Mastering Linear Algebra in 10 Days: Astounding Experiments in Ultra-Learning | Hacker News Reader

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

calnewport.com

280 pointsphenylene76 comments

Cal Newport has the funniest definition of "mastering" and strangest definition of "world’s most efficient studiers" (another blog post of his from a couple years ago)

http://news.ycombinator.com/item?id=2658927

I have ever seen. The shtick is getting old. Gee-whiz posts about a dilettante ramping up to a beginner's knowledge of a subject with little time and effort have nothing to do with the really challenging learning tasks in this world.

I'll be impressed when I see a headline like "Middle East diplomatic issues resolved by undergraduate who completed one course in international relations" or something like that. Show me someone who has solved a genuinely hard problem before proclaiming a new breakthrough in learning. For a refreshing change of pace from the usual blog post on quick-and-dirty learning, see Peter Norvig's "Teach Yourself Programming in Ten Years"

http://norvig.com/21-days.html

or Terence Tao's "Does one have to be a genius to do maths?"

http://terrytao.wordpress.com/career-advice/does-one-have-to...

for descriptions of the process of real learning of genuinely challenging subjects.

I have several concerns about the original article, but if the point of this guest post on Newport's blog is "look, I was able to grind through the MIT requirements in a year with reasonable success" it is not particularly damning that all the person achieved is a beginner's knowledge in several courses. Hopefully readers realize that this is not necessarily such a wonderful achievement while simultaneously respecting the effort made.

My bigger concern is that the overt focus on "time-compressed" learning is that it will devolve to pure hucksterism with no attempt to move beyond anecdote to real research and thought as to how teaching (either by self-directed methods or to students in a traditional way) can be improved. People seem so interested in short-cuts. I personally want to an "efficient studier," but what I mostly mean is that I do not want to waste time using bad learning methods or materials.

We do know that improvements in the learning process are out there - better books, spaced repetition for recall, better guidance and opportunity for early learners than they get in schools in subject-specific areas, etc.

These types of posts along with my reading of immersive learning experiences (like your own math programs, dual language programs, "programming school" opportunities) has me thinking about the innate value that immersion offers to the learner.

Would linear algebra learners be better off to spend 4 weeks focused on only that subject with a professor/mentor, a textbook, and deliberate practice than a single semester of normal lecture instruction?

There was effectively nothing about linear algebra on that page. After some link followings, it appears that http://www.scotthyoung.com/mit/1806-exam.pdf is the exam which the student was happy with (having done worse on the first version). The final score appears to be 66 out of 100.

Based on that test, I think the title is link-bait as it isn't "mastering linear algebra" but "passing an introductory algebra course."

I am quite confused looking at that final; it seems incredibly basic for even an introductory course at MIT (that might have been a midterm when I was the graduate instructor for linear algebra at Berkeley).

18.06 is the very basic, more applied version of linear algebra at MIT. About half of the students that take it aren't in the math department. The more theoretical option is 18.700. And then there's 18.701, Algebra 1, taught by Artin using his book. The latter two are almost completely theoretical/proof based.

To be clear: I mean that it seems too basic even for a final exam of an introductory applied linear algebra course for non-majors.

Yes, that is strange. It looks more like the mid-term of the linear algebra class that I took at MIT: i.e., 18.700. And I have to say that 18.700 was one of the easiest classes that I ever took at MIT.

It's kind of a bummer that they gave me a C, in it though. I found it so easy that I never bothered to do the homework and just showed up for the exams and got A's on them all. For non-lab classes at MIT, they'd usually give you an A -- or at least a B -- if you got an A on all of the exams, even if you neglected the homework.

My thoughts exactly. The author should reconsider what he means by "mastering" something. Not passing a final exam for an introductory course isn't mastering the topic.

I am totally on board with the idea of seeing how fast someone can complete coursework and push the boundaries of what they can learn in a set amount of time, but name the article about it something other than "Mastering Linear Algebra in 10 Days".

This is written from a student perspective, where "mastering" means passing the exam. I'll stick with Norvig's 10 000 hours.

Exactly. When he says "Expertise and mastery give you the career capital to earn more money and enjoy lifestyle perks.", sure it does, but expertise is not achieved by "taming it" in 10 days or a year for that matter.

probably not the sentence I would remember, nor the summary of it all.

What did he try to achieve? Proving you can accelerate the learning process and he did so by example with a MIT graduate level. Even though, it's from MIT, it is a graduate level, nothing more ...

I think the described method is interesting for acceleration or in lean terms, reducing any waste, or even optimizing the learning process. Pick one ...

BTW, 10.000 hours is not from Norvig but from Gladwell, "Outliers".

“Igonvalue” Gladwell is not responsible for the 10,000 hours meme either. The single person who has done most for the expertise research literature is K. Anders Ericsson but he didn't do it alone. To associate intellectuals and researchers with Gladwell is to do them a disservice.

/Redde Caesari quae sunt Caesaris/ ... you're right!

Gladwell widespread the idea to the public though.

And Norvig made usage of this meme for the programming field in a short summary.

Agreed. I had an interesting experience recently when I decided to "relearn" math. I had taken calculus courses in high school and university, and aced all the exams. But when I eventually came back to calculus out of personal interest, I realized that I didn't know what a derivative was! I didn't know what a limit was! How did I pass those classes? And if someone who got the highest marks didn't learn anything, what about the people who were actually struggling? How many people in that class actually learned anything?

And I could say the same for my science classes, foreign language classes, etc. I don't think you really learn anything unless you really want to understand the material and you work hard to do so. And if that were the case, hour for hour you'll get what you put into it. You wouldn't be studying to an exam. You wouldn't be satisfied with 60%+ on that exam. You wouldn't restrict yourself to a specific curriculum. You wouldn't put time limits on your learning. Instead you would learn the thing that you decided you wanted or needed to learn, and however long it took for you to really understand it, that's how much time you would spend.

“Nothing that is worth knowing can be taught.” -- Oscar Wilde

What materials did you consult when relearning math?

The real test is how well you were able to pick up the concepts again. Not using it for, how ever many, years it's natural to forget. However if you can quickly reacquire the knowledge then you did learn it atrophied so to speak.

But I really think that I never learned those concepts in the first place. All I learned were rules to solve the problems given to me. For example I actually did remember the "chain rule". But those rules had no meaning to me, just moving numbers around. Which means I would never be able apply it to anything. For example, calculus clearly has applications all across basic physics. But I never really made that connection. All this makes me think that exams are much, MUCH less effective at measuring comprehension than we think.

I suggest reading very carefully.

I absolutely believe what he writes, because he's quite precise about his experiment and how he did it and this really works for a couple of reasons:

* This guy isn't 20 anymore. He has actually explored and learned and trained "productivity and focus" which he blogs and writes books about - so he doesn't start like a 18 year old directly from school, unexperienced maybe in this level of focus and discipline.

* He was pragmatic in his goals - very much so. He didn't write "becoming the world's foremost expert in linear algebra" but "passing an exam". And so he did. He also didn't write "passing everything with a top grade" but "just pass, if better - wonderful".

* He actually did his math on "hours to put in" - a semester doesn't take full 6 months, you usally don't attend lectures/lab every day 3 hours a day but 1-2 times a week, 2 (university) hours plus preparation. If you carefully add this up, you actually get a surprisingly low count of actual course/lesson hours.

* Taking in a course in a focused manner is actually quite efficient and helps you (at least it does for me) follow the material without interruptions. You also can repeat as often as you like (he mentions a fast forward and replay button in his TEDx talk) - which btw. makes part of the success of e.g. Khan university material.

* He also put some effort and training into the right way of learning and _that_ pays off massively in terms of speed.

Also, one of the points he is actually making is part of what most of you critizise: Going through the list of MIT requirements is something different compared to "becoming an expert in X" - don't mix that up.

Learning for exams and learning for yourself are obviously different kinds of activities, even if the level of depth and rigour are similar.

For maths-heavy subjects, I'm not really inclined to believe that traditional exams are the best way to assess a student's knowledge and understanding of the material (especially with regard to rote memorisation). Exams in such subjects haven't changed fundamentally in many many decades, even though we now have lots and lots of new things we could do with them.

For instance: do more with computers - like getting the students to solve real-world, many-tentacled, hairy problems by numerical methods, rather than giving them some carefully pruned equation that just happens to have nice analytical solutions. Or introduce more computer-assisted mathematical modelling (e.g. use classical mechanics, to start with). Or on the pure front, teach students to write or at least understand some interesting automated theorem prover.

Stuff like that.

I suspect that traditional exams have survived simply because they serve their purpose: a percentage of exam-takers fail the exam (which allows the exam-setters to claim that their standards of assessment are rigorous), and a fair percentage will pass the exam, some with flying colours. Whether or not the actual learning goal was achieved has not been determined, since the exam is deemed to be the only instrument that can measure that.

Yeah, I find the best learning happens when you put that knowledge immediately to work in a real world problem, and preferably one that's meaningful to you, as opposed to most term projects. And that's where learning for yourself makes so much more sense; if you're learning for yourself then you probably already have a real world application for it which got you into the goal of learning it in the first place.

My best bursts of rapid learning are almost always project/puzzle driven. I didn't, for instance, set out to master FFT directly, but it seemed like something that could improve my abysmal performance on a Project Euler that I was working on, so I looked into it. I question (open-mindedly, not snarkily) the efficiency of ploughing through a course or series of courses. On the one hand there's the possibility of cross-pollination that having all sorts of cool bits of knowledge and techniques fraternizing in one's head for as long as possible promotes. On the other hand, there's the sense that the most efficient learning sequence is the one that matches the actual sequence of problems as they present themselves. Just-in-time learning of helicoptering, but if and only if you find yourself in a rooftop gunfight, as it were. Of course, then the issue becomes predicting forthcoming problems with enough lead time to learn the solution.

I also am inclined to believe much of this. I actually did the same thing while at MIT for chemical engineering. Took all the required freshman through senior level classes at the same time, each semester, and finished all the requirements for a chemical engineering degree in a year. I loved MIT for this reason - they had no rules/regulations on the number of classes you could take in any semester, and they didn't enforce prerequisites/corequisites. Very different than other institutions I've trained at. I was still able to participate in extracurricular activities and develop relationships with lots of people.

It's true that I didn't attend a lot of classes (since they all overlapped anyways), and had 2-3exams virtually every week. The only issue I see is that there is only so much you can do online. I also did the same thing with Chemistry and Biology, which had lots of laboratory classes, and I don't see how one could gain the practical experience of putting knowledge to work in those fields without a wet lab class. EECS however is amenable to this (for the most part - likely hard for an optics laboratory), and most of my EECS labs were really done in Athena clusters instead of a distinct laboratory.

People are kind of picking apart his use of the word "mastering," but I'd say that the crux of the article is spot on when it comes to learning techniques.

As an aside, I've never heard it called the "Feynman Techniques." However, one of my favorite things in the world is the so called "Feynman's Algorithm": (1) Write down the problem. (2) Think very hard. (3) Write down the answer. I just found to hilarious, but I digress.

There are two points of his with which I agree 100%.

Firstly, the process of writing a short summary paragraph of what you just read after reading a chapter or big section of a technical book. There is actually a fantastic book -- maybe one of my favorites of all time -- called, somewhat strangely, How to Read a Book. It's all about very active reading over passive, almost to the point of having a "conversation" with the text you're reading.

Ever since reading that book, I've gotten into the habit of writing a summary of each thing that I read. It really forces you to confront whether or not you "got" the point of what the book is saying. I usually find that there are quite a few bits that I either missed, or didn't quite understand, at which point I go through and search for the pieces I'm missing.

Secondly, looking at all of the low level pieces to understand the whole. This is something Salman Khan, of the Khan Academy talks about in (I believe it was) his TED presentation. Quite often, I find that there is some early concept that I glossed over which is slowing my understanding of the current material significantly. For me, doing this makes me being 'honest' with myself over the state of my current understanding -- which was kind of hard at first when I took this new approach to learning. So much of my 'ego' seems to be unfortunately wrapped up in 'what I know,' and thus I convince myself incorrectly that I do understand something, even when I don't, just because it's something that I "should" already know. Admitting to myself that I didn't understand, for instance, some basic math concept that I should have learned in high school was somewhat difficult -- as odd as that may sound. I suppose I have a fragile ego! But sometimes, getting a good grasp on my modern course work, meant stopping what I was doing, and going back a couple of levels and starting at the beginning.

The question of "What do I need to know in order to understand this" is, I find, an extraordinarily powerful one.

Although this is an accomplishment and there is some practical advice of value in the post, the "rules" he posts include correcting his own papers and tests and a minimum 50% passing grade.

http://www.scotthyoung.com/blog/mit-challenge/

Would be more compelling if he was not selling books. Nothing wrong with making a profit but I'm just saying...

Ignoring the semantic controversy on 'mastery' and 'expertise', here's my story.

I dropped out of a CS program after first year. I was the classic case of a student who had always been told he was brilliant, so I never worked very hard. In high school, I coasted along simply on a fantastic memory, often 'studying' for the final exams that determine graduation the night before. I never learned how to learn.

Going to college was like being thrown into a bath of cold water. I had never been particularly conscientious, so being in an environment where I was now responsible for my learning was new to me. I skipped lectures, forgot homework that was due, turned in coursework late; the usual suspects. On raw talent though, I qualified for 2nd year, only failing Pre-Calculus. (I skipped the classes and tried to learn math from 1st principles. Ugh...)

I got a summer job at a small telecom startup. By time 2nd year rolled around, my student loan was denied, so I dropped out. I'd always hated school, so I didn't care. I never applied for leave of absence, nothing. I just didn't show up in September. That was 2006.

I was 20 then. I'm 26 now. I've had a lot of time (6 years!) to reflect on why I did so poorly despite being talented (not being conceited; my lecturers in 1st year said as much). There are quite a few reasons; but the major one is that I didn't know how to learn. So if something didn't immediately click, I'd give up in frustration, and decry the teacher as an idiot who couldn't teach (oftentimes true; but irrelevant). I didn't know there was another way.

Being around HN and places like LessWrong which exposes you to so many thought-leaders brought about some interesting side-effects, which culminated earlier this year. Upon reading an article on LW entitled "Humans are not automatically strategic", which was a reply to a Sebastian Marshall article "A failure to evaluate return on time fallacy", I had an epiphany that being systematic about things was the route to accomplishing great things. "Rationalists should win", the LW meme goes, and it's correct. I came to realize that for every goal, there exists an efficient path to achieve it. My task was to find that path, and execute ruthlessly upon it.

Since then I've made leaps and bounds in my personal development. I still slack off sometimes, but I won't fall into my old perfectionist way of thinking that I'm a failure. It's better to be 80% there than 0%.

I made the decision a few weeks ago to get my CS degree, albeit at a different, larger university. Since then, I've been devouring articles like this one. I recently bought two of Cal's books and wanna sometimes slap myself when I realize that if I had had this knowledge and the discipline to implement it 6 years ago, my life would be so much better. But c'est la vie. These articles on meta-learning are priceless.

So if you're in school now, or are going soon, pay attention to articles like these, Here are a few gems I've dug up recently: http://news.ycombinator.com/item?id=3427762

http://news.ycombinator.com/item?id=818157

http://www.quora.com/The-College-and-University-Experience/H...

http://www.quora.com/Harvard-College/What-are-the-best-Harva...

http://www.quora.com/How-do-top-students-study

Thanks to knowledge like this from Cal Newport and others, I'm going back to college full-time as someone with an above-average cognitive toolset, and a myriad of experiences that will suit me. I'm much more sociable, have a great eye for design having moonlighted as a freelancer some years back, and will now know how to engage my lecturers on an adult level rather than the kid I was 6 years ago. I'm going for a 4.3 GPA. I'm tempted to say wish me luck, but with tools like these, I'll make my own luck.

This rationalist will win.

PS If y'all have more articles like this, let me know. If you wanna chat privately, email's in profile.

EDIT: formatting; clarity

> I didn't know how to learn.

I'm not trolling here, but don't you think it's more accurate to say you didn't know how to work?

Perhaps...

Maybe. Understanding metacognition and how best you, yourself, learn can have major strides in your own knowledge accumulation. Sometimes working harder at something isn't always the best solution. Sometimes the problem needs to be flipped on its head.

I disagree. College is the first time many students have to learn how to teach themselves.

I did quite well in a small town high school with minimal effort. Not perfect, but I graduated 11 out of 399. I can probably count the number of times I did any work or studying at home on my fingers. During the day I listened in class, focused on school, and gave forth effort. It's pretty easy when classes move at a snail's pace lest any student get left behind.

When I went to college my first physics class kicked me in the face so damn hard and I didn't even see it coming. Lectures moved at blistering pace and entire chapters were covered in just one or two class periods. I remember going into the first big test, thinking I did well, and getting a grade so low the teacher pulled me aside and asked if I should drop it. Holy crap that was embarrassing.

After that I realized I needed to learn how to learn. I had to learn how to take the book, break everything down, ask questions when necessary, and master the material without guidance. It was a slow process but my scores got better with every single test to the point I tied for the highest score on the final.

You could argue that I had to learn how to work but I don't think that's accurate. I knew how to put in work rate. I was an Eagle scout and played on the high school soccer team. Both required tons of work. Learning how to learn certainly requires work and effort, but I think it's a skill the same as any other.

I can't speak more to the 'learn how to learn' statement.

I have a very similar story (Eagle scout/football and wrestling team) and had good marks in high school. I arrived at college and was destroyed by Calc 2 and having to learn at that pace when in high school I never studied at all.

After a rough freshman year I knew I had to change how I work and learn. My dad handed me 'Moon-walking with Einstein' and I found calnewport.com (along with other study blogs) and developed a study plan that I still use (I'm currently a Junior).

I'm similar to the author in that I hated school forever, yada yada, but I feel like there's something between learn and work. I've always been (hubris alert) far more learned than my peers in nearly every subject, but the things that didn't come easily I was weak on - higher math was really the only thing that didn't.

I think the main problem wasn't learning per se - I learned whatever I needed to do my technical personal projects with ease (chemistry, programming, electronics, etc.), but what I lacked was something like "how to work" which was really a kind of short-term dedicated focus that math so requires. Higher math is banging your head against a concept until ::pop:: - that's easy! I never banged my head enough - so whatever that is - it's a major problem that we need to overcome.

This all goes back to why so many engineering students, like me, dropout of these programs because we have shortcomings in overcoming these initial problems. Schools need to identify this aggressively and provide some kind of scaffold that will allow these students to learn this focus/work type of skill.

Also - the baggage the term "work" in our (US) culture makes it a bad item to focus on when improving a system. "Bad work ethic" is often a symptom of these types of problems.

Thought experiment: What would you think a struggling college student would try doing if you told them, "you need to learn how to work"? What about if you said, "you need to learn how to learn"?

At least for me, the "work" priming hurts learning, since I do very inefficient work on something I've just started learning.

Are you going to school online or on campus? Full or part time? Working?

On campus, full time. I'm doing consulting. I've been eyeing the online CMU Masters in Software Engineering after undergrad.

LessWrong looks like something I'll enjoy reading. Do you have any favorite or recommended articles -- not necessarily related to op?

Keep up the good work.

Thanks. It's often recommended to start at the Sequences (most of which I haven't read yet): http://wiki.lesswrong.com/wiki/Sequences

Harry Potter & The Methods of Rationality: http://wiki.lesswrong.com/wiki/Methods_Of_Rationality_(fanfi...

Here's a good one on the ways in which LessWrong can improve: http://lesswrong.com/lw/2po/selfimprovement_or_shiny_distrac...

But my 2 favorites are the ones I mentioned: A "Failure to Evaluate Return-on-Time" Fallacy: http://lesswrong.com/lw/2p1/a_failure_to_evaluate_returnonti...

Humans are not automatically strategic: http://lesswrong.com/lw/2p5/humans_are_not_automatically_str...

Particularly the latter. Digesting those 2 are probably responsible for most of the self-improvement gains I've made. I realized that mostly, we operate on autopilot. Now autopilot is great - when you're the one who programmed it. LessWrong is about programming your autopilot so you chart and stay on the correct course as a matter of course.

Also, it would be remiss of me not to mention OvercomingBias ( http://www.overcomingbias.com/ ).IIRC, LessWrong is something of a spinoff from OB

My favorite (not most enlightening but just my favorite) article to date is Yvain's Eight Short Studies on Excuses: http://lesswrong.com/lw/24o/eight_short_studies_on_excuses/

There's quite a lot of philosophical content on less wrong. I liked "Zombies! Zombies?", which is essentially a strong argument against the likelihood of p-zombies.

http://lesswrong.com/lw/p7/zombies_zombies/

> I'd say that if you postulate a mysterious, separate, additional, inherently mental property of consciousness, above and beyond positions and velocities, then, at that point, you have already stuck your neck out as far as it can go. To postulate this stuff of consciousness, and then further postulate that it doesn't do anything—for the love of cute kittens, why?

This sounds like a textbook case of someone being raised to form a "fixed mindset" view of intelligence. Have you read any of Carol Dweck's research, like http://www.scientificamerican.com/article.cfm?id=the-secret-... ?

Yup; it was an article on her work in NYMag that 'diagnosed' me. I think it was 'The Power & Perils of Praise.' I remember reading it and thinking, "holy fuck, that's me!" I think that was also when I was exposed to the "Talent Doesn't Matter" meme, with which I disagree.

Talent does matter - no one disputes that some people have learning disabilities compared to the average; yet seem hesitant to accept that some have learning advantages compared to the average. It's just that talent isn't enough. As a Jamaican, I can tell you that Usain Bolt dominates because of an almost freakish talent AND working till he vomits on the track at training. His training partner, Yohan "The Beast" Blake, is well known to be a much harder worker than Bolt - It was Bolt who nicknamed him "The Beast" when he saw how hard Yohan trained. But Bolt still wins.

I wanna work hard enough to maximize my talent.

About the "talent doesn't matter" issue: It's one of these things where the truth may actually hurt you. It's pretty clear that talent does matter, but it's better for you if you don't know this, since that knowledge may serve as an excuse for you to give up. I don't generally advocate not telling the truth, but this may be one of these cases where everyone is better served by emphasizing the part about malleability and not that about innate talent.

Or one can plainly tell the truth, like my SAT instructor used to say: you're competing against other people with similar capabilities to yours. If you don't bother to do the coursework, they'll get a higher score and you'll get a lower one, and it won't be because of some inherent reason, it will happen simply because they did take the time to study.

(the SAT here is normalized to form a perfect Gauss curve, so essentially the only thing that matters is one's percentile, but I guess this saying is generalizable)

Upvoted. This is something I've thought about as well. My general motto is "We gain nothing by denying the truth," but I've also learned that the mind can sabotage us in very subtle ways. On LessWrong, the idea is that "our brains are untrusted hardware."

>PS If y'all have more articles like this, let me know.

Here's one I was just perusing yesterday, on the origin of the concept of "less wrong".

TLDR: our education system teaches us to strive to get the right answer, or be "right". But in truth there is no "right", just progressively less wrong, and there are multiple undesirable consequences of the emphasis of the former in our education system (from rigid beliefs that can't evolve with new data, to people getting dejecting with fields like hard sciences when they can't be "right" easily):

http://serendip.brynmawr.edu/sci_cult/lesswrong/lesswrong/

"People in our culture, by and large, tend to presume that someone, somewhere knows what is "right," and that each individual's task is either to be that particular someone or to work as hard as they can to learn from that someone what "right" is ... the mindset long predates science as a social activity, but ... science certainly encourages it, and so it is appropriate that science should contribute to correcting it ...

In an enormous variety of distinct fields of inquiry the same general pattern is becoming clear: there is no such thing as "right," the very concept needs to be replaced with "progressively less wrong." The difference is far from semantic. "Right" is measured by proximity to some fixed idea, "progressively less wrong" by how far people have gotten from where they started. It is the aspiration to be "right" that leads to rigid hierarchical social organizations of all kinds, including educational systems. Wanting to be "progressively less wrong" takes one (and societies) in quite different directions entirely: it encourages life-long inquiry by every individual, a respect for past wisdom and enthusiasm for contributing to future understanding, and an appreciation of the enormous value of interactions between unique individuals each of whom has unique perspectives to contribute."

This person, Scott Young, did not "master" linear algebra. If anything, he mastered the curriculum. There's a difference, and in a year he won't remember a word of it.

He is, however, a master of self-marketing:

"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 how other learners have used these techniques)."

I'm inclined to actually believing a lot of this.

When I got into university I found every course very easy, didn't attend any lectures, got all my workshops to run on the same day to reduce my face time and maxed out my free time to do whatever I wanted (work/friends/extra/etc). I'm a STEM major at a top 30 world ranked engineering school with good grades.

I've often asked if I could max out my classes and finish a degree within a year and a half - but I've never been allowed to skip more than a few subjects (tests/bugging the heads of departments).

University shouldn't be time capped or subject load restricted - people should be allowed to do as many as they wish - or you'll find more and more moving towards MOOCs instead.

The predictable response - education isn't about learning stuff, but proving you can work on things which aren't really important.

University shouldn't be time capped or subject load restricted - people should be allowed to do as many as they wish

I'm particularly happy that Math and CS department in my university (University of Warsaw) was precisely like this. It let me take 2-3 times the usual course load, which kept me motivated, prevented from getting bored, and let me learn a lot more things than I would have learned if I followed the standard path. Sadly, it seems like this will soon end, as a side effect of new changes introduced by the government to alleviate a separate problem.

Why not just skip some lower level courses, and catch up using your free time?

What do you mean by skip? You cannot test out of the lower level courses here, though you can just skip lectures and classes, do the required projects/homeworks and show up only on exam, which is what I usually did with easy courses or the ones I didn't care about. Frequently I couldn't even attend these, because other more advanced/difficult courses I took were at the same time.

Oh that is unfortunate. At my school you could take a test and start at whatever course level matched your knowledge. And there were often accelerated versions of courses, where B1 covered the same material as A1 and A2

University in continental Europe is very much like what you describe, though a shift in public attitude towards higher education as a means of job qualification is (sadly) changing this.

unfortunately so... I just loved the "fk education, fk your diploma" I experienced when travelling and working in the USA... unfortunately EU is heading in the opposite direction

what do you mean by that?

(I'm a professor in a University, mostly for first year students.)

The problem with allowing the students to take all the courses they want is that some of them can't correctly measure how much work they can handle. So you will get horror stories like: "A student get enrolled in 3 times the expected courses, has too many homework, too many midterms the same week, and finally don't approve any of them."

Now we have a lost of students that come with questions like "I didn't approve Calculus I last semester. Can I enroll in Algebra I, Calculus I and Calculus II, so I don't lose a semester?" And it is hard to tell them, but most of the times the best thing is to take only "Algebra I" and approve that than taking the three classes and approving none of them.

I also understand that there are special cases, but should be evaluated case by case.

Agreed. I'd like to note I literally have zero problems with either system really.

I'm rather enjoying university right now and the lifestyle I have and am perfectly fine taking the scenic route. I learn plenty on my own and basically consider it a semi retirement stage :-)

I'm glad you feel that way. Those of us with jobs and families snicker at college students who claim to be "so busy". Life is good at this time; do your studies and use those massive amounts of free time to socialize and create new things.

> do your studies and use those massive amounts of free time to socialize and create new things.

I never had massive amounts of free time at college. Maintaining a 3.9 in Computer Science without having the same amount of raw talent (and previous experience) as your peers is really hard, so I had to work my ass off. My schedule was close to 16 hours per day, 7 days per week (including classes). It was "Hell Week" for the ~4 years I was there. I worried my family and friends. It was unhealthy.

Trying to keep up with, frankly, __smarter__ (and, most likely, more intelligent) peers was a real challenge. I tried "Studying Smarter, not Harder", but lacked the skills from K-12 education to do so. Attending classes on "How to Study" and the like really didn't help and, no matter what I tried, I always fell back into investing more time as a solution.

I lacked the bio-hardware (read: brains) to go into Computer Science. I did it anyway. Don't forget about people like me!

> Life is good at this time

No, it wasn't. Not for me.

> Those of us with jobs and families snicker at college students who claim to be "so busy".

I don't. I have more free time now that I'm married and working (a stable and well-paying job, thankfully).

I think it's actually one of the point he made ... nobody teaches students "how to learn".

It might be good adding this to their courses. (And before reaching University would be even better. :))

As someone who at one point enrolled in too many classes and failed all but one of them, I have to say "so what?" I learned a valuable lesson about both my limitations and motivations. Why are we so afraid of letting students fail a little bit once in a while?

I'll leave the discussion of how embellished this post/blog/exercise of MIT Comp Sci in 1 year is to other comments. But! The explanation of Fourier transforms from Scott's notes (http://www.scotthyoung.com/mit/fourier.pdf) is one of the must succinct ones I've read. I've always understood what the transform does, but the nitty gritty on how the equation works was awesome

Yes, it was interesting to see it labelled out like that. I liked to think of the transform as a cross-correlation. You take a wave of a particular frequency (f) and cross-correlate it with your signal s(t) across all time. The fourier coefficients are the results of the cross-correlation, telling you how much of each frequency you have in your signal.

> 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.

This is a useful technique, giving motivation and focus. Though imperfect: it can't detect incorrect understandings that seem consistent. But to be fair, that's a tricky case.

One of the achievements I am most proud of was doing a full year's university course in computer science in 6 weeks and passing. It was pure cramming though and very hard work. I got into a routine of full-on study from 9am-1am with short breaks every hour or so. 16 hours a day for 6 weeks.

Not something I would ever want to repeat and was first year level courses. Basically I was doing a correspondence 3 year degree while working full time. I got heavily involved in my work and decided that I wouldn't continue studying. Then with about 4 weeks to go to the 2 week final exams period I thought, what the heck let's give it a shot...

Amazing what focus and hard work can achieve!

> he completed all 33 courses (...) in less than one year.

> That works out to around 1 course every 1.5 weeks

WTF? What kind of university imposes that you take only one course at any given time? It's not just linkbait, it starts from a wrong assumption. When you take many related courses simultaneously, you see the pieces meshing together and that helps learning. That's different from taking them in a serial manner.

"you see the pieces meshing together"

...or not. Depends on many things, among which the teachers are very important. If your lecturer thinks that his class is the most important and the rest of your courses are trash then you won't see "pieces meshing together". Been there, done that.

Cooper Union or somewhere does that, several short courses one or two at a time.

It's funny because the students at the competitive schools work their ass off for the entire semester/ quarter to learn this material. If you use the weakest possible definition for "learn," then you can claim you have learned anything you want. But that doesn't mean your skill will be comparable to someone who spent 3-5 months practicing non-stop.

...this guy really knows how tomuch puts the "bait" in "link bait" ...nothing about linear algebra in the article but the perfect title to hook the bank of HN fish ...congrats to the OP for pulling this one off :)

I would imagine that the vast majority of students at Universities around the world who take Linear Algebra "master" it in 10 days. That is, the ten days before the exam, having spent most of the term drinking, socialising, falling asleep in lectures (or just staying in bed and skipping the lecture bit). I certainly know I "mastered" elementary linear algebra in about 10 days.

Not seeing this as link bait at all - more method for than what was being learned. Great read that gives a lot of interesting insights and methods - definitely not for everyone. A lot of the same information and ideas have been discussed on Study Hacks though it is great to see the provided examples.

He may have accomplished something impressive, but I had trouble appreciating it because the article seemed so pretentious, and I found that distracting.

It is a marketing scam for a self-help eBook.

Dazzling title, even no Linear Algebra at all, but I like the systematic introduction about "Feynman Technique"

I thought Linear Algebra was the easiest math-class?

Master it in 10 days? Forget most in 10 more.

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