Beyond High School Science Fairs: The Senior Capstone Project

The talk will be structured as an itinerary through a number of themes investigated in my undergraduate research projects (with an emphasis on quadratic residues and their applications to combinatorics, greater prime factor sequences and the relevant open problems in the area, etc). A difficult problem that is worth addressing: what exactly should be considered as a sign of authenticity for a genuine undergraduate research experience, what would make it more than a science fair project (where the emphasis lies - granted with notable exceptions - on contingent data manipulation, with mathematics playing a secondary, albeit cool, "supporting role").  Probably the answer has something to do with a serious dose of mathematical maturity reflected in a significant focus of action/intentionality on abstract objects, in an increased ability of “bracketing out” the contingent world in key moments, and in the sense of freedom implicit in this act.