In Preparation

- S.K. Lucas, When you run out of fingers and toes; a history of
computation, Book, first draft completed.
- S.K. Lucas, How to represent a number, Book draft, 1/3
complete.
- S.K. Lucas, Wallis-type infinite products from the Gamma function.
- S.K. Lucas, So you think you can subtract.
- S.K. Lucas & J.S. Sochacki, Motion down a curved surface.
- S.K. Lucas & J.S. Sochacki, Simple odes with heteroclinic orbits.
- S.K. Lucas & J.S. Sochacki, Powers of integers via Pascal's triangle.
- E. Tu, B. Wastvedt & S.K. Lucas, Variants on algorothm X for NP Complete problems.
- S.K. Lucas, New Formulas for Tangent’s Maclaurin Series and
Bernoulli Numbers
- S.K. Lucas, G.E. Parker, J.S. Sochacki & P.G. Warne, Taylor
series without high order differentiation.
- S.K. Lucas, Changing bases every which-way.
- S.K. Lucas & J.S. Sochacki, Not all differential equations
are created equal.
- S.K. Lucas, An Euler-Maclaurin-like summation formula for
Simpson’s rule.
- S.K. Lucas, C. Collins & K. Stephenson, Placing a circle pack.
- S.K. Lucas & M. Bevis, Generalizing Loves problem.
- S.K. Lucas, R. Martin & K.V. Lever, A direct proof of the
prime number theorem.
- S.K. Lucas & G. Fleury, On extending the weighing puzzle.

Current Research

- Modeling electrospray ionization (with C. Hughey, JMU chemistry).
- Chutes and Ladders and variants via Markov chains (with various
undergraduates).
- Analysis of the game “dreidel” (with C. McGrath, JMU honors).
- Solution of differential equations by polynomial methods (with E.
Parker, J.S. Sochacki, P. Warne, A. Tongen & R. Thelwell, JMU).
Aspects include converting to polynomial form, differential equations
with the same solution but different errors, effectively symplectic
solvers, generating functions and decimal representations of rationals
and roots.
- Mathematics of Sudoku (with E. Arnold, R. Field & L. Taalman,
JMU, & J. Lorch, Ball State).
- Boolean Gröbner Bases (with E. Arnold, JMU).
- Spigot algorithms and continued fractions.
- Generalized exponential distribution functions (with H. Hamdan,
JMU, on hold).
- Game theoretic considerations for duels on graphs (with D.
Lanphier, Western Kentucky, on hold).
- Deformation of elastic half-spaces (with M. Bevis, Ohio State, on
hold).
- An integer-valued logistic equation (on hold).
- Fitting predator prey models to data (on hold).
- Bounded continued fraction representations of reals and rationals
(on hold).
- Properties of Pierce and Engel fraction representations (on hold).