Schools usually have two or three abstract algebra classes just to cover materials in Chapter 1 and a couple later chapters (polynomials, modules, etc).
Not really (though again I emphasize every school is different). At least my school doesn't teach these abstract algebra covered in Chapter 1 except in discrete mathematics, which is not offered to most engineering students.
Sure some axioms, vector spaces, some polynomial, logic, here and there would be covered in calculus, differential and linear. But large part of the content would not be part of a CS/Engineering classes. Only what is relevant.
