Mathematical Principles of the Internet, Volume 1
Mathematical Principles of the Internet, Volume 1

Author: Nirdosh Bhatnagar

Publisher: CRC Press

Published: 2018-11-20

Total Pages: 1022

ISBN-13: 1351379151

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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Mathematical Principles of the Internet
Mathematical Principles of the Internet

Author: Nirdosh Bhatnagar

Publisher: Chapman & Hall/CRC

Published: 2018-12-13

Total Pages: 1768

ISBN-13: 9781138505285

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The purpose of these books is to provide mathematical principles of Internet engineering. They do not aim to provide all of the mathematical foundations upon which the Internet is based. Rather, they cover a partial panorama and key principles. The book is divided into two parts. Volume 1 explores Internet engineering. The supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes. An effort has been made to provide justification and informal proofs as much as possible. Each chapter also begins with a portrait and a brief account of the work of a prominent mathematician/scientist/engineer--

Mathematical Principles of the Internet, Volume 2
Mathematical Principles of the Internet, Volume 2

Author: Nirdosh Bhatnagar

Publisher: CRC Press

Published: 2018-11-21

Total Pages: 694

ISBN-13: 1351379127

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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Mathematical Principles of the Internet, Two Volume Set
Mathematical Principles of the Internet, Two Volume Set

Author: Nirdosh Bhatnagar

Publisher: CRC Press

Published: 2019-03-18

Total Pages: 1768

ISBN-13: 1351379216

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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Introduction to Wavelet Transforms
Introduction to Wavelet Transforms

Author: Nirdosh Bhatnagar

Publisher: CRC Press

Published: 2020-02-18

Total Pages: 268

ISBN-13: 1000768694

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The textbook, Introduction to Wavelet Transforms provides basics of wavelet transforms in a self-contained manner. Applications of wavelet transform theory permeate our daily lives. Therefore it is imperative to have a strong foundation for this subject. Features No prior knowledge of the subject is assumed. Sufficient mathematical background is provided to complete the discussion of different topics. Different topics have been properly segmented for easy learning. This makes the textbook pedagogical and unique. Notation is generally introduced in the definitions. Relatively easy consequences of the definitions are listed as observations, and important results are stated as theorems. Examples are provided for clarity and to enhance reader's understanding of the subject. Each chapter also has a problem section. A majority of the problems are provided with sufficient hints. The textbook can be used either in an upper-level undergraduate or first-year graduate class in electrical engineering, or computer science, or applied mathematics. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject. About the Author: Nirdosh Bhatnagar works in both academia and industry in Silicon Valley, California. He is also the author of a comprehensive two-volume work: Mathematical Principles of the Internet, published by the CRC Press in the year 2019. Nirdosh earned M.S. in Operations Research, and M.S. and Ph.D. in electrical engineering, all from Stanford University, Stanford, California. .

The Principles of Mathematics
The Principles of Mathematics

Author: Bertrand Russell

Publisher: W. W. Norton & Company

Published: 1996

Total Pages: 580

ISBN-13: 9780393314045

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Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.

Mathematical Principles of Optical Fiber Communication
Mathematical Principles of Optical Fiber Communication

Author: J. K. Shaw

Publisher: SIAM

Published: 2004-05-01

Total Pages: 103

ISBN-13: 0898715563

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This book is intended to support and promote interdisciplinary research in optical fiber communications by providing essential background in both the physical and mathematical principles of the discipline. It is written to be as independent as possible while taking the reader to the frontiers of research on fiber optics communications.

Mathematical and Algorithmic Foundations of the Internet
Mathematical and Algorithmic Foundations of the Internet

Author: Fabrizio Luccio

Publisher: CRC Press

Published: 2011-07-06

Total Pages: 224

ISBN-13: 1439831386

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To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating their universality by presenting ideas and examples from various fields, including literature, history, and art. Progressing from fundamental concepts to more specific topics and applications, the text covers computational complexity and randomness, networks and graphs, parallel and distributed computing, and search engines. While the mathematical treatment is rigorous, it is presented at a level that can be grasped by readers with an elementary mathematical background. The authors also present a lighter side to this complex subject by illustrating how many of the mathematical concepts have counterparts in everyday life. The book provides in-depth coverage of the mathematical prerequisites and assembles a complete presentation of how computer networks function. It is a useful resource for anyone interested in the inner functioning, design, and organization of the Internet.

Performance Models and Risk Management in Communications Systems
Performance Models and Risk Management in Communications Systems

Author: Nalân Gülpınar

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 262

ISBN-13: 1441905340

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This volume covers recent developments in the design, operation, and management of mobile telecommunication and computer systems. Uncertainty regarding loading and system parameters leads to challenging optimization and robustness issues. Stochastic modeling combined with optimization theory ensures the optimum end-to-end performance of telecommunication or computer network systems. In view of the diverse design options possible, supporting models have many adjustable parameters and choosing the best set for a particular performance objective is delicate and time-consuming. An optimization based approach determines the optimal possible allocation for these parameters. Researchers and graduate students working at the interface of telecommunications and operations research will benefit from this book. Due to the practical approach, this book will also serve as a reference tool for scientists and engineers in telecommunication and computer networks who depend upon optimization.