Dr James ( Jim ) Macdougall

Biography

I feel my research output has been a productive one. I am grateful for having had the opportunity to have been involved in so much interesting research work with so many helpful colleagues.

Qualifications

• PhD, University of Newcastle, 2005
• Bachelor of Science (Honours), Dalhousie University - Canada
• Master of Philosophy, University of Waterloo
• Master of Arts, Dalhousie University - Canada

Research

Research keywords

• Graph Theory
• Number Theory

Research expertise

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)

Fields of Research

Centres and Groups

Centre

• PRC - Computer Assisted Research Mathematics and its Applications

Memberships

Learned Academy.

• member - American Mathematical Society
• member - Australian Mathematical Society
• member - Canadian Mathematical Society

Awards

Research Award.

Invitations

Teaching

Teaching keywords

• Mathematics

Teaching expertise

40+ years of teaching a wide variety of mathematics courses at university level

Teaching interests

• Graph Theory and Combinatorics
• Number Theory