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3044 results in Probability theory and stochastic processes

Page 46 of 153

  • Preface

  • Henk Tijms, Vrije Universiteit, Amsterdam
  • Book:
    Probability: A Lively Introduction
    Published online:
    06 August 2018
    Print publication:
    06 October 2017, pp ix-x

  • Summary

    Why do so many students find probability difficult? Even the most mathematically competent often find probability a subject that is difficult to use and understand. The difficulty stems from the fact that most problems in probability, even ones that are easy to understand, cannot be solved by using cookbook recipes as is sometimes the case in other areas of mathematics. Instead, each new problem often requires imagination and creative thinking. That is why probability is difficult, but also why it is fun and engaging. Probability is a fascinating subject and I hope, in this book, to share my enthusiasm for the subject.

    Probability is best taught to beginning students by using motivating examples and problems, and a solution approach that gives the students confidence to solve problems on their own. The examples and problems should be relevant, clear, and instructive. This book is not written in a theorem–proof style, but proofs flow with the subsequent text and no mathematics is introduced without specific examples and applications to motivate the theory. It distinguishes itself from other introductory probability texts by its emphasis on why probability is so relevant and how to apply it. Every attempt has been made to create a student-friendly book and to help students understand what they are learning, not just to learn it.

    This textbook is designed for a first course in probability at an undergraduate level or first-year graduate level. It covers all of the standard material for such courses, but it also contains many topics that are usually not found in introductory probability books – such as stochastic simulation. The emphasis throughout the book is on probability, but attention is also given to statistics. In particular, Bayesian inference is discussed at length and illustrated with several illuminating examples. The book can be used in a variety of disciplines, ranging from applied mathematics and statistics to computer science, operations research, and engineering, and is suitable not only for introductory courses, but also for self-study. The prerequisite knowledge is a basic course in calculus.

    Good problems are an essential part of each textbook. The field of probability is well known for being a subject that can best be acquired by the process of learning-by-doing. Much care has been taken to present problems that will enhance the student's understanding of probability.

Page 46 of 153