Methods of Real Analysis

Rating:
Summary: Well worth it.
Review: I come to real analysis from a non-mathematics background. I began with Steven Lay's "Analysis with an Introduction to Proof" which was great for an absolute beginner. Goldberg's text is the next step up. And well worth the money!

Rating:
Summary: Great introduction to Real Analysis
Review: This book reads like an instructor would teach in class. It derives all the important theorems quite rigorously and throws in a few lines of intuition which is very helpful when you are trying to self-study something as intense as real analysis. He also has two or three examples following every major result and shows clearly how to "use" the result just derived to solve an actual math problem.
I went through lots of great analysis books (Rudin, Shilov, Kolmogorov, Aliprantis, Johnsonbaugh, Rosenlicht and Protter among others) until finally learning from this. After getting my foundations and intuitions right, I now feel like I am better equipped to read and understand the results from the above books which, in general, treat proofs more tersely and cover a lot more material in the process.
This book does not cover the origin of real numbers and it's axioms. It covers standard results from elementary set theory, sequences, limits, metric spaces, open and closed sets, completeness, compactness and connectedness, the derivative, Taylor Series, exps and logs, the Lebesgue integral and Fourier Series.

Rating:
Summary: Well worth it.
Review: This is an excellent textbook for an introductory course in Real Analysis. The text is rigorous, but contains enough examples to be readily understood. If you honestly want to learn the subject matter, this book is worth the money. However, if you would rather struggle with it, there are plenty of those books floating around . . .

Rating:
Summary: Clear and to the point
Review: This is an excellent textbook for an introductory course in Real Analysis. The text is rigorous, but contains enough examples to be readily understood. If you honestly want to learn the subject matter, this book is worth the money. However, if you would rather struggle with it, there are plenty of those books floating around . . .