One question for studying Mathematical Analysis

[Shing]

I am self-studying MA, I've learned elementary Calculus ( without vector calculus & Partial Differentiation) I've learned a bit of LA before.

I am using these textbooks:
1. introduction to Analysis (so far there is no difficulty)
2. Principles of Mathematical Analysis (this one is more difficult, and often I got stuck.)

So basically, my question is:
1. What am I supposed to learn before reading Principles of Mathematical Analysis ( so that I can read it more easily) or it is natural that to learn it with some hard time?

Thanks!

 

[Howers]

You need to know introductory analysis. This means Apostol or Spivak, or any kind of "theoretical calc" book. In particular, know epsilon delta proofs,the three hard theorems, and sequences and series. More importantly, know proofs and their techniques. A book like Velleman's How to Prove it will teach you proofs.

The reason you may be have trouble with Principles is that you do not know the rules of logic in math.

 

[ytoruno]

i think rudin (2) is hard to learn from. Since you're just starting, I'd say try out Elementary analysis by Kenneth Ross for single variables.

 

[razored]

Which would be better for a first exposure to Calculus, Spivak or Apostol? I am planning to do the same with other books.

 

[Howers]

I'd say Spivak. I've never used Apostol, but I think he begins with integration first. While it can be done, its not a conventional approach. Simply put, you can't go wrong with Spivak. Its beyond good preparation. Even if Apostol is better, you're not screwed in any way doing Spivak.

 

[Shing]

A bit addition :
introduction to Analysis- by Arthur Mattuck

Thanks to everyone!

I could barely understand Principles of Mathematical Analysis, anyway, that was tough and no fun lol
I am going to finish the introduction to Analysis first! Or it is more proper to start reading the Calculus be Apostol instead?

 

[axeae]

Ross's Elementary Analysis.