More than one math Ph.D. program I am applying to has a section where I am to list relevant coursework. An example is as follows:
"Enter under each category list the two most advanced courses or course sequences you have had or will definitely take before you come to (School)."
Under each class title there is a blank line where I am to list a text or textbooks. (No other instruction)
My question is this: In a few of my courses, the professor has listed a textbook for the course, but whose lectures have not adhered to the structure or level of rigor of the book. The homework also did not come from the course book. If I chose to use another textbook to study out of should I list this one or the one listed in the course syllabus? My reasons for wanting to list the book I used are:
The book on the syllabus is not a good indication of the level of rigor at which the course was taught.
I haven't read a page of the textbook on the syllabus while the book I used is one I own and is the primary reference for the subject on my shelf.
Which book should I write in my application?