S.E. users,
Which one is better for the real analysis, "Mathematical Analysis" by Tom Apostol or "Undergraduate Analysis" by Serge Lang? It is my first time with real analysis, but I will be supplementing either of them with Ross, Abbott, etc. My ultimate plan is to study Rudin's PMA & Pugh's Real Mathematical Analysis after mastering some chapters in APostol or Lang, which will prepare me for my analysis course on this Fall.
Sincerely,
PK
Haven't read Lang. Have only glanced at Apostol and it is not that different to Rudin from what I've seen in terms of sophistication. Abbott is definitely an easier book. My favourite is Elements of Real Analysis by Bartle. Might want to look through this too:Good book for self study of a First Course in Real Analysis
Just googled Ross. Both that and Abbott focus only on the real line. Whereas the books you mention go well beyond it to finite-dimensional Euclidean space and then to general Metric Spaces. So I don't know if Apostol, Pugh or Rudin would "prepare" you for this upcoming course. Having said that I've found it better to sometimes stay ahead of your college courses and know a bit more. So why not challenge yourself by taking a crack at Rudin and Pugh. Even if you only get through the first chapter in Pugh before your course it will be well worth your time.