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Vita: Spencer P. Hurd Department of Mathematics and Computer Science 171 Moultrie St., The Citadel, MSC-25 Charleston, SC, 29409 Email: hurds@citadel.edu Office: (843) 953-5034 Home: (843) 577-2919 Current Position: Professor (with tenure) Military Rank: Lt. Col. Department of Mathematics and Computer Science The Citadel, 171 Moultrie St. Charleston, SC, 29409 Main Work Experience 1984 Mathematics faculty at The Citadel 1977 - 84 Graduate Teaching Assistant, the University of Georgia 1972 - 77 Secondary Math Education, Colquitt County High School, Moultrie, Ga. 1966 - 70 Aerospace Engineer, The Boeing Company (Saturn V program) Education: Ph. D. Mathematics, June 1984, The University of Georgia M.A. Mathematics, June 1981, The University of Georgia M. Ed. Secondary Math Education, June 1977, Valdosta State College, Valdosta, Ga. B.S. Physics, June 1963, Virginia Tech Publications: Refereed Articles in Professional Journals 1. S.P. Hurd, Divisibility in o-Primitive Lattice-ordered Groups, Order, v.3 (1986), 195-205. 2. __________, An Application of the Criteria ASASA for Quadrilaterals, The Mathematics Teacher, v.81 (1988), 124-126. 3. __________, Normal Subgroups of Periodically o-Primitive Ordered Permutation Groups, Houston Journal of Mathematics, v.15 (1989), 85-98. 4. __________, Egyptian Fractions: Ahmes to Fibonacci to Today, The Mathematics Teacher, v.83 (1990), p. 561-568. 5. S.P. Hurd with E.L. Blanton and J.S. McCranie, On the Digraph Defined by Squaring Mod m, When m Has Primitive Roots, Congressus Numerantium, v.82,(1991), 167-177. 6. __________, On a Digraph Defined by Squaring Modulo n, The Fibonacci Quarterly, v.30 (1992),322-334. 7. S.P. Hurd with D.A Trautman, The Knight's Tour on the 15-Puzzle, Mathematics Magazine, v. 66 (1993), No. 3, p.159-166. 8. S.P. Hurd with J. S. McCranie, A Discrete Version of a Stochastic Process: The One-Third Game, Congressus Numerantium, v. 95,(1993), p. 25-30. 9. __________, Quantum Factorials, Congressus Numerantiom, v. 104 (1994), p. 19-24. 10. ____________, Some Conjectures about Primitive Roots Motivated by a Digraph, Congressus Numerantium, v. 107 (1995), p. 41-44. 11. ___________, Small Integer Labels for Egyptian and Super-Egyptian graphs, Congressus Numerantium, v. 132 (1998), pp. 77-84. 12. S.P. Hurd with Hughes H. Hoyle, A combinatorial approach to the 2/n problem, Congressus Numerantium , v. 136 (1999), pp. 136-145. 13. S.P. Hurd with D.G. Sarvate, On c-Bhaskar Rao designs, Journal of Statistical Planning and Inference 90 (2000), 161-175. 14. ____________, All c-Bhaskar Rao designs with block size 3 and c -1 exist, Ars Combinatoria 59(2001), pp. 21-32. 15. ____________, On c-Bhaskar Rao designs with block size three and negative c, Journal of Combinatorial Mathematics and Combinatorial Computing, v. 38 (2001), pp. 21-32. 16. ___________, On c-Hadamard Matrices, Ars Combinatoria, 63(2002), pp. 49-64. 17. S.P. Hurd with D.G. Sarvate, M. Greig, and J.S. McCranie, On cBhaskar Rao Designs with block size four, Journal of Combinatorial Designs, v. 38 (2001), No. 6, 361-386. 18. S. P. Hurd with D.G. Sarvate, On enclosing BIBD(v, 3, ) into BIBD(v+1, 3, +1), Bulletin of the ICA, 36 (2002), 53-61. 19. S.P. Hurd with P. Munson and D.G. Sarvate, Minimal enclosings of triple systems, I: increasing the points by one, Ars Combinatoria 68 (2003), 145-159. 20. S.P. Hurd and D.G. Sarvate, Minimal enclosings of triple systems, II: increasing the index by one, Ars Combinatoria 68 (2003), 263-282. 21. ______________, An application of partition of indices to enclosings of triple systems, Discrete Mathematics 261 (2003), 337-346. 22. ______________, Embeddings and faithful enclosings of GDD's with a constant number of groups, Australasian Journal of Combinatorics 27 (2003), 213-222. 23. S.P. Hurd with M. Greig, and D.G. Sarvate, General constructions of c-Bhaskar Rao designs and the (c-)-spectrum of a c-BRD(v, k, ), Discrete Mathematics 274 (2004), 77-92. 24. S.P. Hurd with D.G. Sarvate and T.S. Purewal, Enclosings of GDD's with group size two, to appear in Congressus Numerantium. 25. S.P. Hurd and D.G. Sarvate, Odd and even group divisible designs with two groups and block size four, submitted 26. S.P. Hurd and D.G. Sarvate, Application of C-BRD's to construct GDD's with two groups, submitted. Paper presented at professional meetings: Jan 1985. Divisibility in o-primitive lattice-ordered permutation groups. AMS/MAA annual meeting, special session on ordered structures. Anaheim, CA. Apr 1988. Egyptian fractions and reciprocal identities, MAA Southeastern Section Annual Meeting, Furman, S.C. Apr 1988. Egyptian fractions, UNCG Number Theory Conference, Greensboro, N.C. Apr 1989. On commuting with y=x+1, MAA Southeastern Region Annual Meeting, Knoxville, Tn. Apr 1989. A combinatorial class of r-partite graphs, UNCG Number Theory Conference, Greensboro, N.C. Nov 1989. Teaching pre-calculus with graphing technology, South Carolina Council of Teachers of Mathematics, Myrtle Beach, S.C. Apr 1990. Cyclic Difference Sets of Order n, UNCG Number Theory Conference, Greensboro, N.C. Nov 1990. What programming on the hand held calculator can do for you, South Carolina Council of Teachers of Mathematics, Annual Conf., Greenville S.C. Feb 1991. On the Digraph Defined by Squaring Mod m, When m Has Primitive Roots, 22nd Annual Southeastern Conference on Combinatorics, Graph Theory and Computing, LSU, Baton Rouge, La. Apr 1991. Picturing Prime Numbers With a Digraph, UNCG Number Theory Conference, Greensboro, N.C. Mar 1992. Computations and Conjectures on Primitive Roots, Southeastern Regional Meeting On Numbers (SERMON IV), The University of Georgia, Athens, Ga. Apr 1992. Laboratory session, WINGZ Spreadsheets on the Macintosh, Citadel Conference on the Use of Spreadsheets in Mathematics, The Citadel, Charleston, S.C. Apr 1992. The Knight's Tour on the 15-Puzzle, MAA Southeastern Region Annual Meeting, Kennesaw State College, Kennssaw, Ga. Jan 1993, How to become famous in mathematics, S.C. Junior Academy of Science, Charleston, S.C. Feb 1993, A discrete version of a stochastic process, 24th Annual Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton, Fl. Mar 1993, A Fibonacci-like congruence for factorial expressions, 5th Southeastern Regional Meeting on Numbers, USC, Columbis, S.C. Apr 1993, The One-Third Game, MAA Southeastern Region Annual Meeting, Conway, S.C. Mar 1994, Quantum Factorials, 25th Annual Southeastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Fl. Apr 1994, Organized Conference: The Sixth Annual Southeastern Regional Meeting On Numbers, The Citadel, Charleston, S.C. Mar 3-10, 1995, Questions about Primitive Roots Motivated by a Digraph. The 26th Annual International Southeastern Conference on Combinatorics, Graph Theory and Compution. Boca Raton, Fla, at Floriad Atlantic University. Mar 1998, Egyptian and Super-Egyptian Graphs, The 29th Annual International Southeastern Regional Meeting on Combinatorics, Graph Theory, and Computing. Boca Raton, Fla., at Florida Atlantic University. Feb 2000, (1) Progress on c-Bhaskar Rao designs, and (2) On c-Hadamard matrices, both at the 31st Annual Southeastern International Copnference on Graph Theory, Combinatorics, and Computing., at Boca Raton, Fl. Feb 2001, Enclosings of triple systems, 32nd International Southeastern Conference on Combinatorics, Computing and Graph Theory, Baton Rouge, LA, at LSU. Sabbatical: Fall 2001 to Fall 2002, to study topics in the study of statistical designs and related combinatorial topics. Results: six papers, 6 accepted. Research grants: 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 Divisibility in o-2-transitive groups. The Citadel Development Foundation. The properties of free lattice-ordered groups. The Citadel Development Foundation. Order relations and group-like structures. The Citadel Development Foundation. Topological Lattice-ordered Groups. The Citadel Development Foundation Egyptian Fractions and Reciprocal Identities. The Citadel Development Foundation. Periodic Ordered Permutation Groups. The Citadel Development Foundation. Finite Fractals and Problems in Number Theory. The Citadel Development Foundation. Problems in Number Theory. The Citadel Development Foundation. Problems in Number Theory. The Citadel Development Foundation. Problems in Number Theory. The Citadel Development Foundation Advanced Study Grants May 1985 Workshop in Lattice-ordered Groups, Bowling Green State University, Bowling Green, Ohio. Jan 1988 Aug 1988 Jan 1989 Aug 1990 Feb 1991 Aug 1991 Jan 1996 Mathematical Association of America Short Courses, (1) LOGO and Problem Solving, and (2) Using Computer Graphics to enhance the Teaching and Learning of Calculus and Precalculus Mathematics, Atlanta Workshop on the Use of Computer Graphing in Instruction, The Ohio State University, Columbus, Oh. M.A.A. Short Courses: (1) Teaching Discrete Mathematics with Computers, and (2) Teaching Elementary Statistics With Computers, Phoenix, Az. M.A.A. Short Course, Teaching Calculus With Mathematica, Ohio State University Baton Rouge Combinatorics Lectures, LSU, Baton Rouge, La. Combinatorial Games, A.M.S. Short Course, Joint Summer Meeting of the A.M.S. and M.A.A., The University of Maine, Orono, Me. M.A.A. Short Courses in Teaching Geometry with Computer Software and Teaching Mathematics with Spreadsheet Applications, AMS/MAA Annual Joint Meeting Orlando, Florida. Other scholarly activities: Mathematical reviewer for ZENTRALBLATT and MATHEMATICAL REVIEWS. Sabbatical Year awarded by the Citadel and The Citadel Foundation for AY 2001-2002. Work in progresss: Manuscript on Statistical Designs: Existence of group divisible designs with two associate classes, with Dr. D.G. Sarvate. Manuscript on coloring of graph designs. Updated Jan 2004.