Immersion
Immersion Is… the opportunity to pursue intellectual curiosities through immersive experiences and culminating projects that are as chosen by you, based on your interests. Studying abroad, conducting research, or fulfilling an internship can be part of your Immersion story.
Immersion Stories
Alberto MagaÑa
Alberto Magaña’s journey to becoming a mathematics major at Vanderbilt University wasn’t a straight line. Initially drawn to 
economics, Magaña discovered a passion for math while taking required courses for his original program. “I realized I didn’t enjoy econ nearly as much as I did math,” Magaña explained. “The draw of mathematics became so strong that I switched majors.” This unexpected turn has led him to a deep appreciation for the beauty and challenge of mathematical thinking, and now, a path toward a PhD.
Magaña cites topology, particularly algebraic topology, as a favorite class, highlighting the challenging and fascinating nature of the subject. His passion for learning extends beyond the classroom, however. A talented guitarist, Magaña also enjoys jazz guitar lessons at Blair School of Music, crediting his instructor, Jerry Kimbrough, for his musical growth. “It’s a great creative outlet for me,” Magaña shared, noting the balance it provides to his analytical work in mathematics.
Research has played a crucial role in Magaña’s academic journey. His summer research experience at the Mathematical Sciences Research Institute (MSRI) in 2023 proved pivotal, solidifying his decision to pursue doctoral studies. “It showed me what research in this field is really like,” he remarked. His recent research project explored the virtual braid group, a complex mathematical object with topological and algebraic properties. Magaña’s work focused on the topological perspective, investigating the spaces on which the group acts and the implications of those actions. He emphasized the importance of his Vanderbilt coursework in topology and abstract algebra, stating, “The concepts and techniques I learned in those classes were essential to my research.”
Beyond academics, Magaña recognizes the impact math has had on his life. “Math has become a significant part of my life, especially during my time at Vanderbilt,” he said. He values the community he’s found through math-related activities, noting the friendships forged through shared intellectual pursuits. He also believes that studying math has fundamentally changed his thinking, improving his reasoning skills and problem-solving abilities.
Looking to the future, Magaña plans to pursue a PhD in pure mathematics, with a strong interest in specializing in topology or geometry. He’s eager to continue learning and contributing to the field. His story is a testament to the power of discovering one’s passion, even when it takes an unexpected turn. From economics student to aspiring mathematician, Alberto Magaña is hitting all the right notes.
Aussie Green
Q: What made you interested in majoring in mathematics?
A: While attending an arts magnet high school, I had planned on studying science journalism in college. But near the end of high school, I found myself addicted to fitting my schedule with as many math classes as possible—taking night and weekend classes at my local community college just to add to my arsenal of math techniques. When starting at Vanderbilt, my introduction to proof-based mathematics in 2500 and 2501 showed me that there exists an intersection between my passions of problem solving and writing. I declared my major in math not long after the start of my sophomore year.
Q: Favorite class?
A: My favorite class at Vanderbilt has been Dr. Schumaker’s special topics course in computing with splines. It was the first course that I took in which the assessments were solely based on algorithm development, which I learned was my strength in upper-level mathematics. Since the course covered material through current research in the field, I had suicient experience to begin my own research the following summer. This experience introduced me to what would become my long- term research interests in numerical analysis and computational geometry.
Q: Favorite math-related activity?
A: I have been solving Rubik’s Cubes and competing in speed-cubing tournaments since 2014. Solving Rubik’s Cubes at an advanced level requires a deep understanding of algorithms. My favorite cubes to solve are the bigger cubes, such as the 6x6x6 and 7x7x7. These puzzles develop a strong intuition in both pattern recognition and how groups of pieces interact with each other. When researching in my current field of computational geometry, I always have a Rubik’s Cube by my side to help visualize how operations and algorithms move data around in 3D space.
Q: Favorite non-math activity?
A: Whenever I have free time, I enjoy driving through the countryside of Tennessee. I love visiting small towns and traveling up steep mountain roads. My favorite roads to drive over the last few years have been Wyoming’s Beartooth Highway, Colorado’s Mt. Evans Road, and East Tennessee’s Tail of the Dragon.
Q: How does math shape your identity?
A: My love of math has connected me to some of my best friends—both throughout my childhood and at Vanderbilt—and has developed me into a leader in my communities. Since 2015, I have organized Rubik’s Cube competitions in Nashville, fostering a large community of Rubik’s Cube enthusiasts in the greater Tennessee region. Last semester, I founded the Vanderbilt Cube Club to establish the first community of cubers on campus. Since then, our club has partnered with the Vanderbilt Department of Mathematics to hold Vanderbilt’s first oicial Rubik’s Cube competition, which hosted a guest lecture on the mathematics of the Rubik’s Cube. The competition attracted attendees from all over the world to share their love for puzzles, shapes, and math.
Q: Describe your research and how you applied what you learned in classrooms into your research.
A: Spline functions, which are piecewise polynomial functions, are especially helpful tools in the field of approximation theory, since they can fit real world data with specified degrees of smoothness and great computational eiciency. Currently, the math behind splines has only been developed to solve problems on domains of one and two dimensions as well as a few simple shapes in three dimensions.
Alongside Dr. Schumaker, I am currently developing methods to apply splines in solving partial dierential equations on complex three-dimensional domains (e.g. shapes with curved surfaces), which has many potential applications in engineering and medical imaging.
A big component of my research regards the “mesh generation problem,” which involves taking complex continuous domains and simplifying them into discrete shapes that are compatible with our numerical methods.
Other than the two courses that directly prepared me for my current research— MATH 3620 (Numerical Analysis) and MATH 3890 (Computing with Splines)—I use the tools and intuition I developed in my linear algebra classes (MATH 2500, 2501, 3330) every day when developing software. With regards to my work with splines, every problem is posed as a solution to a large system of linear equations. Knowledge of least squares solutions, rank, and other linear algebra topics come up frequently. As for computational geometry, I use my linear algebra intuition to geometrically manipulate data. This can look like orienting a 2D plane in 3D space, using normal vectors on a surface to determine where a ray might intersect the shape, etc.
Q: Future plans?
A: Following my undergraduate degree at Vanderbilt, I plan to continue my research in numerical analysis and computational geometry at a PhD program in computational mathematics. My ultimate goal is to develop mathematical techniques that may be used to solve problems in fields that are meaningful to me, such as medical imaging and oncology.