I'm an undergraduate electronics and communication engineering student (sophomore) at an Indian university. I joined this engineering course because I found the areas of quantum computing/information and quantum engineering quite interesting, and I felt an EE background would help me later on to pursue higher studies in these areas.
Lately, although I still have great interest in those areas (quantum computing/information/engineering), I am finding myself very much interested in certain topics in mathematics and mathematical physics. Namely, mathematical foundations of quantum mechanics and quantum information (which involves learning a lot of extra math topics like functional analysis), differential geometry and topology (and their application in theoretical physics), statistical learning (I'm finding the application of statistics in machine learning quite interesting and have been reading quite a few books related to that) and discrete mathematics (graph theory and combinatorics).
The natural thing to do in such a case would be pursue a minor in mathematics. But, unfortunately, our university does not offer any minor degrees or dual major degrees. So, it's not possible for me to formally take extra classes in mathematics. Upon pondering a bit I realize that I might want to pursue my higher studies in some interdisciplinary area which involves knowing things from electronics engineering as well as from the rigorous mathematical physics and statistical learning (machine learning/data science/AI). I'm not sure if such an interdisciplinary area of study even exists at the graduate level (?). But I'm really enjoying learning the new things in mathematics and I don't want my spending time on learning these things go in vain.
So, in short, what would be the correct way to keep proof that I'm actually learning these extra things (so that I can show that I actually know these extra subjects/topics while applying for grad school) ? Should I participate in some research projects in these areas? (But then again professors don't seem to accept people who haven't taken formal courses into their research projects). If it were computer science, I could have taken online courses on sites like EdX and Coursera, for certificates. But for mathematics, no such site exists which gives out certificates based on completion of certain courses.