While in simple mechanics all answers are finite, even in classical electrodynamics one encounters perilous infinities that seem to plague the mathematical consistency of our physical world. In this class we will explore these, mostly focusing on the infinity that appears in the Casimir effect. We'll show you how to get rid of them when they're bugging you, but we'll also develop an intuition for why they occur and give a precise meaning to why some people claim the seemingly false identity $$1+2+3+4+... = \frac{-1}{12}$$. If we have time we'll also talk about why physicists like to work in dimensions really close to 4, but not 4.

While in simple mechanics all answers are finite, even in classical electrodynamics one encounters perilous infinities that seem to plague the mathematical consistency of our physical world. In this class we will explore the different infinites arising in thermodynamics, quantum field theory, and string theory. We'll show you how to get rid of them when they're bugging you, but we'll also develop an intuition for why they occur and give a precise meaning to why some people claim the seemingly false identity $1+2+3+4+... = \frac{-1}{12}$. If we have time we'll also take detours to talk about how quantum mechanics takes away our symmetries and why physicists like to work in dimensions really close to 4, but not 4.

Come act like a real scientist and practice the subtle art of making conclusions with little/no actual data! We'll go a bit into the idea of Fermi Estimation and back-of-the-envelope-calculations, then do some mild examples and then some (hopefully fun and challenging) examples.

We'll explore the appearance of infinities in physical calculations and how to interpret them, as clearly nothing we measure is *Actually Infinite*. So something must be wrong when we calculate answers and get infinitely large values! As a result physicists have developed a bunch of methods to deal with these infinities, and interpretations of how/why they arise. In this class we'll figure out why these infinities tend to pop up and why they don't influence anything we measure. Along the way we'll understand the often quoted result: $$1+2+3+4+5+....=-1/12$$ and how it relates to the Riemann Zeta Function and the distribution of prime numbers. We'll also explore the idea of non-integer dimensions and how we can use them to deal with infinite integrals.

In this class we'll look at some clever manipulations that make infinite sums behave as if they are finite. Take for example: $$x = 1+2+4+8+...$$ $$x = 1+2(1+2+4+8+...)$$ $$x = 1+2x$$ $$x = -1$$ We will discuss the validity of these manipulations and also put them to use to gain insight into problems. In particular we will use the formal sum $$1+2+3+4+...=-1/12$$ to find the force on two parallel conducting plates due to quantum effects. This application will hopefully give some intuitive meaning to what these sums mean.