"On the Convergence of Ergodic Averages Over Zero Density Sequences in Topological Dynamics."  

Advisor - Isak Kornfeld

Most people continue their masters research when they begin work on a PhD.  I changed to Ergodic theory for my dissertation research.   This was a hard  transition because, in the words of one of my professors, "When you study discrete mathematics you become indiscrete."  Ergodic theory uses a little of everything; real analysis, complex analysis, algebra, topology, number theory and geometry.

"On Certain Generalizations of of Ramanujan's Trigonometrical Sum and Their Relation to Mobius Inversion."  

Advisor - Kenneth Johnson

This was a great opportunity to study a number of arithmetic functions and to see how the concept of partial ordering is fundamental to the interpretation of some classic theorems.