Trial by fire: My mission to prove every real analysis theorem from scratch

Proving stuff yourself is hard, and my initial attempts were catastrophic. I wrote one proof that began with a stronger statement than the conclusion I was attempting to draw, rendering the proof useless even in the unlikely case it was otherwise successful. It was not otherwise successful. Jumping through several dodgy implications and logical errors, it eventually arrived at a conclusion that was substantially weaker than what I was attempting to prove. The worst part? I couldn’t even spot my own mistakes, and I thought the proof was probably quite good.

This post is about my approach to real analysis. In many areas of theoretical research, proving things is of paramount importance.  Sadly, I didn’t have the foresight to take a heavy math curriculum as an undergrad, and like many, my skills were lackluster at best. My solution? Prove every theorem in an intermediate analysis course.

Continue reading Trial by fire: My mission to prove every real analysis theorem from scratch

Two Approaches to Learning

Josh Kaufman argues you can learn anything in less than 20 Hours. This seems to contradict research that says it takes (on average) 10,000 hours to master a skill. Josh Kaufman doesn’t mean it takes you 20 hours to master a skill, it just takes that long to get “good enough”. This article explains two approaches and how to apply them effectively.

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Don’t Learn Latin, Don’t Use Translations, Don’t Be a Hack.

I recently read my first book in Spanish. To celebrate, I’m reflecting on how I got here. It was an arduous journey and there are many pitfalls to avoid. Three principles guided my way:

  • Don’t be led astray
  • Eliminate the unimportant
  • Go slow to go fast
Continue reading Don’t Learn Latin, Don’t Use Translations, Don’t Be a Hack.