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.
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