How to address reading courses in cv for Phd application for pure math? How to address reading courses in cv for Phd application for pure math? I can only think of listing topics we covered in the course. But that seems to me very pointless since professors know the major topics of most math courses without reading that. However, I think independent readings are important experiences for math students, they definitely deserve a place in my CV.
It would be helpful to list the topics you looked at, and their sources. Even "standard" courses, with standard names, vary wildly depending on the choice of textbook or other sources, and depending on the instructor (who may be the author of notes or textbook for the course!) 

Similarly, "reading course in X" tells far too little, just as saying "standard course in X" would. Prior to the enforced uniformization of applications to our grad program, as occasional Dir of Grad Studies in Math, I required applicants to not only tell the course name, but also, even more importantly, the (title and) author(s) of the text(s)/source(s) for the course. Reading courses treated the same way.

To repeat: the standard catch-phrases/labels of course names absolutely do not describe the content... so, yes, please do give more details. These details are not at all implied by the general, vague, cliched titles.