I am going to apply to PhD programs in pure mathematics (target programs are mostly in U.S. and Canada). My GPA from state accredited universities is 3,5 for bachelor's and 3,3 for master's. These GPAs are not very good, but above cut-offs for almost all programs.
In my country (Russian Federation) also exists practice when strong worldwide known research centers (like Institute for Theoretical and Experimental Physics, Steklov Mathematical Institute, Independent University of Moscow, etc.) provide free additional classes for senior students. I took 13 such courses and have certifying transcript, but the total GPA for them is about 2,92 out of 4,0.
I am in doubt, is it worth to mention such experience and provide transcript? 13 extra classes in addition to official BSc and MSc degrees are seem to be a good proof of my interest and motivation (I know that in U.S. most students took less 13 math courses in their bachelor studies). On the other hand, I am afraid that a low GPA in these non mandatory activities may affect my application as well.