Probability: A Lively Introduction

Probability has applications in many areas of modern science, not to mention in our daily life. Its importance as a mathematical discipline cannot be overrated, and it is a fascinating and surprising topic in its own right. This engaging textbook with its easy-to-follow writing style provides a comprehensive yet concise introduction to the subject. It covers all of the standard material for undergraduate and first-year-graduate-level courses as well as many topics that are usually not found in standard texts, such as Bayesian inference, Markov chain Monte Carlo simulation, and Chernoff bounds.

Table of Contents:
1. Foundations of probability theory; 2. Conditional probability; 3. Discrete random variables; 4. Continuous random variables; 5. Jointly distributed random variables; 6. Multivariate normal distribution; 7. Conditioning by random variables; 8. Generating functions; 9. Additional topics in probability; 10. Discrete-time Markov chains; 11. Continuous-time Markov chains.

About the Author :
Henk Tijms is emeritus professor at the Vrije University, Amsterdam. He is the author of several textbooks and numerous papers on applied probability and stochastic optimization. In 2008, Henk Tijms received the prestigious INFORMS Expository Writing Award for his publications and books. His activities also include the popularization of probability to high school students and the general public; he also regularly contributed to the Numberplay blog of the New York Times with probability puzzles.

Review :
'This is an attractive textbook for an introductory probability course at the upper undergraduate level. It covers not only the standard material for such a course (discrete probability, the axioms of probability, conditional probability, discrete and continuous random variables, jointly distributed random variables, limit theorems, Markov chains, etc.) but also some topics that might be considered more unusual, such as Kelly betting, renewal-reward stochastic processes, and the law of iterated logarithms. Topics from statistics (confidence intervals, Student-t distribution, Baysian inference, etc.) also appear. The book is quite well-written, nicely motivated, demonstrates considerable enthusiasm for the material, and gives lots of examples of the usefulness of probability. Mark Hunacek, MAA Reviews As with its predecessor, Probability: A Lively Introduction has an engaging and sympathetic tone which will be welcomed by those wrestling with this endlessly fascinating but tricky subject. Robert A. J. Matthews, Significance 'This text serves as an excellent introduction to probability theory. Tijms has achieved the difficult feat of writing a book that is useful as both a textbook and a reference resource. As he wisely points out in the introduction, a key step in attracting students' attention to this field is providing clear, natural examples. In this book, every chapter is full of such examples. Besides covering the topics expected in an entry-level book, the author also covers multivariate normal distributions and the chi-square test, generating functions, and Markov chains (both the discrete time and the continuous time cases). Many students will appreciate the four appendixes at the end of the book. The first three contain the necessary background in enumerative combinatorics, set theory, and calculus, and make the book even more widely accessible in doing so. The fourth appendix introduces a more advanced concept, Monte Carlo simulations. There are plenty of excellent exercises in each chapter, half of which come with detailed solutions (not just numerical answers).' M. Bona, Choice 'In this book, Henk Tijms aims at sharing his passion and enthusiasm for the fascinating world of probability with his readers. I can only say that he convincingly succeeded to do so!' Ivo Adan, European Journal of Operational Research 'A most interesting aspect of this text is its exposition. The text relies heavily on a narrative approach: graphics and lengthy displayed calculations are infrequent. Happily, the author writes well, with an obvious enthusiasm (the 'liveliness' of the title is correct) and a gift for choosing appropriate and revealing examples. Often these examples provide jumping-off points for further discussion or exploration. The material is also presented accurately and at an appropriate level of rigor. One oddity is that theorems are not presented in the classic boxed-off fashion followed by a clearly marked proof. Instead, theorems (which the author calls 'rules') are stated and proofs or sketches of proofs are given within the narrative. The text also features an abundance of interesting exercises, ranging from elementary to challenging. Full solutions to the odd-numbered problems appear at the end of the book, and the publisher offers a password-protected site with solutions to all the exercises in the text.' Thomas Polaski, Mathematical Reviews 'This is indeed a lively introduction to probability theory. The book is addressed basically to undergraduate students and their teachers. All traditional notions, results, ideas and techniques are included and discussed in detail. This is done smoothly and gradually in a master style.' Jordan M. Stoyanov, ZB Math Reviews