I am working through Dummit and Foote's Abstract Algebra this summer in preparation for a class next year. However, this is my first time really trying to learn a subject through only a text. It seems to me that doing every single problem, while probably helpful to understanding, is merely too time-consuming to make the progress I need to make. Do you all still recommend doing so? If not, how do I select exercises to do? I have already learned that skipping all exercises ensures that one learns nothing. =P
If it helps, an example, an example is the fact that there are ~40 exercises following only the axiomatic definition of a group. Should I work through all of them, or only a subset and continue on my way?