Amazing And Aesthetic Aspects Of Analysis - Loya Paul | Libro Springer 07/2019 - HOEPLI.it


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loya paul - amazing and aesthetic aspects of analysis

Amazing and Aesthetic Aspects of Analysis




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 07/2019
Edizione: Softcover reprint of the original 1st ed. 2017





Sommario

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?.




Trama

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 e-N and e-d 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.




Autore

Paul Loya is a professor of mathematics at Binghamton University.







Altre Informazioni

ISBN:

9781493992454

Condizione: Nuovo
Dimensioni: 235 x 155 mm Ø 1116 gr
Formato: Brossura
Illustration Notes:122 Illustrations, black and white
Pagine Arabe: 722
Pagine Romane: xv






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