I am a final year undergraduate in Mathematics at IIT Bombay. Apart from mathematics courses, I have also done courses in Electrical Engineeering. You can find my resume here.
After school, I joined IIT Bombay as an Undergraduate in Electrical Engineering. As my primary interest was mathematics I started pursuing a minor in mathematics. After doing a few courses I was even more interested and therefore changed my major to Mathematics.
Gromov's H-principle: I have read proof of Gromov's theorem for open partial differential relation from the book Introduction to h-principle by Eliashberg and Mishachev. The proof follows the idea of holonomic approximation, that is finding a holonomic approximation of a section of jet bundle near a slightly perturbed submanifold of the original submanifold. This theorem reduces problems of analysis into algebraic/geometric problems. For example it reduces the study of spae of immersions to study of formal immersions.
Professor Akhil Ranjan Lecture notes on Curves and surfaces