Wyniki wyszukiwania:

This text unifies the concepts of information, codes and cryptography as first studied by Shannon in his seminal papers on communication and secrecy systems. The first five chapters cover the fundamental ideas of information theory, compact encoding of messages and the theory of error-correcting codes. After a discussion of mathematical models of English, there is an introduction to the classical Shannon model of cryptography. This is followed by a brief survey of those aspects of computational complexity needed for an understanding of modern cryptographic methods and the recent advances in...

The aim of these notes is to link algorithmic problems arising in knot theory with statistical physics and classical combinatorics. Apart from the theory of computational complexity needed to deal with enumeration problems, introductions are given to several of the topics, such as combinatorial knot theory, randomized approximation models, percolation, and random cluster models.

Cryptography plays a crucial role in many aspects of today's world, from internet banking and ecommerce to email and web-based business processes. Understanding the principles on which it is based is an important topic that requires a knowledge of both computational complexity and a range of topics in pure mathematics. This book provides that knowledge, combining an informal style with strong proofs of the key results to provide an accessible introduction. It includes many examples and exercises, and is based on a highly successful course developed and taught over many years.

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.
A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text...