Most of the following publications are computationally intensive.

1. "Visualizing the Hopf fibration", Mathematica in Education and Research, volume 6, number 1 (1997), pages 9-14.
This article involved the use of Mathematica in a novel visualization of the Hopf fibration. Some materials, including links to Mathematica notebooks, which in part include the article's graphics, are available here.
Copy of text of original article (without the graphics) and copy of figures.
From the introduction: Besides a novel visual rendering of an elusive mathematical object, fundamental concepts in abstract algebra are depicted in an important example The Hopf fibration is a versatile mathematical veteran, arising in numerous and seemingly unrelated situations. Even if you have never heard of it, you may still have encountered it. For instance, the Hopf fibration surfaces in particle physics: it underlies the mathematics of the Dirac monopole (see [Ryder 1996]). It also appears in general relativity, for instance in the Robinson congruence (see [PenRin 1984]). And of course it is found in several pure math contexts, such as in algebraic topology: roughly, there are infinitely many (topologically inequivalent) ways to map the three-dimensional sphere onto the two-dimensional sphere. More precisely, in the language of homotopy groups, π₃(S²) = Z/2Z (see almost any text in algebraic topology, for instance [Whitehead 1978]). Even with all its applications, the Hopf fibration is a mathematical Kilroy: it's been all over the place, but it's difficult to literally 'see'. The Hopf fibration usually arises algebraically, rather than visually. The typical formulation involves S³, the unit sphere in C² (or R⁴), and this in turn is usually visualized by taking ordinary space, R³, and artificially adding a point out at infinity. This is the approach in [Berger 1987 chapters 4 and 18]. While this method of visualization is valuable and interesting and does lead to an actual picture of the Hopf fibration, it is not the approach of this paper. Instead, we present what we think is a new way, and more importantly an elementary way, to honestly visualize this elusive character, emphasizing that we do this without having to venture into C², R⁴ or adding infinity to R³. In fact, we only use some linear algebra, and a basketball. We postpone discussion of the Hopf fibration until after we examine a close relative. Indeed, the object in Figure 1 is our main interest in this article; the Hopf fibration will arise almost as an afterthought. We therefore begin by explaining what the cut-away ball in Figure 1 really is, and then explain what those strings or trajectories inside it represent.
The unit ball model of SO(3) is used to visualize some interesting features of the Hopf fibration.

3. "Using Simpson's rule to approximate sums of infinite series", The College Mathematics Journal, volume 28, number 5 (1997), pages 368-376.
Copy of original article.
From the introduction: "Does the series 1/k³=1+1/8+1/27+... converge or diverge?" A student who knows how to use Simpson's rule could also tackle a followup problem: "Estimate the value of the series to within 0.00001". Equipped with the most primitive of calculators, my students can find the answer in just a minute or two, and demonstrate that their answer is correct to the number of digits claimed. My method for approximately summing such series gives values in the form of a partial sum, plus some correction terms.
The article describes a Newton-Cotes-based competitor to the Euler-Maclaurin summation formula for accelerating the convergence of certain infinite series.

4. "Differentiating among infinite series", Mathematics Magazine, volume 71, number 1 (1998), pages 42-50.
Copy of original article.
From the introduction: Calculus students often spend a lot of time deciding whether or not a series like the sum of 1/j^3/2 for j=1, 2, 3, ... converges. But relatively little time is spent investigating numerical values of such (convergent series). Can't we just use a computer... and keep adding more and more terms..? For many (rapidly converging) series, this logic is... essentially valid. But there are ... many series whose partial sums converge very slowly. For the sum of 1/j^3/2 for j=1, 2, 3... for instance, the 6-digit accuracy we will get below from one of our estimation formula would be atttained by a partial sum only after 160 billion terms were added. As a more dramatic example, we will consider the excruciatingly slow convergence of the sum 1/(j (lnj)²) for j=2, 3, ...; not even the addition of 10¹⁰⁰⁰⁰ terms would match the five digits of accuracy we will obtain for our first, most basic, method.
In the article, numerical differentiation techniques familiar in calculus are used to provide estimates of sums of series. The method is a competitor to Euler-Maclaurin summation for accelerating the convergence of series, using numerical differentiation techniques.

5. "Fun Fractions?! You've got to be kidding!", Mathematics Teacher, volume 91, number 7 (1998), pages 572-575.
Copy of original article.
From the introduction: Well, no, I am not kidding. Consider the following fractions; their decimal expansions, given in parentheses, may surprise you. I urge you to check these expansions on a calculator:
(1) p = 50/49 = 1.020408163265306 ...

(2) o = 10100/9801 = 1.0305070911131517 ...

(3) s = 1010000/970299 = 1.04091625364964820122457 ...

(4) f = 10000/9899 = 1.01020305081321345590463683 ...
The letters denoting the constants were chosen as abbreviations for powers of two, odds, squares, and Fibonacci numbers to remind us of the patterns in the nonzero digits of the decimal expansions. Are these fractions just a fluke? A computer and such software as Derive, Maple, or Mathematica might be better than a calculator for checking the following:
(1') p' = 500/499 = 1.002004008016032064128256513024 ...

(2') o' = 1001000/998001 = 1.003005007009011013015017 ...

(3') s' = 1001000000/997002999 = 1.004009016025036049 ...

(4') f' = 1000000/998999 = 1.001002003005008013021034 ...
Just for fun, if you have found a calculator or computer by now, try 10000/9801, too. In this article, I explain how my class obtained these fractions, as well as how you and your students can find many more. Before doing so, notice one difference between the fractions shown in expressions (3') and (4') and their unprimed counterparts in expressions (3) and (4), respectively. The digits in the decimal expansions for the unprimed fractions, that is, those with the smaller denominators, eventually "bump into one another," a phenomenon that we shall call digit overlap.
The article discusses generating functions and how they can be found, and then used to produce such fractions that have prescribed decimal expansions. One of our favorites is a fraction producing the positive integers, then their squares, in order.

Some other fractions were mentioned in a brief blurb in the College Mathematics Journal; copy here.

6. "Estimating logarithms with college algebra students", International Journal of Mathematical Education in Science and Technology, volume 30, number 2 (1999), pages 197-206. (This site may be better.)
Copy of original article.
From the abstract: Values of logarithms can be estimated using only their algebraic properties, i.e. without appeal to calculus. College algebra students can achieve estimates that are of the order of 1% error, by solving certain linear systems by hand. Improving the accuracy of the approximations naturally leads in two directions: to larger linear systems, requiring a computer; or to least squares solutions, which can bemade natural and accessible to college algebra students in a novel, low-dimensional geometric way. Error bounding, and comparision of the new low-dimensional, geometric least squares method with the traditional higherdimensional approach to least squares provide useful explorations for linear algebra students. Specifically, error bounding is possible for students who (1) are able to compute the distance from a point in R^k to a hyperplane; (2) understand orthogonal matrices, and the basics of the singular value decomposition of a matrix; and (3) know the Taylor series for ln(1+x).

7. "Graphs and matrices in the study of (finite) topological spaces", Missouri Journal of Mathematical Sciences, volume 12, number 2 (2000), pages 96-121 (this site may be better)
Copy of original article.
From the introduction: In a first course in topology one invariably comes across a finite topology, i.e. a topology on a space X with n (finitely many) points. Beginning students (and many instructors) are quite surprised when first told that, for instance, if X has just 6 points, there are 209,527 possible topologies on X. This paper is written in part for those who wonder "why so big a number?", and "how is it obtained?" The main purpose of this article, however, is not to study this specific enumeration problem We instead focus on a productive relationship between graph theory, matrix algebra, and finite topologies. While teaching an introductory topology class, we chanced on a reference that alluded to a graph theoretic approach to the study of finite topologies: each topology on X can be identified with a certain directed graph with n nodes. This gives a nice way to literally visualize a topology. We then show how the adjacency matrix associated to the graph provides many surprises. For one, the left 'eigenvectors' of the matrix directly correspond to the open sets in the topology; and the right 'eigenvectors' correspond to the closed sets.
Several notions of finite topological spaces are also defined and enumerated (e.g. enumerating topological spaces that are not non-trivial products of other topological spaces). Some of these enumerations have been included in the database stored at Neil Sloane's integer sequence website.

8. "Simpson's rule for estimating n! (and proving Stirling's formula, almost)", coauthored with James Graham-Eagle (at U Mass Lowell), International Journal of Mathematical Education in Science and Technology, volume 32, number 3 (2001), pages 466 - 475. (This site may be better.)
Copy of original article.
From the abstract: Using a tool familiar to first-year calculus students (Simpson's rule) surprisingly good estimates are deduced for values of n! - or more precisely ln n! - along with error bounds. These estimates can be implemented on a simple hand-held calculator or computer. Moreover, it is demonstrated how to arrive at analogous, improved estimates (with error bounds) for all higher-order Newton-Cotes integration methods. Along the way, the error bounding naturally, and in short order, leads to the conclusion that n! is approximately C (n/e)ⁿ * sqrt(n). While these methods cannot show the entirety of Stirling's formula (namely that C = sqrt(2 π), they do show how C can be approximated to any desired accuracy.

9. "Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants", in Mathematics of Computation, volume 72 (2003), pages 1379-1397.
Copy of original article.
Several conjectures regarding the Stieltjes constants are made, based on high-precision numerical computations (and graphs) of the Stieltjes constants. This article was probably the first one to actually plot the Stieltjes constants. Some of the figures were incorporated in the Wolfram site Mathworld.

11. "Simpson's rule", invited article in Encyclopedia of Measurement and Statistics, Neil Salkind editor, Sage Publications (2007), Thousand Oaks, CA.
Copy of original article.

12. "Pi (π) to thousands of digits from Vieta's formula", Mathematics Magazine, volume 81, number 3 (2008), pages 201-207.
Copy of original article.
From the introduction: Two infinite products for π, Wallis's and Vieta's, are well-known and striking (and, surprisingly, related). While both formulas are mysterious and beautiful, the convergence of Wallis's formula is painfully slow. Vieta's is much better, although Vieta himself was able to approximate π only to 9 digits past the decimal point in 1593. In this article, we'll describe a way to accelerate the convergence of Vieta that is completely accessible to calculus students, and how we stumbled upon it through experimentation. We were somewhat astonished when we used our accelerated (Vieta) to approximate pi to over 300,000 digits.
The article describes an almost perfect illustration of the use of Richardson extrapolation to dramatically accelerate the convergence of the infinite product in Vieta's formula (or is the formula due to Viete or Vietæ or Viète?).

13. "Visualizing the chain rule (for functions over R and C) and more", International Journal of Mathematical Education in Science and Technology, volume 40, number 2, 277-287 (2009). (This site may be better.)
Copy of original article.
From the abstract: A visual approach to understanding the chain rule and related derivative formulae, for functions from R to R and from C to C, is presented. This apparently novel approach has been successfully used with several audiences: students first studying calculus, students with some background in linear algebra, students beginning study of functions of a complex variable, and current secondary school teachers obtaining professional development.
Besides the chain rule, the article includes discussion of an intuitive approach for formulae for the derivative of the inverse of a function (whether for functions from R to R, or from C to C).

14. "Taylor's theorem: the elusive 'c' is not so elusive", The College Mathematics Journal, volume 41, number 3, 186-192 (2010).
Copy of original article.
The article describes the Lagrange form error term in Taylor's theorem, typically denoted fⁿ⁺¹(c)(b - a)ⁿ⁺¹/(n+1)! for suitably defined functions f on intervals containing a and b; there is interesting structure to the location of the quantity often denoted by the letter c (depending on a, n and b, but in a certain sense much less so on f). The MAA website hosts a supplement to that article; the supplement is also available here.

15. Two entries ("Molecular structure", p672-674 and "Brain", p124-128) for the Encyclopedia of Mathematics and Society, edited by Sarah Greenwald and Jill Thomley, produced by Golson Media, and published by Salem Press, appeared in 2011.

16. "Blockchain: what it is, what we and our students learned - a policy research project", Business Education Innovation Journal, volume 13, number 1, 110-128 (2021) (coauthored with Dr. Carl Wright).

From the abstract: This paper recounts how a narrow policy research project with a multidisciplinary team of undergraduates and faculty, concerning how blockchain might address shareholder-related ownership and voting issues, led to our coming to know, then addressing, the level of understanding of blockchain technology among a subset of the public: state government staff; elected legislators; university students, faculty and staff (including upper-level campus administrators); and other members of the public. We include how the workshops we developed can incorporate hands-on blockchain education into the university-level accounting and business curricula.

OTHER:

Preprint in development for a generalized Wilcoxon rank sum statistical test, and "SO(3) in pictures: a good example of lots of things". Other work in progress includes work on a generalized secant method, on numerical differentiation via the Dirac delta function and numerical integration, on mathematical modeling of ecosystems, and on using random points to aid in plotting graphs of functions f: R²-->R. My unpublished dissertation, "Graded manifolds with spin-conformal structure", is a sheaf-theoretic approach to incorporating spin structures into graded manifolds (which in turn are related to supermanifolds and supergravity).