Welcome to Princeton Splash, a student-run organization at Princeton University

# ESP Biography

## DAVID HERRERA, Princeton junior studying mathematics.

Major: Mathematics

College/Employer: Princeton

## Brief Biographical Sketch:

It's a long story.
I mean, of course it is.

Short version:
I was born. I am still alive.

Slightly longer version:
When I started attending Princeton, I had just started and now I am still going here.
Like an eagle thrown out of the nest for it to learn to fly, I took the introductory math-sequence here in my freshman year and now I am on my second year of helping out with those courses as a course assistant, which I find fun and interesting since I get to see interesting problems and work on/think about them in a new light along with helping run problem and review sessions (helping people learn), which is why I am going to teach a class here, because I enjoy it.
I like reading about math and finding interesting things and the topic I am presenting this year is one of those things I saw and thought was interesting.
I am interested in various mathematical and computer science related things, but particularly in analysis (which is like calculus, but a lot more), topology (like geometry, but kicked up a notch), and algorithms (which describe the process of solving a problem). My class this year is closer to the first and last topics.
I do not know what I am going to do when I graduate, but it might have something to do with what I should be doing now: working on my problem set and finding summer math research programs to apply to.

Even still longer version:
[Insert Book].

## 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 proof-based college level math courses.