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.
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