1. S.K. Lucas & A. Nimbran, Monotonic Series for Fractions near π and its Convergents, The Mathematical Gazette, 106(566), July 2022, 300-309.

2. S.K. Lucas, E. Sander & L. Taalman, Modeling Dynamical Systems for 3D Printing, chapter in The Best Writing on Mathematics 2021, Mircea Pitici (ed), Princeton University Press, June 2022.

3. S.K. Lucas & L. Taalman, Ideal spatial graph configurations, Journal of Mathematics and the Arts, 16(1-2) June 2022, 121-132.

4. S.K. Lucas, E. Sander & L. Taalman, Modeling Dynamical Systems for 3D Printing, Notices of the American Mathematical Society 67(11) 1692-1705 2020.

5. A. Eget, S.K. Lucas & L. Taalman, Optimizing Morton’s Tritangentless Knots for Rolling, Bridges 2020 Conference Proceedings, 2020.

6. D.B. Glass, S.K. Lucas & J.S. Needleman, Chutes And Ladders Without Chutes Or Ladders, The Mathematics of Various Entertaining Subjects (volume 3), J. Beineke & J. Rosenhouse (eds) 2019, 119-138.

7. S.K. Lucas, Representing Numbers Using Fibonacci Variants, The Mathematics of Various Entertaining Subjects, J. Beineke & J. Rosenhouse (eds) 2016, 245-260.

8. E. Arnold, J. Lorch, S.K. Lucas, R. Field & L. Taalman, Nest graphs and minimal complete symmetry groups for magic Sudoku variants, Rocky Mountain Journal of Mathematics 45(3) 2015.

9. J.T. Ratnanather, J.H. Kim, S. Zhang, A.M.J. Davis, & S.K. Lucas, IIPBF: a Matlab toolbox for infinite integrals of products of two Bessel functions, ACM TOMS 40(2) 1-14 (2014).

10. E. Arnold, S.K. Lucas, R. Field & L. Taalman, Minimal complete Shidoku symmetry groups, Journal of Combinatorial Mathematics and Combinatorial Computing 87 209-228 (2013).

11. D.C. Carothers, S.K. Lucas, G.E. Parker, J.D. Rudmin, J.S. Sochacki, R.J. Thelwell, A.L. Tongen, and P.G. Warne, Connections between Power Series Methods and Automatic Differentiation, Proceedings of the 6th International Conference on Automatic Differentiation, July 2012.

12. E. Arnold, S.K. Lucas & L. Taalman, Gr¨obner Basis representations of Sudoku, College Math. J. 41(2) 101-111 (2010).

13. S.K. Lucas & J. Rosenhouse, Optimal strategies for the progressive Monty Hall problem, Math. Gazette 93(528) 410–419 (2009).

14. S.K. Lucas, J. Rosenhouse & A. Schepler, The Monty Hall problem, reconsidered, Math. Mag. 82(5) 332-342 (2009).

15. S.K. Lucas, Approximations to π derived from integrals with nonnegative integrands, Am. Math. Monthly 116(2) 166-172 (2009).

16. S.K. Lucas & W. Whiten, Particle transport through the froth layer in column flotation, 2003 Proceedings of the Mathematics-In-Industry Study Group, MISG 2008.

17. P.D. Haynes & S.K. Lucas, Extension of a short-time solution of the diffusion equation with application to micropore diffusion in a finite system, ANZIAM J. 48 503-521 (2007).

18. V. Ejov, J.A. Filar, S.K. Lucas & P. Zograf, Clustering of spectra and fractals of regular graphs, J. Math. Anal. Appl. 333 236-246 (2007).

19. J. Thredgold, S.K. Lucas & P.G. Howlett, On the contact of a rigid sphere and a plate, Math. Comp. Mod. 43 119-131 (2006).

20. J.L. Nelson, S.K. Lucas, J.A. Filar & V. Ejov, Solving the Hamiltonian Cycle problem using symbolic determinants, Taiwanese Journal of Mathematics 10 327-338 (2006).

21. S.K. Lucas, Integral proofs that 355/113 >π, Gazette Aust. Math. Soc. 32 263-266 (2005).

22. J.A. Filar, A. Gupta & S.K. Lucas, Connected co-spectral graphs are not necessarily both Hamiltonian, Gazette Aust. Math. Soc. 32 193 (2005).

23. M.R. Agrawal, P.G. Howlett, S.K. Lucas, Sunanda Naik & S. Ponnusamy, Boundedness of generalized Cesaro averaging operators on certain function spaces, J. Comp. Appl. Math. 180 333-344 (2005).

24. S.T. Simakov, C.Y. Kaya & S.K. Lucas, Computations for Bang-Bang Constrained Optimal Control Using a Lagrangian Formulation, Optim. Control Appl. Meth. 25 295-308 (2004).

25. A. Torokhti, P. Howlett & S. Lucas, Method of partitioned data orthogonalization for Principal Component Determination, Proc. of XVI International Symposium on Mathematical Theory of Networks and Systems, Leuven, Belgium, ISBN 90-5682-517-8, CD-rom, 2004.

26. S.K. Lucas, On using bounded continued fractions to represent reals, CTAC 2003 conference proceedings, ANZIAM J. 45(E) C921-934 (2004).

27. S.K. Lucas, Maximising flow from oil reservoirs without water breakthrough, ANZIAM J. 45 401-423 (2004).

28. S.K. Lucas, Least squares cubic splines without B-splines, Gazette Aust. Math. Soc. 30 207-211 (2003).

29. D. Panton, M. John, S.K. Lucas & A. Mason, Flight test data cycle map optimisation, European J. OR 146 486-497 (2003).

30. S.K. Lucas & F. Underwood, Women’s success in mathematics: the Hypatia scholarship program, Australasian J. Gifted Education 11(2) 18-25 (2002).

31. S.K. Lucas, Another look at finding continued fractions, Gazette Aust. Math. Soc. 29 216-219 (2002).

32. S.T. Simakov, C.Y. Kaya & S.K. Lucas, Computations for time-optimal bang-bang control using a Lagrangian formulation, Proceedings of IFAC2002, July 2002, Barcelona, (2002).

33. A.C. Mernone, J. Mazumdar & S.K. Lucas, A mathematical study of peristaltic transport of a Casson fluid, Math. Comp. Mod. 35 895-912 (2002).

34. S.K. Lucas & C.Y. Kaya, Switching-Time Computation for Bang-Bang Control Laws, 2001 American Control Conference (ACC), July 2001, 176-181 (2001).

35. S.K. Lucas & J.M. Hill, Testing the fracture of spectacle lenses, 2000 Proceedings of the Mathematics-In-Industry Study Group, MISG, 148-168 (2001).

36. R.A. Frick & S.K. Lucas, Customised student projects in engineering statistics, in EMAC ’98, edited by E.O. Tuck & J.A.K. Stott, Institution of Engineers, Australia (1998).

37. S.K. Lucas, H.A. Stone & R. Sipcic, An integral equation solution for the steady-state current at a periodic array of surface microelectrodes, SIAM J. Applied Math. 57 1615-1638 (1997).

38. S.K. Lucas & A. Kucera, A 3D boundary integral method applied to the water coning problem, Physics of Fluids 8 3008-3022 (1996).

39. S.K. Lucas, Evaluating infinite integrals involving products of Bessel functions of arbitrary order, J. Comp. Appl. Math. 64 269-282 (1995).

40. S.K. Lucas & H.A. Stone, Evaluating infinite integrals involving Bessel functions of arbitrary order, J. Comp. Appl. Math. 64 217-231 (1995).

41. S.K. Lucas & H.A. Stone, A study of reaction-diffusion problems for domains bounded by periodic source/sink distributions on planar surfaces: an application to microelectrode processes, in BEM 17, edited by C.A. Brebbia, S. Kim, T.A. Osswald & H. Power, Wessex Institute of Technology (1995).

42. T. Chou, S.K. Lucas, & H.A. Stone, Capillary wave scattering from a surfactant domain, Phys. Fluids 7 1872-1885 (1995).

43. S.K. Lucas, A collocation expansion approach to the boundary integral method, in Boundary Element Technology VII, edited by C.A. Brebbia & M.S. Ingber, Elsevier Applied Science (1992).

44. S.K. Lucas & A. Kucera, Solving the water coning problem by a three dimensional boundary integral method, Gazette Aust. Math. Soc. 18 105-108 (1991).

45. S.K. Lucas, J.R. Blake & A. Kucera, A boundary integral method applied to water coning in oil reservoirs, J. Aust. Math. Soc. B32 261-283 (1991).

46. S.K. Lucas, Water coning in oil reservoirs, in Computational Techniques and Applications ’89, Hemisphere, (1990).

47. L.A. Maciaszek & S.K. Lucas, A graphical tool to derive network database structure from an enhanced conceptual design, Proceedings of the Conference on Computer Systems and Information Technology, Brisbane, Australia, 39-44 (1987).

Research Experience for Undergraduates (REU) at JMU:

• Brandon Alexander & Stephanie Brown (2013), Applications of the Power Series Method.

• Bjorn Wastvedt & Eddie Tu (2010), Gröbner Bases and NP-Complete Problems.

Honors at JMU:

• Maxwell Cooper (2025-2026), Divisibility Tests and Unusual Bases.

• Natalie Huey (2023-24), Mathematical Modeling of Warfare with Reinforcement.

• Branden Wooten (2013-14), The Karhunen-Loeve expansion and solving stochastic odes.

• Cynthia McGrath (2012-13), Markov chain modeling of chutes and ladders and dreidel.

Independent Study at JMU:

• Timothy Tarter (fall 2024 onwards project) Identifying links in the Peterson family of graphs, and generalizing Y-∆ moves to X-Square.

• Joshua Kunkel (spring 2023 independent study) Optimization for the kissing problem.

• Harley Mead, Abby Eget, William Nettles (2018-21 3d printing) 3d representation of graphs, and ideal dimensions of rolling knots.

• Adam Diehl (2017 independent study) Approximating the Wiener Process

• Volkan Bakirdan (2017 independent study) Parrondo’s Paradox.

• Charles Crook & Zev Woodstock (2015 students in Math 485: Computational Geometry), A comparative study of line segment intersection algorithms and distribution.

• Cole Sebald (2011,2012 independent studies), Project Euler & Integer logistic equation.

PhD at UniSA:

• Kuva Jacobs (2004-2007), Computer animations to teach mathematics (supervised first year).

• Jane Thredgold (2003-2007), Mathematical modeling of the deformation of thin plates (supervised first 2 years).

• Paul Haynes (2003-2007), Modelling of continuous systems (supervised first 2 years).

• Sergiy Kravchuk (2000-2006), Asymptotic study of ideal flows with vorticity. (supervised first 4 years, part time student).

Honors at UniSA:

• Kuva Jacobs (2003), Flash animation and mathematical models.

• Luke Finlay (2003), Comparing convex hull algorithms. 

• Jane Thredgold (2002), Mathematical modelling of the deformation of thin plates. 

• Paul Haynes (2002), Oscillatory systems and microelectromechanical filters. 

• James Caunce (2002), A study of heat flow. 

• Stephen Miller (2000), Chaotic billiards. 

• Deborah Downes (2000), Well-conditioned least squares estimation.

• Jim Rehn (1998), The finite difference method for diffusion problems.

Independent Study at UniSA:

• Amit Gupta (2004 intern), Generating random and co-spectral cubic graphs.

• Glen Ridley (2003 4th year project), Comparing quicksort and its variants.

• Jessica Nelson (2003 Harvey Mudd research exchange), Hamiltonian cycles and Gröbner bases.

• Thu Giang Nguyen (2003 vacation scholar), Investigating some Hamiltonian cycle algorithms.

• Theo Frederiks, (1999 University of Twente research exchange), Optimizing oil flow from an oil-water reservoir.

• S.K. Lucas, Book review: Glimpses of Geometry and Algebra, Gazette Aust. Math. Soc. 30 239-240 (2003).

• S.K. Lucas, Book review: Essential Mathematical Skills, Gazette Aust. Math. Soc. 29 298-299 (2002).