This is a textbook for a course in Honors Analysis (for
freshman/sophomore undergraduates) or Real Analysis (for
junior/senior undergraduates) or Analysis-I (beginning graduates).
It is intended for students who completed a course in "AP
Calculus", possibly followed by a routine course in multivariable
calculus and a computational course in linear algebra. There are
three features that distinguish this book from many other books of
a similar nature and which are important for the use of this book
as a text. The first, and most important, feature is the collection
of exercises. These are spread throughout the chapters and should
be regarded as an essential component of the student's learning.
Some of these exercises comprise a routine follow-up to the
material, while others challenge the student's understanding more
deeply. The second feature is the set of independent projects
presented at the end of each chapter. These projects supplement the
content studied in their respective chapters. They can be used to
expand the student's knowledge and understanding or as an
opportunity to conduct a seminar in Inquiry Based Learning in which
the students present the material to their class. The third really
important feature is a series of challenge problems that increase
in impossibility as the chapters progress. The foundational
material contained in this book is published separately as Paul
Sally's, "Tools of the Trade: Introduction to Advanced
Mathematics," also available from the AMS.