Complex equations, bits of Greek alphabet and brackets of one kind or another often fill a white board in Michele Mosca’s office at the University of Waterloo.
They form numerical sentences about mysterious things in the universe that words inadequately describe.
How those jottings ended up there, in an office occupied by one of Canada’s leading mathematicians, in the Mike & Ophelia Lazaridis Quantum-Nano Centre — one of the most technologically advanced buildings in the country, comes down to this: Waterloo can’t contain its excitement for mathematics.
“If it wasn’t for the math contests and camps, I wouldn’t have come to Waterloo, or gone to Oxford, or co-founded the Institute for Quantum Computing,” Mosca says. “It would never have opened my eyes to all the other opportunities that were out there.”
Every year about 200,000 students in senior elementary classes and high schools around the world try mathematics and computer science contests prepared by Waterloo’s Centre for Education in Mathematics and Computing (CEMC). This year, the mathematics outreach program marks its 50th anniversary.
Mosca remembers his math mind catching fire in Grade 9, thanks to an Essex County teacher who challenged him with increasingly difficult problems to solve.
He went on to write Waterloo contests and travel to Waterloo for math field trips.
And he spent Sundays at math sessions coached by Bruce White, a well-known Windsor-area educator.
Tough mentor
The atrium in Mathematics 3, Waterloo’s newest math and computer science building, bears White’s name. The distinction could have gone to donor John Hele, a Waterloo grad who is now executive vice-president and chief financial officer of MetLife Inc., and donated $500,000 to the Faculty.
Hele opted to honour the tough math teacher he had in high school.
“I teach math as a language, so I teach (students) how to look at questions,” says White, who continues to hold math sessions in Essex County as a retiree. “There are three things I say: ‘What does it say? What does it mean? What does it do?’
“Ninety-nine per cent of the kids I first meet have one question: ‘What’s the answer, what’s the answer, what’s the answer?’”
In Grade 11, Mosca was one of the top 60 math students in the country. In his final year of high school, he won bronze in the (René) Descartes competition, a CEMC product of the time. When he graduated from Waterloo (BMath, 1995), Mosca took home the Mathematics Alumni Gold Medal.
Contests and conferences encourage young students — and their teachers — to celebrate their abilities, and stretch them even further, Mosca says during an interview at his office in the Mike & Ophelia Lazaridis Quantum-Nano Centre.
He uses a sports analogy: “If you never get to play with good people, you’ll never grow as a hockey player. The same is true in other areas … We need to make sure kids experience math in a positive way.”
Ralph Stanton’s legacy
Waterloo has been a pacesetter in mathematics and computer science almost from its start in 1957. When the Faculty of Arts was formed in 1960, mathematics was a department led by Ralph Stanton. Stanton had a passion for Portuguese literature and loud ties, and sharp eye for scholarly talent.
Among his recruits was a young systems engineer, James Wesley (Wes) Graham. Graham would go on to turn Waterloo’s new computer science program into a world leader, pushing computers to be more user-friendly as they processed larger and larger amounts of information.
Stanton argued that mathematics was neither an art nor a science, and should have its own faculty. The university eventually agreed.
His department became the Faculty of Mathematics in January 1967— an achievement that remains unmatched in Canada. Less than 18 months later, the first math and computer science building opened.
Students unfurled a bolt of pink fabric down one side of the structure, a nod to Stanton’s vibrant neckwear. The pink tie endures as the Faculty’s symbol.
“I think we’re a place that attracts students who were the best in their schools,” says Ian Goulden, dean of mathematics. “We’re able to challenge them.”
Mathematics is the Faculty in which the David R. Cheriton School of Computer Science resides. Waterloo’s landmarks in computer science include developing the WATFOR and WATFIV compilers used between the 1960s and 1980s to speed up processing and locate errors when programs went awry.
Waterloo researchers moved the bulky Oxford English Dictionary to a database. Software companies that have spun out of Waterloo’s research in computer science include Maplesoft and OpenText.
Math’s outreach off-campus is just as wide. Waterloo wants students to view math as something that shapes their world instead of so much homework that drags it down.
The joy of competition
To whet their appetites, CEMC develops and delivers more than a dozen competitions, many of them named after famous mathematicians. The list includes Blaise Pascal, Evariste Galois and Hypatia, a Greek mathematician who worked out her calculations about 1,700 years ago. More than 200,000 students register annually for the contests.
The centre runs the Canadian Team Mathematics Competition, the Canadian Computing Competition and the Beaver Computing Challenge. Every September, high school and elementary students sign up for Math Circles on campus.
Formed in 1995, CEMC has roots going back to Stanton and his colleagues.
“They wanted to advance the cause of mathematics and computing by trying to help teachers interest more of their students in mathematics at the high school and elementary levels,” says Ian VanderBurgh, CEMC director.
Today, CEMC oversees an unusual academic offering in Canada — an online Master of Mathematics for Teachers, aimed at high school and college instructors who want to re-energize their methods and material. Every August, CEMC draws math and computer science teachers to campus for conferences.
Stanton’s math department regarded contests as a means of enriching the mathematics experience for students languishing in the conventional school curriculum.
It takes a small army of markers — mostly current and retired high school teachers — to check the problem solutions on almost 45,000 full solution contest entries. They return for marking sessions on campus year after year.
“The people who come are so committed to helping students with math,” VanderBurgh says.
Judy Shanks, a high school mathematics teacher in Ajax, has been marking CEMC contests for 13 years. Contests, she says, bring out “characteristics of curiosity, determination and sheer delight” as students move from understanding a problem to solving it.
“They love the learning process and being able to push themselves past the level they are currently at. Contests provide another opportunity for students to pursue their love of learning in mathematics.”
When Judith Koeller talks to female students, she rolls back the stereotype that math is a geeky, anti-social pursuit.
“That’s really a narrow view of what math is,” says Koeller, one of CEMC’s associate directors. “There is actually a lot of collaboration with other people, and integrating math with other interests that people have …There is a lot of social science to it.
“Somebody with a background in mathematics can collaborate in almost any field …Our goal is to paint an accurate picture of what is involved in math, in the hope that a talented woman wouldn’t turn down the opportunity.”
- The Centre for Mathematical Medicine, of which Waterloo is a founding member. The more math reveals about such things as the function of the brain and the characteristics of cancer, the better doctors become at diagnosing and treating problems.
- The School of Accounting and Finance (within the Faculty of Arts). It studies financial markets, including how executives behave in them.
- Waterloo is also home to WatRISQ — the Waterloo Research Institute in Insurance, Securities and Quantitative Finance.
- WatCAR, the Waterloo Centre for Automotive Research. Researchers apply mathematics in computer modelling to test new materials for lighter automobiles and new systems for safer driving.
Waterloo excels at turning computers into laboratories, and experiments into logarithms.
“With computers, you can replicate experiments several times and share that with other scientists,” says Félix Njap, pointing out a big, clean advantage mathematical modelling has over biological samples.
Njap has joined Sue Ann Campbell, who heads the Department of Applied Mathematics at Waterloo, and Frances Skinner of the Toronto Western Research Institute, to run tests across 30,000 virtual brain cells — digital proxies for real neurons in the hippocampus.
The researchers observe how the virtual neurons respond to conditions that change as the algorithms are altered.
“There are things you can’t get out of a (classical) experiment,’’ Campbell says. “We don’t know which neurons are connected together — who’s talking to who. But with a computer, we can try different things. You might see something you only see when people are sick.”
Waterloo continues to push into new frontiers of mathematics, moving concepts that Ralph Stanton and his colleagues might have discussed 50 years ago closer to reality.
Now deputy director of IQC, Mosca is an expert in the emerging field of quantum cryptography. And he is a founding member of the Perimeter Institute for Theoretical Physics.
Cryptography studies how information can be coded and kept away from adversarial eyes. Quantum adds another layer: The potential for quantum computers — computers than encode and manipulate information in quantum systems, such as atoms and photons — to exploit quantum parallelism and solve problems, including breaking some of the fundamental codes protecting the internet, that were thought to be impenetrable. Complementary to this, quantum physics makes eavesdropping on quantum bits intrinsically detectable, and this leads to cryptographic tools that rely on the laws of physics and are immune to advances in computing technologies.
SUE ANN CAMPBELL, head of Waterloo’s department of Applied Mathematics, applies mathematical modelling to run tests on virtual brain cells. “With computers, you can replicate experiments several times and share that with other scientists,” says postdoctoral researcher FELIX NJAP, who works with Campbell.
Mosca is also a patient advocate for mathematics. In 2006, his name was among 200 on a petition to keep calculus on the Ontario high school curriculum.
Math, he says, shouldn’t be regarded simply as a numerical study; it should be appreciated for how it compels people to apply reason to problems.
Innumeracy is as much a social concern as illiteracy, he adds.
“How can you understand compound interest or climate change if you don’t understand the numbers?” Mosca says.
“People joke about how they can’t do math and fractions, but nobody jokes that they can’t read.”
If it wasn’t for the math contests and camps, I wouldn’t have come to Waterloo, or gone to Oxford, or co-founded the Institute for Quantum Computing.
I think we’re a place that attracts students who were the best in their schools. We’re able to challenge them.
Quantum cryptography: Way beyond the secret decoder ring
Diplomats and spies have used mathematics to hide information from the eyes of snooping adversaries for centuries. Math is at the core of an old and respected science known as cryptography.
The University of Waterloo has its own Centre for Applied Cryptographic Research looking into new ways of keeping communications secure.
Meanwhile, researchers at the Institute for Quantum Computing (IQC) are giving the subject a 21st-century makeover.
With quantum mechanics, cryptography soars to a new level of complexity in the quest for securely moving information among people or machines.
Classical computers use a binary system of ones and zeros to share information. Quantum computers use atomic particles, or qubits. Still under development, quantum computing holds the promise of super-fast processing of rich information. And with that, unbreakable codes.
As a leader in this emerging field, IQC brought the third annual Conference on Quantum Cryptography (QCRYPT) to Waterloo in August. The first QCRYPT conferences were held in Zurich, Switzerland (2011) and Singapore (2012). Paris will host the 2014 conference.
Also in August, IQC convened the International Quantum Key Distribution (QKD) Summer School, drawing 61 graduate students and post-doctoral fellows.
And the institute reaches out to students in Grades 11 and 12 through QCSYS, the Quantum Cryptography School for Young Students. Applications arrive from around the world to take part in the school, which runs annually in August.
In October 2014, IQC provides the venue for PQCrypt 2014, the sixth annual conference on post-quantum cryptography.
