Amazing and Aesthetic Aspects of Analysis (Undergraduate Texts in Mathematics)

Loya, Paul

ISBN 10: 1493967932 / ISBN 13: 9781493967933

Editore: Springer, 2018

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pp. 546. Codice articolo 26375096351

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Titolo: Amazing and Aesthetic Aspects of Analysis (...

Casa editrice: Springer

Data di pubblicazione: 2018

Legatura: Rilegato

Condizione: New

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Riassunto:

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.

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