Introduction to Abstract Analysis (Dover Books on Mathematics)

Book Details

• Author: Marvin Goldstein

• Brand: Dover

• Binding: Paperback

• Number of Pages: 248

• Release Date: 21st January 2015

• ISBN: 9780486789460

• Package Dimensions: 9.1 x 6.1 x 0.6 inches

• Languages: English

About The Book
Developed from lectures delivered at NASA's Lewis Research Center, this concise and insightful text by Marvin Goldstein introduces scientists and engineers with a background in applied mathematics to the fundamental concepts of abstract analysis. Rather than preparing readers for research in the field, this book offers essential background knowledge necessary for understanding the literature of pure mathematics.

The text begins with elementary set theory, gradually moving into key topics such as real numbers, vector and metric spaces, functions and relations, infinite sets, and limits of sequences. Additional sections cover the concepts of continuity and function algebras, Cauchy completeness of metric spaces, infinite series, and sequences of functions and function spaces. The relationship between convergence, continuity, and algebraic operations is discussed within the abstract framework of linear spaces, offering readers a simpler understanding of these crucial mathematical concepts.

This edition, first published by NASA in 1969, features detailed and easy-to-follow proofs and examples that not only clarify these complex topics but also lay the foundation for more advanced mathematical studies. It remains a valuable resource for anyone eager to expand their knowledge of abstract analysis and its applications in mathematics and engineering.

About the Author
Marvin E. Goldstein, a former scientist at NASA's Lewis Research Center, authored this text while working at NASA in 1969. He served as the Chief Scientist at NASA's Glenn Research Center from 1980 to 2004 and was a faculty member at Case Western Reserve University and MIT. Over his career, Goldstein published more than 120 scientific and mathematical papers.

Burt M. Rosenbaum, who co-authored the book, worked in applied mathematics at NASA's Lewis Research Center from 1957 to 1973 and later taught at Cleveland State University.