Overview
- Contains enthusiastic prose and exciting and imaginative exercises that will motivate the reader
- Covers the fundamental ideas, axioms, definitions, and theorems upon which real analysis is built and flourishes
- Motivates the material with historical remarks and well-chosen quotes
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About this book
Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression.
In studying this book, students will encounter:
In studying this book, students will encounter:
- the interconnections between set theory and mathematical statements and proofs;
- the fundamental axioms of the natural, integer, and real numbers;
- rigorous ε-N and ε-δ definitions;
- convergence and properties of an infinite series, product, or continued fraction;
- series, product, and continued fraction formulæ for the various elementary functions and constants.
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Keywords
Table of contents (8 chapters)
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Extracurricular Activities
Reviews
Authors and Affiliations
About the author
Paul Loya is a professor of mathematics at Binghamton University.
Bibliographic Information
Book Title: Amazing and Aesthetic Aspects of Analysis
Authors: Paul Loya
DOI: https://doi.org/10.1007/978-1-4939-6795-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Paul Loya 2017
Hardcover ISBN: 978-1-4939-6793-3Published: 28 May 2018
Softcover ISBN: 978-1-4939-9245-4Published: 25 July 2019
eBook ISBN: 978-1-4939-6795-7Published: 11 May 2018
Edition Number: 1
Number of Pages: XV, 722
Number of Illustrations: 122 b/w illustrations