Can Self-Study Lead to Success in Advanced Subjects Without Coursework?

[Frion]

Do you have any stories of people successfully self-studying a relatively advanced subjected in which they've had absolutely no coursework? Personally, I've taken some honors level courses in high school and then done some extra studying to get on a good enough level to take the AP test. I've studied courses like Differential Equations largely on my own because the professor spoke with too thick of an accent. But I've never actually tried studied a subject completely on my own.

Everyone I know who said they self-studied a subject I was familiar with had serious gaps or misunderstandings. One guy completely self-studied calculus, but he totally wasn't hacking it physics, usually because of math issues. Another guy said he self-studied linear algebra, but he didn't even know the spectral theorem. Lots of amateur mathematicians on the internet are always called out for making obvious mistakes in math that's too advanced for me to judge personally. I've literally never seen a self-studying success story and this makes me very nervous because I'm thinking about self-studying PDEs but it seems nobody succeeds at self-studying.

I'm not even sure what the main obstacles are. Is it just an inevitable fact that a person cannot verify that he learned everything up to a certain standard? Or does one just miss out on subtler points without an instructor?

 

[RichardParker]

Oliver Heaviside was a success, but that was years ago.

 

[MathematicalPhysicist]

The name of the game is to get back feedback that what youv'e done is on the right path.

Most teachers in academia that I met just use notes which use other textbooks (sometimes even just one textbook), so basically going to lectures and writing notes is the same as reading from textbook/s by your own.

So make sure to get textbooks with hints and final answers at the back of the book for self study. (Nowadays you can easily find solutions to most questions in textbooks in the web).

As the subject gets more abstract and more into research there is less such books, and in this respect you need some guidance from an expert.

 

[Leveret]

George Green (of Green's functions and Green's theorem) was almost entirely self-taught. While simultaneously operating and overseeing a mill 24 hours a day. An extraordinary example, to be sure, but an example nonetheless.

Back on the mortal plane of existence, I've held three research positions doing primarily computational work, yet I've never taken a programming class. I'm constantly finding little technical tricks that most people who've had a formal education in the subject would have certainly known about, but I nonetheless have a working knowledge of about half a dozen languages, and the things I'm missing have never really been a problem to-date. Granted, programming strikes me as easier to self-teach oneself than mathematics, but I'd wager that enough time and practice can make it work for math, too.

 

[AlephZero]

If you are still in high school you probably don't have much real experience of this.

People in any profession (medicine, science, engineering, law, etc) spend their whole working lives self-studying. The main point of a degree is to get you to the point where you know enough to be able to self study effectively, not to the point where you know everything you need for the rest of your life.

I graduated 40 years ago. Do you really think advanced engineering or medicine are still done today the same they were back then? I regularly use stuff in my work which hadn't even been invented when I was at university, or was only being worked on by postgraduate researchers.

 

[PhDorBust]

It took me a while to realize the only way that I can self-study is to make a plan that doesn't require much, and follow it over a long period of time. Maybe take a goal as half a chapter a week. You will have a real urge to burn through the material since you set the pace, but for retention you should keep the workload moderate and spread out..

New subjects that you could self-study will strike your fancy. Ignore them at all costs, otherwise you will deviate from your plan continually and end up finishing nothing.

 

[Leveret]

New subjects that you could self-study will strike your fancy. Ignore them at all costs, otherwise you will deviate from your plan continually and end up finishing nothing.

That really depends on why you're self-studying. If it's so you can learn Subject X, then yes, digressions would be detrimental to the attainment of that goal. However, if you're self-studying to increase your general knowledge, I would argue that following whatever piques your interest would be the right course of action. More often than not, doing so will lead you to where your real passions lie, and thereby teach you more directly useful things.

 

[twofish-quant]

New subjects that you could self-study will strike your fancy. Ignore them at all costs, otherwise you will deviate from your plan continually and end up finishing nothing.

Depends on the field. One thing that I've noticed is that a bit of knowledge in some weird area and you come up with something that you are the world expert in.

Call it the chess-boxing strategy. You can be mediocre at chess. Not that great at boxing, but if the situation calls for someone that can play chess *and* box, then you end up being the world expert at the topic.

If you want to be the world expert in applications of computer science to Armenian poetry then it's not that hard to do that. Now you might think that this is totally useless, until one day someone wants to put together a database of Armenian poetry, and you get hired because you are the only one that knows something about databases *and* Armenian poetry.

 

[twofish-quant]

I regularly use stuff in my work which hadn't even been invented when I was at university, or was only being worked on by postgraduate researchers.

The world wide web didn't exist when I was in college, and I'm not that old. Part of the cool thing about teaching yourself stuff is that you get to work on really new technology. I remember when I was trying to figure out how HTML works. I couldn't go out and buy a book on it, because I was probably one of the first people to actually install WWW server, and there were no books on HTML.

 

[twofish-quant]

I'm not even sure what the main obstacles are. Is it just an inevitable fact that a person cannot verify that he learned everything up to a certain standard? Or does one just miss out on subtler points without an instructor?

Anyone that has a Ph.D. has gotten where they are by self-study. They won't hand you the Ph.D. unless you've managed to teach yourself something that wasn't in a textbook. Who watches the watchmen? Who teaches the teachers?

Also self-studying is something of a misnomer. I've studied a huge number of things outside of a formal classroom, but a lot of it involves finding the right person or people and communicating with them.

There will also be gaps in your knowledge, but people that have gone through formal training in something also have gaps, just different ones.