Michael J. Mossinghoff

Curriculum Vitae

Education

• Ph.D., Mathematics, University of Texas at Austin, 1995.
• M.S., Computer Science, Stanford University, 1988.
• B.S., Mathematics, Texas A&M University, 1986, Summa Cum Laude.

Academic Positions and Experience

• Associate Professor, Department of Mathematics, Davidson College, 2006-present.
• Visiting Associate Professor, Department of Mathematics, University of South Carolina, 2008-2009.
• Assistant Professor, Department of Mathematics, Davidson College, 2002-2006.
• Visitor, Simon Fraser University, summers 2002-05 (IRMACS, 2005).
• Adjunct Assistant Professor, Program in Computing, Department of Mathematics, UCLA, 1998-2002.
• Visitor, Centre for Experimental and Constructive Mathematics, Simon Fraser University, and University of British Columbia, summer 1997.
• Assistant Professor, Department of Mathematical Sciences, Appalachian State University, 1995-1998.
• Software Engineer, E-Systems (now part of Raytheon), Garland, Texas, 1988-1989.

Awards

• Lester R. Ford Award, Mathematical Association of America, 2007, for the article A $1 problem, published in The American Mathematical Monthly, 113 (2006), no. 5, 385-402. The citation is available in the prize book.
• Robert Sorgenfrey Distinguished Teaching Award, UCLA, 2000.
• University Fellowship, University of Texas at Austin, 1991-1992.
• Dodd Teaching Excellence Award, University of Texas at Austin, 1990.

Publications

Research Articles

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.
19. The Mahler measure of polynomials with odd coefficients (with P. Borwein and K. G. Hare), Bull. London Math. Soc. 36 (2004) 332-338.
20. Polynomials with restricted coefficients and prescribed noncyclotomic factors, LMS J. Comput. Math. 6 (2003), 314-325.
21. Newman polynomials with prescribed vanishing and integer sets with distinct subset sums (with P. Borwein), Math. Comp. 72 (2003), 787-800.
22. Polynomials with height 1 and prescribed vanishing at 1 (with P. Borwein), Experiment. Math. 9 (2000), 425-433.
23. Rudin-Shapiro-like polynomials in L₄ (with P. Borwein), Math. Comp. 69 (2000), 1157-1166.
24. Polynomials with small Mahler measure, Math. Comp. 67 (1998), 1697-1705, S11-S14.
25. Perturbing polynomials with all their roots on the unit circle (with C. Pinner and J. Vaaler), Math. Comp. 67 (1998), 1707-1726.

Books

1. Combinatorics and Graph Theory (with J. Harris and J. Hirst), second edition, Springer-Verlag, Undergrad. Texts Math., 2008. Table of contents. Errata.
2. Combinatorics and Graph Theory (with J. Harris and J. Hirst), Springer-Verlag, Undergrad. Texts Math., 2000. Table of contents.
3. Maple V Quick Reference (with N. Blachman), Brooks/Cole, 1994.
• German translation, Maple Griffbereit, Vieweg Verlag, 1995.
• Japanese translation, ITP Japan, 1997.

Websites

• Lehmer's Problem.
• Wieferich pairs, Barker sequences, and circulant Hadamard matrices.

Expository Article

• The eccentricities of actors (with J. Harris), Math Horizons, Feb. 98, 23-25. Reprinted (with a new afterword) in The Edge of the Universe: Celebrating Ten Years of Math Horizons, MAA Press, 2006.

Thesis

• Algorithms for the determination of polynomials with small Mahler measure, 1995 (160K gzip'd PostScript).
  Thesis advisor: Jeffrey D. Vaaler.

Research Presentations

Filled disks (•) indicate invited addresses; open circles (o) stand for contributed talks.

Titles of all talks (and some abstracts) are available.

2009

• Special Session on Analytic Number Theory, AMS Fall Eastern Section Meeting, Pennsylvania State University.
• Workshop on Discovery and Experimentation in Number Theory, IRMACS Centre, Simon Fraser University, Burnaby, Canada, and Fields Institute, Toronto, Canada.
• Southeast Regional Meeting on Numbers, University of North Carolina, Greensboro.
• Number Theory Seminar, University of South Carolina, Columbia (April).
• Special Session on Number Theory in the Spirit of Erdös, AMS Spring Central Section Meeting, University of Illinois at Urbana-Champaign.
• Number Theory Seminar, University of South Carolina, Columbia (March).
• Special Session on Experimental Mathematics, Joint Mathematics Meetings, Washington, D.C.

2008

• Palmetto Number Theory Series (PANTS) VIII, University of South Carolina, Columbia.
• Combinatorics Seminar, University of South Carolina, Columbia.
• Mini-Conference on Discrete Mathematics and Algorithms, Clemson University, South Carolina.
• Number Theory Seminar, University of South Carolina, Columbia.
• The Tenth Meeting of the Canadian Number Theory Association, University of Waterloo, Ontario.
• The Mathematical Interests of Peter Borwein, Simon Fraser University, Burnaby, B.C., Canada.
• AMS Spring Western Section Meeting, Special Session on Diophantine Problems and Discrete Geometry, Claremont McKenna College, Claremont, California.

2007

• Palmetto Number Theory Series (PANTS) IV, University of South Carolina, Columbia.
• Palmetto Number Theory Series (PANTS) III, College of Charleston, Charleston, South Carolina.
• Southeast Regional Meeting on Numbers, Wake Forest University, Winston-Salem, North Carolina.
• MAA Southeastern Section Meeting, Georgia Southern University, Statesboro, Georgia.
• AMS Southeastern Section Meeting, Davidson, North Carolina.
• AMS Special Session on Experimental Mathematics in Action, Joint Mathematics Meetings, New Orleans.

2006

• Discrete Mathematics Seminar, Temple University.
• Colloquium, Center for Communications Research, Princeton.
• The Ninth Meeting of the Canadian Number Theory Association, Vancouver.
• Workshop on the Computational Complexity of Polynomial Factorization, American Institute of Mathematics Research Center, Palo Alto, California.
• Number Theory and Polynomials, Heilbronn Institute for Mathematical Research, Bristol, England.
• Southeast Regional Meeting on Numbers, Furman University, Greenvile, South Carolina.
• Mahler Measure in Mobile, University of South Alabama, Mobile.

2005

• Colloquium, Wake Forest University.
• Consortium for Computational Science and High Performance Computing, Appalachian State University, Boone, North Carolina.
• Computer Algebra Seminar, Center for Experimental and Constructive Mathematics, Simon Fraser University, British Columbia, Canada.
• Variations on Mahler's Measure, Centre International de Rencontres Mathématiques, Luminy, France.
• Southeast Regional Meeting on Numbers, University of South Carolina.
• Number Theory Seminar, University of South Carolina.
• Joint Mathematics Meetings, Atlanta, Georgia.

2004

• Workshop on Explicit Methods in Number Theory, Banff International Research Station, Canada.
• The Eighth Conference of the Canadian Number Theory Association, Toronto.
• Southeast Regional Meeting on Numbers, Charleston, South Carolina.
• Colloquium, University of South Alabama, Mobile.

2003

• Western Number Theory Conference, Monterey, California.
• Summer program on Mahler's Measure, Simon Fraser University, Canada (two talks).
• Research Experiences for Undergraduates in Computational Number Theory and Combinatorics, Clemson University.
• Workshop on the Many Aspects of Mahler's Measure, Banff International Research Station, Canada.
• Colloquium, University of South Carolina, Columbia.
• Southeast Regional Meeting on Numbers, Greensboro, North Carolina.
• Algebra and Discrete Mathematics Seminar, Clemson University.
• Joint Mathematics Meetings, Baltimore, Maryland.

2002

• Colloquium, Appalachian State University, Boone, North Carolina.
• Excursions in Computational Number Theory -- Polynomials with Integer Coefficients, MSRI Summer Graduate Program, Simon Fraser University.
• Combinatorics Seminar, Caltech.
• Graduate Student Number Theory Seminar, UCLA.
• Colloquium, Department of Mathematics, Statistics, and Computer Science, Marquette University.
• Joint Mathematics Meetings, San Diego, California.

2001

• Mathematics Department Colloquium, Kansas State University.
• Number Theory Seminar, Kansas State University.
• Center for Computing Sciences, Bowie, Maryland.
• Computer Science Department Colloquium, Clemson University.
• Southeast Regional Meeting on Numbers, Furman University, Greenville, South Carolina.
• Dynamical Systems Seminar, UCLA.
• Combinatorics Seminar, Caltech.

2000

• Western Number Theory Conference, San Diego.
• Number Theory Seminar, University of Texas at Austin.
• Combinatorics Seminar, Caltech.

1999

• Western Number Theory Conference, Monterey.
• The Sixth Conference of the Canadian Number Theory Association, Winnipeg.
• Combinatorics Seminar, Caltech.
• Graduate Student Seminar, UCLA.

1998

• Western Number Theory Conference, San Francisco.
• Southeast Regional Meeting on Numbers, University of North Carolina, Greensboro.
• MAA Southeastern Section Meeting, Charleston, South Carolina.

1997

• Special Session on Concrete Aspects of Real Polynomials, AMS Southeastern Section Meeting, Atlanta, Georgia.
• AMS Special Session on Interactions Between Ergodic Theory and Number Theory, Joint Mathematics Meetings, San Diego, California.
• Conference on Experimental and Constructive Mathematics, Simon Fraser University.
• Southeast Regional Meeting on Numbers, University of Georgia, Athens.
• Colloquium, Appalachian State University.

1996

• The Fifth Conference of the Canadian Number Theory Association, Carleton University.
• Southeast Regional Meeting on Numbers, Wake Forest University.
• Number Theory Seminar, University of Georgia at Athens.
• Colloquium, Appalachian State University.

1995

• International Conference on Analytic Number Theory, Allerton Park, Illinois.
• Number Theory Seminar, University of Texas at Austin.

1994

• Number Theory Seminar, University of Texas at Austin.

1993

• Number Theory Seminar, University of Texas at Austin.

Presentations for Undergraduates and General Audiences

• Shenandoah Undergraduate Mathematics and Statistics Conference, James Madison University, Harrisonburg, Virginia, October 18, 2008.
• Elon University, May 2005.
• Davidson College, February 2005.
• Davidson College, October 2003.
• Pi Mu Epsilon, University of South Carolina, April 2003.
• Super Competition (high school contest), University of North Carolina, Charlotte, March 2003.
• Davidson College, February 2002.
• California Polytechnic State University, October 2002.
• Mathematics Awareness Month Series, UCLA, April 2002.
• California Lutheran University, March 1999.
• Washington and Lee University, September 1997.
• Inaugural Mathematics Colloquium, High Point University, September 1997.
• Western Carolina University, February 1997.
• Davidson College, October 1996.
• Appalachian State University, March 1995.

Selected Titles

• Stop! Are regular octagons optimal?
• Kevin Bacon and small world networks.
• Ordinary lines and extraordinary proofs.
• Fermat's last theorem: As easy as ABC.
• How not to send a secret message.
• Three proofs of the infinitude of primes.

Abstracts of many of these talks are also available.

Teaching

09-10

Combinatorics, real analysis, object-oriented programming, calculus.

08-09

Probability, number theory, calculus.

07-08

Cryptology, object-oriented programming, data structures, calculus.

06-07

Real analysis, combinatorics, number theory, analysis of algorithms, data structures, theory of computation (independent study).

05-06

Number theory, combinatorics, data structures, object-oriented programming, calculus, theory of computation (independent study), cryptology (independent study).

04-05

Analysis of algorithms, data structures, introductory programming, linear algebra.

03-04

Number theory, linear algebra, object-oriented programming, introductory programming, calculus.

02-03

Cryptography, linear algebra, object-oriented programming, data structures and algorithms.

01-02

Cryptography, internet programming, data structures and algorithms, precalculus.

00-01

Data structures and algorithms (introductory and advanced), introductory programming.

99-00

Cryptography, internet programming, data structures and algorithms (introductory and advanced), introductory programming.

98-99

Combinatorics, data structures and algorithms, introductory programming, freshman math seminar (advisor).

97-98

Combinatorics, problem solving, calculus 1, 2, and 3.

96-97

Real analysis (graduate), number theory, cryptography, linear algebra, calculus 1 and 2.

95-96

Real analysis (undergraduate), number theory, calculus 1, precalculus.

94-95 (assistant instructor)

Number theory, mathematics for liberal arts honors students, college algebra.

92-94 (math department computer consultant)

Maple, Mathematica, C programming, Unix, aspects of the computer system.

85-86, 89-91 (teaching assistant)

Business and engineering calculus.

Professional Service

• External examiner, Ph.D. thesis, Keshav Mukunda, Simon Fraser University, Pisot and Salem numbers from polynomials of height one, July 2007.
• Referee for Mathematics of Computation, Proceedings of the American Mathematical Society, American Mathematical Monthly, Experimental Mathematics, Journal of Number Theory, Journal de Théorie des Nombres de Bordeaux, Journal of Combinatorial Theory (Series A), Discrete Mathematics, Illinois Journal of Mathematics, Indian Journal of Pure and Applied Mathematics, Surveys in Mathematics and its Applications, Utilitas Mathematica, Algorithmic Number Theory Symposium, and other publications.
• Reviewer, Mathematical Reviews.
• Question writer/editor, Math Jeopardy, MAA-SE 2004-09, MAA MathFest 2006-08.

Professional Societies

• American Mathematical Society
• Association for Computing Machinery
• Mathematical Association of America