This was an advanced topics course focusing on Prof. Toro's research specialty, Fourier analysis. The basis of Fourier analysis is that, using advanced calculus and infinite series, any smooth function can be recreated using combinations of sinusoidal and exponential functions. I appreciated the emphasis put on developing and proving why the technique works, and though challenging to prove Fourier convergence for any function of a given type, doing so made the process that much mroe enlightening and demonstrated how similar principles can be applied in other settings. We discussed some biomedical and chemical applications, which made the course that much more impactful for my future career.