How can I self study a subject effectively?

[Alexander2357]

There are some classes that are not offered at my university, which I want to self study.

How can I self study them effectively to get the same benefit as doing the class at university?

There is this class MIT 6.024j Mathematics for Computer Science which I very much want to take online because my university doesn't offer such class. My university offers a discrete mathematics class but it is a 3rd year subject and has real analysis as prerequisite. It also doesn't offer number theory for undergrads. I also want to take 1 or 2 other classes which are not offered at my university.

I am highly motivated with respect to my studies but I don't seem to be able to study a subject on my own as effectively as I would be able to at university.

Do you have experience with self-study? What advice can you give me?

 

[Choppy]

One option that might be worth looking into is what's sometimes called a "reading course." This is where a particular subject is not offered as a formal series of lectures, but assuming you can find a suitable professor to mentor you, you can get credit for self-studying the courses (and presenting a summary or report or some other evidence that you have completed and understood the material).

Something else to consider is that if your university is not offering the courses that you want - you could try to transfer somewhere that does. I realize that circumstances may exist that prohibit this, but in situations where this is more than one or two courses, I think that it's reasonable to consider transferring if that's an option. Also, along these lines, bring this up to the department - maybe through the undergraduate student advisor. A single student's interest may not invoke much change, but if half of their graduating class complains that the school is not offering a particular course, the faculty will likely try to find a way to offer it in the future.

As for complete self-directed study, I've never had the discipline to do this. For me it's because I usually have so many other deadlines in my life that anything that doesn't have them doesn't ever percolate to the top of the priority list - at least not often enough to warrant significant progress. I'm not saying it can't be done - just that you need a lot of self discipline.

 

[Alexander2357]

As for complete self-directed study, I've never had the discipline to do this. For me it's because I usually have so many other deadlines in my life that anything that doesn't have them doesn't ever percolate to the top of the priority list - at least not often enough to warrant significant progress. I'm not saying it can't be done - just that you need a lot of self discipline.

Thank you for the reply Choppy.

Although my university is supposed to be a top tier university, I find the online courses, especially those by MIT, to be far better than what my university offers in every way.

If I wanted to take maths classes that serve as the equivalent of that MIT course, I would have to take 4 different classes, which does not fit in my course plan as I am limited to 10 classes per year.

My university is very bureaucratic and has some very limiting and strict rules which annoys me to death, but it seems like nothing can be done about it.

It is very difficult to be motivated to self study, and the fact that I am currently studying full time makes this almost not possible, unless I am motivated enough to take the course over the holidays.

 

[homeomorphic]

I don't think it always takes discipline to self-study. I devoured complex analysis and graph theory when I studied them on my own because I was just so interested in them. There was not much need to motivate myself. So, there's a clue. If you can make a sales pitch to yourself on how cool the subject is, you'll be in good shape, and part of that is finding a really good book or online source to learn it from. Another way to look at it might be to take courses for the less interesting stuff, when you need someone to force you to do it, and self-study the good stuff.

In fact, usually, at the end of the semester, it was like party time for me, not because I was free to go party, but because I was free to read that book I had been wanting to read the whole semester, but was forcing myself not to because it would be too distracting. That's often the first thing that I would do after finals were over. Only after I had indulged myself for a while would I relax a a bit and enjoy the break.

 

[Alexander2357]

In fact, usually, at the end of the semester, it was like party time for me, not because I was free to go party, but because I was free to read that book I had been wanting to read the whole semester, but was forcing myself not to because it would be too distracting. That's often the first thing that I would do after finals were over. Only after I had indulged myself for a while would I relax a a bit and enjoy the break.

That is how I usually feel to be honest, there are many topics that I am super interested in that are either not offered at my university or are offered in 3rd/4th year or master level.

Could you please tell me how you self-learned complex analysis and graph theory? What resources did you use and how long did it take you to finish them? I am most likely not going to take complex analysis and graph theory because they don't fit into my timetable but I very much want to do them.

My problem is that I don't take examining myself too seriously when I self-study. I usually don't examine myself at all but I want to change that. I want to actually do the problem sets and exams to get the same benefit form self studying as taking a course at university. At university there are deadlines and the results actually matter so I always do the problem sets and exam.

 

[Arsenic&Lace]

Homeomorphic wins the thread I think, that's true of myself as well. I can read endlessly about what I find interesting but find it torturous to read through anything I'm not interested in. I will point out though that graph theory at least is a relatively "atomic" subject; in principle, as long as you are used to the basic notation that mathematicians use you can begin to learn it without prior background in anything (maybe topological or algebraic graph theory would be challenging without background I have no idea). Quantum field theory, on the other hand, was very challenging to understand (for me anyway) without a background in other physics even though I was very interested in it.

 

[homeomorphic]

I first learned complex analysis from Visual Complex Analysis, which is an expensive book, but might be available at your library. I learned graph theory from a free online book by Diestel, which you can just google and find pretty easily. Back then, the whole book was online. Most of it still is, but you have to buy the book to get the full contents now.

You might also have to do a sales pitch to yourself on doing the exercises and just pick some that look fun and force yourself to do them. And from there, try to get interested in doing them.