Splash Biography

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.