"A Transition to Advanced Mathematics" (0-534-38214-2) at the end of my 6th grade school year, just as summer was starting.<p>I would give this book to myself because it's a bridge between finishing the final class in high school math and learning how to read proofs on arXiv. The world would be a better place today if I'd known how to manipulate mathematical proofs a decade ago.<p>During fourth grade and fifth grade, i walked across the street to the other school for my math classes. To this day, people i never knew recognize me on sight as "that kid from math class". When sixth grade ended at age 12, the school ran out of math to teach me (at pre-calculus). I was offered a choice: bus to the high school miles away for math classes, or take music instead. I worried that the bus would ostracize me further from my peers. I would be someone else today if i had chosen the bus. Fluent in math, certainly!<p>In the years since, I've harbored a desire for a textbook that will teach advanced mathematics to someone with my experience. I've had this dream of understanding how to consider and construct equations with Hilbert spaces. I know it sounds arcane and weird, but it's just a few steps away from cosines and bitwise operators. You can reach into an equation and "flip" things over into this weird space with dimensionality that is not constant, enabling solutions that cannot be had simply from high school algebra alone.<p>Two months ago, while surfing a used bookstore's Math section, I came across a textbook with the singularly direct title "A Transition To Advanced Mathematics". It is amazing. I am reading sections, doing the exercises, checking against the teacher's guide, redoing until I get a right answer or at least "get it". So far, I can handle one section a week, which means I will complete the book in 39 weeks. (Coincidentally, 39 weeks is precisely 75% of a year, just like American school years.)