Mastering linear algebra within ten days: an amazing speeding learning experiment

Reprinted from: http://www.read.org.cn/html/2070-zhuan-zai-shi-tian-nei-zhang-wo-xian-xing-dai-shu-jing-ren-de-chao-su-xue-xi-shi-yan.html

I just saw a very wonderful article in the translation, which was specially reproduced for sharing by more people.

• Source: calnewport.com
• Original article title: Mastering linear algebra in 10 days: astounding experiments in ultra-Learning
• Address: http://calnewport.com/blog/2012/10/26/maste
• Translator: mapleflying
• Address: http://select.yeeyan.org/view/94114/329073/author

Full-text directory

1 Article: Challenge mit Computer Courses

2. How can I take mit computer science courses (Scott Yang)

2.1 Why is it useless to hold your feet temporarily?

2.2 can you speed up your understanding?

3. Study: You learn faster

3.1 Stage 1: Knowledge coverage

3.2 Stage 2: Exercise

3.3 Stage 3: Introspection

4 Feynman skills

4.1 dealing with the concept that you are completely confused

4.2 deal with various processes

4.3 dealing with various formulas

4.4 deal with content that needs to be remembered

5. Form a deeper intuition

5.1 analogy, visualization, and simplification

5.2 learn faster strategies

5.3 study, even if you are not a student

1 Article: Challenge mit Computer Courses

Recently, my friend Scott Young made an amazing feat: within a year, he completed all 33 of the legendary mit computer science curriculum, from Linear Algebra to Computational Theory. The most important thing is that he is self-taught. He watches online tutorial lectures and uses actual tests for self-evaluation. (Go to Scott's FAQ page to see how he can accomplish this challenge)

He proved that it would take about 1.5 weeks to complete a course. I firmly believe that the ability to quickly grasp complex information is crucial to achieving a remarkable career (read my new book and blog at any time ). Therefore, I naturally asked Scott to share his learning mysteries with us. Fortunately, he agreed. Next we will provide a detailed explanation of Scott, in-depth analysis of his learning skills (including specific examples), and show him how to win the MIT challenge. The following time will be handed over to Scott ......

2. How can I take mit computer science courses (Scott Yang)

I was so excited to learn faster and get faster. Master the important knowledge. professional knowledge and skill will be your professional capital, helping you earn money and enjoy your life. If you have a good life, your goal is to attract you to the desired place (the book has its own gold house, and the book has its own face as Jade ).

Although learning faster has many advantages, most people do not want to learn "how to learn ". Probably because we refuse to believe in such a good thing, in our opinion, the speed of learning depends only on good genes and talent. It is true that some people have a natural capital, but research shows that your learning method is also very important. More in-depth knowledge processing, and repeated updates, in some cases, will increase your learning efficiency. Yes, research on deliberate exercises shows that learning will never stop if there is no correct method.

Today, I want to share my learning strategies and learn how to complete the four-year MIT computer science course in 12 months. This set of strategies has been honed by 33 courses, trying to find out the tips for faster learning and the useful and useless methods.

2.1 Why is it useless to hold your feet temporarily?

Many students may laugh at me and want to spend only one year learning four years of courses. After all, I can always stick to my feet temporarily, and I can still pass the test without knowing anything, right? Unfortunately, this policy does not work at MIT. First of all, MIT's tests require problem-solving skills and often produce questions that have never been seen before. Second, the MIT course is step-by-step. Even if you are lucky enough to pass an exam, the Seventh Course in the same series may not be able to keep up. In addition to rote memorization, I have to find another way to accelerate the process of understanding.

2.2 can you speed up your understanding?

"Aha !" When we finally figured it out, we were all excited. The problem is that most people do not think systematically. The classic path for students to study is to listen to lectures and read books. If they do not understand it, they have to do a lot of exercises or take notes. There is no systematic approach, and it seems impossible to understand it more quickly. After all, the psychological mechanism of epiphany is completely unknown.

Even worse, understanding itself is hard to be called a switch. It is like an onion layer-by-layer skin, from the most superficial understanding to a deep understanding, layer by layer to consolidate the cognition of the scientific revolution. Peeling such an onion is a process of understanding that is rarely known and easy to ignore.

The first step in accelerating learning is to reveal the secrets of this process. How to understand the problem and deepen your understanding depends on two factors: 1. Establishing knowledge connections; 2. Self-debugging and troubleshooting. Knowledge connections are important because they are the access points for understanding an idea. I had struggled with Fourier transformation until I realized that it was converting pressure into pitch or radiation into color. These insights are often established between what you know and what you don't understand. Debugging troubleshooting is equally important because you often make mistakes. The root cause of these errors is incomplete knowledge. Poor understanding is like a software program with hundreds of errors. If you can debug yourself efficiently, the learning process will be greatly accelerated. Establishing accurate knowledge connections and debugging and troubleshooting are sufficient to form profound insights. However, mechanized skills and rote memorization often benefit only when you have a certain intuition on the nature of the problem.

The Drilldown method: You learn faster

Over the years, I have improved a method to accelerate the process of increasing understanding layer by layer. This method has so far been used by me in various subjects, including mathematics, biology, physics, economics and engineering. You only need to make a few changes. It also works well for mastering practical skills, such as programming, design, or language. The basic structure of this method is knowledge, practice, and introspection. I will explain each stage, show you how to execute them as efficiently as possible, and give detailed examples to show how I apply them to practical courses.

3.1 Stage 1: Knowledge coverage

You cannot organize an attack if you don't even have a topographic map. Therefore, the first step of in-depth study is to have a general impression on what you need to learn. If you are in the classroom, this means you have to read handouts or textbooks. If you are studying by yourself, you may want to read more books on the same subject and study each other.

A common mistake made by students is that this stage is the most important. In many ways, this stage is the most efficient, because your investment per unit of time is only for the minimum amount of knowledge returns. I often perform acceleration at this stage, which is very helpful. In this way, I can invest more time in the next two stages.

If you are watching a video of the course lecture, it is best to set it to 1.5x or 2x speed forward. This is easy to achieve, as long as you download the video, and then use the player (such as VLC) "Speed Control" function. I used this method to watch the course video for one semester in two days. If you are reading a book, I suggest you do not spend time highlighting the text. This will only make your understanding of your knowledge stay at a low level, and in the long run, it will also make your learning efficiency low. A better way is to take (sparse) Notes occasionally during reading, or write a summary after reading each major chapter.

Here is an example of my notes on Machine Vision.

3.2 Stage 2: Exercise

Exercise questions can greatly promote your knowledge understanding. However, if you are not careful, you may fall into two efficiency traps: 1. No immediate feedback is received: research shows that if you want to learn better, you need immediate feedback. Therefore, it is best to answer the questions in hand (I have the answer in the world), and review the answers each time I finish a question. Without feedback or feedback, learning efficiency is severely restrained. 2. Question-sea tactics: just as some people think that learning begins with the classroom, some students also think that most of their knowledge is produced by exercises. Yes, you can always establish a knowledge framework through the sea of questions tactics, but the process is slow and inefficient.

Exercise questions should highlight your need to build a more intuitive field of knowledge. Some tips, such as the Feynman technique I will talk about, are quite effective. For non-technical disciplines, it requires you to master concepts rather than solve problems. Therefore, you often only need to complete a few exercises. For these subjects, you 'd better spend more time in the third stage to form disciplinary insights.

3.3 Stage 3: Introspection

Knowledge coverage and exercise questions are designed to let you know what else you do not understand. This is not as easy as it sounds (it's hard to know, not to know ). You think you understand it. Actually, it's not, so you always make mistakes. Or, you have no idea about a comprehensive subject, but you cannot understand it clearly.

The next technique, I call it the "Feynman technique", will help you identify missed vacancies and go further on the way to knowledge. When you can accurately identify what you don't understand, this technique helps you fill in the gaps in your knowledge, especially those that are the most difficult to fill. This skill can also be used. Even if you really understand an idea, it can also associate you with more ideas, so you can continue to study and deepen your understanding.

4. The Feynman Technique)

This technique was inspired by Richard Feynman, the Nobel Physics Prize winner ). In his autobiography, he mentioned that he had been entangled in a difficult research paper. His approach is to carefully review the paper's auxiliary materials (supporting material) until he has mastered the knowledge base and is sufficient to understand the difficult ideas.

This is also true for Feynman's skills. To deal with a complicated idea of knowledge, such as hair and connotation, you should divide it into small pieces of knowledge and then deal with them one by one (recursion). In the end, you can fill in all the knowledge gaps, otherwise, these gaps will impede your understanding of this idea. For more information, see this short tutorial video.

Feynman's skills are simple: 1. Take a piece of white paper; 2. Write an idea or process on the top of the White Paper; 3. Explain it in your own words, it's like you are teaching others this idea. The most important thing is to separate an idea, although it is possible to repeatedly explain some knowledge points that have already been understood. However, you will eventually reach a critical point and cannot explain it clearly. There is exactly the knowledge gap you need to fill. To fill in this gap, you can check textbooks, ask teachers, or search for answers on the Internet. Generally, it is easier to find the exact answer once you accurately define your puzzles or misunderstandings.

I have used this Ferman technique for hundreds of times and are sure it can cope with various learning situations. However, because the learning situation has its own characteristics and needs to be flexible, it seems difficult to get started, so I will try to give some different examples.

4.1 dealing with the concept that you are completely confused

In this regard, I still insist on using the Feynman technique, but open the textbook and find the chapter to explain this concept. I first browsed the author's explanation, then carefully imitated it, and tried to elaborate on it with my own thoughts. In this way, the "guided" Feynman technique is useful when you cannot write down any explanation in your own words. Here is an example of how I understand photography.

4.2 deal with various processes

You can also learn about a process you need through the feeman technique. Looking at all the steps not only explains what each step is doing, but also how it is executed. I often understand the process of mathematical proof, the chemical equation, and the fermentation process of biology. Here is an example to show how I want to achieve mesh acceleration.

4.3 dealing with various formulas

Formulas should be understood, not just memorized. Therefore, when you see a formula, but you cannot understand its operating mechanism, try to separate it with the Feynman technique. Here is an example to show how I understand the Fourier analytical equation.

4.4 deal with content that needs to be remembered

The Feynman technique can also help you to check whether you have mastered the profound knowledge concepts of non-technical disciplines. For a topic, if you can successfully use the Feynman technique without referring to the original materials (handouts, textbooks, etc.), it proves that you have understood and remembered it. Here is an example to illustrate how I recall the concept of price (Economics ).

5. Build a deeper intuition (deeper intuition)

Combined with exercises, feeman's skills can help you strip the superficial skin of knowledge and understanding. But it can also help you study it further, not just a superficial understanding, but a profound knowledge intuition (keen insight ). It is not easy to understand an idea intuitively. It seems a little mysterious, but it is not its original phase. Most intuition of an idea can be categorized as follows:

5.1 analogy, visualization, and simplification

Analogy: You understand an idea by recognizing its important similarities with a more understandable idea. Visualization: abstract concepts are often useful intuition, as long as we can build pictures (imagination and composition) for them in the brain, even if this picture is just an incomplete expression of a larger and more diverse idea, simplified: a famous scientist once said, if you cannot explain something to your grandmother, it means you have not fully understood it. Simplification is an art that strengthens the thinking connection between basic concepts and complex ideas.

You can use the Feynman technique to stimulate these instincts. Once you have a general understanding of an idea, the next step is to analyze it in depth to see if the above three instincts can be used to explain it. During this period, it is also excited to borrow the existing images. For example, it is difficult to put the plural in a two-dimensional space to understand it. However, it allows you to visualize the concept (the concept is structured in your mind ). DNA replication is imagined as a one-way zipper, which is not a perfect analogy, but it will become useful as long as you know the similarities and differences in your mind.

5.2 learn faster strategies

In this article, I describe three stages of learning: knowledge, practice, and introspection. However, this may make you misunderstand that they are always executed in different periods and never overlap or repetition. In fact, as you continue to understand your knowledge, you may go through these stages again and again. You can only have a superficial impression when you first read a chapter, but after you have done exercises and built intuition, you can come back and read them again, we will have a deeper understanding (learn new things from the past ).

5.3 study, even if you are not a student

This process is not only applicable to students, but also helps to learn complex skills or accumulate professional knowledge on a topic. Learning skills like programming or design, most people follow the first two stages. They read a related basic book and then experience it in a project. However, you can use the Feynman technique to further lock and clearly express your insights. The only difference is that you need to collect learning materials, including related research articles and books, before building up your knowledge. In any case, as long as you have figured out the field of knowledge you want to know, you can study it in depth.