If there’s one thing I’ve learned about mathematics during my many years at school, it’s that having a solid foundational understanding of the main components can go a long way towards learning new subjects within mathematics. Unfortunately, this is what is often lacking for students, and it can have the knock-on effect of making later concepts more difficult to grasp.

Despite needing to compute many quantities in my various physics and mathematics classes, I like to take a slightly different approach to studying for a test. First, I will do a bunch of practice problems in order to strengthen the “muscle memory” of how to do certain types of questions. This usually means going over assignments and doing examples. This particularly helps with refreshing my mind for questions I haven’t done in a few weeks.

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.

I’ve already mentioned this before, but there are more and more high-quality shows and sites on science and mathematics out there. Whether it’s popular science like what you’d find on Nautilus, or mathematics channels like 3Blue1Brown, there’s a lot of potential to learn science and mathematics in a way that is both informative and beautiful.