This new undergraduate text offers a concise introduction to probability and random processes. Exercises and problems range from simple to difficult, and the overall treatment, though elementary, includes rigorous mathematical arguments. Chapters contain core material for a beginning course in probability, a treatment of joint distributions leading to accounts of moment-generating functions, the law of large numbers and the central limit theorem, and basic random processes.

Probability: An Introduction

Science & Math

Grimmett, Geoffrey

Welsh, Dominic

History & Philosophy

Oxford University Press

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 public key cryptography, password systems and authentication techniques. Because the aim of the text is to make this exciting branch of modern applied mathematics available to readers with a variety of interests and backgrounds, the mathematical prerequisites have been kept to an absolute minimum. Problems and solutions are included.

Codes and Cryptography

Computers & Technology

Computer Science

Mathematics

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 is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

Complexity and Cryptography: An Introduction

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.

Politics & Social Sciences

Talbot, John

Social Sciences

Cambridge University Press

See the best price to sell, buy, or rent books by Welsh, Dominic. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Welsh, Dominic