B.Math (Hons), B.Ed., M.Sc., PhD

Inst. Math.& Statistics & Coordinator
School of STEM
Faculty of Arts and Sciences
Mathematics & Statistics

604.986.1911 ext. 3409
Fir Building, room FR477
paulottaway@capilanou.ca

Education

PhD, Mathematics, Dalhousie University, 2009.

M.Sc., Mathematics, Dalhousie University, 2003.

B.Ed., Queen's University, 2002.

B.Math (Honours, Dean's List), Combinatorics and Optimization, University of Waterloo, 2002.

"Finding the answer to a mathematics problem is often only the first step in finding a solution."

Bio

Paul Ottaway (PhD, Dalhousie, 2009) is a mathematician whose main research is in the field of combinatorial games. He also holds interests in math competitions and math education.

After completing degrees at University of Waterloo, Queen's University and Dalhousie University, Ottaway completed post-doctoral work at the University of British Columbia. He has held positions at Thompson Rivers University and Capilano University as well as an adjunct professorship at Dalhousie University. He has served as Coordinator of the Mathematics and Statistics department at Capilano University since 2018.

The most significant of Ottaway's research in combinatorial games is his contribution to the analysis of "misere" games in which both players are trying to lose. Recently, he has explored connections between combinatorial and economic games along with Melissa Huggan.

Ottaway has served on the Canadian Mathematics Competition (CMC) committees since 2001, helping design national math contests for students in grades 7 through 12.

My passion for mathematics stems from the challenge of solving puzzles. I believe mathematics is a toolbox of skills rather than a set of procedures to be memorized.

As such, I'm always looking for new and interesting ways to use the tools at my disposal to approach problems in novel ways and to find multiple solutions using a different set of techniques. I try to instill this in my students by frequently revisiting problems and asking for another way to arrive at the answer or asking questions which are unlike any they have seen before.

The true test of mastery is not repeating what is shown in class but to apply your knowledge to new and different situations.

Combinatorial games are defined as having two players (denoted Left and Right) complete information and no element of chance. Under "normal play", a player loses if they cannot make a legal move on their turn. A simple game that falls into this category includes NIM. Many other games such as HEX, chess and go can be analyzed using similar techniques by making only small modifications to their rules.

My own research largely focuses on "misere play" where both players are trying to lose. The mathematics is much less intuitive and was unknown for many decades since its formal introduction in "Winning Ways" but has now been the topic of numerous theses and research papers as the area becomes more developed.

Finbow, S., Gaspers, S., Messinger, M.E., Ottaway, P. A Note on the Eternal Dominating Set Problem, International Journal of Game Theory, 2018.

Harding, P., Ottaway, P.Impartial Edge Deletion Games with Parity Rules, INTEGERS, 2013.

Milley, R., Nowakowski, R. J., Ottaway, P.. The Misre Monoid of One-Handed Alternating Games, INTEGERS, 2012.

Nowakowski, R. J., Ottaway, P. Option-Closed Games, Contributions to Discrete Mathematics, 2011.

Mesdal, G. A., Partizan Splittles, Games of No Chance 3, 2009.

Mesdal, G. A., Ottaway, P. Simplification of Partizan Games in Misre Play, INTEGERS, 2007.

Nowakowski, R. J., Ottaway, P. Vertex Deletion Game with Parity Rules, INTEGERS, 2005.

Ottaway, P., Polyas Paragon. Non-refereed Monthly Column, Mayhem/CRUX, 2002-2003.

*Authors are listed in alphabetical order, the names of student co-authors are underlined, and G.A.Mesdal is a pseudonym representing the participants of the 2006 Games-At-Dal conference, including myself.

Izaak Walton Killam Memorial Scholarship, Dalhousie University, 2004-07.

Postgraduate Scholarship D, National Science and Engineering Research Council (NSERC), 2003-06.

Postgraduate Scholarship A, National Science and Engineering Research Council (NSERC), 2002-03.

I. Miller Scholarship, University of Waterloo, January 2001.