So I recently joined university for a BSc in mathematics. I have never been exposed proofs but I have knowledge of algebra, trigonometry, and some differentiation/integration. Now I'm struggling with proofs. I'm having trouble figuring out the best way to write the proofs, since everything seems so random. I don't know where to begin.
After some Googling, I came across some tutorials but they do not help much. I think I lack the basics of proof solving and I think I lack the mathematical language to express what I need. Would anyone experienced have any suggestions for me on where to start and gradually be able to tackle most proofs(contradiction, induction) and I would really appreciate it if you could suggest some great introductory proof-based books which will give me a head start and gradually move to advanced stuff.