I want to learn the art of constructing proofs but it proves difficult namely because I don't know how to begin. I've become familiar with a variety of methods such as proof by contradiction, deduction, exhaustion, induction etc.
How I approach trying to prove something is that I read it out in words and then write it down. It's as if I know it's true but I struggle to piece it together through maths though. I've come from an engineering maths syllabus and I enjoyed it so much it's become an addiction but I feel like I lack the essence and purity of it all. I've taken a step back and decided to study the theory of sets and grammar books for a start. I'm absorbing definitions and theorems a lot more seriously now, but again its the rigor.
Could any members suggest some good books or even provide a learning curve for where to begin in learning how to prove?