Elements of Real Analysis

Rating:
Summary: A good introduction to real analysis
Review: The proofs of the book are clear and detail.

Rating:
Summary: A Spoon-Feeding Book on Analysis
Review: This book is essentially the same book as the "Foundation of Analysis" by the same auther, which I used in an undergrad analysis class. I found it to be an outstanding book. A later analysis class used the baby Rudin, and I like Gaskill so much better. I dare say I did not learn anything new from the baby Rudin that I did not already know from Gaskill.

Some of the features I appreciate are (1) the plain language explanations of proofs and motivations before/after each theorem, and (2) graphs to illustrate the idea behind the theorems/examples. I wish other authors would include more graphs and illustrations!

If you want to understand the concepts behind how calculus works at Riemann level, this is a great book to start with. And I like Stromberg as a follow-up book. (There are some but not a lot of new things to learn even from Stromberg once you master Gaskill.)

However, this book does not mention analysis in R^n whereas the baby Rudin does. And the chapter on topology could be better in providing motivation and concrete examples. Things clicked for me when another book started out by saying that compactness can characterize a closed interval as versus an open interval in R.
And I would have like to see how this book would introduce Lebesgue measure. (Neither does the baby Rudin, but Stromberg does, and I appreciate learning something concrete like Lebesgue measure before abstract measure.)