I'm taking some time off between my undergraduate and graduate studies. I've definitely kept up the practice of my field during this time through self-study. My question relates to how I can show this to graduate admissions next year. Let's say I've been working through some very important books/papers of my field which prepare me for research. What's a good way to show this? Simply stating this on my statement of purpose isn't sufficient as I've seen first hand people mentioning or exaggerating the extent of their study/projects and there'd be no way to tell if what I'm doing is any different. Should I be typing up notes as I go along and uploading them somewhere? This to me seems like a tedious task which would take time away from the actual study. Or should I upload my hand-written notes? This on the other hand seems a bit unprofessional.
Edit: For clarification, I should mention that my field is theoretical physics.