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Amazing and Aesthetic Aspects of Analysis de Paul Loya

Amazing and Aesthetic Aspects of Analysis

Autor Paul Loya
en Limba Engleză Hardback – 28 mai 2018
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.
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Specificații

ISBN-13: 9781493967933
ISBN-10: 1493967932
Pagini: 558
Ilustrații: XV, 722 p. 122 illus.
Dimensiuni: 155 x 235 x 48 mm
Greutate: 1.29 kg
Ediția:1st ed. 2017
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States

Cuprins

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​.

Recenzii

   

Notă biografică

Paul Loya is a professor of mathematics at Binghamton University.

Textul de pe ultima copertă

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.

Caracteristici

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