Hello Mathematicians .
I am a first year PhD student in Mechanical engineering.
Since I was in high school I always loved maths and used to watch all sort of documentaries . That made me want to do research . However in engineering school I have had an overwhelming number of classes and subjects at once that I couldn't keep up ( obviously I did good enough to graduate) but I have never felt that I fully grasp the mathematical foundation and formal proofs .
So recently I started to circle back to my undergrad lectures in my free time and I want to re-inforce my understanding of fundamental mathematics because I want to study some advanced branches ( most notably deferential geometry and functional analysis ) .
Do you have any recommendations ? Ressources ? Or advices ?
Thank you for Reading . Have a great day !