In Preparation
  1. S.K. Lucas, When you run out of fingers and toes; a history of computation, Book, first draft completed.
  2. S.K. Lucas, How to represent a number, Book draft, 1/3 complete.
  3. S.K. Lucas, Wallis-type infinite products from the Gamma function.
  4. S.K. Lucas, So you think you can subtract.
  5. S.K. Lucas & J.S. Sochacki, Motion down a curved surface.
  6. S.K. Lucas & J.S. Sochacki, Simple odes with heteroclinic orbits.
  7. S.K. Lucas & J.S. Sochacki, Powers of integers via Pascal's triangle.
  8. E. Tu, B. Wastvedt & S.K. Lucas, Variants on algorothm X for NP Complete problems.
  9. S.K. Lucas, New Formulas for Tangent’s Maclaurin Series and Bernoulli Numbers 
  10. S.K. Lucas, G.E. Parker, J.S. Sochacki & P.G. Warne, Taylor series without high order differentiation. 
  11. S.K. Lucas, Changing bases every which-way. 
  12. S.K. Lucas & J.S. Sochacki, Not all differential equations are created equal. 
  13. S.K. Lucas, An Euler-Maclaurin-like summation formula for Simpson’s rule. 
  14. S.K. Lucas, C. Collins & K. Stephenson, Placing a circle pack.
  15. S.K. Lucas & M. Bevis, Generalizing Loves problem. 
  16. S.K. Lucas, R. Martin & K.V. Lever, A direct proof of the prime number theorem.
  17. S.K. Lucas & G. Fleury, On extending the weighing puzzle.
Current Research
  1. Modeling electrospray ionization (with C. Hughey, JMU chemistry).
  2. Chutes and Ladders and variants via Markov chains (with various undergraduates).
  3. Analysis of the game “dreidel” (with C. McGrath, JMU honors).
  4. 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.
  5. Mathematics of Sudoku (with E. Arnold, R. Field & L. Taalman, JMU, & J. Lorch, Ball State). 
  6. Boolean Gröbner Bases (with E. Arnold, JMU).
  7. Spigot algorithms and continued fractions.
  8. Generalized exponential distribution functions (with H. Hamdan, JMU, on hold). 
  9. Game theoretic considerations for duels on graphs (with D. Lanphier, Western Kentucky, on hold).
  10. Deformation of elastic half-spaces (with M. Bevis, Ohio State, on hold).
  11. An integer-valued logistic equation (on hold). 
  12. Fitting predator prey models to data (on hold). 
  13. Bounded continued fraction representations of reals and rationals (on hold). 
  14. Properties of Pierce and Engel fraction representations (on hold).