Principles of Mathematical Analysis by Rudin

[Menomena]

I am curious as to where this book falls in the hierarchy of mathematical education.

Could it be used effectively before a calculus course? Is calculus necessary before analysis?

 

[micromass]

Well, you could use it before a calculus course. But you'll find it much too difficult and without motivation.

To tackle Rudin, one needs to know calculus and one needs to be very familiar with proofs. Furthermore, some mathematical maturity is needed.

And even then, Rudin is still hard.

 

[Menomena]

To tackle Rudin, one needs to know calculus and one needs to be very familiar with proofs. Furthermore, some mathematical maturity is needed.

And even then, Rudin is still hard.

I know its subjective, but what is the definition of "mathematical maturity"?

 

[Number Nine]

I know its subjective, but what is the definition of "mathematical maturity"?

Comfort with abstract mathematical concepts. In general, if you haven't taken calculus yet, then you don't have any (because you've never even encountered abstraction in mathematics). Rudin is something you read after you've already been introduced to real analysis; you are not ready. There are a few good introductory analysis texts (e.g. Elementary Analysis by Ross, which is quite good), but some of the motivation may be lacking if you haven't studied calculus (which isn't to say that you couldn't do it, just that you may not understand the importance of the some of the topics quite yet).