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Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis.
The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds.
Key Features:
- Meets and aligns with various student backgrounds
- Pays explicit attention to basic formalities and technical language
- Contains varied problems and exercises
- Drives the narrative through questions
List of contents
Preliminaries: Numbers, Sets, Proofs, and Bounds. Sequences and Series. Limits and Continuity. Derivatives. Integrals.
About the author
Paul Zorn was born in India, and had his primary and secondary schooling there. He did his undergraduate degree, in mathematics and English, 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.
In 1987 Paul Zorn received the Allendoerfer Award for mathematical exposition from the Mathematical Association of America (MAA). He was chief editor, from 1995 to 2000, of the MAA journal Mathematics Magazine. He has also served on the Council of the American Mathematical Society and on the Board of Governors of the MAA. In 2011 and 2012 he served as President of the MAA.
The first edition of Understanding Real Analysis was published by AK Peters in 2010. The present (second) edition was published by CRC Press in 2017. Paul Zorn has also published (with his late co-author, Arnold Ostebee) a series of calculus textbooks that draw on computing to promote graphical, numerical, and symbolic viewpoints.
Summary
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.
