How can I select ( identify) the exercise which I have solve in Dummit book ?

Maths Lover

How can I select ( identify) the exercise which I have solve in Dummit book ?
and avoid these exercises which I have not to solve ?

I talk about Identified book " Dummit and Foote "

homeomorphic

I don't think there are any firm rules to it. Do them all if you want a lot of practice. That's probably overkill. Just look at them and try to get enough practice with each concept. It may help if you can identify which concepts you want to cover the most thoroughly for later purposes. That would depend on what subjects you want to study later.

Maths Lover

in the truth , I didn't select the subject which I want to use abstract algebra in it later , because I don't know what is the subjects I can use abstract algebra in it !!

moreover , there is no teacher can help me in this matter , I study Abstract Algebra because I think it's an interesting subject ,

anyway , I want to devolope my knowlege in maths to a high level , so I thing I have to study Abstract algebra , linear algebra , set theory and number theory and other subjects
before I catch university .

rasmhop

Everyone is different, but the following are some approaches I have used when self-studying.

Look at the exercises. If any look particularily scary or you have no idea how to begin on some, then do that exercise.

Another approach is simply to do the last 5 exercises or so in each section (unless they are very similar, then just pick 5 late exercises that look different). They tend to be the hardest so if you have problems with those try some of the earlier ones that looks to have a similar theme, and once you understand the ideas go back to the later ones.

The idea is that ideally you should be able to solve all exercises, but only actually solve a few. It is pretty hard to pick exercises because books like Dummit Foote are optimized for classroom exposition, and therefore way too many exercises are included so professors can pick and choose.

If you tend to breeze through all exercises, then you may be doing too many. If you tend to struggle with most exercises you are likely doing too few, or too easy ones.