[billfruit]

As someone who have struggled to self-study abstract algebra, I do find subject lacking in 'motivation', Eg: why do we define groups, fields, in the way that they are defined? Why do we need them at all?

Also most treatments do not cover categories, which seems to have its own separate literature.

Perhaps having some geometric intuition will greatly help, viz coordinate systems in 3d Eucliden space, answering interesting questions like when is it legal to take dot product of two vectors? and if two unit vectors are parallel are they the same vector?

[jsmith45]

the lack of providing motivation is a huge problem with math courses on every level.

I feel that mathematical topics almost always benefit from positing some problem, and then "inventing" the mathematics that allow you to answer the question, followed immediately by some examples of other questions this topic can help you answer (as at least an informal justification of some of the seemingly arbitrary choices made).

Then show a similar topic you cannot quite answer and build on it with that. Eventually you will have built up the majority of the topic with motivations for each part.

Abstract algebra might be trickier to motivate than many subjects, but it still should be possible. Yet given how much trouble there seems to be in writing out motivation for more concrete topics finding a textbook that provides motivation throughout for this area seems tricky at best.