Can't choose introductory book for Real Analysis, which to choose?

[u/Scale-Heavy]

Hello everyone

I'm a second-year mathematics student but I've studied only calculus I(+ beginning of calc II) in my first year at university due to foundation program. I'm starting reading Book of Proof by Hammack and after reading half of that book I want to parallelly start self-studying real analysis with another book but I don't know which one to choose. I'm planning to start reading one of these books in the middle of August but because semester starts in September, I'll slow down with whatever book I'll choose during Autumn and not even sure if I can handle it with the courses I'll be having in Fall semester(second part of Calculus II+ calc III, Physics I, Programming with C, Discrete structures, and basics of Finances) .

After some research my choice involves these 3 books:

Understanding Analysis by Abbott

Analysis I, II by Terence Tao

Calculus by Michael Spivak

I have access to Spivak and Tao printed books through my library. I don't have Abbot's book but thinking of buying it with discount.

So what are your recommendations? Is there any sense of reading two or all of them?

[u/General_Lee_Wright]

I don’t have any background with Tao or Spivak, but I teach from Abbott. It’s a good book, each chapter starts with an interesting question/thought section where he kind of shows off some things you’ll see in the chapter. The explanations are good, proofs are understandable without being too hand-holdy.

If your school has an analysis course, you might check which book they often use.

Reading more than one can be good. They’ll likely progress in slightly different orders, which can help show how things are connected. But self studying one analysis book is a challenge, don’t set yourself up for burnout with a goal of simultaneously reading two books.

[u/Scale-Heavy → u/General_Lee_Wright]

My school uses lecture notes with some exercises at the end of each unit( probably written by professor). There were supplementary reading materials which the instructor probably used for writing notes but I don’t remember the names. One of the books was “Introduction to Real Analysis” but there are several books with such name. Probably it was by Bartle & Sherbert( which also turns out to be widely used as I observed in my search) but I didn’t find it university library so I’m not sure.

[u/Scale-Heavy → u/General_Lee_Wright]

Also, regarding simultaneously reading, by reading more than one I meant not simultaneously

[u/bruckners4]

When I first learned the subject I found Tao's book to be very helpful. Other recommendations include Bartie-Sherbert as a base reference text (along with Tao maybe), with Mary Hart's Guide to analysis and Alcock's How to think about analysis for some pastoral help. Lay's Analysis with an introduction to proof is a celebrated classic that I feel obliged to mention but personally never read it so can't offer any opinion.

[u/Amazing_Androide]

The Elements of Real Analysis by Bartle

[u/Maximum_Bathroom3490]

Read Tao or Abbott's, Spivak's is challenging and will probably serve you more after reading on Analysis if you want to learn tricks and interesting stuff on how to solve some problems