Статья: Mastering Linear Algebra in 10 Days: Astounding Experiments in Ultra-Learning

Despite the advantages of learning faster, most people seem reluctant to learn how to learn.

understanding is hardly an on/off switch. It’s like layers of an onion, from very superficial insights to the deep understandings that underpin scientific revolutions.

Getting insights to deepen your understanding largely amounts to two things:

1. Making connections
2. Debugging errors

making connections between something you do understand and the material you don’t.

Debugging errors is also important because often you make mistakes because you’re missing knowledge or have an incorrect picture. 

1. Coverage
2. Practice
3. Insight

You can’t plan an attack if you don’t have a map of the terrain.
For a class, this means watching lectures or reading textbooks. For self-learning it might mean reading several books on the topic and doing research.
 In many ways this is the least efficient stage because the amount you can learn per unit of time invested is much lower. I often found it useful to speed up this part so that I would have more time to spend on the latter two steps.

if you want to learn, you need immediate feedback. 

Practice problems should be used to highlight areas you need to develop a better intuition for

The goal of coverage and practice questions is to get you to a point where you know what you don’t understand.

By digesting the big hairy idea you don’t understand into small chunks, and learning those chunks, you can eventually fill every gap that would otherwise prevent you from learning it.

1. Get a piece of paper
2. Write at the top the idea or process you want to understand
3. Explain the idea, as if you were teaching it to someone else

1. Analogies – You understand an idea by correctly recognizing an important similarity between it and an easier-to-understand idea.
2. Visualizations – Abstract ideas often become useful intuitions when we can form a mental picture of them. Even if the picture is just an incomplete representation of a larger, and more varied, idea.
3. Simplifications – A famous scientist once said that if you couldn’t explain something to your grandmother, you don’t fully understand it. Simplification is the art of strengthening those connections between basic components and complex ideas.

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