Since my university doesn't have algebraic geometry courses or professors (*), I'm self studying algebraic geometry with the goal of finishing prerequisites before transferring. I've already started on commutative algebra and algebraic toplogy, next my goal is to read Royal Road to Algebraic Geometry. After that, I'll finally start Hartshorne.
How do I put my efforts on my transfer application for U.S. schools? I'll mention how I self-studied and what exactly I did in more detail on my statement of purpose, but is that enough? My primary goal in studying is to prepare, but my secondary goal is to convince universities that I'm putting in a ton of work on my own and thereby boost my application. I'm certain to succeed in my primary goal, but I'm unsure about the secondary goal since even if they do believe I studied, they have no reason to believe I carefully studied. I could type up exercise solutions, but they're not gonna spend time reading through all of them when there's so many students applying.
A similar question was already asked here but there are 2 differences: the topics are more advanced and I'm applying to transfer. The answers given there are to excel in the math subject GRE and get a professor to vouch for your knowledge through a letter of recommendation. The 1st difference makes the former answer irrelevant (besides, I already got 96%), and the 2nd difference + (*) makes the latter impossible unless I get someone from another university to vouch for me. What's the best way to do that, knowing full well that I would be approaching faculty just to get them to check my work?