UWEC CERCA 2026

This talk provides a broad introduction to Fourier series and Fourier analysis, concepts first introduced in the early nineteenth century by Joseph Fourier. We will explore the central idea behind Fourier methods: representing complex functions as sums of simpler trigonometric components. The presentation will briefly discuss the historical origins of these ideas, the basic mathematical framework, and how Fourier methods are used today. Along the way, we will highlight examples of applications in areas such as signal processing, engineering, and applied mathematics. This talk is intended as a short crash course that gives an overview of the ideas and why they are so widely used.