# Splash Biography

## MICHAEL FRIM, ESP Teacher

Major: Not available.

College/Employer: Not available.

## Brief Biographical Sketch:

Michael Frim is currently a sophomore at Harvard College studying archaeology and physics.

## Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M573: Euler's Identity in Rainstorm Fall 2020 (Dec. 05 - 06, 2020)
We are going to be deriving what has been described as the most beautiful theorem in mathematics: Euler's identity. A simple one-line equation that elegantly relates $$e,i,\pi,1,$$ and $$0$$, five fundamental constants of the universe. We will start by deriving the general form of Taylor expansion. We will then expand into the realm of complex numbers to see the beauty of the universe come alive. If time allows, we will discuss some of the applications of Euler's identity, from differential equations to quantum mechanics.

S106: Calculating the Speed of Light: the Electromagnetic Wave Equation in Rainstorm Spring 2020 (May. 30 - 31, 2020)
We will derive the general wave equation using Newton's Second Law, generalize it to 3 dimension, and from there find the electromagnetic wave equation. From this, the speed of electromagnetic waves can easily be found. Since light is an electromagnetic wave, we will have calculated the speed of light.

M107: Euler's Identity in Rainstorm Spring 2020 (May. 30 - 31, 2020)
We will first explore Taylor expansions and calculate some examples of Taylor series using sine, cosine, and $$e^x$$. Then, we will expand into the realm of complex numbers and understand exactly how the fundamental constants of mathematics $$e, i, \pi, 1, \text{ and } 0$$ are all interrelated.