Upper School Intersession 2025

How many ways can you make $0.97 from quarters, dimes, nickels and pennies?
How can you derive a closed-form formula for the sum of the first n squares or cubes? Or for the n-th Fibonacci number?

These all sound like inherently discrete counting problems--yet there are ideas from the realm of continuous functions, which have an essentially non-discrete, infinite character, that can be used to solve them. We'll explore generating functions, which encode solutions in polynomials, and touch on finite calculus, which extends ideas of calculus to the discrete realm.

Prerequisites: most of the class will just use ideas through precalculus, but familiarity with basic derivatives and integrals will be helpful for the last part of the class.