The following is a list of my research publications. In most cases both the paper itself (in dvi format and/or pdf format) and a brief abstract (in text format) are available.
- Strongly sufficient sets and the distribution of arithmetic sequences in the $3x+1$ graph. (with Keenan Monks, Ken M. Monks, and Maria Monks) Discrete Mathematics, Volume 313, Issue 4, 28 February 2013, Pages 468-489.
- A Category of Topological Spaces Classifying Acyclic Set Theoretic Dynamics – submitted
- The Autoconjugacy of the 3x+1 Function– (with J. Yazinski) – Discrete Mathematics, 275, (2004) pp 219-236
- 3x+1 minus the +, Discrete Mathematics and Theoretical Computer Science, 5, no. 1, (2002), 47-54
- Groebner Bases and the Cohomology of Grassmann Manifolds with Application to Immersion, Bol. Soc. Mat. Mexicana (3) 7 (2001) no. 1, 123-136
- Change of basis, monomial relations, and bases for the Steenrod algebra, Journal of Pure and Applied Algebra, 125 (1998) 235-260
- The Nilpotence Height of $P_t^s$, Proc. Amer. Math. Soc., 124 (4), April (1996) 1297-1303
- Polynomial Modules Over the Steenrod Algebra and Conjugation in the Milnor Basis, Proc. Amer. Math. Soc., 122 (2), October (1994) 625-634
- Nilpotence in the Steenrod Algebra, Boletin de la Sociedad Matematica Mexicana (special edition in honor of Jose Adem), 37 (1992) 401-416
- Nilpotence and Torsion in the Cohomology of the Steenrod Algebra, Trans. Amer. Math. Soc. 333 (2), October (1992) 903-912
- h0-torsion bounds in the cohomology of the Steenrod algebra, Proc. Amer. Math. Soc. 114 (1992) 5-9
- From Formal to Expository: Using the Proof-Checking Word Processor Lurch to Teach Proof-Writing (with Nathan Carter, in Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing Across the Curriculum, eds. Schwell, Steurer, and Vasquez, MAA Notes 85 (2016), ISBN 978-0-88385-195-1
- Lurch: a word processor that can grade students’ proofs. (with Nathan Carter) Proceedings of the Work in Progress session, CICM 2013, Bath, UK, July 9-10. Lange, et al. editors.
- Lurch: a word processor built on OpenMath that can check mathematical reasoning. (with Nathan Carter) Proceedings of the OpenMath Workshop, CICM 2013, Bath, UK, July 9-10. Lange, et al. editors.
- Integral-Free Antiderivatives – preprint
- Fractal Themes at Every Level – in Fractals, Graphics, and Mathematics Education, edited by M. Frame and B. Mandelbrot, MAA Press, (2002), ISBN: 0-88385-1695
Slides from Selected Professional Talks
- Talk slides and supporting materials – are available for some professional talks I have given.
Mathematical Images in Print
- The Pharaoh’s Breastplate – an image I produced for the cover of Multifractals and 1/f Noise by Benoit Mandelbrot.
- Mandelbrot Zooms – images of the Mandlebrot set that appear on the cover of and inside The Nature and Power of Mathematics by Don Davis.
- Special Session on Homotopy Theory (in Honor of Donald M. Davis’s and Martin Bendersky’s 60th Birthdays) 2005 Spring AMS Eastern Sectional Meeting Newark, DE, April 2-3, 2005