Principles of Mathematical Analysis - First Edition vs Later

Question

I've decided to learn some analysis and so I have settled on Rudin's Principles of Mathematical Analysis, I found a 1st edition copy at my local library.

I have gone through the first chapter and have realised that later editions have a different approach to constructing the reals (Dedekind cuts are used in the first edition). I am wondering now if there are any other important differences between the editions.

Should I get a later edition or is it ok for me to keep working on this one?

Answer 1

From the Preface to the third edition:

Experience has convinced me that it is pedagogically unsound (though logically correct) to start off with the construction of the real numbers from the rational ones. At the beginning, most students simply fail to appreciate the need for doing this. Accordingly, the real number system is introduced as an ordered field with the least-upper-bound property, and a few interesting applications of this property are quickly made. However, Dedekind's construction is not omitted. It is now in an Appendix to Chapter 1, where it may be studied and enjoyed whenever the time seems ripe.

So, bottom line: don't let this stop you from using the First Edition. If you enjoy seeing the construction of the reals, then go right ahead. If you are one of those who "fail to appreciate the need for doing this", then skim through it and go on.

Answer 2

I suggest you to read TOM APOSTOL real analysis before reading mathematical analysis by WALTER RUDIN . It make you able to handle mathematical analysis by WALTER RUDIN.