An Intuitive Guide to Linear Algebra

Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”.

Why? Well, let’s try this course format:

  • Name the course “Linear Algebra” but focus on things called matrices and vectors
  • Label items with similar-looking letters (i/j), and even better, similar-looking-and-sounding ones (m/n)
  • Teach concepts like Row/Column order with mnemonics instead of explaining the reasoning
  • Favor abstract examples (2d vectors!
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Why Do We Learn Math?

I cringe when hearing "Math teaches you to think".

It's a well-meaning but ineffective appeal that only satisfies existing fans (see: "Reading takes you anywhere!"). What activity, from crossword puzzles to memorizing song lyrics, doesn't help you think?

Math seems different, and here's why: it's a specific, powerful vocabulary for ideas.... Read article

How To Understand Derivatives: The Product, Power & Chain Rules

The jumble of rules for taking derivatives never truly clicked for me. The addition rule, product rule, quotient rule — how do they fit together? What are we even trying to do?

Here’s my take on derivatives:

  • We have a system to analyze, our function f
  • The derivative f’ (aka df/dx) is the moment-by-moment behavior
  • It turns out f is part of a bigger system (h = f + g)
  • Using the behavior of the parts, can we figure out the behavior of the whole?
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