This manual provides comprehensive information for the Introduction to Abstract Analysis, a text developed from lectures delivered at NASA's Lewis Research Center. Authored by Marvin E. Goldstein and Burt M. Rosenbaum, this concise volume is designed for scientists and engineers with backgrounds in applied mathematics, offering essential background for understanding the literature of pure mathematics. It covers fundamental concepts such as elementary set theory, real numbers, vector and metric spaces, functions, infinite collections of sets, and limits of sequences, progressing to topics like continuity, function algebras, Cauchy completeness, infinite series, and sequences of functions. The book emphasizes the relationship between convergence and continuity within linear spaces, providing detailed proofs and examples to illustrate its foundational role in advanced mathematical subjects.
The purpose of this manual is to serve as a detailed guide to the concepts presented in "Introduction to Abstract Analysis." It aims to equip readers with the necessary understanding of abstract mathematical principles, facilitating their comprehension of more complex mathematical literature. The content is structured to build from basic set concepts to advanced topics in analysis, including metric spaces and function spaces. By offering clear explanations, proofs, and illustrative examples, this manual supports both self-study and academic learning, ensuring readers can effectively grasp and apply the principles of abstract analysis.
Developed from lectures delivered at NASA's Lewis Research Center, this concise text introduces scientists and engineers with backgrounds in applied mathematics to the concepts of abstract analysis. Rather than preparing readers for research in the field, this volume offers background necessary for reading the literature of pure mathematics.
Starting with elementary set concepts, the treatment explores real numbers, vector and metric spaces, functions and relations, infinite collections of sets, and limits of sequences. Additional topics include continuity and function algebras, Cauchy completeness of metric space, infinite series, and sequences of functions and function spaces. The relation between convergence and continuity and algebraic operations is discussed in the abstract setting of linear spaces in order to acquaint readers with these important concepts in a fairly simple way. Detailed, easy-to-follow proofs and examples illustrate how the material relates to and serves as a foundation for more advanced subjects.
Author: Goldstein, Marvin E.
Author: Rosenbaum, Burt M.
Publisher: Dover Publications
Illustration: N
Language: ENG
Title: Introduction to Abstract Analysis
Pages: 00256 (Encrypted EPUB)
On Sale: 2014-10-27
SKU-13/ISBN: 9780486789460
Category: Mathematics : Complex Analysis
Category: Mathematics : Calculus
Developed from lectures delivered at NASA's Lewis Research Center, this concise text introduces scientists and engineers with backgrounds in applied mathematics to the concepts of abstract analysis. Rather than preparing readers for research in the field, this volume offers background necessary for reading the literature of pure mathematics.
Starting with elementary set concepts, the treatment explores real numbers, vector and metric spaces, functions and relations, infinite collections of sets, and limits of sequences. Additional topics include continuity and function algebras, Cauchy completeness of metric space, infinite series, and sequences of functions and function spaces. The relation between convergence and continuity and algebraic operations is discussed in the abstract setting of linear spaces in order to acquaint readers with these important concepts in a fairly simple way. Detailed, easy-to-follow proofs and examples illustrate how the material relates to and serves as a foundation for more advanced subjects.
Author: Goldstein, Marvin E.
Author: Rosenbaum, Burt M.
Publisher: Dover Publications
Illustration: N
Language: ENG
Title: Introduction to Abstract Analysis
Pages: 00256 (Encrypted EPUB)
On Sale: 2014-10-27
SKU-13/ISBN: 9780486789460
Category: Mathematics : Complex Analysis
Category: Mathematics : Calculus
