This is an invitation and an introduction to the fascinating world of knot theory: the study of knots. We discuss questions such as when two knots are the same and how hard it is to tell?. I will then describe some of the current research problems that are surprisingly easy to understand. Unlike the title seems to suggest, this will be a fun course for every student, and even more so if you look for mathematics in every thing you do.

The axiom of choice is deceivingly straightforward: "Let L be a collection of nonempty sets. Then we can choose a member from each set in that collection.". However this statement cannot be proved, or disproved and hence the name 'axiom'. While the axiom of choice seems intuitively true, it can lead to bizarre consequences, like the Banach Tarski Paradox which says you can break up a sphere into finitely many parts and re-glue them to form 2 spheres of the same size!. We look at other bizarre consequences in a world where this axiom is true. We then look at what could happen if it was not.

What is infinity? Can it be thought of as a number? If so, what is one added to infinity, or even infinity added to infinity? What happens when we add infinitely many numbers? If you think that these questions sound interesting, this is the class for you. We will discuss infinity, its types and connections with the cardinality of sets like the natural numbers and real numbers. We will briefly talk about infinite sums all through fun discussions and activities.