Alice Zielinski is currently an MIT undergraduate studying aeronautical & astronautical engineering and computer science & electrical engineering. In this article, she tells us that
“Many MIT students recount questions about their GPA, test scores, magnificent things they’ve built, other accomplishments—while I often find myself trying to convince people that I actually attend MIT. The reactions that I’ve received from people range from amusing to borderline offensive, from delightful to ‘what??’”
Scott Young recently finished an astounding feat: he completed all 33 courses in MIT’s fabled computer science curriculum, from Linear Algebra to Theory of Computation, in less than one year. More importantly, he did it all on his own, watching the lectures online and evaluating himself using the actual exams. Check out the link for more in depth info.
The first step in learning anything deeply, is to get a general sense of what you need to learn.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.
Take sparse notes while reading, or do a one-paragraph summary after you read each major section.
Practice problems should be used to highlight areas you need to develop a better intuition for.
Non-technical subjects, ones where you mostly need to understand concepts, not solve problems, can often get away with minimal practice problem work. In these subjects, you’re better off spending more time on the third phase, developing insight.
THE FEYNMAN TECHNIQUE
The technique is simple:
a)Get a piece of paper
b) Write at the top the idea or process you want to understand
c)Explain the idea, as if you were teaching it to someone else
What’s crucial is that the third step will likely repeat some areas of the idea you already understand. However, eventually you’ll reach a stopping point where you can’t explain. That’s the precise gap in your understanding that you need to fill.
Formulas should be understood, not just memorized. So when you see a formula, but can’t understand how it works, try walking through each part with a Feynman.
Most intuitions about an idea break down into one of the following types:
a)Analogies – You understand an idea by correctly recognizing an important similarity between it and an easier-to-understand idea.
b)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.
c) 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.