SUAMI Offers Students, Mentors Connections

When Carnegie Mellon University's Department of Mathematical Sciences hosts the Summer Undergraduate Applied Mathematics Institute (SUAMI), not just undergraduate students spend the summer in Pittsburgh conducting research. Visiting professors come too.

Ryan Moruzzi Jr., assistant professor at the California State University, East Bay, served as one of several summer mentors and project leaders for SUAMI. He spent eight weeks helping students work on problems analyzing the zero-forcing numbers of different families of graphs.

"The students took ownership of their work and looked into a lot of options," Moruzzi said.

Zero forcing is an iterative coloring process on a graph. Suppose a subset B of the vertices of a graph G are colored blue, and all vertices not in B are colored white. The researcher can proceed with the following color change rule: a blue vertex v will force a white adjoining u blue if u is the only white neighbor of u. After carrying out this iterative color change process, either all the vertices in the vertex set of G will be colored blue, or there will be at least two white vertices stopping the researcher from coloring the entire graph.

The size of the smallest initial blue vertex set required to force all the vertices in G blue is called the zero forcing number of G. One can think about how to adapt this color change rule; for example, to be less restrictive than needing a unique white neighbor. Questions like the previous on variations of forcing have been adapted for different applications and research into these variations of forcing bring about new directions.

David Offner, associate teaching professor, directs the SUAMI program. For more than 30 years, the Department of Mathematical Sciences has provided students with strong academic records — regardless of background — the opportunity to work on projects related to applied mathematics under the direction of research faculty or postdoctoral researchers. Along with Moruzzi's work other research opportunities included projects in number theory, partial differential equations and discrete mathematics.

"We have an incredibly strong and hard-working group of mentors and students engaged in cutting edge research," Offner said.

Along with Moruzzi's group, other mentors included Theresa Anderson, assistant professor, and Elisa Bellah, postdoctoral teaching fellow, both of CMU's Department of Mathematical Sciences, who resolved open questions about doubling measures in the field of analysis. A group mentored by Rachel Kurchin, an assistant research professor, and Jerry Wang, an assistant professor of civil and environmental engineering, both from CMU's College of Engineering, assessed the robustness of algorithms for Bayesian parameter estimation. And the group mentored by Juergen Kritschgau, a postdoctoral researcher in math, proved new theorems in anti-Ramsey theory.

Wohua Zhou, a rising senior, who — like Moruzzi — is from California State University, East Bay, worked with Kritschgau.

"Working with Juergen on anti-Ramsey theory problems made me realize I want to try different things with Ramsey theory," Zhou said. "This was my first time being away from home and conducting research. It was pretty amazing."

Moruzzi said that when he was an undergraduate at California State Polytechnic University, he thought his only path with a bachelor's degree in math would be to teach at a high school.

"I was involved in a high school classroom at that point and when I moved to Michigan for my master's program, I was able to teach in the college classroom at that point," he said. "Pretty early on in graduate school I had felt as though I wanted to be involved with students both in the classroom and teaching and being able to provide students with research experiences."

He went on to finish his doctorate at University of California, Riverside, and a postdoctoral teaching position at Ithaca College in New York. Moruzzi and his four SUAMI students will stay in contact as they work on writing up some of their results for publication, and the students figure out what comes next.

"It's not just about the research experience but also connecting with students differently than in the classroom. I viewed that time as valuable for helping to shape their perceptions on what they're able to do with mathematics. It's not just about going and being a teacher. It's opening conversations about graduate school and other careers."

SUAMI alumni have gone on to become leaders in the financial industry, education advocates in government, professors and more.

Anna Rittenhouse, a rising senior from Clark Atlanta University, worked with Offner, Kurchin and Wang.

"I was applying to REUs to get a taste of the graduate student experience, and it seemed liked SUAMI was the most well rounded," she said.

Along with research, the students participate in the Mellon College of Science's Summer Scholars Program, which provides social and professional learning and development opportunities for students in several undergraduate research programs.

"There was such a good cohort of people. I got to know a lot of physics, chemistry and biology, and it was really interesting to hang out with them and hear them explain their work."

SSP participants went white water rafting, visited the Kennywood amusement park, rock climbed, toured the Carnegie Museums and caught a Pirates baseball game. They also participated in faculty mentor dinners.

"That was really good, especially having time to chat with students outside of research meetings. Part of the mentoring process is getting to know the students and share different experiences of life beyond the research," Moruzzi said. As part of their SUAMI experience, Moruzzi would set aside time for each student for checking in with them. "It created even more of a collaboration feel. We're doing this as a group. It's not just an opportunity to mentor students but to create a collective where they also had agency and ownership of the research project."

Michael Young, the Mellon College of Science associate dean for diversity, equity and inclusion and an alumnus of CMU, initially invited Moruzzi to come to Carnegie Mellon for the summer.

"I had been thinking about trying to get involved in a summer research program, and when he brought it up it piqued my interest," Moruzzi said. "Especially because of the point I was at in my research and where I had at ideas of what undergrad research projects could be."

Not only did Moruzzi help students work on problems, he also read applications and worked behind the scenes to recruit students and learn about the process of setting up a summer research experience.

"As an undergrad it wasn't on my radar to do a program like this," he said. "As I went through graduate school I saw how important it is for students to get experience as an undergraduate. It helps students realize if they want to try new research or if this is a path that is not quite one that they want to go down."

Young, participated in SUAMI as an undergraduate at the University of Florida. He said that SUAMI continues to be a recruiting tool not just for students. Faculty are often considered for programs such as the Shelley Distinguished Professorship, which is an opportunity for experienced mathematics professors to teach at CMU for an academic year.

"We typically have a faculty mentor for SUAMI who is from another institution," Young said. "It provides them with an opportunity to work on campus, meet our faculty and other students and offer opportunities for their home institution."