My topology curriculum is an example of How To: Learn a New Discipline.

#### 0. Build the map.

*The map* is a high level representation of important concepts and connections — the threads that compose the subject.

I started by working through these two:

Where “work through” $\equiv$ read carefully and annotate the text, take notes on important concepts, and complete a few exercises from each chapter.

*“Catherine, you said you’d teach me math. Why are you drawing squiggles?”*

*“Math is formalized art! I get to draw these squiggles on a page, describe them with symbols, and call it math.”*

#### 1. Learn by working through complementary perspectives in parallel.

- Hatcher: Intuitive & Geometric Perspective: $\rightarrow$ understand it.
- May: Category Theoretical Perspective: $\rightarrow$ believe that you understand it.

#### 2. Give weekly lectures on what you’ve learned.

I’m giving informal lectures to a small group of people on what I’m learning. These people ask questions and tolerate pauses to look things up.

*Don’t forget to ask for help when you get stuck! *

If you can’t find a satisfactory explanation online:

- talk to professors/PhDs/postdocs at your local university (they’re people too!)
- post your question to a website such as MathOverflow or Quora.

Hi Rin! I’ve been reading your website for a while, and I really enjoy what you’re writing. I also enjoy teaching myself tons of new things, and I’ve even gotten into teaching myself some mathematics topics (I missed out in university (I was a liberal arts student), but curiosity got the best of me). Your posts are very inspiring for a fellow autodidact- thanks!