Amazing and Aesthetic Aspects of Analysis

Authors: Loya, Paul

  • ​​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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eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4939-6795-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-1-4939-6793-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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:

  • 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.
Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.

About the authors

Paul Loya is a professor of mathematics at Binghamton University.

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Table of contents (8 chapters)

  • Very Naive Set Theory, Functions, and Proofs

    Loya, Paul

    Pages 3-28

  • Numbers, Numbers, and More Numbers

    Loya, Paul

    Pages 29-146

  • Infinite Sequences of Real and Complex Numbers

    Loya, Paul

    Pages 147-236

  • Limits, Continuity, and Elementary Functions

    Loya, Paul

    Pages 237-376

  • Some of the Most Beautiful Formulas in the World I–III

    Loya, Paul

    Pages 377-416

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4939-6795-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-1-4939-6793-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Amazing and Aesthetic Aspects of Analysis
Authors
Copyright
2017
Publisher
Springer-Verlag New York
Copyright Holder
Paul Loya
eBook ISBN
978-1-4939-6795-7
DOI
10.1007/978-1-4939-6795-7
Hardcover ISBN
978-1-4939-6793-3
Edition Number
1
Number of Pages
XV, 722
Number of Illustrations
122 b/w illustrations
Topics