Ph.D. mathematics application: Disclosing course textbooks

I am the Graduate Coordinator for a math department in which we ask graduate applicants to list their course textbooks.

I encourage you to follow the directions and list the textbooks that were used. By and large, this is a good way for us to figure out the approximate level and content of courses like "algebra," "analysis" and "topology" with standard names but widely varying content. A complex analysis course taught out of

A First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka

is likely to be quite different from one taught out of

Complex Analysis, Lars Ahlfors

If you feel that the chosen textbook was below the level of the course and you supplemented with a more advanced/rigorous textbook, you may as well list that textbook too, saying something like "I myself used..."

If the instructor has online lecture notes, definitely include a link to them: that gives a really good idea of what was covered.

Note to international readers: having standard textbooks for advanced undergraduate math classes is much more, um, standard in the United States than in many other parts of the world. We certainly know that international students may come from less of a "textbook culture." (This need not be a bad thing in itself, but it is one of several ways in which it can be harder to evaluate the profile of an international applicant than a domestic one.)