(Source: Complex Variables with Applications, Second Edition, A. David Wunsch)
I started transporting my professional books to my new office this week, five books at a time. One of the books I brought today was my old textbook from when I took Complex Analysis in university, about 20 years ago. I decided to skim through the book to see how much of those two courses I remember, and as it turns out, the answer is not much.
I stumbled upon this notation that I was unfamiliar with very early on in the textbook, and decided to work my way back through the textbook to see if I could find out where this notation was introduced, and found the only reference to a definition of the notation above.
It occurred to me that this is not so much a failure of the author, but a failure of the medium, and one that could be addressed in a digital medium much more easily. One cannot easily link to notation, especially notation used often in a traditional textbook, back to it’s origin. However in a digital textbook every single instance of this notation could be made linkable (perhaps in an unobtrussive way so as not to be distracting) back to not only the first instance of the notation, but to carefully constructed examples of the notation in use.
On a related note, in my classroom, I try my best to introduce vocabulary and notation as it is needed to describe mathematical (or otherwise) objects that the students have been gaining some familiarity with. This way the vocabulary or notation is meeting a need; labelling something that we want to discuss, rather than being artifically introduced "because we will need to know this later."