Publications
The following is a list of my publications and preprints. In most cases both the paper itself and a brief abstract are available. They are grouped roughly by topic, but some papers fit into more than one category.
Algebraic Topology
- Monks, Kenneth G., Groebner Bases and the Cohomology of Grassmann Manifolds with Application to Immersion, Bol. Soc. Mat. Mexicana (3) 7 (2001) no. 1, 123-136
- Monks, Kenneth G., Change of basis, monomial relations, and bases for the Steenrod algebra, Journal of Pure and Applied Algebra, 125 (1998) 235-260
- Monks, Kenneth G., The Nilpotence Height of $P_t^s$, Proc. Amer. Math. Soc., 124 (4), April (1996) 1297-1303
- Monks, Kenneth G., Polynomial Modules Over the Steenrod Algebra and Conjugation in the Milnor Basis, Proc. Amer. Math. Soc., 122 (2), October (1994) 625-634
- Monks, Kenneth G., Nilpotence in the Steenrod Algebra, Boletin de la Sociedad Matematica Mexicana (special edition in honor of Jose Adem), 37 (1992) 401-416
- Monks, Kenneth G., Nilpotence and Torsion in the Cohomology of the Steenrod Algebra, Trans. Amer. Math. Soc. 333 (2), October (1992) 903-912
- Monks, Kenneth G., $h_0$-torsion bounds in the cohomology of the Steenrod algebra, Proc. Amer. Math. Soc. 114 (1992) 5-9
- Monks, Kenneth G., A Category of Topological Spaces Classifying Acyclic Set Theoretic Dynamics – preprint
Dynamical Systems and the Collatz Conjecture
- Monks, Monks, Monks, and Monks, 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.
- Monks, Kenneth G. and Yazinski, Jonathan, The Autoconjugacy of the 3x+1 Function, Discrete Mathematics, 275, (2004) pp 219-236
- Monks, Kenneth G., 3x+1 minus the +, Discrete Mathematics and Theoretical Computer Science, 5, no. 1, (2002), 47-54
- Monks, Kenneth G., A Category of Topological Spaces Classifying Acyclic Set Theoretic Dynamics – preprint
Combinatorics
Lurch
- Carter, Nathan C. and Monks, Kenneth G., A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics. Proceedings of CICM 2017, eds. Herman Geuvers and Jacques Fleuriot, Springer Lecture Notes in Artificial Intelligence (LNAI 10383) (2017).
- Carter, Nathan C. and Monks, Kenneth G. From Formal to Expository: Using the Proof-Checking Word Processor Lurch to Teach Proof-Writing 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
- Carter, Nathan C. and Monks, Kenneth G., Lurch: a word processor that can grade students’ proofs. Proceedings of the Work in Progress session, CICM 2013, Bath, UK, July 9-10. Lange, et al. editors.
- Carter, Nathan C. and Monks, Kenneth G., Lurch: a word processor built on OpenMath that can check mathematical reasoning. Proceedings of the OpenMath Workshop, CICM 2013, Bath, UK, July 9-10. Lange, et al. editors.
Teaching
- Carter, Nathan C. and Monks, Kenneth G., 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
- Monks, Kenneth G., 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
- Integral-Free Antiderivatives – preprint
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.