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The Resource Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson
Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson
Resource Information
The item Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary

 Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse problem, one starts with a sumset hA and attempts to describe the structure of the underlying set A. In recent years, there has been remarkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an ndimensional arithmetic progression
 Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and selfcontained account of this subject. In particular, it contains complete proofs of results from exterior algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis
 Language
 eng
 Extent
 xiv, 293 pages
 Contents

 1. Simple inverse theorems
 2. Sums of congruence classes
 3. Sums of distinct congruence classes
 4. Kneser's theorem for groups
 5. Sums of vectors in Euclidean space
 6. Geometry of numbers
 7. Plunnecke's inequality
 8. Freiman's theorem
 9. Applications of Freiman's theorem
 Isbn
 9780387946559
 Label
 Additive number theory : inverse problems and the geometry of sumsets
 Title
 Additive number theory
 Title remainder
 inverse problems and the geometry of sumsets
 Statement of responsibility
 Melvyn B. Nathanson
 Language
 eng
 Summary

 Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse problem, one starts with a sumset hA and attempts to describe the structure of the underlying set A. In recent years, there has been remarkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an ndimensional arithmetic progression
 Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and selfcontained account of this subject. In particular, it contains complete proofs of results from exterior algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1944
 http://library.link/vocab/creatorName
 Nathanson, Melvyn B.
 Index
 index present
 LC call number
 QA241
 LC item number
 .N3468 1996
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/subjectName

 Number theory
 Nombres, Théorie des
 Number theory
 Getaltheorie
 Nombres, Théorie des
 Additive Zahlentheorie
 Label
 Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson
 Bibliography note
 Includes bibliographical references (p. [283]291) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1. Simple inverse theorems  2. Sums of congruence classes  3. Sums of distinct congruence classes  4. Kneser's theorem for groups  5. Sums of vectors in Euclidean space  6. Geometry of numbers  7. Plunnecke's inequality  8. Freiman's theorem  9. Applications of Freiman's theorem
 Dimensions
 25 cm.
 Extent
 xiv, 293 pages
 Isbn
 9780387946559
 Lccn
 96012929
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
 System control number

 (OCoLC)34471461
 (OCoLC)ocm34471461
 Label
 Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson
 Bibliography note
 Includes bibliographical references (p. [283]291) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1. Simple inverse theorems  2. Sums of congruence classes  3. Sums of distinct congruence classes  4. Kneser's theorem for groups  5. Sums of vectors in Euclidean space  6. Geometry of numbers  7. Plunnecke's inequality  8. Freiman's theorem  9. Applications of Freiman's theorem
 Dimensions
 25 cm.
 Extent
 xiv, 293 pages
 Isbn
 9780387946559
 Lccn
 96012929
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
 System control number

 (OCoLC)34471461
 (OCoLC)ocm34471461
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