2021 EXPO Honors Cross (Mathematics)

A Brief Introduction to the Calculus of Complex Valued Functions

Michael Cross | Mathematics | Sara Quinn
Honors Project

Abstract 

In this paper, I will discuss, show examples, and prove theorems related to the calculus of complex valued functions. Starting with the history of complex numbers, we will work through facts about the complex numbers as a set, facts about complex functions, limits and derivatives of those functions, and finally working up to the integration of complex valued functions. The motivation for this project is that the complex numbers were originally discarded as "impossible solutions" to cubic equations by Gerolamo Cardano in the 16th century. Yet, now the understanding of complex numbers is now crucial to understanding some of the most important unsolved problems in modern mathematics.

Presentation - Zoom (9:30 - 9:55 a.m.)

  • Zoom link: https://dom.zoom.us/j/99752595915
  • Meeting ID: 997 5259 5915

 

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