The Real Numbers - An Introduction to Set Theory and Analysis (Hardcover, 2013 ed.)

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory-uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis-the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schroeder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Undergraduate Texts in Mathematics
Release date:	October 2013
First published:	2014
Authors:	John Stillwell
Dimensions:	235 x 155 x 21mm (L x W x T)
Format:	Hardcover
Pages:	244
Edition:	2013 ed.
ISBN-13:	978-3-319-01576-7
Categories:	Books > Science & Mathematics > Mathematics > History of mathematics Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
LSN:	3-319-01576-1
Barcode:	9783319015767

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!