Gröbner bases: A Natural Extension of Gaussian Reduction and the Euclidean Algorithm

In this introduction to Gröbner  bases, we motivate their salient features by considering the Euclidean algorithm and Gaussian row reduction of matrices from a slightly different point of view.

Patrick Flinn received a Bachelor's Degree in mathematics from the University of Dayton, where an excellent faculty, and in particular Professor K.C. Schraut, prepared him for and inspired him to pursue a Ph.D. The latter was obtained in functional analysis at the Ohio State University, under the direction of Professor William Davis. Pat met his future wife, Barbara Brown, a brilliant mathematician who would earn her Ph.D. in complex analysis at the University of Michigan, while both were on fellowship at Cambridge University, England. Interestingly, Barb's father and Pat are from Sidney, Ohio, but Barb and Pat had to "cross the pond" to meet. While Barb was at the University of Texas in Austin on her postdoc and Pat was on the faculty of Texas A&M University, Bob Karkoska, a classmate of Pat's at both Dayton and Ohio State, and his new bride, stopped in Austin to visit on their honeymoon. Bob suggested a solution to the problem of finding collocated jobs for research mathematicians in a difficult job market for mathematicians: The National Security Agency (NSA). Now, twenty years later, Barb and Pat are senior cryptologic mathematicians at NSA, Pat running a division of 150 mathematicians, computer scientists, and engineers on the front line of cryptomathematical research and applications.

The Kenneth C. Schraut Memorial Lecture was established entirely with the generous support of alumni donations in memory of Dr. Kenneth C. Schraut. The Memorial Lecture was established for the purpose of sponsoring invited lectures by noted mathematicians for undergraduate students.