Reddit mentions of Introduction to Real Analysis

My university took an analysis approach to calculus. Our classes were 95% proofs and 5% application. I believe this gave us a better understanding for what calculus really is and a good introduction to later pure math courses. I would recommend you look in to [Introduction to Real Analysis by Robert G. Bartle & Donald R. Sherbert] (http://www.amazon.ca/Introduction-Real-Analysis-Robert-Bartle/dp/0471433314). The first few pages teach you the basics of proofs (proof structuring, sets, axioms, theorems such as well ordering property and etc) and then it dives into calculus. Good luck!

I also have a lot of love for the Bartle real analysis text. It's light on prerequisites other than calculus and the text spends time explaining the logical reasoning. A lot of upper-level math texts are simply a collection of theorems. The good ones present a coherent narrative that give context as each theorem is presented.

I used Intro to Real Analysis by Bartle and Sherbert for my first analysis course. I just checked, and it has quite a few examples for most sections. The book was sufficient without lecture, as far as learning proofs and applying theorem goes. It was also relatively easy to read; there are a lot of analysis books which are hard to read due to terseness. You can probably find it for cheaper too. Good luck.

I hear that Rudin's book is pretty dense, so initially, I won't be using it, though I'm not entirely familiar with Spivak/Rudin beyond the comments on Amazon/Reddit.

Instead, I'm reading from Ross and [Bartle] (https://www.amazon.ca/Introduction-Real-Analysis-Robert-Bartle/dp/0471433314) right now, which I hear are good books for people starting out in Analysis. As I progress through the series, I might start teaching from Rudin and a variety of other sources.