© 2017

Amazing and Aesthetic Aspects of Analysis


Table of contents

  1. Front Matter
    Pages i-xv
  2. Some Standard Curriculum

  3. Extracurricular Activities

    1. Front Matter
      Pages 417-417
    2. Paul Loya
      Pages 419-531
    3. Paul Loya
      Pages 589-699
  4. Back Matter
    Pages 701-722

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:
  • 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.


real analysis fundamental theorems of continuous functions infinite sequences of real numbers infinite series mathematical induction cardinality

Authors and affiliations

  1. 1.Department of MathematicsBinghamton UniversityBinghamtonUSA

About the authors

Paul Loya is a professor of mathematics at Binghamton University.

Bibliographic information