The papers and dissertation below explore exotic topologies on Topological Vector Spaces. The 1995 paper and thesis resolved a question first posed in the early 1970's.
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Jan Jaworowski, Nguyen To Nhu, Nguyen Nhuy, and Pham Quang Trinh, "Rigid Spaces and the AR-Property", Tsukuba Journal of Mathematics 25 (2001), no. 2, 413–442.
- Nguyen To Nhu and Paul Sisson,
"A Rigid Space Homeomorphic to Hilbert
Space,"
Proceedings of the American Mathematical Society 126 (1998), no. 1, 85–95.
- Paul Sisson, "A Rigid Space Admitting Compact Operators,"
Studia Mathematica 112 (1995), no. 1, 137–147.
- Compact Operators on Trivial-Dual Spaces. PhD Thesis, University of
South Carolina, 1993.
The following paper uses techniques from
differential geometry and analysis to arrive at a surprisingly simple
answer to a question that can be understood by a general audience.
- Ralph Howard and Paul Sisson,
"Capturing the Origin with Random Points: Generalizations of a Putnam Problem," College Mathematics Journal 27 (1996), no. 3,
186–192.
More recently, involvement with Mathematica and a look at the notorious Collatz Problem (through the lens of complex numbers) led to many irresistible images. These, in turn, led to irresistible involvement with students, including a class devoted to mathematical art and complex variables, an HP Technology for Teaching Grant, and a
gallery showing the work of the students. Some of this, and some technical aspects of making the pictures, is described in the article below.
- Fractal Art Using Variations on Escape Time Algorithms in the Complex Plane, Journal of Mathematics and the Arts 1 (2007), no. 1, 41–45.
After a few years of teaching calculus and precalculus, it seemed easier to write a textbook than to adapt to the texts of others. The following have since been in use at LSUS and are gaining popularity at other schools.
- Precalculus, Hawkes Publishing, 2006 (ISBN 0-918091-89-6).
- College Algebra, 2nd ed., Hawkes Publishing, 2008 (ISBN 1-932628-27-4).
Here are other assorted mathematical thoughts that found their way into print.
- Michael Avidon, Richard Mabry, and Paul Sisson, "Row Enumeration of Three Species", Mathematics Magazine 74 (2001), no. 2, 130–134.
- Paul Sisson, "Polynomials of Arbitrarily High Degree, Descartes’ Rule of Signs, and the
Calculation of Effective Rate of Return", Proceedings of the Spring 2000 LA/MS MAA Meeting.
- Paul Sisson, "The Ratio of Volume to Surface Area" (solution to Problem 10352), American Mathematical Monthly 104 (1997), no. 1, 80–81.
- Paul Sisson, "Integrating Calculus and Algebra to the Benefit of Both", Proceedings of the 10th International Conference on Technology in Collegiate Mathematics, 1997.