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Foundations of Abstract Analysis (Hardcover, 2nd ed. 2013, Corr. 2nd printing 2014)
Loot Price: R3,435
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Foundations of Abstract Analysis (Hardcover, 2nd ed. 2013, Corr. 2nd printing 2014)
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Foundations of Abstract Analysis is the first of a two book series
offered as the second (expanded) edition to the previously
published text Real Analysis. It is written for a graduate-level
course on real analysis and presented in a self-contained way
suitable both for classroom use and for self-study. While this book
carries the rigor of advanced modern analysis texts, it elaborates
the material in much greater details and therefore fills a gap
between introductory level texts (with topics developed in
Euclidean spaces) and advanced level texts (exclusively dealing
with abstract spaces) making it accessible for a much wider
interested audience. To relieve the reader of the potential
overload of new words, definitions, and concepts, the book (in its
unique feature) provides lists of new terms at the end of each
section, in a chronological order. Difficult to understand abstract
notions are preceded by informal discussions and blueprints
followed by thorough details and supported by examples and figures.
To further reinforce the text, hints and solutions to almost a half
of more than 580 problems are provided at the end of the book,
still leaving ample exercises for assignments. This volume covers
topics in point-set topology and measure and integration.
Prerequisites include advanced calculus, linear algebra, complex
variables, and calculus based probability.
General
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