Summary: I’m building a calculus course from the ground-up focused on permanent intuition, not the cram-test-forget cycle we’ve come to expect.
Limits, the Foundations Of Calculus, seem so artificial and weasely: “Let x approach 0, but not get there, yet we’ll act like it’s there… ” Ugh. Here’s how I learned to enjoy them:
- What is a limit? Our best prediction … Read article
The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations:
Yikes. Rather than deciphering it symbol-by-symbol, let's experience the idea. Here's a plain-English metaphor:
- What does the Fourier Transform do? Given a … Read article
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), … Read article
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… Read article
I’ve studied probability and statistics without experiencing them. What’s the difference? What are they trying to do?
This analogy helped:
- Probability is starting with an animal, and figuring out what footprints it will make
- Statistics is seeing a footprint, and … Read article
What’s algebra about? When learning about variables (x, y, z), they seem to “hide” a number:
What number could be hiding inside of x? 2, in this case.
It seems that arithmetic still works, even when we don’t have the… Read article