I am taking a real analysis course next year and I want to start slowly preparing for that class now, so I hope you can help me.
The class is quite challenging and the fail rate is relatively high. The class uses Rudin's Principles of Mathematical Analysis.
To prepare for the class, I decided to go through Abbott's Understanding Analysis, Book of Proof by Hammack and work on inequalities. I read that it is important to be good with proving inequalities so can you give me advice on how I can do that? Are there books that can help me with that?
What else do you think I should work on, what books do you recommend? Is it necessary to go through a more rigorous calculus textbook? The courses I did in calculus used Thomas' Calculus, which I think is much less rigorous than something like Spivak's.
Would very much appreciate your advice.