Tyler Genao, a postdoctoral associate at Ohio State, has brought his passion for mathematics into his teaching. Credit: Courtesy of Tyler Geneao. Graphic: Lily Pace | Managing Campus Editor
Many students walk into their first year of college calculus with nervous anticipation, bracing for a whirlwind of equations, integrals and derivatives.
However, for students taking calculus with Postdoctoral Associate Tyler Genao, anticipation quickly gives way to understanding and appreciation for the intricacies of the often dreaded topic.
For Genao, his interest in mathematics began early when he took a discrete mathematics class as part of his high school’s dual-enrollment program.
“It was unlike any mathematics class I had taken before,” Genao said. “I really enjoyed it.”
While pursuing his undergraduate degree at Florida Atlantic University, Genao continued to pursue math courses, and eventually began mathematics research, which solidified his love for the subject.
“It convinced me to pursue a math Ph.D., and to eventually become a professor and organize research projects of my own,” Genao said.
He would go on to complete his Ph.D. at University of Georgia in 2023 before heading to Ohio State to begin his postdoc that same fall.
Genao said he was initially drawn to the university because of the size of the school.
“The math department is great, and it’s quite big, meaning we get lots of interesting math speakers each year, as well as lots of funding to invite collaborators,” he said.
As a postdoc at Ohio State, Genao organizes research projects, conducts mathematics research and instructs a number of mathematics classes, with a primary focus on calculus.
With several hundred students taking his classes each year in addition to research work, Genao manages a substantial workload. Even so, he works to ensure that none of his students are left behind — regardless of their educational background or comfort with math.
“I really try not to assume that everyone has taken calculus before,” Genao said. “I try to clarify each step or conclusion as carefully as I can.”
Genao does this through a unique approach to complex problems, turning them into mnemonics.
These acronyms, which he calls “processes,” break down difficult problems into individual steps that can be easily memorized. Genao said he found the technique resonated with students while instructing at University of Georgia, and has continued to use it since.
Niel Patel, a first-year in aerospace and one of Genao’s calculus I students, said he has found Genao’s instruction methods especially helpful.
“Instead of spamming you with numbers, equations, calculations, it’s more broken down into words… like a checklist almost,” Patel said. “If you’re someone who has a hard time understanding math like I do, it really helps.”
Patel said Genao focuses on working through problems in class rather than a pure lecture, allowing students to apply new knowledge while in an environment where they can ask questions and clarify problems.
“He’ll definitely try and say, ‘Hey, if you don’t understand it this way then he’ll show us a different way to look at the problem,’” Patel said. “He takes the time to answer any questions, no matter how elementary they are.”
However, what stands out most to Patel is Genao’s commitment to his students — from staying late after office hours to answer questions to checking in with students on how they are doing.
“He really does go out of his way,” Patel said. “If you don’t understand something, and you make it known and reach out, I feel like he will go to all ends to make sure you understand.”
Despite working with several hundred students each semester, Genao says he tries to connect with students as much as he can.
“I try to take the time to get to know as many of them as possible,” he said.
He also encourages students to attend his office hours, where he can work with them more directly and get to know them better.
“It’s really touching to be told that they appreciate me, and their appreciation is also reflected in their continued participation in office hours and class,” Genao said. “It really makes me feel like my efforts are valued.”
While Genao has primarily instructed calculus and precalculus, he has also instructed advanced classes related to his research focus: number theory and arithmetic geometry.
In simple terms, he explains his research as the “study of integers and their relations,” and using “algebraic and geometric techniques to study the integers.”
He is especially interested in torsion points on elliptic curves, which have unique mathematical properties and their Galois representations. Genao noted the interesting history of the subject.
“Galois is named after Évariste Galois, a 19th-century mathematician who came up with Galois theory as a teenager,” he said. “He died at 20 in a duel!”
A lot of research has been conducted on torsion points and individual elliptic curves, but Genao said he is especially interested in a different angle.
“I am always thinking about what can be said about large collections of elliptic curves at the same time,” Genao said. “I hope to continue to add pieces to this beautiful mosaic of the theory of elliptic curves.”
Elliptic curves are used extensively in the realm of cryptography, Genao said, from radio networks to digital communications.
Companies like Apple, Google and CloudFlare use Elliptical Curve Cryptography, known as ECC, to encode and authenticate messages, according to an article on ECC by TechTarget.
Genao said the future of the technology is in quantum computing — not developing it, but defending against it.
Industry researchers are using elliptical curves to develop security systems that can “defend against a quantum computer attack,” he said.
Genao said while there are many industry applications for the subject, his research is “pure math,” and he intends to stay in the academic world where he can continue to follow both of his passions — research and teaching.
Genao won’t be at Ohio State much longer, as his postdoc contract finishes this spring.
While he may be heading out the door, Genao said what he’s enjoyed most at Ohio State is working with students.
In a time where the world is unpredictable, and many may feel disconnected, Genao said he’s found Ohio State students to be open and motivated.
“I really appreciate my students; they’ve been so kind and friendly to me,” Genao said. “It’s made my job and life so much more enjoyable.”
