By Jake Viscusi, Upper School Math Teacher
Differential Equations
Machine Learning
Digital Signal Processing
Chemical Equilibrium Reactions
Molecular Orbital Theory
Quantum Light Polarization
These are the second semester topics of study selected by the exceptional students in MAT501—Linear Algebra. The unique structure of the course aims to nurture the creative and aesthetic mathematical senses in each student, giving them the tools to confidently pursue their own areas of interest in the future. The particular students enrolled this year (Katherine Connolly ’24, Siddharth Kancharapu ’24, Grayson Kyle ’24, Veer Pahwa ’24, William Sommers ’24 and Anish Vakalapudi ’24) each had the opportunity to grow through the Tower Hill math curriculum from ninth through 12th grade and as a result, had the strong foundations necessary to approach the classroom setting in a slightly different manner.
A typical class period of MAT501 begins with a single question: “What are some options to describe the distance between two functions?” or “How can we rigorously define the pseudoinverse of a map?”
The class spends the bulk of their period answering this question, though the path to a solution is rarely direct. Instead, a thoughtful meandering begins where students find new ways to apply the concepts they have already mastered and develop connections between previously separate topics. In this way, the curriculum forces participants to be agents in their own learning. This guided discovery aims to give students the experience of having ‘figured it out’ on their own, and, in doing so, provides them with the confidence to know they can do it again!
This unconventional approach works when the students have the appropriate prerequisite content knowledge—fortunately, these soon to be Tower Hill alumni are well-equipped, which comes as no surprise. When asked about math experiences at Tower Hill, Kyle expressed, “The entirety of Tower Hill math excels at exploring topics in depth while simultaneously broaching the overlap between differing subjects.”
Math League president and AIME participant Pahwa echoed, “Tower Hill math has exceeded my expectations. The curriculum is thorough in its coverage of topics, ranging from trigonometry to algebra to calculus, and helps students build a strong foundation for future mathematical studies.”
With the enrollees of MAT501 being so close to graduation, the course bears a special responsibility in preparing its scholars for their years beyond Tower Hill, which is the express purpose of the second semester project. Having spent the first semester honing the skills of discovery and risk-taking in the classroom, students are given the chance to apply their “weapons of maths destruction” to problems of their own choosing. To be truly invested in the project, a student needs to find a piece of themselves in what they are studying. Fortunately, it is no exaggeration to say that linear algebra is a pivotal course for any STEM field, and, as a result, its applications run the gamut. This means that every student can find some application of linear algebra that is relevant to their future goals.
When asked how he chose his topic, All-State Jazz Band member Sommers shared, “I’ve been interested in both music and computer science for many years, so I naturally became interested in the intersection of these areas, which introduced me to the mathematical discipline of digital signal processing. As tends to be the case with loads of things in math, this secretly involves quite a bit of linear algebra, and I’m excited to explore this in more depth during my second semester project.”
The group this year has seemingly taken it as a challenge to cover as diverse a range of topics as possible. With just six students, there are topics from pure math, computer science, chemistry and physics, which is a testament to the broad range of interests found in the Tower Hill student body.
“Linear algebra in particular has fostered a sense of interconnectedness that’s difficult to truly appreciate in any other class,” Kyle goes on. “In exchange for a more difficult and abstract subject matter, the course delivers a unique kind of satisfaction, especially as it spans an incredible breadth of material without giving up quality or depth of information.”
In exchange for a more difficult and abstract subject matter, the course delivers a unique kind of satisfaction, especially as it spans an incredible breadth of material without giving up quality or depth of information.
Sommers agrees, “Linear algebra is pretty different from any other math course I’ve taken at Tower Hill. There’s a lot more room for exploration, and the occasional class-derailing tangent contributes to a course that, although challenging, strives to make intimidating concepts feel as simple as addition and subtraction. Because of this, it’s a very rewarding class, and I’d recommend it to anyone even remotely interested in math.”
