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Foundations of Real and Abstract Analysis (Hardcover, 1998 ed.)
Loot Price: R2,092
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Foundations of Real and Abstract Analysis (Hardcover, 1998 ed.)
Series: Graduate Texts in Mathematics, 174
Expected to ship within 12 - 17 working days
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The core chapters of this volume provide a complete course on
metric, normed, and Hilbert spaces, and include many results and
exercises seldom found in texts on analysis at this level. The
author covers an unusually wide range of material in a clear and
concise format including elementary real analysis, Lebesgue
integration on R, and an introduction to functional analysis. This
makes a versatile text also suited for courses on real analysis,
metric spaces, abstract analysis, and modern analysis. The book
begins with a comprehensive chapter providing a fast-paced course
on real analysis, and is followed by an introduction to the
Lebesgue integral. This provides a reference for later chapters as
well as an introduction for students with only the typical sequence
of undergraduate calculus courses as prerequisites. Other features
include a chapter introducing functional analysis, the Hahn-Banach
theorem and duality, separation theorems, the Baire Category
Theorem, the Open Mapping Theorem and their consequences, and
unusual applications such as weak solutions of the Dirichlet
Problem and Pareto optimality in Mathematical Economics. Of special
interest is the unique collection of nearly 750 exercises, many
with guidelines for their solutions. The exercises include
applications and extensions of the main propositions and theorems,
results that fill in gaps in proofs or that prepare for proofs
later in the book, pointers to new branches of the subject, and
difficult challenges for the very best students.
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