Splash Biography

From light diffracting into rainbows and tectonic plates shearing into earthquakes, to black holes generating gravitational waves in the fabric of spacetime — Despite how different these phenomena may seem at first, with the magic of calculus, they can all be reduced to one simple type of equation. In this class, we will dive into the general theory of wave propagation, also known as the theory of linear, homogeneous differential equations. We will use these equations to examine both fundamental physics — light waves in electromagnetism, matter waves in quantum mechanics, and gravitational waves in general relativity — as well as emergent phenomena in the macroscopic world — shear waves, sound waves, and water waves.

How can we describe the way populations, chemical reactions, or infectious diseases evolve over time? Can we use this to come up with a way to predict how these systems will behave? In this class, we will dive into the essence of calculus, the tool that allows us to work towards answering such questions. From physics to economics and biology to chemistry, calculus permeates nearly every aspect of the world around us. We will start by introducing the fundamental concepts of limits and derivatives, then focus on modeling the physical world using differential equations, which gives us a way of relating different variables. Whether you are interested in understanding the language of the universe or just looking to sharpen your mathematical skills, this class will equip you with the necessary tools to solve problems across different disciplines!

Ever wanted to make an animated film? This class will teach you the basics! Available animation software: - Wick Editor (https://www.wickeditor.com), free, works for all computers, including Chromebooks - Krita (https://krita.org), free, works for Windows, MacOS, and Linux - Adobe Animate, paid, works for Windows and MacOS I will teach using Wick Editor since it's the most accessible for everyone. However, you are welcome to install Krita or Adobe Animate on your computer and bring it to class. The workflow is similar for all of them.

An gentle introduction to tensors, the mathematical objects whose implicit weaving of space and time serves as the framework to build the theories of special and general relativity.

Five decades ago, the Big Bang theory faced a crisis: Compared to its predictions of how the universe began, actual large-scale observations showed that our universe is, in a sense, too boring — Its density is too "uniform", its shape too "flat", and its magnetic monopoles? seemingly nonexistent! What resolved this crisis came to revolutionize the field of theoretical cosmology. This course will start off by deriving a model of our expanding universe from some basic principles of introductory physics. Applying this model to real-world data, we will discover for ourselves the aforementioned paradoxes. Then, in the second hour, we will introduce the theory of inflationary cosmology: its physics are too complex to derive, but we can glean from simple approximations how it is able to resolve these paradoxes, and make new predictions about our universe.

How do video games and 3D animations look so real? An introduction to the physics, then the code, of raytracing and raymarching algorithms.

In the early 20th century, physicists made a surprising discovery: light appear to travel at the same speed in space no matter how fast you are moving. From this seemingly paradoxical observation, and a little bit of geometry, we present a derivation for the basics of Einstein's theory of special relativity.