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Introduction to Probability Theory with Contemporary Applications

Lester L. Helms
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Patricia Humphrey
, on

This re-issue of an old text originally published by W. H. Freeman is suited to lower-level graduate students or advanced undergraduate students. As the title suggests, it is theoretical in nature, and to this reviewer, does not seem suited for a first course in probability. No measure theory is involved; student preparation is limited to Calculus II (power series, convergence and induction). I found it well-written and very readable. The historical context notes in the introduction to each chapter I found interesting.

As a text for probability theory course, it has all the standard topics, including nice treatments of discrete and continuous Markov processes. Each section has seven to 10 exercises (primarily proofs) for the student to attempt; however, answers/solutions to all are included, making it of limited use in a class setting. This reviewer is somewhat puzzled by the “contemporary applications” of the title — applications in the text are primarily classical (urns, flipping coins, defective items, etc) but some examples and exercises do mention such applications as cracking passwords, and some exercises are stated as requiring Mathematica or Maple to solve them.

The MAA Guides series has the intent of refreshing an individual’s knowledge of a topic (similar to that required for a student to pass a comprehensive exam). A book like this one would fit into that series very well.



Patricia Humphrey is an Associate Professor of Statistics in the Department of Mathematical Sciences at Georgia Southern University. She is a past Chair of the SIGMAA-StatEd for 2008 and is a member of the MAA-ASA Joint Committee on Statistics Education, and a member of the Dolciani Expositions Series Editorial Board.  At the Section level, she has been a member of Project NExT-SE, one of its organizers, and is Vice Chair for Programs for the Southeastern Section for 2010-2012. She is the author of numerous ancillary technology manuals for introductory statistics.


1. Classical Probability
2. Axioms of Probability
3. Random Variables
4. Expectation
5. Stochastic processes
6. Continous Random Variables
7. Expectation Revisited
8. Continous Parameter Markov Processes
Solutions to Exercises
Standard Normal Distribution Function