After earning an applied math degree and teaching math for years, Darren realized he doesn’t really understand math as well as he should.
In college, he “could calculate my butt off, but so often didn’t fully understand what I was doing.”
As an example, in differential equations I could calculate eigenvalues all day long, but to this day I don’t know what an eigenvalue is or what it does for me or why I need to calculate it. I’ve taught myself plenty –sometimes just days before I had to teach it to my students.
He told a student bound for Cal Poly “not to make the mistake I made; ask the questions, go for the deeper understanding.” And Darren decided to go for it himself.
I’ve never understood the Fundamental Theorem of Calculus. Why, exactly, are an integral and an antiderivative the same thing? I’ve followed the steps in my calculus books, and understood each step, but never really understood how they all fit together. So today I pulled a different calculus book out of my closet and I started studying. I found one that provided a very user-friendly explanation, which then allowed me to understand the very rigorous (read: dry and difficult) proof in a second text. It took a few minutes to replace decades of deficit.
In the fall, Darren will start a masters program in Teaching Math through the University of Idaho’s Engineering Outreach Program.
Most of us never have the courage to face our eigenvalues, much less blog about it.