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Hi everyone! I want to thank Tom Lee for inviting me to join the MaplePrimes community. I feel very enthusiastic about the creative potential of this wonderful collaborative resource and want to take a moment to introduce myself. My first blog post includes a brief biography and states some of my Maple plans and research goals. I completed my PhD in Applied Mathematics with an emphasis in Symbolic Computation at the University of Waterloo under the supervision of Keith O. Geddes in 2003. I'm now working with Prof. Geddes as a Postdoctoral Fellow in the School of Computer Science. Please don't be fooled by these clever disguises—applied mathematician, computer scientist—I'm really a pure mathematician at heart! In my PhD thesis, I invented the Geddes Series Scheme for the interpolation and approximation of multivariate functions, which I named in honor of my thesis supervisor. (I was inspired by the example of Bruno Buchberger, who invented Groebner bases in his PhD thesis and named them after his thesis supervisor.) In the years ahead, I look forward to developing and sharing many Maple worksheets, Maple packages, Maplet applications, and MapleNet demos which feature Geddes series expansions. I hope to accomplish two things by doing this:
  1. Geddes series expansions of multivariate functions have many interesting theoretical and computational properties. I want to help the mathematical community develop a hands-on understanding of these properties by providing guided interactive explorations in Maple.
  1. Geddes series are very powerful, versatile, accurate, and efficient. I want to demonstrate these strengths by showing how to use Geddes series in Maple to solve many different kinds of important and challenging problems in applied analysis.
For more detailed information about the Geddes Series Project, please see my formal Research Statement, which I have attached below as a PDF file. Feel free to contact me if you would like to know more about Geddes series and the many advantages they offer over traditional series expansions. With best wishes, Fred Chapman -- Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo http://www.scg.uwaterloo.ca/~fwchapman/
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