I am in an extremely stressed out situation right now. I am pursuing Mathematical Sciences, as of now. I experience absolutely no difficulty in understanding the motivation or meaning underlying the several concepts and ideas one is taught in undergraduate courses. I am taking a few advanced and graduate courses as well and recently obtained a scholarship to pursue a research project.
I am extremely enthusiastic regarding what I do and I really love and have a passion for mathematics.
But the major problem I am facing right now is that I find myself incompetent in writing proofs in flawless rigour. I figure out the solution to any assigned problem as a rough intuitive idea, which in almost all cases is the underlying idea behind an elegant solution to the given problem. But once I can "see" the solution, I can no longer formulate it into a standard rigorous proof and this incompetence is hurting me severely in every step in "my career of exploration ". As a result, though I find that I can solve almost every problem assigned to me (provided I am given time to ponder over it), however hard they might seem to be, still I feel I lack the skill to formulate it into a perfect solution.
I am passing through an extremely depressing phase of my life and I would be highly indebted to anyone who lends me a helping hand in this regard. You can suggest me any literature to study, any class or lecture to attend or anything else that you feel would be beneficial for me.