Michael J. Mossinghoff
	Department of Mathematics Office: Chambers 3039 Davidson College Office hours: TTh 2:30-4:00, WF 3:30-4:00 Box 6996 Phone: 704-894-2238 Davidson, NC 28035-6996 Fax: 704-894-2005

My vita is available, and so are titles and abstracts of many mathematical talks of mine.

You can view my academic family tree.

Teaching

• Fall 2012: Math 113, Calculus II.
• Fall 2012: Math 108, Mathematics & Politics.

Research

• I am an associate editor of Mathematics of Computation.
• SERMON 2010 was held at Davidson College April 16-18, 2010.
• 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

Books

• The second edition of my textbook Combinatorics and Graph Theory, written with John Harris and Jeffry Hirst, appeared in 2008. It is published by Springer, in the series Undergraduate Texts in Mathematics.
• Table of contents (pdf).
• Publisher's information.
• Amazon.
• MathSciNet review.
• Errata.
• The first edition of Combinatorics and Graph Theory, also published by Springer, appeared in 2000.
  • Table of contents (pdf).
• I am co-author of the Maple V Quick Reference (Brooks/Cole, 1994), with Nancy Blachman.

Preprints and Recent Reprints of Research Papers (PDF)

1. Sporadic Reinhardt polygons (with K. Hare), submitted for publication.
2. Between the problems of Pólya and Turán (with T. Trudgian), J. Aust. Math. Soc., to appear.
3. Negative Pisot and Salem numbers as roots of Newman polynomials (with K. Hare), Rocky Mountain J. Math., to appear.
4. The distance to an irreducible polynomial, II (with M. Filaseta), Math. Comp. 81 (2012), no. 279, 1571-1585.
5. Average Mahler's measure and L_p norms of unimodular polynomials (with K.-K. S. Choi), Pacific J. Math. 252 (2011), no. 1, 31-50.
6. Enumerating isodiametric and isoperimetric polygons, J. Combin. Theory Ser. A 118 (2011), no. 6, 1801-1815.
7. The distance to an irreducible polynomial, in Gems in Experimental Mathematics, T. Amdeberhan, L. A. Medina, and V. H. Moll, eds., Contemp. Math. 517, Amer. Math. Soc., 2010.
8. Heights of roots of polynomials with odd coefficients (with J. Garza, M. I. M. Ishak, C. G. Pinner, and B. Wiles), J. Théor. Nombres Bordeaux 22 (2010), no. 2, 369-381.
9. Lower bounds for heights in cyclotomic extensions, (with M. I. M. Ishak, C. Pinner, and B. Wiles), J. Number Theory 130 (2010), no. 6, 1408-1424.
10. Wieferich pairs and Barker sequences, Des. Codes Cryptogr., 53 (2009), no. 3, 149-163. (The original publication is available at www.springerlink.com.) Some data associated with this research is also available.
11. Lower bounds for Z-numbers (with A. Dubickas), Math. Comp., 78 (2009), no. 267, 1837-1851.
12. Minimal Mahler measures (with G. Rhin and Q. Wu), Experiment. Math., 17 (2008), no. 4, 451-458.
13. Sign changes in sums of the Liouville function (with P. Borwein and R. Ferguson), Math. Comp. 77 (2008), no. 263, 1681-1694.
14. An isodiametric problem for equilateral polygons, in Tapas in Experimental Mathematics, T. Amdeberhan and V. H. Moll, eds., Contemp. Math. 457, Amer. Math. Soc., 2008, pp. 237-252.
15. 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.
16. Slices, slabs, and sections of the unit hypercube (with J.-L. Marichal), Online Journal of Analytic Combinatorics 3 (2008), #1, 11 pp.
17. Irreducible polynomials and Barker sequences (with P. Borwein and E. Kaltofen), ACM Commun. Computer Algebra 41 (2007), no. 4, 118-121.
18. Lehmer's problem for polynomials with odd coefficients (with P. Borwein and E. Dobrowolski), Ann. of Math. (2) 166 (2007), no. 2, 347-366.
19. Generalizations of Gonçalves' inequality (with P. Borwein and J. D. Vaaler), Proc. Amer. Math. Soc. 135 (2007), 253-261.

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

Upcoming Conferences

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

• Service Academy Student Mathematics Conference, United States Naval Academy, Annapolis, Maryland, April 19-20, 2012.
• REU program in Computational Algebraic Geometry, Combinatorics, and Computational Number Theory, Clemson University, South Carolina, June 4, 2012.
• Simon Fraser University, June 12-16, 2012.
• The Twelfth Meeting of the Canadian Number Theory Association, University of Lethbridge, Alberta, June 17-22, 2012.
• Palmetto Number Theory Series (PANTS) XVIII, Wake Forest University, Winston-Salem, North Carolina, September 15-16, 2012.
• AMS Eastern Sectional Meeting, especially the Special Session on Analytic Number Theory, Rochester Institute of Technology, New York, September 22-23, 2012.
• Palmetto Number Theory Series (PANTS) XIX, University of South Carolina, Columbia, December 1-2, 2012.
• Joint Mathematics Meetings, especially the AMS Special Session on Mathematics of Computation: Algebra and Number Theory, San Diego, California, January 9-12, 2013.
• MAA Southeastern Section Meeting, Winthrop University, Rock Hill, South Carolina, March 15-16, 2013.
• Southeast Regional Meeting on Numbers (SERMON), High Point University, North Carolina, spring 2013 (dates TBA).

Last modified May 11, 2012.