Teaching:
Semester A, 2011: Linear Algebra/Linear Algebra for Engineers, MATH253-11A/ENGG283-11A.
Course material for this subject is on MOODLE.
MOODLE can be accessed via http://www.waikato.ac.nz/student
Research:
My research interests are chiefly in combinatorics, which is a branch of discrete mathematics, which is a branch of pure mathematics.
Within combinatorics, I do a lot of work on latin squares, latin trades or bitrades and graph decompositions. Latin trades connect with many branches of pure mathematics including geometry (eg: partitioning an integer-sided triangle into smaller, integer-sided triangles), finite field theory (in particular Weil’s theorem has been useful), group theory (some latin trades may be defined in terms of a group with specified properties) and linear algebra.
A latin square of order n is an nxn array of symbols 1,2,....,n such that each symbol occurs exactly once in each row and once in each column. Below is a latin square of order 4. Note that a completed Sudoku puzzle is a type of latin square of order 9.
|
3 |
4 |
1 |
2 |
|
4 |
2 |
3 |
1 |
|
2 |
1 |
4 |
3 |
|
1 |
3 |
2 |
4 |
Problems in combinatorics are often easy to state but sometimes hard to solve. For potential research students who enjoy puzzles, I have many fun potential thesis topics!
Biography:
Dr Nick Cavenagh was awarded a PhD in Pure Mathematics from The University of Queensland, Australia, in October 2003. Since then he has worked as a postdoctoral research fellow at Charles University (Czech Republic), the University of New South Wales (Australia) and Monash University (Australia). His chief research interests are latin squares, latin trades and graph decompositions which are topics within combinatorics. Latin trades in particular have connections to geometry, topological graph theory, group theory and finite field theory. Dr Nick Cavenagh was awarded a Kirkman medal in 2008 from the Institute of Combinatorics and its Applications.