Listing books read on a CV for undergraduate research in mathematics I am currently making my CV for undergraduate research internships in Pure Mathematics. I have read many graduate level books on the field out of my own interest. Whenever I was stuck on a difficult concept, I have sought the help of my professors and they can vouch for my understanding of these topics. Adding a section titled "Books Mastered" seems a bit narcissistic but I believe mentioning these books would add weight to my application.How can I leverage this experience and incorporate it into my CV?
How can I leverage this experience and incorporate it into my CV?


I'm not convinced there's any good way to incorporate this experience into your CV.  The basic problem is that it's unclear what it means to have studied a book: there's a huge range of levels of mastery that could all legitimately fall into this category.  Furthermore, many undergraduates have trouble accurately assessing their own knowledge and accomplishments, so a self-assessment of mastery is not convincing even if it's completely honest.  And of course honesty and bias are important issues.

The net effect is that these claims are vague, subjective, and unverifiable, which is exactly the opposite of what belongs in your CV.

You could always try to say something more precise.  For example, "I wrote out solutions to every problem in Hartshorne's algebraic geometry textbook" is much more compelling than "I studied Hartshorne" or "I mastered Hartshorne".  It's still not ideal; for example, it leaves open the question of whether your solutions were actually correct.  However, it at least gives a much clearer idea of how much you might have learned, and it allows the possibility of verification by requesting to see the solutions.  (Don't say this if you lost them!)

I wouldn't recommend trying to make precise claims like this for all your independent reading, since it would still come across as eccentric.  However, that would at least be a better option than just listing some books.