I want to self study Real Analysis, and I want to choose between these books.
This is my background
I am a teacher of mathematics for highschool, which means (at least) in my country, that I had seen abstract algebra untill ring theory and calculus untill integral in several variables, but not things like Stokes theorem (because standards for teachers in my country solicites some very basic ODE and, so I had seen ODE instead Stokes). This calculus class was a mix level between engineering and pure mathematics
Could you tell me about the pros and cons of each of the following Real Analysis books? (Suitable or not for self-study, content quality, difficulty of the exercises, etc.)
- Real Mathematical Analysis, by Charles Pugh
- Mathematical Analysis, by Tom Apostol
- Principles of Mathematical Analysis, by Walter Rudin
As Thomas said, background matters a lot and well resources too.
Real mathematical analysis by Charles Pugh:
Pros : Pugh's real analysis is a fantastic book filled with lots of exercises/pictures. Difficulty of exercises range from easy to really hard. Book is readable as well.
Cons : Solution manual isn't available (Author did that on purpose though -.-, read the preface) Other than math forums, it's quite difficult to find solutions of the problems.
Rudin's Principles of Real analysis : (What I'm currently using.)
Really good exercises. Yes, Rudin's tough, but i believe that if you supplement your text with some lectures notes or lectures you will gain a lot, trust me here.
The supplements i suggest are : (Solely for Rudin) https://people.math.harvard.edu/~auroux/112s19/Notes_Math_112_may5.pdf (*45 pages) and https://dec41.user.srcf.net/notes/IA_L/analysis_i.pdf (*61 pages)
Now, Rudin(book) is dry, there aren't many examples or easier problems to get familiar with definitions or theorems, it throws a mountain of tough things at you. So these will will help as well.
Um, If it's for self study, Abbot's Real analysis will do the job as well, and it's a good read.