Transition to Analysis with Proof

By: Steven Krantz

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Paperback | 6 November 2017 | Edition Number 1

At a Glance

Paperback
364 Pages

Dimensions(cm)
23.39 x 15.6 x 1.91

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Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered.

The text opens with an introduction to basic logic and set theory, setting students up to succeed in the study of analysis. Each section is followed by graduated exercises that both guide and challenge students. The author includes examples and illustrations that appeal to the visual side of analysis. The accessible structure of the book makes it an ideal refence for later years of study or professional work.

Combines the author's previous works Elements of Advanced Mathematics with Foundations of Analysis

Combines logic, set theory and other elements with a one-semester introduction to analysis.

Author is a well-known mathematics educator and researcher

Targets a trend to combine two courses into one

Industry Reviews

This book is designed for undergraduate students and provides an introduction to analysis including an introduction to proofs. Namely, it starts with basic logic along with set theory and suggests plenty of instructive examples on how to do a correct mathematical reasoning. Then, he moves to functions, sequences, basic topology, differentiation, and integration. The text ends with power series and elementary transcendental functions. Each section of the book has a clear and convenient structure. It opens with "Preliminary remarks", which in a few sentences explain what the following passage is about. Then, the main text follows in which every statement is equipped with an instructive proof. Examples and exercises help master the material of the topic. A look back" blocks consist of a few simple questions (like "What is a monotone sequence?") and serve as a test if you understand the basics.

General remarks. The language of the book is quite vivid and lively, at the same time it is available for non-native students. The text has useful navigation tools like glossary, index, and the table of notations. The only disadvantage, in my opinion, is the lack of solutions and answers to the exercises.

Nikita Evseev (Novosibirsk)

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