Bridge to Abstract Mathematics

Bridge to Abstract Mathematics is what it sounds like. This course is the bridge that leads to the level of thinking needed to learn, work with, and understand abstract math. The goal of this course is to prepare students for upper-level math courses that require abstract thinking and the ability to prove ideas by teaching them concepts of logic, strategies for proofs, and introductory ideas of many upper-level courses. The concepts learned in this course can then be applied to any area of math, including set theory, number theory, modern algebra, and real analysis.

We will start this section by going over the basics of set theory. Then, we will introduce relations along with two special types, equivalence and ordering relations. Next, we will look at a specific type of relation known as a function. We will look at what it means for functions to be one-to-one and onto and how to prove that a function possesses these characteristics. Finally, we will discuss cardinality and how this connects to finite and infinite sets. So, without further ado, let’s begin our discussion of some of the topics learned in Bridge to Abstract Mathematics.