Through four editions this popular textbook attracted a loyal readership
and widespread use. Students find the book to be concise, accessible,
and complete. Instructors find the book to be clear, authoritative, and
dependable.
The primary goal of this new edition remains the same as in previous
editions. It is to make real analysis relevant and accessible to a broad
audience of students with diverse backgrounds while also maintaining the
integrity of the course. This text aims to be the generational
touchstone for the subject and the go-to text for developing young
scientists.
This new edition continues the effort to make the book accessible to a
broader audience. Many students who take a real analysis course do not
have the ideal background. The new edition offers chapters on background
material like set theory, logic, and methods of proof. The more advanced
material in the book is made more apparent.
This new edition offers a new chapter on metric spaces and their
applications. Metric spaces are important in many parts of the
mathematical sciences, including data mining, web searching, and
classification of images.
The author also revised the material on sequences and series adding
examples and exercises that compare convergence tests and give
additional tests.
The text includes rare topics such as wavelets and applications to
differential equations. The level of difficulty moves slowly, becoming
more sophisticated in later chapters. Students have commented on the
progression as a favorite aspect of the textbook.
The author is perhaps the most prolific expositor of upper division
mathematics. With over seventy books in print, thousands of students
have been taught and learned from his books.
