Dr Jim Macdougall

Biography

I am grateful for having had the opportunity to have been involved in so much interesting research work with so many helpful colleagues.  Graph labelings, in particular magic and anti-magic labelings. Related combinatorial arrays such as sparse magic and anti-magic squares (collaboration with W. D. Wallis, SIU and J. S. Kimberley and M. Miller, U of Newcastle). Diophantine problems - problems in algebra and geometry that give rise to diophantine equations, especially elliptic curves. These include characterizing polynomials some or all of whose derivatives split into linear factors over the rational integers, and characterizing rational-sided polygons or polyhedra which have rational areas, volume or other parameters. (collaboration with R. H. Buchholz, DSTO) Various problems in graph theory: the structure of the subgraph poset and universal graphs, graphs saturated with respect to triangles or other subgraphs (collaboration with R. B. Eggleton, ISU). Linear algebras with various properties, including homogeneous algebras with a view to describing the structure of various classes, e.g. anti-commutative algebras, nilpotent algebras or quasi-division algebras; spaces of matrices of fixed rank or nilindex. (collaboration with L.G. Sweet, U of PEI)

Research Interest

Mathematics