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.

Label
Additive number theory : inverse problems and the geometry of sumsets
Title
Title remainder
inverse problems and the geometry of sumsets
Statement of responsibility
Melvyn B. Nathanson
Creator
Subject
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 n-dimensional arithmetic progression
• Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and self-contained 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
Member of
DLC
1944-
Nathanson, Melvyn B.
Index
index present
LC call number
QA241
LC item number
.N3468 1996
Literary form
non fiction
Nature of contents
bibliography
• Number theory
• Nombres, Théorie des
• Number theory
• Getaltheorie
• Nombres, Théorie des
Label
Additive number theory : inverse problems and the geometry of sumsets, Melvyn B. Nathanson
Instantiates
Publication
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
Publication
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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