstract: In this course, we shall learn about ordinal numbers and how they are used in mathematics. In the first part of the course, we shall first introduce ordinal numbers, transfinite generalizations of induction and recursion, and ordinal arithmetic. In the second part of the course, we shall see how ordinals naturally appear in mathematics and how to use them to prove interesting theorems. For example, we shall prove Goodstein’s theorem, show the existence of Cantor-Bendixson rank of a Polish space, construct various pathological subsets of plane with special combinatorial properties.
Language: TR, EN