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Probability through Algebra

Bowen Kerins, Benjamin Sinwell, Al Cuoco, and Glenn Stevens
American Mathematical Society and IAS/Park City Mathematics Institute.
Publication Date: 
Number of Pages: 
IAS/PCMI-The Teacher Program Series
Problem Book
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Charles Ashbacher
, on

I tutor a boy about to enter the eighth grade and the topics are math and science. While most of our work is within the curriculum we do some free-form work. One of the main topics in the free-form area is in probability and expectation. He follows college and professional sports so he is really interested in problems related to those fields. For example, in basketball one can shoot a two or a three-point basket. He was really interested when I showed him how to compute the expectation of points per shot based on the percentage of success when a player shoots from two versus the three-point area.

This book describes what is called a “course” in the algebraic properties of expected value and variance. The quotes are used in the book because the activities consist of problem sets that step the reader through many different manifestations of expectation and variance in many different games. Mathematical or otherwise. The problems are very illustrative and understandable and solutions are included.

The target audience is precollege teachers, although college teachers of courses such as discrete mathematics and basic statistics will also find material of great value. Children and adults are often into sports and so the types of problems in this book will give them a real world perspective on how math is used that they will understand and enjoy. Pre-existing knowledge of the specific sport is not necessary, a few seconds of background instruction and the problem will be understandable. 

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Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.