Interesting. In Mathematics classes, you usually have what are called 'motivating examples'. For instance, you might take an object and then see that you can't

Interesting. In Mathematics classes, you usually have what are called 'motivating examples'. For instance, you might take an object and then see that you can't tell something about it, but if you restrict it in a certain way then it starts having certain interesting properties. The difference between a good lecturer and a poor lecturer is often whether they can give you good motivating examples. The textbooks though are frequently as you describe. They execute like a computer program. Hartshorne's Algebraic Geometry is the classic example for me: it takes so much work just to go through each page. Even chapter 1 you have to skip forward to see that you can get the Nullstellensatz before you can come back to see why you're restricting your object in a certain way. This is no way to learn.