Mastering Linear Algebra in ten days:astounding experiments in ultra-learning

The MIT Challenge

My friend Scott Young recently finished a astounding Feat:he completed all the courses in MIT's fabled computer science C Urriculum, from Linear Algebra to Theory of computation, in less than one year. More importantly, he does it all in his own, watching the lectures online and evaluating himself using the actual exams. (see Scott's FAQ page for the details about how he ran this challenge.)

That works out to around 1 course every 1.5 weeks.

As you know, I ' m convinced that the ability to master complicated information quickly are crucial for building a remarkable Career (see my new book as well). So, naturally, I had-ask Scott to share he secrets with us. Fortunately, he agreed.

Below is a detailed guest post, written by Scott, which drills down to the exact techniques he used (including specific Exa Mples) to pulling off his MIT challenge.

Take It away Scott ...

How I tamed MIT's computer science curriculum, by Scott Young

I ' ve always been excited by the prospect of learning faster. Being good at things matters. Expertise and Mastery give you the career capital to earn more money and enjoy lifestyle perks. If being good is the goal, learning are how you get there.

Despite the advantages of learning faster, most people seem reluctant to learn how to learn. Maybe it's because we don t believe it's possible, that's learning speed is solely the domain of good genes or talent.

While there'll always be people with unfair advantages, the "the" the "the" Method "the" "use" to shows learn a lot. Deeper levels of processing and spaced repetition can, in some cases, double your efficiency. Indeed The deliberate practice shows us, without the right method, learning can plateau forever.

Today I want to share the strategy I used to compress the ideas from a 4-year MIT computer science curriculum down to M Onths. This strategy is honed over-classes, figuring out what worked and what didn ' t in the method for learning faster.

Why cramming doesn ' t work

Many student might scoff at the idea of learning a 4-year program in a quarter of the time. After all, couldn ' t just cram for every exam and pass without understanding anything?

Unfortunately this strategy doesn ' t work. First, MITs exams rely heavily on problem solving, often with unseen problem types. Second, MIT courses is highly cumulative, even if you could sneak by one exam through memorization, the seventh class in A series would is impossible to follow.

Instead of memorizing, I had to find a by-speed up the process of understanding itself.

Can you speed up understanding?

We ' ve all had those, "aha!" moments when we finally get a idea. The problem is the very most of us don ' t has a systematic of finding them. The typical process a student goes through in learning are to follow a lectures, read a book and, failing this, grind out p Ractice questions or reread notes.

Without a system, understanding faster seems impossible. After all, the mental mechanisms for generating insights is completely hidden.

Worse, understanding is hardly an on/off switch. It's like layers of a onion, from very superficial insights to the deep understandings that underpin scientific revolutio Ns. Peeling that onion is often a poorly understood process.

The first step is to demystify the process. Getting insights to deepen your understanding largely amounts to both things:making connections debugging errors

Connections is important because they provide an access point for understanding a idea. I struggled with the Fourier transform until I realized it is turning pressure to pitch or radiation to color. Insights like these is often making connections between something you does understand and the material you don ' t.

Debugging errors is also important because often do mistakes because you ' re missing knowledge or has an incorrect p Icture. A poor understanding is like a buggy software program. If You can debug yourself on an efficient-in-a-do, you can greatly accelerate the learning process.

Doing these-things, forming accurate connections and debugging errors, is the most of the creating a deep understanding. Mechanical skill and memorized facts also help, but generally if they sit upon the foundation of a solid intuition About the subject. The Drilldown method:a strategy for learning Faster

During the yearlong pursuit, I perfected a method for peeling those layers of deep understanding faster. I ' ve since used it on topics in math, biology, Physics, economics and engineering. With just a few modifications, it also works well for practical skills such as programming, design or languages.

Here's the basic structure of the Method:coverage practice Insight

I ' ll explain each stage and how can go through them as efficiently as possible, while giving detailed examples the How I used them in actual classes.

Stage one:coverage

You can ' t plan an attack if you don't have a map of the terrain. Therefore The first step in learning anything deeply, was to get a general sense of what do 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.

A mistake students often make are believing this stage are the most important. In many ways 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 has more time to spend on the latter II steps.

If you ' re watching video lectures, a great a-do-it-to-watch them at 1.5x or 2x. This can is done easily by downloading the video and then using the Speed-up feature on a player like VLC. I ' d watch Semester-long courses in, and via this method.

If you ' re reading a book, I would recommend against highlighting. This was processes the information at a low level of depth and was inefficient in the long run. A better method would is to take sparse notes while reading, or does a one-paragraph summary after your read each major secti On.

Here's an example of notes I took and doing readings for a class in machine vision.

Stage Two:practice

Practice problems is huge for boosting your understanding, but there is both main efficiency traps you can get caught in If you ' re not careful.

#1 –not Getting Immediate Feedback

The clear:if is a want to learn and you need immediate feedback. The best-of-the-go question-by-question with the solution key in hand. Once you ' ve finished a question, check yourself against the provided solutions. Practice without feedback, or with delayed feedback, drastically hinders effectiveness.

#2 –grinding Problems

Like the students fall to the trap of believing that most learning occurs in the classroom, some students believe UN Derstanding is generated mostly from practice questions. While you can eventually build a understanding simply by grinding through practice, it ' s slow and inefficient.

Practice problems should is used to highlight areas the need to develop a better intuition for. Then techniques like the Feynman technique, which I'll discuss, handle that process much more efficiently.

Non-technical subjects, ones where you mostly need to understand concepts, not solve problems, can often get away with min iMAL practice problem work. In these subjects, you ' re better off spending more time on the third phase, developing insight.

Stage three:insight

The goal of coverage and practice questions is for get you to a point where you know what you don ' t understand. This isn ' t as easy as it sounds. Often you can be mistaken to believing you understand something, but don ' t, or do might not feel confident with a gener Al subject, but isn't see specifically what's missing.

This next technique, which I call the Feynman technique are about narrowing down those gaps even further. Often when you can identify precisely what do you don't understand, that's gives you the tools to fill the gap. It's the large gaps in understanding which is hardest to fill.

The technique also has a dual purpose. Even when does understand a idea that it provides you opportunities to the create more connections so can drill down to a Deeper understanding. The Feynman technique

I first got the idea from this method from the Nobel prize winning physicist, Richard Feynman. In the He autobiography, he describes himself struggling with a hard and a paper. His solution is to go meticulously through the supporting material until he understood everything that is required to UN Derstand the hard idea.

This technique works similarly. 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 the from learning it.

For a video tutorial of this technique, watch this short video.

The technique is simple:get a piece of paper Write at the top the idea or process you want to understand Explain the idea , as if you were teaching it to someone else

What's crucial is that the third step would 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 so need to fill.

From this gap, you can be the answer from a textbook, teacher or online. Generally, once you ' ve narrowly defined your misunderstanding it becomes much easier to find the precise answer.

I ' ve used this technique hundreds of times, and I ' ve found it can tackle a wide variety different learning situations. However, since each might is slightly different, it may seem hard to apply as a beginner, so I'll try to walk through some Different examples.

For Ideas you Don ' t Get at all

The I handle this was to go through the technique but has the textbook open to the chapter explaining that concept. Then I go through and meticulously copy both the author's explanation, but also try to elaborate and clarify it for myself . This "guided" Feynman can is useful when trying to write anything on your own would is impossible.

Here's a example I used for trying to understand photogrammetry.

For procedures

You can also with the method to fully understand a process you need to use. Go through all the steps and explain isn't only what they does, but how they execute it. I would often go through proof techniques by carefully explaining all the steps. I also used it in understanding chemical equations or in organizing the stages of glycolysis in biology.

You can see the This example I used when trying to the figure of how to implement grid acceleration.

For formulas

Formulas should is 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.

Here's an example I used for the Fourier analysis equation.

For Checking Your Memory

Feynmans also offer a-to-self-test your knowledge of the big ideas for non-technical subjects. Being able to finish a Feynman on a topic without referencing the source material means you understand and can remember it .

Here's one I did for an economics class, recalling the concept of predatory pricing. developing a deeper intuition

Combined with practice questions, the Feynman technique can peel those first few layers of understanding. But it can also drill deeper if your want to go from not just have an understanding, but to have a deep intuition.

Understanding an idea intuitively isn ' t easy. Once again, getting to this-is often seen as a quasi-mystical process. But it doesn ' t has to be. Most intuitions-about-an-idea-break-into-one of the following types: analogies –you understand an I DEA by correctly recognizing a important similarity between it and an easier-to-understand idea. Visualizations –abstract ideas often become useful intuitions when we can form a mental picture of them. Even if the picture was just an incomplete representation of a larger, and more varied, idea. Simplifications –a famous scientist once said 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.

You can use the Feynman technique as a to encouraging these types of insights. Once you ' ve gotten past a basic understanding of the idea, the next step was to go further and see if you can explain it us ing some combination of the three methods above.

The truth is plagiarism are okay too, and not every insight needs to be unique. Understanding complex numbers as being and dimensional is hardly original, but it allows a useful visualization. DNA replication working like a one-way zipper are not a perfect analogy, but so long as you understand where it overlaps, i T becomes a useful one.

The strategy to learn Faster

Learning faster doesn ' t need to being a trick to work well. It simply means recognizing what's actually going on if we reach a new level of insight and finding tools to help us re Ach those stages consistently.

In this article I described learning as being three stages:coverage, practice and insight. This gives the false impression that these three occur always in distinct phases and never overlap or repeat.

In truth you could find yourself going between them in a loop as you successfully peel down to deeper layers of Understandin G. The first time you read a chapter if get only superficial insights, but after doing practice questions and Buildin G intuitions, you could go back and read for deeper understandings.

applying the Drilldown Method for non-students

This process isn ' t one of you need to is a student to apply. It also works for learning complex skills or building expertise on a topic.

For skills like programming or design, most people follow the first and the stages. They read a book teaching them the basics and then they practice with a project. You can extend this process however, and use the Feynman technique to better lock in and articulate the insights you creat E.

For expertise on a topic, the only difference are that, prior to doing coverages, you need to find a set of material to Lear N from. That could is articles or several books on the topic. In either case, once you ' ve defined the chunk of knowledge you want to master, you can drill down and learn it deeply.

To find out more about this, join Scott's newsletter and you'll get a free copy of his rapid Learning ebook (and a set of Detailed case studies of what other learners has used these techniques).