True. Examples are necessary for both motivation, and for showing how the formalisms work, at this level. One good undergraduate textbook that has plenty of exa

True. Examples are necessary for both motivation, and for showing how the formalisms work, at this level. One good undergraduate textbook that has plenty of examples is Dummit & Foote. However, that doesn't mean that you don't define anything properly, and solely use examples to show how to crunch certain computations. The student is then stuck with a bunch of patterns in their heads, with little mathematical understanding.