The Resource Elementary number theory, group theory, and Ramanujan graphs, Guiliana Davidoff, Peter Sarnak, Alain Valette

Elementary number theory, group theory, and Ramanujan graphs, Guiliana Davidoff, Peter Sarnak, Alain Valette

Label
Elementary number theory, group theory, and Ramanujan graphs
Title
Elementary number theory, group theory, and Ramanujan graphs
Statement of responsibility
Guiliana Davidoff, Peter Sarnak, Alain Valette
Creator
Contributor
Subject
Language
eng
Summary
This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background material from graph theory, number theory, group theory and representation theory. The text can therefore be used as a brief introduction to these subjects as well as an illustration of how such topics are synthesised in modern mathematics
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Davidoff, Giuliana P
Illustrations
illustrations
Index
index present
LC call number
QA166
LC item number
.D35 2003
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Sarnak, Peter
  • Valette, Alain
http://library.link/vocab/subjectName
  • Graph theory
  • Number theory
  • Group theory
  • Graph theory
  • Group theory
  • Number theory
  • Endliche Gruppe
  • Graphentheorie
  • Elementare Zahlentheorie
Label
Elementary number theory, group theory, and Ramanujan graphs, Guiliana Davidoff, Peter Sarnak, Alain Valette
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 138-141) 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
Ch. 1. Graph Theory -- 1.1. The Adjacency Matrix and Its Spectrum -- 1.2. Inequalities on the Spectral Gap -- 1.3. Asymptotic Behavior of Eigenvalues in Families of Expanders -- 1.4. Proof of the Asymptotic Behavior -- 1.5. Independence Number and Chromatic Number -- 1.6. Large Girth and Large Chromatic Number -- Ch. 2. Number Theory -- 2.1. Introduction -- 2.2. Sums of Two Squares -- 2.3. Quadratic Reciprocity -- 2.4. Sums of Four Squares -- 2.5. Quaternions -- 2.6. The Arithmetic of Integer Quaternions -- Ch. 3. PSL[subscript 2] (q) -- 3.1. Some Finite Groups -- 3.2. Simplicity -- 3.3. Structure of Subgroups -- 3.4. Representation Theory of Finite Groups -- 3.5. Degrees of Representations of PSL[subscript 2] (q) -- Ch. 4. The Graphs X[superscript p,q] -- 4.1. Cayley Graphs -- 4.2. Construction of X[superscript p,q] -- 4.3. Girth and Connectedness -- 4.4. Spectral Estimates -- App. 4: Regular Graphs with Large Girth
Dimensions
23 cm.
Extent
viii, 144 pages
Isbn
9780521531436
Lccn
2002074057
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)50253269
  • (OCoLC)ocm50253269
Label
Elementary number theory, group theory, and Ramanujan graphs, Guiliana Davidoff, Peter Sarnak, Alain Valette
Publication
Bibliography note
Includes bibliographical references (p. 138-141) 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
Ch. 1. Graph Theory -- 1.1. The Adjacency Matrix and Its Spectrum -- 1.2. Inequalities on the Spectral Gap -- 1.3. Asymptotic Behavior of Eigenvalues in Families of Expanders -- 1.4. Proof of the Asymptotic Behavior -- 1.5. Independence Number and Chromatic Number -- 1.6. Large Girth and Large Chromatic Number -- Ch. 2. Number Theory -- 2.1. Introduction -- 2.2. Sums of Two Squares -- 2.3. Quadratic Reciprocity -- 2.4. Sums of Four Squares -- 2.5. Quaternions -- 2.6. The Arithmetic of Integer Quaternions -- Ch. 3. PSL[subscript 2] (q) -- 3.1. Some Finite Groups -- 3.2. Simplicity -- 3.3. Structure of Subgroups -- 3.4. Representation Theory of Finite Groups -- 3.5. Degrees of Representations of PSL[subscript 2] (q) -- Ch. 4. The Graphs X[superscript p,q] -- 4.1. Cayley Graphs -- 4.2. Construction of X[superscript p,q] -- 4.3. Girth and Connectedness -- 4.4. Spectral Estimates -- App. 4: Regular Graphs with Large Girth
Dimensions
23 cm.
Extent
viii, 144 pages
Isbn
9780521531436
Lccn
2002074057
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)50253269
  • (OCoLC)ocm50253269

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