We start by building intuition and proving formulae for Fourier series as well as the Fourier transformation and the Fourier inversion theorem. We then use our intuition to generalize our notion of the Fourier transform. Then, we delve into the numerous applications of the Fourier transform, including solving differential equations, signal processing, and the Riemann-Zeta function. We culminate with an exploration of the fundamentality of the Fourier transform to the Uncertainty Principle and Quantum Field Theory.

We will start with an altogether too fast introduction to Lagrangian and Hamiltonian Mechanics (poetry for physicists would be a good class to take for a more in depth presentation). Then, we will explore the movement from classical to quantum theory under what the process of canonical quantization. Using canonical quantization, we will "prove" Schrodinger's equation and work out some simple problems in quantum mechanics. We will demonstrate how to derive the uncertainty principle and how it is hidden within classical mechanics itself. Finally, if time permitting, we will extend our notion of quantization to quantum field theory.

In the past couple years, the "flat earth" conspiracy theory has seen a rise in publicity. In a way, this theory is actually true! Locally, the Earth is "the same" as a flat plane. In this class, we will introduce students to concepts of topology, continuity, homeomorphism, and finally define and give numerous examples of manifolds.

We start by building intuition and proving formulae for Fourier series as well as the Fourier transformation and the Fourier inversion theorem. We then use our intuition to generalize our notion of the Fourier transform. Then, we delve into the numerous applications of the Fourier transform, including solving differential equations, signal processing, and the Riemann-Zeta function. We culminate with an exploration of the fundamentality of the Fourier transform to the Uncertainty Principle and Quantum Field Theory.