What is the best way to study this kind fo books ?

[Maths Lover]

Hi ,

I hope that you are all fine ,

I want to ask a question which I need to know it's answer soon,

when I study a subject like Abstract algebra or calculus or linear algebra or any subject , after very section or unit or lesson in my , there is lot's of exercises which need lot's of time to solve it ! and some books put very very difficult exercises , for example , some books put important theorems as an exercises and the reader have to get his own proof ! and that is tiring , so , what is better ? we slove all the exercises ? or solve some of them and just look to the others ?! if the better is to solve some of them only , how can I choose the exercise which I need to solve and leave the one which I shoudn't solve ??

some books do this , artin's book as an example !


my greetings
Maths Lover

 

[Fredrik]

I prefer to focus on the theorems and their proofs.

My approach to exercises is to just solve a few exercises chosen more or less at random until I feel that I know how to solve problems of the type that the section of the book is trying to teach us to solve.

 

[micromass]

In my undergrad, I never really solved any exercises from a textbook. I found it enough to just read the theory and make up my own examples. Eventually, I found out the hard way that my method was not a good one. Now, whenever I read a math book, I (try to) solve all the exercises. Certainly for a thing like abstract algebra, you will want to solve a lot of exercises.