You have one minute and an index card to write down the biggest number you can think of. We'll talk about Busy Beaver Numbers, Turing Machines, the Ackermann function, different sizes of infinity and other strange and interesting things. Then we'll play again. Who can name the bigger number? Inspired by Scott Aaronson's essay of the same name.

What's a good way to efficiently contain and describe an infinite sequence? What about as coefficients of a power series? We'll see some benefits of considering a sequence in this form. For example, we'll find a (relatively) simple expression for the terms of the Fibonacci sequence and other sequences. We'll also talk about how these expressions help us manipulate sequences that are otherwise hard to get a handle on. For example, how many ways can you write a positive integer as the sum of other positive integers, where order doesn't matter? Surprisingly, there's no (simple) great answer--but using generating functions, we can deal with them anyway!