Mathematical Theory of Communication Theory

This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars.

This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research.

This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars.

This book is dedicated to new mathematical instruments assigned for logical modeling of the memory of digital devices. The case in point is logic-dynamical operation named venjunction and venjunctive function as well as sequention and sequentional function. Venjunction and sequention operate within the framework of sequential logic. In a form of the corresponding equations, they organically fit analytical expressions of Boolean algebra.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption.

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics. It includes exercises and examples at the end of each section.