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Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features:
The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds
The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems
Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.
Summary
Basic Real Analysis
and
Advanced Real Analysis
systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features:
* The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds
* The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems
Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.
Additional text
"Basic Real Analysis and Advanced Real Analysis are two companion volumes of a comprehensive treatment unifying numerous branches of classical and functional analysis that can, with more or less assurance, be named as Real Analysis... Summing I can repeat that this volume is useful and interesting for all who deal with Analysis and its applications. I suppose, any mathematical library must have a copy of this book and can recommend it for students and lecturers."
---Zentrablatt MATH
Report
"Basic Real Analysis and Advanced Real Analysis are two companion volumes of a comprehensive treatment unifying numerous branches of classical and functional analysis that can, with more or less assurance, be named as Real Analysis... Summing I can repeat that this volume is useful and interesting for all who deal with Analysis and its applications. I suppose, any mathematical library must have a copy of this book and can recommend it for students and lecturers."
---Zentrablatt MATH
