I would love to hear about how you study math books

[nox]

Summary: self study math books

I wanted to make a post, been a while since my last one.

I been taking a few weeks off but back studying linear algebra done right, and i notice a few things.
First i will find myself reading the chapter, and fooling myself i get it, but then struggle with the exercises, so i move on to the next chapter.

In the next chapter whenever the author uses earlier results i find myself lost, and need to return.
It is at this point i find myself taking notes through the earlier chapters, and this time the exercises makes much more sense.

Like today i did chapter 3, ex 18, and found that the author tried to throw a curved ball, he made it very tempting to use a specific theorem, until you realize you can't apply it like that. Very illuminating when i saw that, and a good lessons in learning when you can apply a theorem.

My current process to mastering the material, is to read a chapter, until i can do some exercises touching each major topic in the chapter. Then move to the next one, if i find problem with building new topics on top of earlier ones, i revisit and write detailed notes on that sub chapter, and do more problems. So it is an iterative process where i spend a day or two initially on each chapter, but regularly revisit them, and if need be do detailed notes on them as the need arise.

Slowly i feel i start to grasp concepts in non trivial ways, but i still got allot more thinking to do before i really have gained what i want from the book.

I am super curious, how do you study a math book, what methods do you do to really learn the material deeply and in the event you get interrupted for weeks, how do you pick up where you left off?

 

[lavinia]

A long but ultimately fruitful road is to try the exercises first and only read the chapter when you figure out what it is that you do not know but need to know to solve the problem. This takes many tries and fails. Theorems should also be attempted first before reading the proofs.

This may be impractical since it takes a long time but I feel it is worth it to learn the mathematical way of thinking.

 

[RJLiberator]

I'd be interested in hearing how more people 'study' textbooks.

In my experience, when I start a tough textbook I fail miserably after a few days. I read a chapter, do some problems, then almost immediately forget the knowledge.

I'd love to hear more!

 

[WWGD]

There is this SQ3R method that seems to have worked out for many: Survey, Question, Read, Review, Recite. First just browse to get an overview. Maybe do it the night before doing the rest. Do then a second read where you ask questions. These first two steps have now allowed you to break down the material and then you jump in in full and read again. Then you give it a reread for review. Lastly, recite it; to yourself or others. Check too that you are well rested, etc.
.

 

[WWGD]

To me the issue is mostly the dauntingly complex notation in some areas. Once i get it down everything else falls into place more easily.

 

[Infrared]

Reading a serious math text on your own can be very difficult, especially if you don't already have a lot of mathematical maturity. Try to find a professor (or anyone who knows the topic well) you can consult with when you have questions or get stuck.