I couldn't find this question anywhere else, so just thought I would ask it here. There is a series of 4 analysis books written by Stein and Shakarchi (sometimes called the Princeton Lectures in Analysis), and as I intend to study from them, I was wondering whether it is important or not to learn the material in the order that the books were written:
-
Fourier Analysis
-
Complex Analysis
-
Real Analysis
-
Functional Analysis
For example, is the Fourier analysis in the first volume a prerequisite to understanding the complex analysis in the second volume? Or can one just proceed straight to complex analysis while having just a basic background in real analysis (like Tao or Rudin)? Thanks.
Best Answer
Most math books contain an introduction that outlines the prerequisites. I have only read Vol III, but that one was generally self-contained. I doubt an introductory complex analysis book would require Fourier analysis. Quoting from the intro to Vol III:
In my opinion the chief prerequisite is "mathematical maturity", i.e., familiarity with proving stuff. They may not be so good as an introduction to proof-writing.