### Research Publications

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*h*, Proc. Amer. Math. Soc. 114 (1992) 5-9_{0}-torsion bounds in the cohomology of the Steenrod algebra

### Other Publications

*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.

### Conferences Organized

- 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