# Dr. David Hecker

I have taught at St. Joseph's University since Fall 1980. I received my Ph.D. in mathematics from Rutgers University in Spring 1981.

## Office Hours

My office is in Room 236 of the Barbelin Building. My office phone number is (610) 660 - 1560. I will be on sabbatical in Fall 2012, and so will not be available.

## Courses

I teach a wide variety of the mathematics courses that the department offers.

## Research and Publications

My Ph.D. dissertation involves characterizing the conditions under which an operator within a certain class of psuedodifferential operators is subelliptic (a topic in partial differential equations).

I co-authored an article with William J. Sweeney (Rutgers University), my thesis advisor, that was published in the Feb. 1986 issue of the Journal of Differential Equations, entitled "Subelliptic Estimates for Certain Complexes of Psuedodifferential Operators", which was an extension of the results in my dissertation.

I also co-authored an article with Ranan Banerji (St. Joseph's University) that was published in the Sept. 1985 issue of Mathematics Magazine entitled "The Slice Group in Rubik's Cube". This article uses Rubik’s cube to discuss several topics covered in an undergraduate abstract algebra course, and could be used as enrichment material for such a course.

Ranan Banerji and I, and several other department members, have been playing with the 3n+1 problem in our spare time. This problem involves a conjecture regarding the following function: f(n)=3n+1 if n is odd, and f(n)=n/2 if n is even. The conjecture states that, if k is any positive integer, than some iterate of k under f (that is, f(k), f(f(k)), f(f(f(k))), ...) will equal 1. The conjecture is still an open problem. Computers have been used to search for counterexamples up to very high values for k with no success. We have some partial results and are looking for the appropriate journal in which to publish them. (Ranan Banerji has already published some earlier partial results on this problem.)  For a preview of our joint paper,  click here .

I have written an article describing how to use a straightedge and compass in the Euclidean plane to draw a "line" in the Poincare disk model for hyperbolic geometry. This appeared in the November 2003 edition of the College Mathematics Journal.

I published a joint paper with Dr. Deborah Lurie on using least squares to solve for eigenvectors. The article, “Using Least-Squares to Find an Appropximate Eigenvector” appeared in the Electronic Jouranal of Linear Algebra, Volume 16, pp. 99-110, March 2007.

In 1984, I began working with Stephen Andrilli (LaSalle University) on a textbook for a course in linear algebra. The manuscript was completed in 1992, and published in Spring 1993. In 1997, we received the copyright back from our publisher. We published a second edition (January 1999) with our new publisher, Academic Press.  In Spring 2002 we began working on revising the second edition. The third edition appeared in 2003. We have since revised that, and a fourth edition of Elementary Linear Algebra is now available from Elsevier/Academic Press.

Last Updated: 7/31/2012