Quantum Computing is often explained as some mysterious, mythical computer which can do anything because of “quantum weirdness.” Going beyond these vague and sometimes misleading descriptions, I’ll dive into the actual math/physics underlying the weirdness, and give some concrete examples showing what Quantum Computing can and cannot do. Topics will include unitary time evolution, quantum gates, the Deutsch algorithm, and if time permits the full Deutsch-Jozsa algorithm.

A mathematically rigorous introduction to general relativity, Einstein's legendary theory of gravity. This class will explore the motivation behind geometric curvature and its connection to gravity. Topics will include: the basic theory of manifolds and differential geometry, geodesics, the Einstein Field Equations, Black Holes, Gravitational Waves, and (time permitting) the cosmological constant and models of the universe. Get ready to learn about this beautifully geometric theory and the bizarre consequences of Einstein's elegant field equations connecting energy to space-time curvature, $$R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu} $$

This class will cover the basics of tensors without going deep into abstract definitions. We will then apply this to 4-vectors and special relativity - a topic made far more elegant by the introduction of tensors.

An intense introduction to the mathematics of relativistic quantum mechanics. This class will introduce Lorentz transformations, relativistic mass-energy, the Klien-Gordon equation (and why it fails), and finally the magnificent Dirac equation. We will show that the odd phenomenon of spin is a necessary consequence of including relativity in quantum mechanics.