Proofs form the core of mathematics – they are how we know what mathematics claims are true or false. In this course, we are going to develop our ability to come up with proofs, write proofs, and analyse proofs.
We will start at the beginning, assuming no formal prerequisite knowledge beyond just general exposure and an interest in mathematics. We will start with basic ideas of logic and inference that allow us to write down our first compelling proofs. As we build up our mathematical sophistication, we will see proofs in contexts like set theory and number theory, and develop a range of proof techniques. We will wrestle with ideas of infinity and finally close out the course by exploring some of Dr. Trefor’s favourite proofs in multiple areas of mathematics.
A proof needs to be logical and rigorous so we can be completely convinced that it demonstrates a mathematical fact. But coming up with proofs also takes creativity and inspiration, writing proofs can be a joyful experience, and the proofs can have a beauty to them.