## Perron-Who Theorem?

#### Anya Mondragon | May 11th, 2023

Postdoctoral scholar Peter Huston hosted Vanderbilt’s Undergraduate Math Seminar on the Perron-Frobenius theorem on March 28th. The Undergraduate Math Seminar offers the opportunity for any interested Vanderbilt students to learn more about different topics in mathematics presented by graduate students and enjoy free pizza.

While the talks are marketed as being accessible to any student, even those with no background in mathematics, the intricacies of proving the Perron-Frobenius theorem were a bit beyond my pay grade as a student enrolled in their first linear algebra course. For anyone interested in math hesitant to attend out of a fear of not being able to follow the lesson, I would still encourage giving it a chance.

The benefit of attending these undergraduate math seminars is the chance to participate in a thoughtful discussion about math. Conversation, not usually present in traditional math courses, has been shown to have great benefits in promoting understanding of new material and engagement with math (Sfard 2001). The journal article “Cooperative Learning in Mathematics” published in the journal *The Mathematics Teacher* reinforces this idea, concluding that “while learning mathematics in certain cooperative-learning settings, students often improve their problem solving abilities, solve more abstract mathematical problems, and develop their mathematical understanding” (Leikin et al. 1999). The atmosphere of the seminar was relaxed and friendly. Upon learning what math courses I was in, one of the other attendees recommended a youtube channel with instructional videos that had helped them through similar courses.

Furthermore, even without a solid background in math on eigenvalues and vectors, involved in the proof of the Perron-Frobenius theorem, it was fascinating to follow the line of reasoning of the theorem. One of the points of Huston’s talk was the idea that even for theorems with conclusions that seem a bit abstract, often there are important real-world applications. For example, the main idea of the Perron-Frobenius theorem, which “places constraints on the largest eigenvalues and positive eigenvectors of matrices with non-negative entries,” has applications for economics, dynamical systems, and technology.

As a student it can often feel like there are too many different things demanding your time and attention, from athletics, academics, clubs, to social commitments. But for any Vanderbilt student interested in math who is available every other Tuesday in Stevenson 1320 from 5:30-6:30 P.M., I would recommend looking out for Vanderbilt’s undergraduate math seminar. For those interested in what topics the seminar has covered in the past, all previous talks since the program’s beginning in 2001 can be found on their website.

Works Cited

Leikin, R., & Zaslavsky, O. (1999). COOPERATIVE LEARNING IN MATHEMATICS. The Mathematics Teacher, 92(3), 240–246. http://www.jstor.org/stable/27970923.

Sfard, Anna. ( 2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher, C. Walter (Eds), Proceedings of 21st Conference of PME-NA (pp. 23-44). Columbus, Ohio: Clearing House for science, mathematics, and Environmental Education. https://www.researchgate.net/profile/Anna-Sfard/publicatio/252619091_Learning_mathematics_as_developing_a_discourse/links/0f31753c8e5cc02dbd000000/Learning-mathematics-as-developing-a-discourse.pdf.

https://math.osu.edu/sites/math.osu.edu/files/What_is_2018_Perron-Frobenius_Theorem.pdf

Undergraduate Seminar in Mathematics. https://my.vanderbilt.edu/undergradseminar/.