Undergraduate Projects

“Number Theory: The Queen of Mathematics”, explores the idea that Number theory is not limited to simple investigation of numerical arithmetic, nor abstract mathematical considerations, but also may be used to contextualise the analysis of thought and meaning in general, in addition to having direct applications to the real world. I begin by covering some well-known properties of Integer Arithmetic, and prove the Chinese remainder theorem for co-prime moduli. I go on to explore how philosophical concepts may be analysed from a mathematical standpoint, using the necessity to order symbols for meaningful communication to demonstrate a possible foundation for a “mathematical philosophy”. Here, the Chinese remainder theorem may be used as an analogy for how we may piece together novel concepts from earlier ones. This leads into explorations in abstract algebra and ideals, with the “theoretical” portion of the report culminating in proving the Chinese remainder theorem for ideals. Finally, I outline an application of Number theory in modelling biochemical reaction systems, with a focus on the Chinese remainder theorem. Using formal mathematical notation, intuitionist logic, and the presentation of an application, I demonstrate that Number theory truly is the Queen of Mathematics.