2024

Jun

17

• Smashing through “Linear algebra done right”. Actually doing all the exercises and learning a lot from the failures. Failing truly is the fastest way to learn because you’re correcting your mistakes and updating your mental model. How can you verify your mental model if you never apply it? You will assume it always right :)
• Actually understanding fractions now — might do a quick article for them. Math is all about what can you add to your toolbox.
• Understanding matrix multiplication super well — wrote about it in one of my blogs.
• Learned about sigma notation.

18

• Learned that proofs are super important. I’m at a point in my linear algebra book (inverse matrices) where it introduced “prove this” questions and I really don’t know how to write them. I make examples are write the logic but the actual explanation in the way it wants me to do it is just wrong. So i googled how important is proof righting and damn, heres a quote from reddit: “this skill of being able to explain how something is true instead of just accepting it as fact, even if it seems obvious, is really important, especially if you later learn topics like analysis where you learn there’s a lot of things that seem like they’ll obviously be true and turn out to be false. ” and “Math isn’t necessary all about theorems, it’s about discovering new structures and learning how to solve problems within these structures. Roughly “structure” means “properties of the objects” you study.”. Proofs are like a programming language that constructs a library which you use in your code application.
  • Proofs will be essential down the life for inventing new formulas for shit we encounter when building AGI.
  • They are extremely important for accelerating math learning. The better you understand proofs the faster you’ll understand somethings intuition. It’s essentially reading the code of someone else. You may be able to construct a better proof then these textbook ones! Understanding is how you truly know something. Not accepting that it’s true.
• Actually understand Gaussian Elimination now.
• Didn’t really do much overall in the day. Struggled with inverse matrices. Very slow day didn’t get many pages done — plus had a ton of calls and distractions to stop focus.

19

• ”Proofs explain why mathematics works and not just how”, from p108 in “Linear Algebra Step By Step”.