About this book
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.
real analysis fundamental theorems of continuous functions infinite sequences of real numbers infinite series mathematical induction cardinality
- Book Title Amazing and Aesthetic Aspects of Analysis
- DOI https://doi.org/10.1007/978-1-4939-6795-7
- Copyright Information Paul Loya 2017
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-1-4939-6793-3
- Softcover ISBN 978-1-4939-9245-4
- eBook ISBN 978-1-4939-6795-7
- Edition Number 1
- Number of Pages XV, 722
- Number of Illustrations 122 b/w illustrations, 0 illustrations in colour
Sequences, Series, Summability
- Buy this book on publisher's site