Michael J. Mossinghoff
	Department of Mathematics Office: Chambers 3039 Davidson College Office hours: 209 Ridge Road, Box 6996 Phone: 803-777-5218 Davidson, NC 28035-6996 Fax: 704-894-2005

My vita is available.

You can view my academic family tree.

Teaching

On sabbatical for the 2008-2009 academic year at the University of South Carolina.

Research

My research interests lie in number theory, including analytic, computational, combinatorial, and transcendental aspects. I am particularly interested in extremal problems concerning integer polynomials, especially problems dealing with Mahler's measure of a polynomial, and problems regarding factors of polynomials with restricted coefficients. I am also interested in some problems in discrete geometry.

A nice introduction to many of the problems I work on can be found in the book of P. Borwein, Computational Excursions in Analysis and Number Theory (Springer-Verlag, 2002).

I maintain a site on Lehmer's problem concerning Mahler's measure of polynomials with integer coefficients.

I also maintain a site on Wieferich pairs, Barker sequences, and circulant Hadamard matrices.

Selected Publications

Preprints and Recent Reprints of Research Papers (PDF)

1. The distance to an irreducible polynomial, submitted for publication.
2. Heights of roots of polynomials with odd coefficients (with J. Garza, M. I. M. Ishak, C. Pinner, and B. Wiles), submitted for publication.
3. Lower bounds for heights in cyclotomic extensions, (with M. I. M. Ishak, C. Pinner, and B. Wiles), submitted for publication.
4. Wieferich pairs and Barker sequences, Des. Codes Cryptogr., to appear. (The original publication is available at www.springerlink.com.) Some data associated with this research is also available.
5. Lower bounds for Z-numbers (with A. Dubickas), Math. Comp., 78 (2009), no. 267, 1837-1851.
6. Minimal Mahler measures (with G. Rhin and Q. Wu), Experiment. Math., 17 (2008), no. 4, 451-458.
7. Sign changes in sums of the Liouville function (with P. Borwein and R. Ferguson), Math. Comp. 77 (2008), no. 263, 1681-1694.
8. An isodiametric problem for equilateral polygons, Tapas in Experimental Mathematics, T. Amdeberhan and V. Moll, eds., Contemp. Math. 457, Amer. Math. Soc., 2008, pp. 237-252.
9. Barker sequences and flat polynomials (with P. Borwein), Number Theory and Polynomials (Bristol, U.K., 2006), J. McKee and C. Smyth, eds., London Math. Soc. Lecture Note Ser. 352, Cambridge Univ. Press, 2008.
10. Slices, slabs, and sections of the unit hypercube (with J.-L. Marichal), Online Journal of Analytic Combinatorics 3 (2008), #1, 11 pp.
11. Irreducible polynomials and Barker sequences (with P. Borwein and E. Kaltofen), ACM Commun. Computer Algebra 41 (2007), no. 4, 118-121.
12. Lehmer's problem for polynomials with odd coefficients (with P. Borwein and E. Dobrowolski), Ann. of Math. (2) 166 (2007), no. 2, 347-366.
13. Generalizations of Gonçalves' inequality (with P. Borwein and J. D. Vaaler), Proc. Amer. Math. Soc. 135 (2007), 253-261.
14. Isodiametric problems for polygons, Discrete Comput. Geom. 36 (2006), no. 2, 363-379. (The original publication is available at www.springerlink.com.)
15. A $1 problem, Amer. Math. Monthly 113 (2006), no. 5, 385-402.
16. Traceability in small claw-free graphs (with J. M. Harris), Util. Math. 70 (2006), 263-271.
17. Auxiliary polynomials for some problems regarding Mahler's measure (with A. Dubickas), Acta Arith. 119 (2005), 65-79.
18. Small limit points of Mahler's measure (with D. W. Boyd), Experiment. Math. 14 (2005), 403-413.

Information on published papers, and some more reprints, are available on my vita.

Books

• The second edition of my textbook Combinatorics and Graph Theory, written with John Harris and Jeffry Hirst, is now available. It is published by Springer, in their series, "Undergraduate Texts in Mathematics." You can view the table of contents (PDF format) and the publisher's information on the text.
• The first edition of Combinatorics and Graph Theory, also published by Springer, appeared in 2000. You can view its table of contents, and a brief review at Zentralblatt für Mathematik.
• I am co-author of the Maple V Quick Reference (Brooks/Cole, 1994), with Nancy Blachman.

Upcoming Conferences

You can find me at the following upcoming meetings and conferences.

• Workshop on Discovery and Experimentation in Number Theory, Fields Institute, Toronto, Canada, and IRMACS Centre, Simon Fraser University, Burnaby, Canada, September 22 - 26, 2009. I will attend the western site of the workshop, at IRMACS.
• Southeast Regional Meeting on Numbers (SERMON), Davidson College, Davidson, North Carolina, Spring 2010 (dates to be announced).

Last modified June 3, 2009.