Mathematical Notation for Recommender Systems

Over the years of teaching and research, I have gradually standardized the notation that I use for describing the math of recommender systems. This is the notation that I use in my classes, Joe Konstan and I have adopted for our MOOC, and that I use in most of my research papers. If you haven't already settled on a notation, perhaps you would consider adopting this one. I have tried to strike a balance between clarity and clutter. I slightly overload the meaning of some symbols; in particular, I am loose with distinctions between sets and matrices, because it is generally clear from context which is being invoked; I do not overload external referents, however.