2006 Section Meeting

Invited talks

Aparna Higgins, University of Dayton

Demonic Graphs and Undergraduate Research

Abstract: My work with undergraduates on mathematical research has been one of the most satisfying aspects of my teaching career. This talk will highlight some of the beauty and depth of the research done by my former undergraduate students on line graphs and pebbling on graphs. We will consider iterated line graphs, some pioneering results in pebbling graphs, and pebbling numbers of line graphs. The results of some of the later students built on work done by the earlier ones, and have spawned some of my own recent research.

Carl Pomerance, Dartmouth College

Primal Screens

Abstract: Prime numbers, the very building blocks of the integers, remain an enigma. Yet we make progress in our quest to understand these very basic objects. This non-stressful talk will highlight recent progress and some of the many problems that are still unsolved.

Jim Reynolds, Clarion University

Equal Areas, Apple Orchards, and Fun with The Fundamental Theorem

Abstract: One part of the Fundamental Theorem of Calculus states conditions about the differentiability of functions defined as the integral (with respect to t) of f(t) from t=a to t=x. Because many students' first impression of this result is that it is abstract and useless, problems that utilize it in unexpected ways have always been favorites of mine.This presentation deals with two such problems.

One problem starts with functions g(x)=kx^n and h(x)=x^n with n>0 and k>1 then seeks to determine a function y=f(x) (passing through the origin) such that for any Quadrant I point P on g(x) the area bounded by g, h, and the vertical line through P is always equal to the area bounded by f, g and the horizontal line through P. The other problem looks at a typical yield function Y(t), in tons per year, for an apple orchard and considers when the orchard should be replanted.