Amazing and Aesthetic Aspects of Analysis - (Undergraduate Texts in Mathematics) by Paul Loya (Paperback)

Book Synopsis

​​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

From the Back Cover

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 Author

Paul Loya is a professor of mathematics at Binghamton University.