Organizing Self-Study: Advice from Others

[Buri]

Just wondering how some of you guys have done self-study? That is, how have you organized it all? Any advice would be greatly appreciated :)

Thanks!

 

[fss]

1. Buy book.
2. Read.
3. Profit.

 

[Caramon]

https://www.physicsforums.com/showthread.php?t=459157

 

[radou]

Whatever you intend to study, solve as much problems as you can. I assume you are about to self-study something which involves problems. :) Theory itself is necessary, but far from enough.

 

[DrummingAtom]

1. Buy book.
2. Read.
3. Profit.

Haha, elegant.

When I self study I understand the most when I just play around with ideas. I have a certain pet peeve of starting from the beginning of a book and going through each chapter. It can be frustrating at times but it's just how I need to learn from a book. I figure they set those chapters up for a reason so I feel I need to follow it.

Anyway, after studying for a bit I find an idea I like then explore it until I've had my fix. I usually try some problems at a medium level; just by reading through a problem I can get a feel if it's trivial or not. I pick ones that give a slight challenge until I feel comfortable with the concepts. Then I find a challenging problem that I can let simmer for days or even weeks. Doing this gives me the motivation to stay focused and eventually finish that concept/chapter.

Opening up a challenge problem let's me try off the wall ideas and "play" without being confined to a certain structure. It also forces me to research a topic further than what the book is designed for.

 

[Hurkyl]

Self studying something because you have an application for it is often helpful. I learned a lot of commutative algebra in the process of trying to learn algebraic geometry.

 

[Buri]

How would you guys organize the time you actually self-study? A couple of hours each day?

See my thing is that I feel that when I don't have a deadline I don't cover as much as I could. I know if I was doing it all because of a class I'd probably do more. But at the same time, by setting deadlines I feel like I could not be understanding something fully because I'm 'rushing'. And since I don't know anything of the material before hand, I have no clue what to give more time (for harder concepts and stuff).

 

[Buri]

Self studying something because you have an application for it is often helpful. I learned a lot of commutative algebra in the process of trying to learn algebraic geometry.

Thanks for answering!

See, I don't really have an application for anything yet because I still haven't studied the main areas in math yet - in reality, I have no clue which area I find the most interesting (everything I read seems cool lol). That's the reason I'd like to self-study because I find school goes too slow and I'd like to start concentrating on something I really like.

 

[dkotschessaa]

I re-taught myself basic algebra and trig over the last few months. It was doable because I'm not employed and I did have a deadline for myself which was that I wanted to be done before going back to school in January.

The most important thing is to have some structure which to me means you have one *primary* book that you're studying from, or some kind of structured material. More flexible than X hours per day is something like X material covered per week.

My pacing was something like 2 to 3 chapters a week. The book I was using had tons of problems so just the homework alone took a good 8 hours in each chapter. I used my main books primarily and then used other resources such as those available at khanacademy.org and whatever else I could find as supplements.

You have to be flexible enough in your structure that you can spend more time on things that are difficult and less time on things that are easy, but not so flexible that you never achieve your goal. The problems you've outlined are simply problems inherent in self-study and you have to balance them.

Thing is, we're inevitably our own worst teachers no matter what we do. If you really want to learn something well, taking a class is the way to go. I did self study mostly as a review, and I sometimes do it for things that I'm really super interested in or motivated by. But I have a lot of unfinished self-study project lying around, like my attempt to read the complete works of Shakespeare, Kant's Critique of Pure Reason, and a host of other unrealistic goals. Of course my attempt to self-learn physics has been going on for over a decade now which is why I'm going back to school for math.

-DaveKA

 

[dsking]

Depending on the topic you may be able to find a free online course that will guide you through. One example is MIT open courseware. http://ocw.mit.edu/courses/mathematics/

 

[Buri]

I re-taught myself basic algebra and trig over the last few months. It was doable because I'm not employed and I did have a deadline for myself which was that I wanted to be done before going back to school in January.

The most important thing is to have some structure which to me means you have one *primary* book that you're studying from, or some kind of structured material. More flexible than X hours per day is something like X material covered per week.

My pacing was something like 2 to 3 chapters a week. The book I was using had tons of problems so just the homework alone took a good 8 hours in each chapter. I used my main books primarily and then used other resources such as those available at khanacademy.org and whatever else I could find as supplements.

You have to be flexible enough in your structure that you can spend more time on things that are difficult and less time on things that are easy, but not so flexible that you never achieve your goal. The problems you've outlined are simply problems inherent in self-study and you have to balance them.

Thing is, we're inevitably our own worst teachers no matter what we do. If you really want to learn something well, taking a class is the way to go. I did self study mostly as a review, and I sometimes do it for things that I'm really super interested in or motivated by. But I have a lot of unfinished self-study project lying around, like my attempt to read the complete works of Shakespeare, Kant's Critique of Pure Reason, and a host of other unrealistic goals. Of course my attempt to self-learn physics has been going on for over a decade now which is why I'm going back to school for math.

-DaveKA

Thanks for the advice. The reason why I give 'X hours a week' is because I'm a student so I can't really spend a lot of time on things other than school work. But I'll try to do the X material covered in a week instead. Seems like it would probably work better. Thanks!

 

[Buri]

Depending on the topic you may be able to find a free online course that will guide you through. One example is MIT open courseware. http://ocw.mit.edu/courses/mathematics/

Thanks for the link! Didn't know about it!

 

[dkotschessaa]

Thanks for answering!

See, I don't really have an application for anything yet because I still haven't studied the main areas in math yet - in reality, I have no clue which area I find the most interesting (everything I read seems cool lol). That's the reason I'd like to self-study because I find school goes too slow and I'd like to start concentrating on something I really like.

That's a good reason. I was hoping this wasn't another "I just want to learn math and physics on my own without going to school" threads. :)

My motivation was similar. I was so excited about finally going back to school after 13 years in the workforce that I couldn't wait for the semester to start. So I basically taught myself pre-calculus, hoping that when I have the class it will deepen my understanding, since, as a math major, I want to have a deeper grasp of the fundamentals.

In that case I didn't worry so much about not spending enough time on anything, since I know I'll cover it again. If your case is similar in some way, then you might want to think similarly. Rather than spend a ton of time self-studying, give yourself a basic course. If you find you'll take the course in school then you'll be ahead of your classmates. If you don't - then great - you've learned something that may penetrate into other areas of study or warrant a revisit later. The point is, if you really want to understand something - take a course - whether it's now or later.

Of course you mind find that you study something on your own, love it, understand it thoroughly and have no need to take a class on it, and that's ok too.

-DaveKA

 

[Buri]

That's a good reason. I was hoping this wasn't another "I just want to learn math and physics on my own without going to school" threads. :)

My motivation was similar. I was so excited about finally going back to school after 13 years in the workforce that I couldn't wait for the semester to start. So I basically taught myself pre-calculus, hoping that when I have the class it will deepen my understanding, since, as a math major, I want to have a deeper grasp of the fundamentals.

In that case I didn't worry so much about not spending enough time on anything, since I know I'll cover it again. If your case is similar in some way, then you might want to think similarly. Rather than spend a ton of time self-studying, give yourself a basic course. If you find you'll take the course in school then you'll be ahead of your classmates. If you don't - then great - you've learned something that may penetrate into other areas of study or warrant a revisit later. The point is, if you really want to understand something - take a course - whether it's now or later.

Of course you mind find that you study something on your own, love it, understand it thoroughly and have no need to take a class on it, and that's ok too.

-DaveKA

I've thought of it that way.

I'm a 2nd year pure mathematics student and so I do plan on doing all the required courses for my BSc even if I have taught myself the material - I find it important to learn things from someone very knowledgeable as a professor. There's just so much out there that I'd like to start reading, but my program breaks up (i.e. into Topology, Real Analysis, Complex Analysis, Differential Geometry, Abstract Algebra, Combinatorics/Graph Theory, Number Theory and Set Theory) until 3rd year into the program. Technically speaking, I can tackle all of these courses now (I've done Analysis I which was taught from "Calculus" by Spivak, Algebra I & II taught from "Linear Algebra" by Friedberg, Insel and Spence and "Groups and Symmetry" by Armstrong, Advanced ODE's taught from "Differential Equations, Dynamical Systems, and An Introduction to Chaos" by Hirsch, Smale and Devaney, and currently in the process of completing Analysis II taught from "Analysis on Manifolds" by Munkres). And so I've picked up a lot of books recently that I'm using for self-study and quite amazed by how much I could have read already - I know mathematical maturity is important and I do feel like I've gotten the hang of abstract mathematics. So I've just become thirsty for more since school goes too slow. See, my university taught complex analysis and topology the first half and they're courses I could have done, but I didn't since they over lapped with Analysis II. This coming January, however, I'll be doing Number Theory and Differential Geometry. See NT and DG are 3rd year courses and so I had to ask for permission to take them and I asked both professors if there was anything I should take a look at before just in case I'm not fully prepared and they said I should be fine. So I'm just left wondering, why on Earth are they 3rd year courses then! Also, it seems that the really top students always know more so they just breeze through a class since they know it all and the course basically serves more for consolidating what they already know. So that's also another reason why I'd like to do self-study.

Currently, I'm reading Complex Analysis and Real Analysis by Stein Shakarchi, Topology by Munkres, Abstract Algebra by Dummit and Foote and Introduction to Analytic Number Theory by Apostol. I know some of you guys may object to some of these choices, but they are the ones they use at my university and so far I'm not having any troubles reading them due to "lack of prerequisites".

So that's where I stand lol Sorry if that was long...

 

[dkotschessaa]

No problem Buri. I'm interested in your experience since I'm entering a pure math degree and may encounter some of the same things. My self study from this point forward is going to consist of a few things, first being that I want to study just a bit ahead of my courses whenever possible. This is more of a strategy for me personally since I tend to space out in lectures. Secondly I'm taking Mathwonk's advice (See this thread if you haven't already: https://www.physicsforums.com/showthread.php?t=122924) about reading the great mathematicians. Thirdly I'm still doing a bit of physics as I may double major at some point.

Good luck with all of this. Sounds like you're doing great.

-DaveKA

 

[Buri]

"Space out in lectures" - I do the same. Well, partly at least since it seems when I actually read my lecture notes I recall what he's said, but I usually don't follow during lecture. It just doesn't seem like its the right setting for me to actually learn something on the spot. I guess that's also another reason to do self-study because depending on the professor sometimes lectures can be very useless especially when they regurgitate the textbook. And struggling with the material on my own is something I've always liked doing since it sort of forces you to figure it out on your own.

Anyways, thanks for showing interest in all of this. You've helped! Wish you the best with your studies