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City Campus 
515 LOYA

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 Description
 xv, 722 pages : illustrations ; 24 cm
 Notes
 Contents: Preface  Some of the most beautiful formulas 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 IIII  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.Includes bibliographical references and index.Summary: 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 wellchosen 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 εN and εδ 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.