Splash Biography

Heisenberg’s Uncertainty Principle tells us that some pairs of physical properties are fundamentally uncertain at the quantum scale. For example, if you try to confine a particle into a small space, quantum mechanics require you to simultaneously give up knowledge about the particle’s speed; Conversely, if you can measure the speed of a particle very precisely, your measurement apparatus has to become oblivious to its spatial position. We can prove this principle, as well as the general duality between position and momentum, with Fourier’s theory of wave analysis. In this class, we will gain an intuitive understanding of Fourier transforms and use them to understand why quantum uncertainty is unavoidable. By exploring the properties of waves and how to construct them, we will be able to unlock this strange, yet fundamental structure of reality.

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!

To what extent can we predict the behavior of systems? From population dynamics to fluid convection to an irregular heartbeat, there is a degree of uncertainty that prevents us from knowing the exact outcomes of these situations. This class will take you through some of the unsettling math of nonlinearity and bifurcation that unites these systems, setting the foundations for ideas in chaos theory.