Fundamentals of Mathematical Analysis
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Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
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Product details:
- Publisher OUP Oxford
- Date of Publication 9 March 2021
- ISBN 9780198868781
- Binding Hardback
- No. of pages480 pages
- Size 241x159x27 mm
- Weight 906 g
- Language English
- Illustrations 8 85
Categories
Short description:
Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology.
MoreLong description:
Fundamentals of Mathematical Analysis explores 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.
Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later 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. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and 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.
Table of Contents:
Preliminaries
Set Theory
Vector Spaces
The Metric Topology
Essentials of General Topology
Banach Spaces
Hilbert Spaces
Integration Theory
