School of Mathematics
Georgia Institute of Technology
Atlanta, GA 303320160
(404) 8949231
h e i l @ m a t h . g a t e c h . e d u
C. Heil:
Introduction to Real Analysis,
Springer, Cham, 2019 (xvii + 400 pp.).
From the preface:
This text is an introduction to real analysis.
There are several classic analysis texts that I keep close by
on my bookshelf and refer to often.
However, I find it difficult to use any of these as the textbook
for teaching a first course on analysis.
They tend to be dense and, in the classic style of mathematical
elegance and conciseness, they develop the theory in the most
general setting, with few examples and limited motivation.
These texts are valuable resources, but I suggest that
they should be the second set of books on analysis
that you pick up.
I hope that this text will be the analysis text
that you read first.
The definitions, theorems, and other results are motivated and explained;
the why and not just the what of the subject is discussed.
Proofs are completely rigorous, yet difficult arguments
are motivated and discussed ...

Table of contents.

Preface.
 See the book at:
 Book Reviews:
 Mathematical Association of America.
Quote: "Heil has understood that what does not draw attention has little chance of being thought about, and what is not thought about cannot possibly be learned."
Quote: "This challenge has been met hands down."

MathSciNet.
Quote: "This book gives an accessible introduction to real analysis that is suitable for firstyear graduate students."

Zentralblatt Math.
Quote: "The main aim of the author is to clarify the central ideas of modern analysis."

Amazon customer review.
Quote: "This book is amazing."
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