Research - I received my Ph.D. from the University of Pittsburgh in 2002. My thesis title is "Fatou, Julia and Mandelbrot Sets for Functions with Non-Integer Exponent." It is available as a PDF file by email. My article called, "Fractals for functions with rational exponent", appeared in the journal Computers and Graphics, volume 28, number 4, published by Elsevier. The article can be viewed through the Science Direct website (institutional membership required - email me for a copy).
My second article, “Difficulties in Complex Multiplication and Exponentiation” can be found in the Cornell University Electronic pre-print server. The direct link to this paper is here. This paper was the subject of a talk at the 75th MAA Allegheny Mountain Section meeting at the University of Pittsburgh in 2008, and led to another talk with a student (Justin Ryan) and the 2010 Section meeting in Johnstown, PA. The (zipped) slideshow from that presentation can be found here, and the computer code that generated the images is available here. I am currently revising a paper discussing these results and post more information about it after submission.
I was asked to
participate in some "Harry Potter" parties here at school, so I went
as the only math professor mentioned in the books, Professor Vector.
Unfortunately, Professor Vector is a witch, so I went in a dress (It's a horrid
visual - you have
been warned!) I did also include a "Harry Potter" problem on several
exams in my algebra courses. I have it as a PDF file for your enjoyment. What is the value of