Welcome to Princeton Splash, a studentrun organization at Princeton University 
ESP Biography
DAVID HERRERA, Princeton junior studying mathematics.
Major: Mathematics College/Employer: Princeton Year of Graduation: 2017 

Brief Biographical Sketch:
It's a long story. Short version: Slightly longer version: Even still longer version: Past Classes(Look at the class archive for more.)Finite Sums in Splash Spring 16
The class will be on finite sums. The goal is to develop some of the tools of "finite calculus"/"discrete calculus" which is a very elementary (meaning that you kinda just need to know algebra to do it) method of calculating sums.
First, we will discuss sequences and finite sums with sigma notation. Then we will go over the discrete derivative and discuss the relationship between it and finite summation which is basically the discrete integral. Then we will discuss induction and calculate a few sums using induction and the "standard tricks" that one learns in high school for calculating the arithmetic or geometric series. Then we will look at these calculations from the viewpoint of discrete calculus, discuss how to calculate the series $$\sum_{k=1}^{n}k^\ell$$ for any integral $$\ell \geq 1$$ and prove that the series of any polynomial is another polynomial whose leading term (the term with the highest degree) is easy to calculate.
My goals for this is for it to be interesting and accessible for high school level students yet pushing toward some of the skills used in proofbased college level math courses.
