# ESP Biography

## NOAH MILLER, Columbia University senior studying physics

Major: Physics/Math

College/Employer: Columbia University

Year of Graduation: 2018

## Brief Biographical Sketch:

Noah Miller is primarily interested in the the intersection of math and physics. And what an intersection!

## Past Classes

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

S658: Special Relativity in Splash Spring 18 (Mar. 31, 2018)
In this class, I'll cover the basics of Einstein's theory of special relativity! (That's the theory of light, space, and time. Not the one about gravity, that's general relativity.)

S659: Superfluid Helium in Splash Spring 18 (Mar. 31, 2018)
I probably shouldn't teach this class, but what the heck. I'll try to explain some of the awesome properties of super fluid helium starting from first principles. It's a liquid at absolute zero, for starts, and can flow without any viscosity! And that's not even mentioning the quantized vortex lines... If you know about calculus and complex numbers, that'd be very helpful. I don't expect you to know quantum mechanics, but that would awesome if you did. Hopefully this course should be fun, but take it at your own risk.

S593: What is quantum mechanical spin? in Splash Fall 2017 (Nov. 04, 2017)
What's the deal with spin? How can an electron only be "spin up" or "spin down" when space is three dimensional? In this class we will cut past the confusing analogies and jump right into the math! We'll talk about spin states, SchrÃ¶dinger's equation, Pauli matrices, and the dank topology lurking right beneath the surface! Bring paper and pencils!

M320: Crash Course in Calculus in Splash Splash Fall 2015 (Nov. 14, 2015)
If there's one branch of math to know, it's calculus. Its beauty and applicability is so insane that it's not even worth discussing. Most people, however, fear it as if the subject is hard: it is not. Calculus, very simply, answer two questions: what is the slope of a tangent line to a graph, and what is the area under a graph? These two questions are intimately linked, and will be explored accessibly in great detail during this class. I plan to cover the essentials of a full year senior calculus course in a way accessible to anyone (with the prerequisites). I will also prove Euler's Identity (e^ix = cos x + i sin x)

M243: The Calculus Of Variations - Minimization / Maximization Principles in Physics in Splash Spring 2015 (Apr. 18, 2015)
What do optics, classical mechanics, relativistic mechanics, and quantum mechanics all have to do with each other? They can all be expressed elegantly using the Calculus of Variations! What is that, you ask? Well, what's the shape of a rope hanging from 2 endpoints? It's the curve that minimizes the gravitational potential energy, but how do you calculate that shape? This course will discuss the mathematics necessary to solve questions like that, and explain the minimization principles that unite seemingly disparate branches of physics. This isn't your grandpa's calculus!