C. V. - 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: Colonel
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
Books:
Essential Calculus, 2nd Edition, 2007, Hawkes Learning Systems, Charleston, SC.
Publications: Refereed Articles in Professional Journals, and Current Work
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 c-Bhaskar 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 Institute of Combinatorics and Its Applications, 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 D.G. Sarvate, and T.S. Purewal, Faithful enclosings of group divisible designs
formed by adding an additional group, Congressus Numerantium 161(2003) 129-138.
24. S.P. Hurd, D.G. Sarvate, and M. Greig, General constructions of c-Bhaskar Rao designs and the
(c, ) spectrum of a c-BRD(v, k, ), Discrete Mathematics 274(2004), 77-92.
25. S.P. Hurd and D.G. Sarvate, Odd and Even Group Divisible Designs With Two Groups and
Block Size Four, Discrete Mathematics 284(2004), 189-196.
26. S.P. Hurd and D.G. Sarvate, Pair resolvability and tight embeddings for path designs, J. of
Combinatorial Mathematics And Combinatorial Computing 58 (2006), 113-127.
27. S.P. Hurd, with M.A. Francel, G. Rudolph, and D.G. Sarvate, The anatomy of a design,
Congressus Numerantium 181 (2006), pp. 77-88.
28. S.P. Hurd with D. Henson and D.G. Sarvate, Group divisible designs with three groups and
block size four, Discrete Mathematics 307 (2007), 1693-1706.
29. S.P. Hurd and D.G. Sarvate, An edge-coloring problem for designs, Bulletin of the Institute of
Combinatorics and Its Applications 49 (2007), 15-20.
30. S.P. Hurd and D.G. Sarvate, Balanced Ternary Designs, p. 330-333 in The CRC Handbook of
Combinatorial Designs, 2nd Edition, Ed. By C.J. Colbourn and J.H. Dinitz, CRC Press, Boca Raton,
2007.
31. S.P. Hurd, D.G. Sarvate and N. Mishra, A new construction for group divisible designs with
block size five and few groups, Ars Combinatorica, 84(2007), p. 243-245.
32. S.P. Hurd with D.G. Sarvate, GDDs with two groups and block configuration (1, 4), Journal of
Combinatorics, Information and System Sciences, Vol. 32 (2007), No. 1-4, p. 297-306.
33. S.P. Hurd and D.G. Sarvate, On c-Bhaskar Rao Designs and Tight Embeddings for Path
Designs, Discrete Mathematics 308 (2008), 2659-2662.
34. S.P. Hurd and D.G. Sarvate, Group divisible designs with block size four and two groups,
Discrete Mathematics, 308 (2008), 2663-2673.
35. S. P. Hurd and M. A Francel, Nested balanced ternary designs and c-Bhaskar Rao designs,
Australasian Journal of Combinatorics Vol 42 (2008), 3-19.
36. S.P. Hurd and M.A. Francel, Packed and Monadic Balanced Ternary Designs With Common
Reductions, Congressus Numerantium, 192 (2008), 161-168.
37. S.P. Hurd with D.G. Sarvate, Embedding multiple BIBDs into BIBDs or projective planes,
Journal of Statistics and Applications,Vol 4, No. 2-3, (2009), 277-284.
38. S.P. Hurd, D.G. Sarvate and N. Mishra, Group divisible designs with two groups and block size
five with fixed block configurations, J. Combin. Math. Combin. Comput. 70 (2009), 15--31.
05B05
39. S.P. Hurd and M.A. Francel, Monadic Balanced Ternary Designs, to appear in volume 70 in
JCMCC in 2010.
40. S.P. Hurd and D.G. Sarvate, Group divisible designs with two association classes and with
groups of sizes 1,1, and n, accepted 2009 (JCMCC).
41. S.P. Hurd and D.G. Sarvate, Group association designs with two association classes and with
many small groups, submitted 2009.
42. S.P. Hurd, D.G. Sarvate, N. Punnim, Loop Designs, submitted 2009 (JCMCC)
43. S.P. Hurd and D.G. Sarvate, Cyclic Loop Designs, submitted 2009 to JCMCC
44. S.P. Hurd, D.G. Sarvate, and Peter Dukes, It’s Hard To Be Different, Bulletin of the Institute of
Combinatorics and Its Applications, Vol. 60 (2010), 86-90.
45. S.P. Hurd, D.G Sarvate, N. Punnim, and A. Chaiyasena, GDDs With three groups of different
sizes, preprint, submitted 2010.
46. S.P. Hurd and D.G. Sarvate, GDDs with 3 unequal groups and larger first index, preprint,
submitted 2010
47. S.P. Hurd and D.G. Sarvate, Graph Decompositions of K(v,) into Modified Triangles, preprint
Paper presented at professional meetings:
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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 Florida Atlantic
University.
Mar 1998, Egyptian and Super-Egyptian Graphs, The 29th Annual International Southeastern Conference 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.
Mar 8-12, 2004, Pair resolvability and tight embeddings for path designs, 35th Annual Southeastern Conference on
Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton, FL.
March 7-11, 2005, On c-Bhaskar Rao designs and tight embeddings of path designs, 36 th Annual Southeastern
Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic Univ., Boca Raton, FL.
March 2006, On c-Bhaskar Rao Designs and Balanced Ternary Designs, 37 th Annual Southeastern Conference on
Combinatorics, Graph Theory and Computing, Florida Atlantic Univ., Boca Raton, FL.
Oct 13-15, 2007, Three constructions using BIBD(v, k, u)s to construct GDDs with two groups and block size k+2,
21st Midwest Conference on Combinatorics, Cryptography and Computing, Charleston, SC.
Oct 13-15, 2007, Balanced ternary designs with a constant number of doubletons per block (presented by coauthor
M.A. Francel), 21st Midwest Conference on Combinatorics, Cryptography and Computing, Charleston, SC.
Oct 2008, Balanced Ternary Designs With Common Reductions, 22nd Mid-West Conference on Combinatorics,
Cryptography and Computing, University of Nevada at Las Vegas.
Oct 2009, Loop Designs, Rochester, NY, 23rd Midwest Combinatorics Conference.
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
1994-present
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
Numerous Faculty Presentation Grants
Advanced Study Grants
May 1985
Jan 1988
Aug 1988
Jan 1989
Aug 1990
Feb 1991
Aug 1991
Jan 1996
Jan 3-6, 2008
Workshop in Lattice-ordered Groups, Bowling Green State University, Bowling Green,
Ohio.
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.
Short Course in the History of Combinatorics, AMS/MAA Meeting
Other scholarly activities:
Mathematical reviewer for ZENTRALBLATT and MATHEMATICAL REVIEWS
Work in progresss:
Group divisible designs with few groups, with D. Sarvate
Updated Sept 2010.