Have you ever had to do anything that was really hard, and frustrated you at every turn?
That's the boat I'm in right now--I'm plugging away very, very, very slowly at my pre-calculus course. It's insanely frustrating to work with--intense, complicated problems that I often get wrong.
The worst part is when I get super emotionally involved in my work-- I have to grade my own problem sets. There are few things more discouraging than finding I screwed up problems that took me twenty or thirty minutes of hard work to solve. Some days I just want to throw the textbook across the room.
This has been my situation since January of last year, when I finished Algebra II and went on to pre-calculus.
I am very grateful for winter break, but I still dread the day when I have to take of pre-calculus again--perhaps the bane of my very existence.
But then my Mom--who is also my teacher--told me to look at math like a piano concerto. She insists that finishing pre-calculus and moving on to calculus will keep doors to whole career paths open if my career as a pianist doesn't happen. You know, I thought then, she's right.
She suggested I write a blog post comparing the many skills required to solve pre-calculus problems like graphing a sinusoid curve, finding roots of complex numbers calculating the distance between a point and a line, etc. to the years of experience and many skills required to learn, say, a piano concerto. I liked that idea, and since I love to analyze anything I can get my hands on--I decided to go right ahead.
I picked a movement from one of my favorite concertos of all time, the third movement of the piano concerto No. 3 in C minor by Beethoven. This will most likely be my piece for my senior year recital at the National Federation of Music Clubs recital in spring 2018 (so I have plenty of time to learn it!). Here's a recording I particularly enjoy, by Krystian Zimmerman. https://www.youtube.com/watch?v=R1QNhRNxvTI. The third movement is at 28:37, unless you want to watch the whole thing, which I highly recommend. :)
I'm not going to go into a minute-by-minute analysis of the piece, which would be tiresome to all but the most dedicated musicologists. But, among other things, this concerto requires solid scale, arpeggio, chromatic and octave technique. Many times, the pianist needs to balance a dense, rolling accompaniment with a singing melody.
I've heard many people say that calculus is easier than pre-calculus, which at first didn't make any sense to me. If these problems I'm doing now are hard, what will calculus be like???
In the same way, learning pieces like this can be as daunting as taking on a calculus course.
But then, I thought, what if I were to break it up?
Calculus is only hard because of the pre-calculus necessary to solve it. And, in the same way, once I've learned the individual skills by themselves--the scales, the arpeggios, the octaves, the balance, the interpretation--it's like the pre-calculus in calculus. It takes years of experience to build up to repertoire like this, just like in math, one goes from beginning arithmetic to fractions to algebra to geometry to pre-calculus to calculus.
This particular concerto is not as complex or long as, say, Rachmaninoff's or the Tchaikovsky concertos--to which one might describe as the linear algebra of music. But nevertheless, it is still very difficult in its own way, and attempting this piece requires the endurance and many skills comparable to solving calculus problems. So, perhaps I can look forward to my schoolwork this coming winter. It's a welcome outlook, I think.