I had studied abstract algebra long time ago. Now, I would like to review some material, particularly about Galois theory (and its application).
Can anyone recommend an abstract algebra book which cover Galois theory (and its applications)?
I have been a software engineer for past many years. Ideally, I would like an algebra book with programming assignments or exercise (help me to understand concept.) For example, homework assignments to write a program to verify Galois theory, or to construct 'solvable Group", or anything like that. (Of course, I can think some random questions, but I prefer a text book with well designed, and meaningful home works).
I felt that I was not good at deriving formula anymore, I would like to use my programming skills to help me to understand subject, do more hand-on exercise and calculations.