In this recent blog post the author lists several interesting concepts he has discovered pertaining to learning. One thing he mentions is the following:
Mastery is more important than passing grades. You will reach limits in learning when you have a "Swiss cheese" foundation full of misconception holes. Master each concept before building on top. ~Salman Khan
(This is actually from Salman's TED talk which you can view here.) My questions is as follows: I graduated about a year ago with a Master's in Applied Physics from a reputable university. I've been a B student throughout my academic career and I feel like I started building on un-mastered concepts somewhere towards the end of high school. Despite obtaining a relatively tough engineering degree, I cut corners whenever possible. If I could pass an exam by being able to do all the exercises, I would get to that level and stop there. I would rarely - if ever - go for complete mastery. As a result I feel like I have Swiss cheese holes in my understanding that date back to high school.
If Albert Einstein's quote is anything to go by:
If you can't explain it simply, you don't understand it well enough.
I'm afraid I can't simply explain a whole lot. For instance I would not be able to explain simply:
- What is the proof of Euler's identity?
- Why can you express a wave as an imaginary exponential?
- How does a photon have momentum, but not mass?
- What is the intuitive understanding of eigenfunctions, eigenvalues and their physical manifestations?
With the wealth of knowledge available today on the internet, I could look up any one of my knowledge gaps, and with some effort I feel confident I would be able to fill them. My question is, would that be worth it?