A Mentor Perspective on the SIAM-Simons Undergraduate Summer Research Program

By Karen Bliss, Malena Español, Alicia Prieto-Langarica, and Padmanabhan Seshaiyer

2023 was the inaugural year of the SIAM-Simons Undergraduate Summer Research Program, which provides annual support for ten undergraduate students to embark on a focused summer curriculum of mentorship, scholarship, and research in applied mathematics and computational science. The program establishes mentors at five research sites across the U.S. and assigns two students to each location; participants receive a weekly stipend and funding for lodging, meals, and travel. Over the course of either six or eight weeks, the students work with their mentors and learn how to conduct scientific research, effectively communicate mathematical and computational science principles, and prepare for a scientific career.

The SIAM-Simons program targets U.S. students from groups that are typically underrepresented and historically marginalized in science, technology, engineering, and mathematics (STEM) — specifically ethnic minorities. Although many individuals from these groups are interested in applied math and computational science, it can be difficult for them to find role models and experiential opportunities that allow them to envision themselves forging successful careers in these disciplines. The SIAM-Simons program therefore seeks to foster a strong sense of community and belonging among participating students and instill confidence as they continue on their academic paths.

In addition to the program’s immersive research component, recurring virtual meetings provide a forum for students to share their work, build their networks, and learn from others in the field via question-and-answer panel discussions about career development and graduate school. Participants also visit the Simons Foundation’s Flatiron Institute in New York City to meet each other in person, tour the Institute, and learn about the work of its employees. Students who took part in the inaugural cohort reported feeling more confident, connected, and capable as a result of the program.

The 2023 mentors, sites, and research projects were as follows:

• Heiko Enderling and Renee Brady-Nicholls of Moffitt Cancer Center: “Identifying Novel Biomarkers for Cancer Treatment Personalization”
• Malena Español of Arizona State University (ASU): “Computational Methods for Inverse Problems in Imaging”
• Illya Hicks of Rice University: “Minimum Cycle Basis for Pose Graph Optimization”
• Alicia Prieto-Langarica of Youngstown State University (YSU): “Cost/Benefit Analysis of Yearly Mammograms: A Social Justice Approach to Individualized Medicine”
• Padmanabhan Seshaiyer of George Mason University (GMU): “Program MASTER: Modeling, Analysis, and Simulation for the Grand Challenges Through Innovative Training, Education, and Research.”

Here, three of the mentors from the 2023 cohort discuss their respective projects, reflect on their experiences, and advocate for the importance of research and professional development opportunities for undergraduate students.

Malena Español of ASU: “Computational Methods for Inverse Problems in Imaging”

At the ASU site, students Ashley Ramsay-Allison of Florida State University and Kelsi Anderson of St. Mary’s College of Maryland worked to determine parameters for curve fitting in nonlinear models. The students’ invaluable contributions throughout the summer included calculating Jacobian matrices for various nonlinear functionals and implementing them via MATLAB. They also utilized both synthetic and real data to produce a comparative analysis of the Gauss-Newton method, alternating least squares, and variable projection methods. Throughout the eight-week program, Ashley and Kelsi developed and honed their proficiency in MATLAB, LaTeX, and Overleaf, and enhanced their communication and teamwork skills.

SIAM provided everyone with mentor-participant guidelines but encouraged mentors and student pairs to modify them to suit their unique personalities and needs. Agreeing on expectations and communication strategies from the project’s onset was especially helpful, and the whole experience was very rewarding. The students were motivated, independent, and otherwise outstanding in their mathematical and programming capabilities.

Alicia Prieto-Langarica of YSU: “Cost/Benefit Analysis of Yearly Mammograms”

The U.S. Preventative Services Task Force recommends that women who are 40 years of age and older receive biennial breast cancer screenings via mammography. In light of this guideline, participants of the six-week YSU project examined breast cancer risk factors, screening techniques, inequities in screening access and healthcare in the U.S., and different types of screening protocols in other countries. The SIAM-Simons program ran concurrently with a National Science Foundation Research Experience for Undergraduates (REU) at YSU; as such, SIAM-Simons students Amira Claxton of the University of Tampa and America Jarillo-Montero of Simpson College collaborated with REU student DiDi Tensley of YSU. Using a public database of risk factors and cancer diagnoses, the trio employed clustering algorithms and classification methods to group women into three categories based on their level of breast cancer risk.

Amira, America, and DiDi joined other REU students every weekday morning for a “working breakfast” that included various community-building activities (led by myself or a YSU student assistant). Next, the SIAM-Simons participants met with me to discuss the previous day’s progress; together, we would make a plan for the remainder of the morning. After a break for lunch, most afternoons began with a professional development session. These sessions covered a variety of topics, such as professionalism in STEM, careers in mathematics, graduate school, CVs and branding, and effective research presentations. After a mid-afternoon progress update and goal-setting session, the student researchers continued with their daily tasks. We hosted a group trip for them every weekend and organized other outings as well. After the summer activities concluded, Amira and America attended the 2023 SACNAS National Diversity in STEM Conference—which took place in Portland, Ore., last October—and presented a poster about their work.

As a YSU professor, I seldom see students of color in my mathematics classrooms; working with math majors or research students of color is even more uncommon. I love engaging with all of my students, but collaborating with Amira, America, and DiDi—three women of color—was the most rewarding professional experience of my career thus far. Due to our shared backgrounds and experiences, it was easy to build connections; understand their concerns, fears, and hesitations; and address them effectively and promptly. I highly recommend this program to interested students and professors. There is nothing like being able to be your full self and do math.

Padmanabhan Seshaiyer of GMU: “Program MASTER”

As mentors and educators, it is important to expose students to work that expands beyond mere discovery and addresses real-world problems with tangible impacts on society. This mentoring philosophy helps me better connect with my students, so I was pleased to learn that I was selected to serve as a mentor in the inaugural 2023 SIAM-Simons program. In addition to coaching two motivated undergraduates on advanced topics in mathematics, problem solving, data-driven modeling, computing, visualization, and multidisciplinary applications, I sought to enhance their awareness of the ever-increasing utility of mathematical approaches in biological, engineering, and bio-inspired systems.

I was excited to meet the students that were assigned to my site at GMU: Adan Baca of the University of Arizona and Diego Gonzalez of the University of La Verne. As a research mentor in this new program, I aimed to nurture their curiosity; encourage them to explore real-world, global challenges; guide and support them as they navigated the complexities of mathematical modeling; create interdisciplinary connections beyond mathematics; and provide opportunities for scientific and professional growth. During the program, GMU graduate student Alonso Ogueda also served as a co-mentor. He met individually with the students to discuss the merits of graduate school and otherwise serve as a sounding board for their professional development.

For their project, Adan and Diego modeled, simulated, and analyzed a patient detox journey. They utilized a modified susceptible-infected-recovered (SIR) epidemiological framework to generate a mathematical model that treats addiction as an infectious disease, accounts for its unique factors, and depicts its perpetuation throughout communities and populations. This novel model examines the impact of different types of treatment interventions, demonstrates the efficacy of recovery and treatment programs in lowering addiction rates, and holds promise for public health decision-making and resource allocation.

Although Program MASTER was hosted within GMU’s Department of Mathematical Sciences, the SIAM-Simons participants also engaged with Holly Matto from the College of Public Health, who specializes in social work and is an expert in addiction research. She helped us identify missing compartments in our SIR model and incorporate important state transitions; I encourage future mentors to employ a similarly multilayered approach.

Adan and Diego presented this work as both a poster and full talk at the 16th Annual International Symposium on Biomathematics and Ecology Education and Research at Virginia Commonwealth University in November 2023. Both students also delivered two different presentations on this topic at the 2024 Joint Mathematics Meetings, which took place in San Francisco, Calif., in early January. We are currently preparing to submit our results to a peer-reviewed journal for consideration.

Undergraduate research provides students with a valuable experience that goes beyond academic learning to shape their skills, knowledge, and attitudes; prepare them for future careers; and contribute to the advancement of knowledge in STEM. I commend both SIAM and the Simons Foundation for creating a partnership that promotes such impactful undergraduate research in applied mathematics.

Conclusions

The inaugural 2023 cycle of the SIAM-Simons Undergraduate Summer Research Program was a tremendous success, and participating students offered overwhelmingly positive feedback. 97 percent of students reported either good or great gains in research skills, and 90 percent reported good or great gains in attitudes (i.e., enthusiasm and interest in applied math, confidence, and so forth). “I gained so many great things from this [program],” America Jarillo-Montero of Simpson College, who worked with Alicia Prieto-Langarica of YSU, said. “I met fantastic people, made great memories, got one step ahead in my career, and gained resources and information about things I always considered out of my reach.” Kelsi Anderson of St. Mary’s College of Maryland spoke about her positive experience with Malena Español at ASU, increased sense of self-assurance, and newfound appreciation for mathematics. “I felt more connected to applied math when working with people who look like me and share similar interests,” she said. “Realizing my capability throughout this program also helped me feel more in touch with the field.”

All 2023 participants are encouraged—and will receive funding—to present their research at the in-person component of the 2024 SIAM Annual Meeting, which will take place from July 8-12 in Spokane, Wash. In the meantime, SIAM is already gearing up for the program’s 2024 cycle. The 2024 mentors, sites, and research projects are as follows:

• Henry Boateng of San Francisco State University: “Fun at the Intersection of Linear Algebra and Probability”
• John Jungck of the University of Delaware: “Biomimetic Design Criteria for Self-assembly and Self-folding Viral Capsid Models”
• Sooie-Hoe Loke of Central Washington University: “Interest Rate Modeling and Asset Pricing in Incomplete Markets”
• Marilyn Vazquez Landrove of Simpson College: “Data Augmentation Applied to Tabular Data”
• Alexandria Volkening of Purdue University: “Characterizing Biological Patterns Using Optimal Transport and Topological Data Analysis.”

Details about each of these projects is available online. Student applications for the 2024 cohort must be submitted by February 7th, and letters of recommendation are due by February 14th. If you are an interested student, visit the online portal to submit your application today.

The application window for SIAM members who wish to serve as mentors for the 2025 cycle of the SIAM-Simons Undergraduate Summer Research Program will open in July, with a deadline of September. The importance of undergraduate research and mentorship cannot be overstated, so please consider hosting a research project at your institution next year.

	Karen Bliss is the Senior Manager of Education and Outreach at SIAM.
	Malena Español is an assistant professor in the School of Mathematical and Statistical Sciences at Arizona State University. Her research interests include inverse problems, image processing, and materials science.
	Alicia Prieto-Langarica is a distinguished professor in the Department of Mathematics and Statistics at Youngstown State University. Her research focuses on applied mathematics in fields like biology, sociology, and public policy.
	Padmanabhan Seshaiyer is a professor of mathematical sciences at George Mason University who previously served as chair of the SIAM Diversity Advisory Committee. He works in the broad area of computational mathematics, mathematical biology, data science, biomechanics, design thinking, and STEM education. Seshaiyer is also chair of the U.S. National Academies Commission on Mathematics Instruction and Associate Director for Applied Mathematics at the Math Alliance.