Items related to Basic Real Analysis and Advanced Real Analysis Set...
Synopsis
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.
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From the Back Cover
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) 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 of Basic Real Analysis:
* Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations
* Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces
* The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments
* The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems
Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its 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, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician.
Review
"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
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