Department of Mathematical Sciences
Combinatorics and Optimization
The Department of Mathematical Sciences has a small active group with interests in discrete mathematics, matroid theory, combinatorial optimization, graph theory and probabilistic methods. Each year the department offers 5-6 combinatorics and optimization courses at the junior, senior and graduate levels. These courses cover the methods, the models, and the theory of discrete optimization, linear programming and graph theory. An important component in these courses is the use of technology software such as LINDO. In alternate semesters, special topics courses in combinatorics and optimization are offered at the graduate level. Recent topics have included algebraic combinatorics, matroid theory, and linear algebra methods. In addition there is a weekly seminar on combinatorics and optimization - recent topics have included: probabilistic methods in discrete mathematics, randomized algorithms, discrete geometry and convex polytopes. Usually two or three distinguished researchers from academia or industry visit our department each year to give invited lectures and consult. The group organizes the NSF- sponsored Big Sky Conference on Discrete Mathematics, which brings together researchers from neighboring states and provinces. A conference highlight is the evening President's Lecture in which the beauty and wonder of mathematics are shared with the general public. The Presidential Lecturer for 2000 was John H. Conway of Princeton University.
Combinatorics and Optimization Faculty
Prof. Mark Kayll, Ph.D., Rutgers University, 1994
Research interests: discrete mathematics, probabilistic methods, optimization, theoretical computer science.
Selected publications:
  • On the Stochastic Independence Properties of Hard-core Distributions, Combinatorica 17 (1997), 369-391 (with J. Kahn).
  • Asymptotics of the total chromatic number for multigraphs, Australasian Journal of Combinatorics 19 (1999), 279-281. 
  • Asymptotically good choice numbers of multigraphs , Ars Combinatoria, to appear. 
  • On pebbling threshold functions for graph sequences (with Andrzej Czygrinow, Nancy Eaton and Glenn Hurlbert), submitted for publication. 

Prof. Jenny McNulty, Ph.D., University of North Carolina at Chapel Hill, 1993 Research interests: matroid theory, combinatorics. Selected publications:
  • Connected Hyperplanes in Binary Matroids, Journal of Combinatorial Theory, Series B 79 (2000), 87-97, (with H. Wu).
  • The Matroid Ramsey Number n(6,6), Combinatorics, Probability & Computing 8 (1999), 229-235, (with J. Bonin and T.J. Reid).
  • On Amalgams and Density of Uniform Matroids, Congressus Numerantium 136 (1999), 193-199, (with J. Corp).
  • Ports and Oriented Matroids, Congressus Numerantium, 96 (1993), 11-20.
 		Prof. George McRae, Ph.D., University of Washington, 1967
Research interests: homological algebra, ring theory, category theory, operations research. Selected publications:
  • A Network Model for Determining Trunk Lines with Redundancy, Ninth Annual Proceedings of American Institute for Decision Sciences, (1980) 187-190. (with Hien Nguyen).
  • On Karmarkar's New Projective Algorithm-Theory and Applications (invited address), Decision Sciences Institute (Phoenix 1986).

Other faculty members with interests and backgrounds in probability, statistics, algebra, analysis, computing and mathematical modeling often interact with and participate in the combinatorics and optimization activities of the department.

Mathematical Sciences | The University of Montana