Monday, November 12, 2012

Beyond High School Science Fairs: The Senior Capstone Project

On October 31, 2012, I was invited to speak in the University of Findlay (OH) Mathematics Colloquium. The title of my talk was "Beyond High School Science Fairs: The Senior Capstone Project". The talk was 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 I tried to address: 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").  I suppose 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, and in the sense of freedom implicit in this act.

Monday, November 5, 2012

A nice picture

A nice "Paley digraph" picture - with outgoing edges from x to x+1, x+2, x+3, x+4, x+6, x+8, x+9, x+12, x+13, x+16 and x+18 (modulo 23) for x = 0,1,...,22.