During the next quarter at uni, I'll be taking a course in real analysis and since I prefer studying with an additional text I thought I'd come here to look for some book recommendations.
My background: I'm comfortable with linear algebra and single variable calculus, but shakey on multivariable calculus. I did have a slight introduction in to geometry.
For linear algebra I found the common recommendation of Hoffman & Kunze to be very helpful (although the abstractness came as a bit of a kicker at first).
For Single variable calculus I used the book Calculus by Adams and Essex, which I found frustrating to work with, because it often left me guessing at what they were trying to do or why they were doing it. I also felt that they exercised a certain lack of rigour. (Which may be due to the subject which would make it hard to derive from axioms.)
Details: Though it would be a complementary text, I'd prefer one which will still hold value as a work of reference at a later point in my studies. I've heard that Rudin's Principles of mathematical analysis is one of the better textst out there, but also read several comments discouraging Rudin's book as a first introduction to real analysis, hence my quest to gather more information and maybe get some more personalised recommendations.
The course: The mandatory course literature will consist of lecture notes, but 4 texts are suggested as recommended reading.
T.M. Apostol, Mathematical analysis. Addison-Wesley (1974) J.
Dieudonné, Foundations of Modern Analysis. Academic Press (1960) A.
van Rooij, Analyse voor Beginners.Epsilon Uitgaven, no. 6 (2003)
- R.S. Strichartz, The way of analysis (1995)
Thanks in advance!