Real Analysis book with Solved Answers

Question

I'm a self-learner in maths & starting with real analysis. I looked for many books and many suggestions here (like this and this and many more) & finally choose Tao's Analysis volume. It's beatifully written, giving a beautiful overview and connected one aspect with another.

But since my mathematical maturity is still not that developed, sometimes I had to struggle pretty hard in undestanding simple things (like "$\varepsilon$ follow the axiom of substitution for equality", etc.). Another challenge I'm facing is many of the propositions in this book are given as exercise. This might be good, but for newcommer like me, it's bit difficult.

So, I was looking for a companion book which might help me practice my understanding while reading this book. The ordering of this alternative book's chapter might not be the same as Tao's (not even the entire scope as I think when I start understanding analysis bit more I can start walking with Tao on my own), but very similar. I don't want to go with Rudin as I want to use it after finishing Tao as test of my understanding.

Thanks!

Answer 1

Well, I really like the book of R.P. Burn: Numbers and Functions - Steps into Analysis.

Publisher: Cambridge University Press Online publication date: May 2018 Print publication year: 2015 Online ISBN: 9781316018392 https://doi.org/10.1017/CBO9781316018392

Answer 2

The Way of Analysis by Robert Strichartz may suit your needs.

The author explains well what his intents are at the beginning of each chapter. Most proofs are often explained with not much left for the reader to figure out, and there's quite a bit of intuition accompanied with this explanations. There's even a preliminary chapter as well for the information concerning logical quantifieres, proofs, and sets.

https://www.amazon.com/Analysis-Revised-Jones-Bartlett-Mathematics/dp/0763714976/ref=sr_1_1?ie=UTF8&qid=1547313840&sr=8-1&keywords=strichartz+way+of+analysis

Answer 3

Spivak's Calculus is a classic texts for people who want a gentle introduction to real analysis.

The book contains many problem and there are completely solved exercise sheets online for all exercices. The author also included solutions/answers to selected problems in the back.

You can't go wrong with this text. Spivak learns to think you as a mathematician.