I am a high school student really into algebra and algebraic geometry.
I want to expose this sort of math to other high school students that have the motivation and ability.
For a long time, I had no idea how to learn more math after learning calculus, and I feel my middle school and early high school years were wasted as a result. One day, I coincidentally found a post on r/math that had a link to a bunch of Springer PDFs that were being given out for free. This experience was incredibly eye-opening, and I was exposed to all sorts of math that I had never seen before.
I want to find similar students to me that never got the chance to find an online copy of Lang, or their father's calculus textbook. Furthermore, I want to give a mathematical experience better than picking up a random book and struggling through it while you're supposed to be doing homework.
In short, I want to teach advanced mathematics (leaning towards abstract algebra/foundations) to high school (or even middle school) students, with no prerequisites other than demonstrated commitment to learning and calculus.
In order to accomplish this goal, I have a few questions.
(1) When I first asked this question, I thought that we were going to go through parts I and II of Lang's Algebra, all of Mendelson's logic book, and Axler's linear algebra book. I based the curriculum and pacing heavily on Math 55 at Harvard. But then the answers made me realize that the majority of students are not willing to neglect their grades and social life to study math for 60 hours a week. Should I postpone the project to the summer looking for the students who can, or lower my standards?
(2) How do I find and recruit students? Nobody at my school is interested, and even if they were, I doubt most of them would put in the effort.
(3) What general methods for teaching should I know of? How do I write a lesson plan, schedule a curriculum, and grade proofs?