Over the next few months I will be posting about many of the independent projects and research projects I did as an undergraduate. They range from metabolic models to full process designs and cover a diverse selection of chemical engineering principles, several with significant real world applications. Starting things off will be a walk through of a proof I wrote in response to a test grade I did not agree with and how the results of the proof may be used both to simplify and enhance a graphical method for predicting distillation column behavior. This proof will be the basis for a paper I will be writing on the subject as well.