Sinossi
Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes that have applications in many areas of mathematics, says Goldbring, and are typically presented to students in specialized courses such as logic, functional analysis, or geometric group theory. Here, however, he presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of them, then applies these techniques to a wide variety of topics. He covers ultrafilters and their applications, classical ultraproducts, metric ultraproducts and their applications, and advanced topics. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
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Ultrafilters Throughout Mathematics
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American Mathematical Society, 2022
ISBN 10: 1470469618
ISBN 13: 9781470469610
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Paperback. Condizione: new. Paperback. Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes which have applications to many areas of mathematics. Typically, this topic is presented to students in specialized courses such as logic, functional analysis, or geometric group theory. In this book, the basic facts about ultrafilters and ultraproducts are presented to readers with no prior knowledge of the subject and then these techniques are applied to a wide variety of topics. The first part of the book deals solely with ultrafilters and presents applications to voting theory, combinatorics, and topology, while also dealing also with foundational issues.The second part presents the classical ultraproduct construction and provides applications to algebra, number theory, and nonstandard analysis. The third part discusses a metric generalization of the ultraproduct construction and gives example applications to geometric group theory and functional analysis. The final section returns to more advanced topics of a more foundational nature.The book should be of interest to undergraduates, graduate students, and researchers from all areas of mathematics interested in learning how ultrafilters and ultraproducts can be applied to their specialty. Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781470469610
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Ultrafilters Throughout Mathematics
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Ultrafilters Throughout Mathematics
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Paperback. Condizione: New. Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes which have applications to many areas of mathematics. Typically, this topic is presented to students in specialized courses such as logic, functional analysis, or geometric group theory. In this book, the basic facts about ultrafilters and ultraproducts are presented to readers with no prior knowledge of the subject and then these techniques are applied to a wide variety of topics. The first part of the book deals solely with ultrafilters and presents applications to voting theory, combinatorics, and topology, while also dealing also with foundational issues.The second part presents the classical ultraproduct construction and provides applications to algebra, number theory, and nonstandard analysis. The third part discusses a metric generalization of the ultraproduct construction and gives example applications to geometric group theory and functional analysis. The final section returns to more advanced topics of a more foundational nature.The book should be of interest to undergraduates, graduate students, and researchers from all areas of mathematics interested in learning how ultrafilters and ultraproducts can be applied to their specialty. Codice articolo LU-9781470469610
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Ultrafilters Throughout Mathematics (Graduate Studies in Mathematics)
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Ultrafilters Throughout Mathematics
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Condizione: New. Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters the second part presen. Codice articolo 595975516
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