Welcome!

Proof is the language of higher mathematics; it is the art of logically deducing new properties of some kind of mathematical object or system from ones we are more familiar with.  All of advanced theoretical mathematics is built by proving successively less obvious things about such an object and in doing so understanding it more deeply.

The main goal of this course is to learn what constitutes a proof, how to write one, and how to communicate mathematical ideas rigorously. To do so, we will mostly be thinking about basic properties of numbers, sets, and functions, but we may also see some more advanced topics.