Amazing and Aesthetic Aspects of Analysis

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Sprache: Englisch

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Beschreibung

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 ¿-N and ¿-¿ 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.

In studying this book, students will encounter:

Über den Autor

Paul Loya is a professor of mathematics at Binghamton University.

Zusammenfassung

¿¿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

Inhaltsverzeichnis

Preface.- Some of the most beautiful formulæ in the world.- Part 1. Some standard curriculum.- 1. Very naive set theory, functions, and proofs.- 2. Numbers, numbers, and more numbers.- 3. Infinite sequences of real and complex numbers.- 4. Limits, continuity, and elementary functions.- 5. Some of the most beautiful formulæ in the world I-III.- Part 2. Extracurricular activities.- 6. Advanced theory of infinite series.- 7. More on the infinite: Products and partial fractions.- 8. Infinite continued fractions.- Bibliography.- Index¿.

Details

Erscheinungsjahr:	2018
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xv 722 S. 122 s/w Illustr. 722 p. 122 illus.
ISBN-13:	9781493967933
ISBN-10:	1493967932
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Loya, Paul
Auflage:	1st ed. 2017
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Maße:	241 x 160 x 45 mm
Von/Mit:	Paul Loya
Erscheinungsdatum:	28.05.2018
Gewicht:	1,262 kg

Artikel-ID: 111055513