What is the one thing in mathematics or physics you feel completely comfortable with? In other words, which concept do you find you have grasped to such a degree that you’re able to get a good grasp on any problem concerning it? For myself, the mathematic concept that I feel pretty comfortable with is the idea of tangent lines and planes to certain functions (multivariable or not). I’m not saying that I understand a problem within three seconds, but I’m generally able to figure out the solution without too much difficulty. In physics, the concept I’m comfortable with is waves. I’m able to write equations for the wave-like motion of various objects and phenomena, and I’m good at extracting information out of them. Therefore, that would be my most comfortable area at the moment.
(Of course, it may come as no surprise that I’m comfortable with these two areas because I’ve recently taken a class on them. As such, it’s not exactly surprising that I’m used to them.)
However, there are plenty of concepts which I am not familiar with. In mathematics, I always get caught up when I have to deal with chords in a circle or if I have to use hyperbolas and other not-frequently used functions. In physics, the concepts of energy, torque, moments of inertia, and other physics related to rotating bodies can often throw me for a loop.
The reason, I think, is that I never had a full, thorough explanation of most of these concepts. As such, I’m always operating on a level that includes a bit of knowledge, but not necessarily one that makes me confident that I know what to do. In other words, I have a shaky foundation. And, as we all know, a shaky foundation has consequences for later on. When we aren’t comfortable with a subject, the problems will only resurface in other concepts later on.
To combat this, I’m setting myself a goal of filling the holes of my knowledge and finding those full explanations that I might have missed at different points in my education. That way, I’ll be improving my foundation so that I can actually move forward and not be so confused with concepts.
If I can offer one piece of advice, it is this: don’t settle for half-explanations. When learning, make sure that you understand the concepts to a point that you are completely comfortable with the ideas. If you have questions, make sure you ask them. Don’t worry about seeming “dumb” or not knowing enough. What’s more important is that you understand, and nothing else.