Katherine Naismith

Katherine Naismith, PhD Candidate 
Katherine Naismith

Degrees: Honours BA Mathematics (Wilfrid Laurier University), Master of Mathematics: Combinatorics and Optimization (University of Waterloo)

Supervisor: Bertrand Guenin

What program are you in? What is your research area?

I am currently pursuing a PhD in Combinatorics and Optimization. My research area is in graph theory.

Why did you choose to study in the Faculty of Mathematics? Why did you choose the University of Waterloo?

I started my undergraduate career as a music major, taking some math courses as electives. I soon discovered that I have an aptitude for (and just really enjoy) math – as long as there aren’t any numbers involved! As a result, I switched my major to mathematics, and fell in love with graph theory.

I chose to pursue graduate studies at the University of Waterloo because of UW’s C&O department, which is the only such department in the world, and is also highly regarded by the mathematical community at large. Because the C&O department brings together experts in several different areas, including those I am personally interested in (structural graph theory, topological graph theory, matroid theory), studying at UW seemed like a natural choice.

What are your career goals?

I’d like to pursue a career in academia as a professor.

What has been the most rewarding moment in your graduate career so far?

Probably finishing my Master’s thesis. It’s very exciting to see all the pieces of a challenging research project finally come together, after spending such a long time working on it.

What has been the most challenging part of life as a graduate student?

Time management. As a graduate student, I take far fewer courses at a time than I did during my undergraduate studies, but I also have added academic responsibilities outside of class time, such as doing research for my thesis, and TA duties. So learning the discipline of being hard at work during much of my flexible-seeming time has been something of a change.

What has been your favourite course or project so far in grad school?

My Master’s thesis. It brings together a few different areas of mathematics, and it was particularly interesting to see how results and techniques from these different areas could be used together in powerful ways. The project was also at a level of difficulty where completing it was quite challenging, but very satisfying.

How do you describe combinatorics and optimization to your friends and family?

My area of research is called graph theory, and (not surprisingly) the objects I study are called “graphs”. (Not the graphs from high school math!) A graph is basically a collection of dots, and lines between pairs of dots. How we draw the dots and lines on a piece of paper doesn’t really matter, as long as everything is joined up correctly. We can use this kind of dot-and-line system to represent real-world information, and draw conclusions from it.

For example, each dot might represent a person working in a company, and we could draw a line between two of these dots if the corresponding people communicate directly with each other at work. Then drawing the dots and lines out might tell us something useful about the company: for example, maybe we notice that if we get rid of two particular dots and all the lines attached to them, then the dot-and-line picture falls apart into two pieces. This would tell us that if the corresponding two people are both sick on the same day, then there would be no way for people in the two different parts of the company to communicate, potentially a big problem. Graph theory can also be used in scheduling, shipping, trip planning, and other problems.

How do you spend your time outside of school?

I enjoy knitting, sewing, and other crafts. I also spend a lot of time helping kids in my neighbourhood with homework, both informally and through the Learn English Make Friends program at the Victoria Hills Community Centre.

Do you have any words of advice for people considering or planning graduate studies at the University of Waterloo? What about for people who may be interested in C&O?

UW’s C&O department is a great environment to pursue graduate studies in, and the faculty are very knowledgeable, approachable, and encouraging.