Amazing and Aesthetic Aspects of Analysis

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 studen...

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Bibliographic Details
Main Author: Loya, Paul
Format: eBook
Language:English
Published: New York, NY Springer New York 2017, 2017
Edition:1st ed. 2017
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Description
Summary: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
Physical Description:XV, 722 p. 122 illus online resource
ISBN:9781493967957