Lee's introduction to smooth manifolds

12 Apr, 2026

today i read Lee's introduction to smooth manifolds

with help of Claude, reading thru a textbook in top-down style is now easier. I pondered myself should i read top-down or keep building bottom-up. I used to be familiar with basic linear algebra, calculus, topology, abstract algebra, complex analysis.

There are 3 major reasons, I choose to read top-down again:

1. More confident: With help of LLM, I can quickly look up anything.
2. It motivates me. It keeps the flame alive.
3. I already have enough scaffolding that "hitting the wall" will be productive rather than demoralizing. When someone with no background hits a wall in reading top-down, they're lost. When I hit a wall, I'll recognize which room I'm in

If It takes too much time to "patch" the knowledge holes, it'll demoralize the passion.

topological manifold

Think about a class of objects, that look like subspaces ${ℝ}^n$ but more abstract. We constraint a set of conditions, then let's see how far it goes.