“I have always been fascinated by math and the beauty of its complexity,” said Gauri Purohit ’21. Upper School math teacher Carolyn Licata, who is teaching her Linear Algebra class, shares her wonder. “I love introducing students to new concepts in mathematics,” said Licata. “Even at the beginning of the course, the idea of n-dimensional space really intrigues the students.”

This academic year, Poly is offering Linear Algebra as a new course. Previously, Licata had taught Linear Algebra at Poly as an independent study for students who had completed all the math courses at Poly. “There was enough interest from students who love mathematics to offer the course to all students who have successfully completed a calculus course,” Licata said.

“In Linear Algebra,” Licata explained, “systems of equations and matrices are used as vehicles for the introduction to vector spaces, subspaces, independence, and dimensions. Since Linear Algebra is primarily about defining and transforming spaces using matrices, many applications are a direct result of these transformations. Some of the applications are graphs and networks, which are used in engineering, especially electrical engineering, and in computer science.”

The Linear Algebra course at Poly will give our students the foundation for higher level math and computer science courses in college.

Students in Licata’s class are very enthusiastic about this opportunity. “I hope to learn mathematical properties and calculation methods that I can apply to future math, science, and computer science studies,” said Robert Magnus ’21. “I plan to pursue computer science or a concentration of computer science as my major in college.”

Licata, an MIT graduate, said she had used Matrix Theory in courses in electrical engineering during her graduate school years. “In addition,” she said, “matrix operations are used in image processing and compression, and facial recognition. Eigenvectors and eigenvalues of very large matrices are used in determining the closest matches for internet searches. Other applications are in fast Fourier transforms, systems of differential equations, finding the covariance matrix in statistics, genetic variation within populations, and many others.”

“As I am also interested in computer science and physics,” said Purohit, “I hope that I will be able to use what I learn from Linear Algebra to apply to these areas of study, with a deeper, more complex understanding of vectors specifically. I also think there is a certain level of abstract and conceptual thinking and understanding in Linear Algebra that is unlike that of any other class I have taken so far, which also seems to be quite valuable as it is pushing me out of my comfort zone and will be necessary if I pursue a future in math.”

Since Middle School, Purohit has enjoyed the opportunities Poly’s Mathematics Department has offered. “I was really grateful to be able to take Advanced Geometry while still in eighth grade, which was quite intimidating at first, but I soon was able to form tight-knit bonds with so many of my older peers that I would otherwise not have had the chance to form,” she said. “Since then, I have loved being able to push myself in math class each year and challenge myself with concepts from beyond the standard advanced curriculum. I would also have to say that by pursuing this more advanced track, I am able to take an independent study in Multivariable Calculus, Linear Algebra, and AP Statistics this year, which would not have been possible otherwise, and cater my schedule more toward STEM [science, technology, engineering, and mathematics].”

Likewise, Magnus said of his studies this year, “One highlight for me was studying for the AP Calculus AB exam virtually and being one of the first math students to experience the first digital version of the test. It was very mysterious, as even though I was prepared content wise, no one knew how the two questions would be formatted to test a year’s worth of learning.”

As for the future, Purohit said, “I have always been fascinated with computer science and mathematics, which happen to go very well together. I hope thatby enriching my own schedule and taking advantage of as many STEM classes that Poly offers as I can that I will be a little more prepared for what is to come in college!”