PUBLICATIONS

"**Multivariate Polynomial Interpolation in Newton Forms**"

*SIAM Review*, Vol. 61, No. 2, June 2019, pp. 361-381, https://doi.org/10.1137/17M1124188 (reprint).

"**Comparing High-Order Multivariate AD Methods**" with Benjamin Altman,

*Optimization Methods and Software*, Vol. 33, No. 4-6 (special issue: Advances in Algorithmic Differentiation), 2018, pp. 995-1009, https://doi.org/10.1080/10556788.2018.1472256 (pdf preprint).

MATLAB Forward Corner implementation of direct forward multivariate series.

MATLAB Comparison Test Codes.

"**Avoiding Plagiarism in Mathematics**"

*Math Horizons*, Vol. 23, No. 4, April 2016, pp. 16-17, doi.org/10.4169/mathhorizons.23.4.16.

"**A Fair-Bold Gambling Function is Simply Singular**"

*American Mathematical Monthly*, Vol. 123, No. 1, January 2016, pp. 1-18, doi.org/10.4169/amer.math.monthly.123.1.3.

"**Efficient Recurrence Relations for Univariate and Multivariate Taylor Series Coefficients**"

*Dynamical Systems and Differential Equations, DCDS Supplement 2013, Proceedings of the 9th AIMS International Conference (Orlando, USA)*, Nov. 2013, pp. 587-596.
open access

"**A Classroom Note: Newton’s Method Doubles Digit Improvement**"

*Mathematics and Computer Education*, Vol. 48, No. 1, Winter 2014, pp. 19-22. pdf scan

"**Introduction
to Automatic Differentiation and MATLAB OOP**"

*SIAM Review*, Vol. 52, No. 3, pp. 545-563, Sept. 2010 pdf file.

zip file of accompanying MATLAB
m-files.

For MATLAB versions prior to release 2008a, here are older m-files.

"**Letter
to the Editor: Archimedes, Taylor, and Richardson**"

*Mathematics Magazine*, Vol. 82, No. 1, February 2009, p. 41. pdf preprint

"**Problem
200. A Spherical Average**

(Characterization of one radian as the average azimuthal (from z-axis) angle over a hemisphere.)

*Math Horizons*, Vol. 14, September 2006, pp. 41-42 (proposed in Vol. 13,
February 2006, p. 33).

"**Directions
for Computing Truncated Multivariate Taylor Series**"

*Mathematics of Computation*, Vol. 74, No. 249, January 2005, pp. 321-340. article
and MATLAB implementation

"**Series
as a Computational Differentiation Tool**"

*Mathematica in Education and Research*, Vol. 9, No. 2, 2000, pp.
5-14. Mathematica
Info. Center download

"**Sample
Calculus**" with Walter G. Spunde,

*Mathematics Magazine*, Vol. 72, No. 3, June 1999, pp. 171-182. web supplement.

"**Infinite
Series Supplement for a Differential Equations Course**" with Donna K.
Molinek,

Davidson College course pack, first version 1999, latest
version November 2008 pdf file.

"**Mathematica
Notebooks for ATLAST**"

(Augmenting the Teaching of Linear Algebra through the use of Software
Tools) available in Mathematica
Info. Center. These notebooks accompany the book *ATLAST Computer
Exercises for Linear Algebra*.

"**Programming
Paradigms via Mathematica**" with Todd G. Will and John R. Swallow,

in Mathematica
Info. Center, originally posted 1998 as Mathematica 2.2 notebooks, later
updated to 4.0 notebooks, with contributions by Stephen L. Davis.

"**The
Road to Chaos is Filled with Polynomial Curves**" with R. John Annen
III,

*American Mathematical Monthly*, Vol. 103, No. 8, October
1996, pp. 640-653. web supplement.

"**Recursive
Algorithms for IFS Fractals**"

*Mathematics and Computer Education*, Vol. 30, No. 1, Winter
1996, pp. 83-100. pdf scan

"**Computing
Multivariable Taylor Series to Arbitrary Order**"

APL95 Conference Proceedings, *APL Quote Quad*, Vol.
25, No. 4, June 1995, pp. 134-144. link

"**Neural
Networks from Idea to Implementation**" with Kenneth M. Lane,

*APL Quote Quad*, Vol. 25, No. 3, March 1995, pp. 27-37.

"**Array-Oriented
Programming in Education**"

*APL Quote Quad*, Vol. 24, No. 2, December 1993, pages 17-18.

"**Differential
Equations are Recurrence Relations in APL**"

APL92 Conference Proceedings, *APL Quote Quad*, Vol.
23, No. 1, July 1992, pp. 165-174.

"**An
Efficient Method for the Numerical Evaluation of Partial Derivatives of
Arbitrary Order**"

*ACM Transactions on Mathematical Software*, Vol. 18, No. 2, June 1992,
pp. 159-173.

"**An
APL Approach to Differential Calculus Yields a Powerful Tool**"

APL89 Conference Proceedings, *APL Quote Quad*, Vol.
19, No. 4, August 1989, pp. 285-288.

"**Automatic
Differentiation and APL**"

*College Mathematics Journal*, Vol. 20, No. 3, May 1989,
pp. 238-251.

"**Survey
on Preparation for Graduate School**"

*FOCUS*,
newsletter of the MAA, Vol. 8, No. 4, September, 1988.

"**Concepts
in the real interpolation of Banach spaces**"

*Functional Analysis*, Lecture Notes in Mathematics, 1332, Springer-Verlag, New
York, 1988, pp. 43-53.

"**Factoring
operators through hereditarily-lp spaces**"

*Banach Spaces*, Lecture Notes in Mathematics, 1166, Springer-Verlag, New
York, 1985, 116-128.

"**Norm-attainment
of linear functionals and characterizations of Tauberian operators**"
with H. P. Rosenthal,

*Pacific Journal of Mathematics*, Vol. 118, 1985, pp.
215-228.

"**Schachermayer's
result concerning RNP and KMP equivalence**"

*Longhorn Notes*, 1983-84, pp. 111-123.

"**Characterizing
Tauberian operators by closed images**" with H. P. Rosenthal,

*Longhorn Notes*, 1982-83, pp. 211-221.

Last updated on June 11, 2018.