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Fourth-year student gets an early taste of mathematical research, scores top marks for thesis presentation
By: Clara Wong
June 02, 2021
Ali Syed

Ali Syed, fourth-year Math and Its Applications student

The undergraduate thesis course (MTH40A/B) has been around for a while, but this year, the department began recognizing the highest achieving student. The inaugural award goes to fourth-year Math and Its Applications student Ali Syed.

Syed’s winning work is entitled “Decidable Locally Finite Discriminator Varieties Arising from Varieties of Groups", supervised by professor Dejan Delic. The experience was a pivotal springboard — one that bolsters Syed’s plan to return in September to study math at the master’s level.

What’s an Undergraduate Thesis Anyway?

The undergrad thesis is not your typical textbook course. No classes, tests, assignments or midterms. Just a year-long, independent project. One student, one professor, working together on a single research question — all culminating in a final written thesis and oral presentation.

While a thesis might seem daunting at first, Delic says the course is a capstone, with opportunities and benefits for any upper-year student contemplating graduate school.

“The undergraduate thesis gives students a firsthand look into how mathematical research is done — similar to how it works in grad school,” he says. “You learn to critically analyze existing research, look into advanced material that interests you, and formulate and present your own results in a rigorous way.”

Early Taste of Research & Collaboration

Teaming up during the academic year, both mentor and mentee clearly relished the process.

“Working with Dr. Delic was the most important part of my thesis,” says Syed. “We met weekly to exchange ideas, and when I couldn’t figure out how some things were related, he always pointed me in the right direction. Thanks to him, I got to work on a really exciting problem with ideas from a variety of fields, and was introduced to areas of math that are totally new to me.”

For Delic, the respect was mutual. “Ali’s commitment to hard work was exceptional, as well as his eagerness to absorb new knowledge. Working together on this project was extremely enjoyable.”

Prize-Winning Presentation

Syed spent the year applying tools from his favourite area, abstract algebra, along with some new tools in universal algebra, model theory and logic. Using these, he investigated certain discriminator varieties obtained from groups of algebras. His goal was to identify which ones are decidable — that is, ones that can produce a correct answer to a true/false decision problem.

Syed elaborates: “Generally, we can show that a class of algebras is undecidable by using a concept called semantic embedding. We came up with a way to show that if a group fails a certain condition that we set, then it’s undecidable. Otherwise, we know that it’s decidable.”

Under Delic’s guidance, Syed produced his first written thesis detailing his results. He also polished his presentation skills to deliver a 20-minute defense before a review committee. His achievements earned him an A+ and the department’s first Undergraduate Thesis Award.

Reflecting on the experience and his path forward, Syed is elated. “I was totally caught by surprise by the award, but extremely happy! Now, I’m planning to come back to Ryerson to study for my master’s degree.”

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