Cook Papers

Bill Cook's Publications:

"Transcendental Function Meditations"
     with William Bauldry & Michael Bosse
     The Electronic Journal of Mathematics & Technology, Volume 18 (2024) Number 3 (October)
     Associated Reader Investigations (.mw) (Maple Worksheet).
"Fuchs' Problem for Small Groups"
     with Josh Carr & Lindsey Wise
     Involve, a Journal of Mathematics 17-3 (2024), 441—463. DOI 10.2140/involve.2024.17.441
     A preliminary version of the paper is posted here.
     Slides from a related talk.
     [Note: Dihedral and Dicyclic groups are indexed differently in the slides vs. the paper.]
"Patterned Transcendental Numbers"
     with William Bauldry & Michael Bosse
     The Electronic Journal of Mathematics & Technology, Volume 18 (2024) Number 1 (February)
     Associated Patterned decimal calculator (Sage demo).
"Number Systems Tower"
with William Bauldry, Michael Bosse, Katrina Palmer, & Jaehee Post
Journal of Humanistic Mathematics, Volume 13 Issue 2 (July 2023), pages 398-426.
"A Generalized Method of Undetermined Coefficients"
with James Cook
CODEE Journal, Vol. 15 (2022), Article 4. [(.pdf)]
"Repeating Decimal Expansions in Different Bases"
     with Michael Bosse
     The Electronic Journal of Mathematics & Technology, Volume 16 (2022) Number 3 (October)
     A preliminary version of the paper is posted here.
     Associated Becimal Calculator (Sage demo).
"Synthetic Division: Connecting with Other Mathematical Ideas"
     with William Bauldry, Michael Bosse, Katrina Palmer, & Jaehee Post
     The Electronic Journal of Mathematics & Technology, Volume 15 (2021) Number 3 (October)
     A preliminary version of the paper is posted here.
     Associated Horner's Method (Sage demo).
"Types of Infinity"
     with Michael Bosse
     The Electronic Journal of Mathematics & Technology, Volume 15 (2021) Number 2 (June)
     A preliminary version of the paper is posted here.

     Reprinted in Research Journal of Mathematics & Technology, Vol. 10, Nr. 2 (December 2021)

"Infinite Talk" slides.
"Crossing Through and Bouncing Off $\infty$: Graphing Rational Functions"
     with Michael Bosse
     MathAMATYC Educator, Winter Issue 2021, Vol. 12 Number 1.
     A preliminary version of the paper is posted here.
"Quantifying the Curvature of Curves: An Intuitive Introduction to Differential Geometry"
     with Jason Osborne and Michael Bosse
     PRIMUS, DOI: 10.1080/10511970.2019.1636432, August 2019
     A preliminary version of the paper is posted here [the published version looks much better].
"Leibniz algebras with low dimensional maximal Lie quotients"
     with John Hall, Vicky Klima, and Carter Murray
     Involve, a Journal of Mathematics 12-5 (2019), 839—853. DOI 10.2140/involve.2019.12.839
     A preliminary version of the paper is posted here.
"Finding Real Roots of Polynomials Using Sturm Sequences"
     with Michael Bosse and Joseph Castonguay
     PRIMUS, DOI: 10.1080/10511970.2018.1501626, April 2019
     A preliminary version of the paper is posted here.
     Related software (Sage interacts) can be found here.
"On the minuscule representations of type $B_n$"
     with Noah Hughes
     Involve Vol. 11 (2018), No. 5, 721—733.
     A preliminary version of the paper is posted here.
     Related GAP code (appearing in the paper's appendix) is posted here (.g).
     Our original submitted long version is posted here.
     MathSciNet review MR3784022
"Fitting the Extreme Value Theorem into a Very Compact Paper"
     with Katie Mawhinney and Michael Bosse
     MathAMATYC Educator, February 2018, Vol. 9 Number 2.
     A preliminary version of the paper is posted here.
"The Simplicity and Beauty of Topology: Connecting with the Intermediate Value Theorem"
     with Katie Mawhinney and Michael Bosse
     MathAMATYC Educator, September 2016, Vol. 8 Number 1.
     A preliminary version of the paper is posted here.
"15.6: Parametric Surfaces" & "15.7: Surface Integrals"
in Sullivan & Miranda's Calculus
"An n-dimensional Pythagorean theorem"
     College Math. J. 44 (2013), no. 2, 98—101. DOI 10.4169/college.math.j.44.2.098
     A preliminary version of the paper is posted here.
     Slides from an accompanying talk are posted here.
"Two Proofs of the Existence and Uniqueness of the Partial Fraction Decomposition"
     with William (Tyler) Bradley
     International Mathematical Forum. 7 (2012), no. 31, 1517—1535.
     The paper can be found here.
     MathSciNet review MR2967371
"On a symmetry of the category of integrable modules"
     with Christopher Sadowski
     New York J. Math. 15 (2009) 133—160.
     The paper can be found here.
     Related Maple code is posted here.
     MathSciNet review MR2501481.
"A recurrence relation for characters of highest weight integrable modules for affine Lie algebras"
     with Haisheng Li and Kailash C. Misra
     Commun. Contemp. Math. 9 (2007), no. 2, 121—133. DOI 10.1142/S0219199707002368
     A copy of this paper can be found here.
     MathSciNet review MR2313509.
"Affine lie algebras, vertex operator algebras and combinatorial identities"
My Ph.D. thesis from NCSU. My thesis is posted here [backup copy].
"On the constructive inverse problem in differential Galois theory"
     with Claude Mitschi and Michael F. Singer
     Comm. Algebra 33 (2005), no. 10, 3639—3665. DOI 10.1080/00927870500243304
     A copy of this paper can be found here or here.
     Related Maple code used for some of the calculations in the paper can be found here.
     MathSciNet review MR2175456.