Foreword

Linear algebra, my old flame - how I missed you. At my undergraduate institution, linear algebra was my introduction to proof-based mathematics. There are people who shake hands, and there are people who shake hands. You know the type - you grasp their hand, and they clamp down and pull you in, agitating so wildly you fear for the structural integrity of your joints. My first experience with proofs was an encounter of the latter variety.

I received my first homework grade, and I was not pleased with my performance. I promptly went to the library and vowed not to leave until I learned how to write proofs adequately. The hours passed, and, (thankfully for my stomach), I got it. I didn't let up all semester. Immediately before the final exam, I was doing pushups in the hallway, high-fiving my friends, and watching the 'Michael Jordan Top 50 All Time Plays' video while visualizing myself doing that to the test. Do that to the test I did indeed.

This time around, the appropriately-acronymized LADR is the first step on my journey to attain a professional-grade mathematical skillset.

Tight Feedback Loops

In a (possibly maniacal) effort to ensure both mastery of the material and the maturation of my proof skillset, I did nearly $^{1}$ every one of the 561 exercises provided. I skipped problems only when I was confident I wouldn't learn anything, or calculus I didn't remember was required (and the payoff didn't seem worth the time spent relearning it now in a shallow manner, as opposed to thoroughly learning more calculus later). If I could sketch a solid proof in my head, I wouldn't write anything down. Even in the latter case, I checked my answers using this site (additional solutions may be found here, although be warned that not all of them are correct).

I also sometimes elected to give myself small hints after being stuck on a problem for a while; the idea was to keep things at the difficulty sweet spot. Specifically, I'd spend 10-20 minutes working on a problem by myself; if I wasn't getting anywhere, I'd find a hint and then backpropagate the correct mental motion instead of what I had been trying to do. I think that focusing on where you were going wrong and what insight you should have had, in what direction you should have looked, is more efficient than just reading solutions.

Over time, I needed fewer hints,... ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Becoming Stronger