Real Analysis and Infinity - Hassan Sedaghat

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Real Analysis and Infinity

By: Hassan Sedaghat

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Hardcover | 31 March 2022

At a Glance

Hardcover
576 Pages

Dimensions(cm)
24 x 16.4 x 3.2

Hardcover

$240.99

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Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions.

Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge.

Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.

Industry Reviews

Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. * MathSciNet *
This is a thorough introduction to the subject for undergraduates. There are very few prerequisites (less than in most similar textbooks) because topics such as infinity, countable and uncountable sets, and even the principle of mathematical induction are discussed in an early chapter. [...] The main advantage this book offers is its reader-friendly style. * Miklos Bona, University of Florida, Department of Mathematics *
Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. * zb Math Open *

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