>I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific.

You made my point far better than I ever could. When I am faced with a general abstraction I have to conceptualize it in terms that I understand (the specific). Yet when the general case is presented, very little is said about the specific so I have to grind for months until I can finally maybe understand what was being meant. All of that could have been prevented had the concept been communicated in a more friendly, yet still mathematical, manner.

>All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in.

That's how I felt constantly in college and it is actually part of the the reason I dropped out. It almost felt as if this alienation is intentional. Which makes me somewhat sad!