"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.