Elementary Number Theory Group Theory And Ramanujan Graphs
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Elementary Number Theory Group Theory And Ramanujan Graphs
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Author : Giuliana Davidoff
language : en
Publisher: Cambridge University Press
Release Date : 2003-01-27
Elementary Number Theory Group Theory And Ramanujan Graphs written by Giuliana Davidoff and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-27 with Mathematics categories.
This text is a self-contained study of expander graphs, specifically, their explicit construction. Expander graphs are highly connected but sparse, and while being of interest within combinatorics and graph theory, they can also be applied to computer science and engineering. Only a knowledge of elementary algebra, analysis and combinatorics is required because the authors provide the necessary background from graph theory, number theory, group theory and representation theory. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.
Elementary Number Theory Group Theory And Ramanujan Graphs
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Author : GIULIANA P. DAVIDOFF
language : en
Publisher:
Release Date : 2002
Elementary Number Theory Group Theory And Ramanujan Graphs written by GIULIANA P. DAVIDOFF and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Random Graphs Geometry And Asymptotic Structure
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Author : Michael Krivelevich
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-25
Random Graphs Geometry And Asymptotic Structure written by Michael Krivelevich and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-25 with Mathematics categories.
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
A First Course In Graph Theory And Combinatorics
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Author : Sebastian M. Cioabă
language : en
Publisher: Springer Nature
Release Date : 2022-07-07
A First Course In Graph Theory And Combinatorics written by Sebastian M. Cioabă and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Graph Theory And Additive Combinatorics
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Author : Yufei Zhao
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Graph Theory And Additive Combinatorics written by Yufei Zhao and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Mathematics categories.
An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
Lectures On Profinite Topics In Group Theory
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Author : Benjamin Klopsch
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-10
Lectures On Profinite Topics In Group Theory written by Benjamin Klopsch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Mathematics categories.
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
Adventures In Graph Theory
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Author : W. David Joyner
language : en
Publisher: Birkhäuser
Release Date : 2017-12-28
Adventures In Graph Theory written by W. David Joyner and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-28 with Mathematics categories.
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.
Random Walks And Geometry
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Author : Vadim Kaimanovich
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Random Walks And Geometry written by Vadim Kaimanovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.
Cryptographic Boolean Functions And Applications
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Author : Thomas W. Cusick
language : en
Publisher: Academic Press
Release Date : 2009-03-04
Cryptographic Boolean Functions And Applications written by Thomas W. Cusick and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-04 with Mathematics categories.
Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic
Probability On Discrete Structures
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Author : Harry Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Probability On Discrete Structures written by Harry Kesten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.