How do you read textbooks on your own?

Forum for the GRE subject test in mathematics.
dasgut
Posts: 250
Joined: Thu Jan 21, 2010 12:20 am

How do you read textbooks on your own?

Postby dasgut » Wed Feb 08, 2012 11:40 am

So I have a question for you guys...

I love learning new quantitative disciplines on my own, but I struggle with figuring out the best way to read the textbooks. I usually try and do every problem in the book, but then invariably get frustrated and just put the book down when I can't solve a problem. Obviously, if I'm doing the reading on my own I don't really have a professor I can consult. How would you guys read texts on your own? Do some of the problems? Learn to develop a sufficient understanding of the material w/o doing problems?

gromov
Posts: 38
Joined: Sun Feb 13, 2011 6:49 pm

Re: How do you read textbooks on your own?

Postby gromov » Wed Feb 08, 2012 9:19 pm

It would depend how deeply I want to learn the subject. If just a rapid introduction, I would pick a few exercises to work out just to stay honest. If I wanted a deeper understanding, I'd probably take a look at nearly every exercise suggested, if it's known to be a book that is very foundational to entering the field in question.

bemonocled
Posts: 35
Joined: Sun Jul 31, 2011 6:54 pm

Re: How do you read textbooks on your own?

Postby bemonocled » Thu Feb 09, 2012 10:38 am

I usually like to try to find one of those textbooks that inserts exercises in the body of the text at appropriate points and do all of those. Then if there are exercises at the end of a section I try to do a couple and at least think about the more interesting looking ones. If possible, I try to find a course online that had used that textbook previously and do whatever problems the professor assigned for that class since good professors tend to pick the most instructive problems to do and it is difficult for someone new to know which ones those are.

I also take notes as I go, reading a paragraph or two at a time and then trying to write down what I just learned without looking in the text (unless it is just things like definitions, then I'll just copy them down).

sywisy
Posts: 18
Joined: Fri Jan 20, 2012 1:25 am

Re: How do you read textbooks on your own?

Postby sywisy » Sun Feb 12, 2012 6:39 pm

To address the questions portion of your post, StackOverflow has a nice web 2.0 question/answer format that is like playing a video game. Of coure, there are many other web forums dedicated to this, I just find this one to be best.

But basically, just work at it. You will probably fail at first, and then probably the next time too, and so on.... But eventually you will get a methodology that works for you. If you're at a place where you can find motivated friends, then that will help.

Cihan
Posts: 3
Joined: Mon Feb 06, 2012 11:15 am

Re: How do you read textbooks on your own?

Postby Cihan » Mon Feb 13, 2012 6:14 pm

dasgut wrote:So I have a question for you guys...
I usually try and do every problem in the book, but then invariably get frustrated and just put the book down when I can't solve a problem.

Trying to solve every problem is of course nice if you want a good understanding of the subject but with a good textbook there will almost always be some exercises you can't solve at your first try. When I fail at solving such an exercise I try not to spend too much time on it (this is sometimes easier said than done, I sometimes feel like I "should be able to" solve that specific exercise) and move on to other exercises or new subject matter. It is really inefficient spending hours on a single exercise. I take note of the exercises that I couldn't solve to return in the future though.

Taking time off trying to solve an exercise can be useful, I often come up with solutions much quicker on my second try. When I spend so much time on a problem I often feel like there is a particular approach which should work, and that results in tunnel vision which makes me ignore other possibilities. Giving up on the problem after some failed attempts and visiting it later avoids that.

goombayao
Posts: 53
Joined: Sun Oct 16, 2011 9:17 am

Re: How do you read textbooks on your own?

Postby goombayao » Mon Feb 13, 2012 6:56 pm

Cihan wrote:
dasgut wrote:So I have a question for you guys...
I usually try and do every problem in the book, but then invariably get frustrated and just put the book down when I can't solve a problem.

Trying to solve every problem is of course nice if you want a good understanding of the subject but with a good textbook there will almost always be some exercises you can't solve at your first try. When I fail at solving such an exercise I try not to spend too much time on it (this is sometimes easier said than done, I sometimes feel like I "should be able to" solve that specific exercise) and move on to other exercises or new subject matter. It is really inefficient spending hours on a single exercise. I take note of the exercises that I couldn't solve to return in the future though.

Taking time off trying to solve an exercise can be useful, I often come up with solutions much quicker on my second try. When I spend so much time on a problem I often feel like there is a particular approach which should work, and that results in tunnel vision which makes me ignore other possibilities. Giving up on the problem after some failed attempts and visiting it later avoids that.


Good advice. Sometimes I'll bang my head against the wall trying to solve a difficult problem for hours, only to solve it during my sleep that night and wake up with the answer.

dasgut
Posts: 250
Joined: Thu Jan 21, 2010 12:20 am

Re: How do you read textbooks on your own?

Postby dasgut » Mon Feb 13, 2012 6:59 pm

goombayao wrote:Good advice. Sometimes I'll bang my head against the wall trying to solve a difficult problem for hours, only to solve it during my sleep that night and wake up with the answer.


And that's the problem! I think I'm going to only dedicate 30 minutes to any given problem. At the end of the day I'm reading the textbooks to have an understanding of new knowledge that might further my research and not my ability to do problem sets!

Cihan
Posts: 3
Joined: Mon Feb 06, 2012 11:15 am

Re: How do you read textbooks on your own?

Postby Cihan » Tue Feb 14, 2012 1:10 am

I'd like to add that what I said for exercises apply (at least for me) to textbooks in general too. It can be the case that I was unable to do much more than a couple exercises or really didn't get much of a feel of the subject while reading. Then naturally I may lose enthusiasm towards self studying from that particular textbook. In this case pushing myself with the thought of "I do want to learn this subject soon, come on!" works less optimal than switching to another textbook which is about another subject I want to study. I am usually in better condition to digest the material in the previous textbook after I spend some time away from it.




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