Abstract Academics

Junior Grant Koh Presents His Independent Study on Abstract Algebra


Photo credit: Sam Forst

Junior Grant Koh studies abstract algebra.

At Parker, you are first introduced to algebra in eighth grade and continue to delve into the various topics surrounding it through freshman year. Junior Grant Koh decided to take the concept of algebra a step further by conducting an independent study on something called Abstract Algebra. Koh defined the concept as “generalizing the process of algebra, which is useful towards studying specific algebraic problems.” Abstract algebra is usually a topic taught in college, which doesn’t follow the basic math patterns that students learn earlier on — it’s a totally different concept.

Parker’s upper school math curriculum introduces algebra at the beginning of a student’s high school career because it’s a backbone of the math concepts that are taught later on. Algebra comes up almost everywhere, whether solving a proof in geometry or the derivative in calculus. 

“The reason why I wanted to study this,” Koh said, “is that algebraic concepts permeate the rest of mathematics. Whenever you have structure, you have algebra.” Koh’s curiosity led to a deep dive throughout the first semester, where towards the end, he could notice patterns to group specific problems as a ring or a field. Koh is one to think slowly and deeply about a topic and be thorough to make sure that he didn’t miss anything. He would check in with math teacher Ethan Levine throughout the semester. “When he works on whiteboards, he’ll be pacing, lost in thought until an idea pops into his head,” he said. “He’s a very thorough, methodical thinker.”

Koh found a textbook online that he would refer to throughout the study. Using this textbook, he would go through each chapter and all of the new problems. He would then have brief discussions with Levine and summarize all of the new concepts that he had learned. “I was willing to go along for the ride to help whenever he needed it,” Levine said.

At the end of the semester, they decided it would be a good idea to present all of the material that Koh had learned and experimented with during the study. “The idea was that the viewers could walk away from the presentation with a conversational ability of abstract algebra,”Koh said, “and I think it went well. I think a lot of people got a technical understanding of the concept and to see a new view of a higher level of mathematics.” Kumiko Muro, a junior who went to Koh’s presentation, said, “It was really refreshing to learn about something we usually wouldn’t in school from another student.” 

Because Koh had been working on his independent study for a full semester, he had to figure out how to summarize all of it within an hour or two for people who had never heard of the subject matter. Muro said, “He made sure to explain things in the context of the theories he used so that people could make sense of what he was talking about.”

“Abstract algebra has a scary reputation,” Levine said, “and Grant was able to stick with this topic for months, which was very impressive.” The fact that college students avoid delving into this topic demonstrates Koh’s curiosity and his ability to slow down and process very complicated ideas.