Understanding Real Analysis 1st Edition by Paul Zorn (PDF)

Description

This book is a one-semester text for an introduction to real analysis. The author’s primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of mathematical “apparatus” work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques.

User’s Reviews

Editorial Reviews: Review This is a textbook designed to teach students who are new to analysis what it’s all about. … The path Zorn takes is based on several very reasonable principles. These include: building on calculus basics; focusing on mathematical proof, structure and language; staying with the basics; offering many examples and many solved exercises; and gradually increasing technical sophistication. … There are plenty of exercises. They tend to follow a pattern where an exercise that is not completely straightforward is broken into multiple parts to guide the student to a solution. — Bill Satzer, MAA Reviews, June 2010 From the Back Cover In this introduction to real analysis, a branch of mathematical analysis dealing with the set of real numbers and their operations, Paul Zorn (St. Olaf College) aims to develop ideas already familiar from elementary calculus in a rigorous manner. The text will help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of the mathematical “apparatus” work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques. About the Author Paul Zorn was born in India and completed his primary and secondary schooling there. He did his undergraduate work at Washington University in St. Louis and his Ph.D., in complex analysis, at the University of Washington, Seattle. Since 1981 he has been on the mathematics faculty at St. Olaf College, in Northfield, Minnesota, where he now chairs the Department of Mathematics, Statistics, and Computer Science. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Pedagogically this is a fine text: the basic ideas of limits, continuity, Cauchy sequences, convergence, et cetera are explained very well. But there is little coverage of convergence tests for infinite series (e.g., even the root test is missing). And there is no coverage of power series. Two other texts that are close to this book in spirit and level of exposition are Howie’s “Real Analysis” (Springer) and Dangello and Seyfried’s “Introductory Real Analysis” (Houghton Mifflin). Yet both have more coverage of infinite series and both cover power series. Zorn’s book might be fine for a weak class or for an “analysis for liberal arts majors” kind of course. But I doubt it will suffice as the text for a first course in analysis for prospective math majors.

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