This article provides an impresssive mathematical basis for optimizing communications fidelity. Shannon builds his case very clearly, which can serve as a model for mathematical theory building. The resource material does an excellent job of distinguishing between the technical problem of delivering a message and the problem of understanding what a message means. This step allowed engineering discipline to focus on the message delivery system. With this in mind, it successfully solved problems for a very abstract (thus widely applicable) model of a communication system that includes both discrete (digital) and continuous (analog) systems. This is a clear demonstration and reinforces the core concepts and relationships between each other. The material includes examples of real-life situations that can be used as prompts for assignments. The resource material is easily integrated into the discipline's current curriculum and pedagogy. Finally, it provides a comprehensive guide to mathematical theory of communication, allowing students/professionals to gain knowledge quickly and easily apply it to academic work or any field of specialization. Even without much mathematical knowledge, students are likely to be impressed with the deep analysis of communications failure -- and optimization.