Publisher Description

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 featureis 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 withproblems (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 followingthree 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 indiscrete 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.

Author Biography

Geoffrey Grimmett is Professor of Mathematical Statistics at the University of Cambridge and Master of Downing College, Cambridge. His research interests lie in disordered physical systems, including percolation and related processes. He has written numerous research articles in probability theory and statistical mechanics, as well as three research books and two successful textbooks on probability and random processes at the undergraduate and postgraduate levels.Dominic Welsh is Professor Emeritus of Mathematics at the University of Oxford and Emeritus fellow of Merton College, Oxford. He held the John von Neumann Professorship at Bonn in 1990-91, and was appointed Professor of Mathematics at Oxford in 1993. His research interests include combinatorics and complexity theory, and he has written more than a hundred papers in these areas. He retired from Oxford University in 2005, and has since then held visiting positions in New Zealand and Barcelona.

Table of Contents

Part A BASIC PROBABILITY1: Events and probabilities2: Discrete random variables3: Multivariate discrete distributions and independence4: Probability generating functions5: Distribution functions and density functionsPART B FURTHER PROBABILITY6: Multivariate distributions and independence7: Moments, and moment generating functions8: The main limit theorems9: Branching processes10: Random walks11: Random processes in continuous time12: Markov chains

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A compact account of the basic features of probability and random processes

Long Description

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.

Feature

Directed at first and second year undergraduates
A concise introduction to probability
An honest approach to mathematical rigour
Careful choice of material, from probability to stochastic processes
Enhanced by exercises and problems

Details