I study electronic engineering at university, 3rd course. I had to use mathematics a lot, from basic algebra to analysis. Yesterday, after watching some mathematics-related videos and reading some posts I made a conclusion that I don't have a general understanding of this beautiful field of science. I don't know if this kind of question is appropriate here but I want to ask a basic but nontrivial (for me) question:
What is mathematics?
That is, what branches it has, what is the foundation, the starting point, etc. This question emerged when I decided to get a more profound insight of the matter and start learning mathematics from scratch to form a systematized knowledge and after all I love using and studying it.
P.S.: I apologize for my English: it isn't my first language.