This was a question Jason Klusowski asked himself when he embarked on his first year at the University of Manitoba. Jason, along with his two siblings, were home-schooled for their entire K-12 education. After finishing grade 12, Jason didn't go directly to post-secondary education, but spent a year working at Investors. His original intention was to go to university and take business and finance. So, he started taking first-year courses: namely calculus and algebra, to satisfy the program pre-requisites.
As a home-schooled student, Jason wasn't sure how he would do at university. Was his education up to snuff?
Jason attributes his change in plans to what he saw as the challenge posed by Dr. Sasho Kalajdzievski in first-year calculus. Kalajdzievski said: "Calculus is perhaps the most difficult first-year mathematics course!" Jason understands this as a defining moment. Despite his concerns about homeschooling, he made calculus THE course where he had to prove himself. As a result, he really pushed himself in his course work - especially in calculus.
In retrospect, Jason muses: "Home-schooling teaches you to be an independent thinker. You have to hammer away at problems and find the solutions on your own. You don't have other people to help you. I think it is the challenge of working through something that is difficult that ultimately drew me to mathematics."
Jason recalls: "I worked really hard. You have to work really hard in Mathematics; solutions don't come easily. I challenged myself by solving the problems at the back of the textbook: the most difficult yet elegant problems. I drew a tremendous amount of satisfaction from cracking them; it turned out to be highly rewarding."
The Possibilities of Probabilty
In his second year, Jason was drawn to what he saw as the tremendous insights associated with working with probability. He explains: "Probability showed me how intuition can so easily be wrong. I would work on problems, expecting to find the answer in one direction, but instead discovering the result to be much different. Probability is a powerful tool that we humans need to teach us how intuition can be faulty."
Jason is now a Statistics/Mathematics student in a Joint Honours Program in the Faculty of Science. He explains: "It made sense for me to choose the only program that would give me an in-depth exposure to fields of enormous interest and challenge to me."
Jason's hard work paid off, not only did he do well, he excelled, and he subsequently applied for and was awarded a National Science and Engineering Research Council (NSERC) Undergraduate Summer Research Award (USRA). It was just the beginning of the academic accolades to come.
"I first found out about the undergraduate awards from Dr. Katherine Davies of the Department of Statistics. She announced the competition at the beginning of one of the classes she was teaching," says Jason. He followed-up with the process and was granted his first award in 2011. The 2012 award is his second.
During his 2012 NSERC summer research award, he spent a lot of time on percolation theory and branching processes.
Percolation theory describes the properties of a liquid flowing through a disordered porous medium. It is the mathematical analysis of the behaviour and properties of clusters in a randomly generated graph. Imagine the existence of edges in the graph as indicating whether liquid can flow from one point to another.
One type of branching process models a population whose members may have off-spring and whose descendants branch out as new members are born, (as in a family tree). He spent some time working on the Galton-Watson process: one of many different branching processes.
In Victorian times, there were concerns that certain aristocratic family name lines were dying out. Francis Galton posed the statistical problem in an 1873 journal, and the Reverend Henry William Watson proposed a solution. Together they wrote a paper describing what was to become the Galton-Watson process.
Jason also worked on some occupancy and urn type problems, and problems in stochastic processes and martingales.
Jason says: "This particular Undergraduate Student Research Award (USRA) was a rare opportunity for me explore anything that peaked my curiosity. My supervisor, Dr. David Gunderson from the Department of Mathematics has unending supply of stimulating problems in combinatorics, graph theory, and probability."
As part of the USRA, Jason gave a presentation at the Canadian Undergraduate Mathematics Conference at the University of British Columbia, Okanagan campus. The presentation called, Flows, Branching, Numbers, and Percolation on Trees, discussed some concepts and results in branching processes and percolation theory.
"I think it's crucial to put some time into researching your potential supervisor for the award. Choose someone whose interests match yours. This may involve doing some website research and speaking with a few potential supervisors to get an idea of what they do and what they expect from you during the summer. Also, since the awards are competitive, achieving high grades in your classes will increase your chances of being successful in your application."
"I would like to attend graduate school to study mathematical statistics and probability. It is my hope that this will lead to a PhD and a career in academia."
Jason is also interested in the psychology behind certain behaviours. For example, given what statisticians know about gambling, what is their propensity to become gamblers?
Jason continued to work hard and to excel in his university courses. In 2013, he graduated with a B.Sc. (Hons.) in Mathematics and Statictics, and was awarded the Bachelor of Science Gold Medal in the Honours program and the Univeristy of Manitoba Governor General's Silver Medal. The Governor General's medal is granted to the student who achieves the highest academic standing at the University of Manitoba at the undergraduate level. An outstanding accomplishment!
Undergraduate student research award projects in the Faculty of Science are funded by various sources such as the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Faculty of Science and the grants held by professors at the University of Manitoba.
Students apply for awards during the Fall Term. Check with the Departments in Science for deadlines.
Jason with his NSERC supervisor, Dr. David Gunderson
A rooted tree with a path of length three - the dotted lines.
Illustration from Jason's July 2012 Math conference presentation at UBC