Structures in Mathematics

Mathematics is often motivated by and tries to model patterns that appear in real life. In this course, we will study the patterns that so often appear in mathematics itself. Motivated by The Joy of Abstraction by Eugenia Cheng, we will travel through some of the abstractions that math majors in college are introduced to. We will then look at various mathematical structures and the interesting and unexpected analogies between them. For example, a common theme is studying a specific type of mathematical object by considering appropriate functions between such objects (for example, studying sets by studying functions between them). We will try to move towards a theory of mathematical structures that provides a solid philosophical viewpoint about how we can think about mathematics as a whole.