Amazing and Aesthetic Aspects of Analysis

• Main Author: Loya, Paul (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2017.
• Edition: 1st ed. 2017.
• Subjects: Sequences (Mathematics).; Functions of real variables.; Sequences, Series, Summability.; Real Functions.

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...

Table of Contents:

• 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 .