Fundamentals Of Mathematical Analysis Paul Sally Pdf
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Fundamentals of Mathematical Analysis
Adel N. Boules
Abstract
Fundamentals of Mathematical Analysis is a beginning graduate textbook on real and functional analysis, with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Instructors can choose material from this part as their students' background warrants. Chapter 4 is the spine of the book and is essential for an effective reading of the rest of the book. It is an extensive study of metric spaces, including the core topics of completeness, c ... More
Fundamentals of Mathematical Analysis is a beginning graduate textbook on real and functional analysis, with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Instructors can choose material from this part as their students' background warrants. Chapter 4 is the spine of the book and is essential for an effective reading of the rest of the book. It is an extensive study of metric spaces, including the core topics of completeness, compactness, and function spaces, with a good number of applications. The remaining chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. The entire book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology, real analysis, or functional analysis. The book is designed as an accessible classical introduction to the subject, aims to achieve excellent breadth and depth, and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.
Keywords: number field, set theory, vector space, metric space, topology, Banach space, Hilbert space, measure theory, Lebesgue measure, integration theory
Bibliographic Information
| Print publication date: 2021 | Print ISBN-13: 9780198868781 |
| Published to Oxford Scholarship Online: May 2021 | DOI:10.1093/oso/9780198868781.001.0001 |
Authors
Affiliations are at time of print publication.
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Fundamentals Of Mathematical Analysis Paul Sally Pdf
Source: https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198868781.001.0001/oso-9780198868781
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