Linear Algebra: Record-Breaking Interest in Casady’s Post-AP Course

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Thirteen: the whopping number of students who decided to take on the post-AP linear algebra class at Casady this year. It’s safe to say that our math program has never seen anything quite like this. Math-department-head Chris Halpern expressed that in recent years, “we were seeing one here, two here, maybe even four or five [students] at most. This year, however, there’s something a little more significant that’s happened.” This particular group of students is making Casady history as its largest post-AP math course. 

Mr. Eric Ebert, the man responsible for educating our post-AP mathematicians, informed me that last year, there were nine students in Casady’s other post-AP math course, multivariable calculus. It excites Mr. Ebert that so many students are taking linear algebra, particularly because it “gives them another opportunity to explore mathematics from a different perspective. It’s a place where you can see where the theory has the weight.”

Although the number of students who choose to pursue higher-level math has only recently spiked, Casady hadn’t offered full-blown linear algebra and multivariable calculus classes until five years ago. Before then, students at the post-AP level of mathematics participated in independent studies. For example, in a partnership with the University of Central Oklahoma, Casady alum Nathan Prabhu (’11) took multivariable calculus. Aside from a few individuals here and there, students’ high school math careers typically capped off at BC calculus.

In recent years, classes like linear and multivariable calculus have garnered increasing interest from Casady’s mathematicians. While impressive that more and more students are reaching such a high level of math, such advanced placement sometimes comes at a cost. “It’s a little bit of a risk. There’s no guarantee that this is the right move for a certain student, and I think that there’s a little misconception about the race. To where? To theoretical mathematics? You can get there too soon, and you can lose your fire.” Halpern recommends that students build strong foundations and become well-rounded mathematicians before pursuing expedited math paths. After all, all mathematicians, regardless of age or grade-level, eventually arrive at proof-based theoretical mathematics, and only a very small portion of the world has the interest and ability to pursue that caliber of math, much less appreciate or enjoy it. According to Halpern, it takes “a special mentality and a special kind of person.”

So… we were all wondering it, but what exactly is linear algebra? When asked to put linear algebra into simple terms, Mr. Ebert’s eyes enlarged, but he managed to give a run-down of the course: “The place that you start is an Algebra 2 problem. You have lines and you want to know if they intersect. And then, a line is a one-dimensional thing. Then you look at two dimensional things, like two planes… do they intersect at a line? Are they parallel to each other? The next question becomes: What does any of that mean when you’re sitting in an ‘n’ dimensional space? You have two n dimensional linear objects. Do they intersect? It was the purview of mid-19th Century mathematicians trying to figure out these things. From there, mathematicians discovered that maps between mathematical objects were as important as trying to understand the objects themselves. This leads one down the path of trying to understand linear transformations.”

If that sounded really complicated, that’s because, well, it is. I spoke with current linear algebra student Saadia Naazir (‘20) to find out how she has fared in the class so far. She informed me that linear algebra has without a doubt been the hardest math course she has taken. She also expressed that although math has never come easy to her, linear algebra has transformed her approach to the subject, as it has forced her to shift her perspective. “I can’t say I 100% understand everything we learn, but it’s incredibly inspiring to see how people have used abstract math to achieve tangible results through application and synthesis.”

A glimpse at one of Naazir’s homework problems.

When I asked Mr. Ebert how he believed the students are handling the class, he looked into space as a slow grin spread across his face. He nodded his head up and down, and after a few seconds of pondering, he erupted into laughter: “Like all things, it’s been a journey, and it is something that is more abstract than has been encountered before.” Ebert admitted that after a rough start with adjustments to the new schedule, new school year, and a new concept of math, the students adjusted to the class quite well.

While linear algebra challenges any student who decides to brave its course, its appeal seems to grow with each passing year. Many of the students currently enrolled in the course plan to pursue a STEM field, and they will undoubtedly find the lessons they have learned extremely useful.