Cover image for Mathematical fallacies, flaws and flimflam
Title:
Mathematical fallacies, flaws and flimflam
Author:
Barbeau, Edward, 1938-
Personal Author:
Publication Information:
Washington, D.C. : Mathematical Association of America ; Cambridge : Cambridge University Press, [2000]

©2000
Physical Description:
xvii, 167 pages : illustrations ; 23 cm
Language:
English
ISBN:
9780883855294
Format :
Book

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Q172.5.E77 B37 2000 Adult Non-Fiction Central Closed Stacks
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Summary

Summary

Through hard experience, mathematicians have learned to subject even the most evident assertions to rigorous scrutiny, as intuition and facile reasoning can often lead them astray. However, the impossibility and impracticality of completely watertight arguments make it possible for errors to slip by the most watchful eye. They are often subtle and difficult of detection. When found, they can teach us a lot and can present a real challenge to straighten out. Presenting students with faulty arguments to troubleshoot can be an effective way of helping them critically understand material, and it is for this reason that I began to compile fallacies and publish them first in the Notes of the Canadian Mathematical Society and later in the College Mathematics Journal in the Fallacies, Flaws and Flimflam section. I hoped to challenge and amuse readers as well as to provide them with material suitable for teaching and student assignments. This book collects the items from the first eleven years of publishing in the CMJ. One source of such errors is the work of students. Occasionally, a text book will weigh in with a specious result or solution. Nonprofessional sources, such as newspapers, are responsible for a goodly number of mishaps, particularly in arithmetic (especially percentages) and probability; their use in classrooms may help students become critical readers and listeners of the media. Quite a few items come from professional mathematicians. The reader will find in this book some items that are not erroneous but seem to be. These need a fuller analysis to clarify the situation. All the items are presented for your entertainment and use. The mathematical topics covered include algebra, trigonometry, geometry, probability, calculus, linear algebra, and modern algebra.


Reviews 1

Choice Review

Barbeau (Univ. of Toronto) offers an unusual and interesting book. If one believes that one can learn from other's mistakes, then this is the mathematical source book to turn to. It contains more than 200 errors in mathematical understanding, calculation, or logic. Textbooks, newspaper articles, journal articles, and submissions from individuals provided the original sources for these fallacies and mistakes. Some have been published in a regular column in College Mathematics Journal. The intent was to challenge and amuse readers, as well as to provide them with material suitable for teaching and student assignments. The topics range from arithmetic all the way to advanced undergraduate mathematics. They are amusing and often require real thought and understanding to find the flaws. This is a book in a series published by the Mathematical Association of America, directed toward a broad range of readers. The origin of each fallacy is noted, and there is a short bibliography pointing the reader to similar books. The book is suitable for general readers interested in mathematics and potentially valuable for undergraduates and their teachers. Recommended for acquisition by all academic libraries. All levels. D. Z. Spicer; University of Maryland


Table of Contents

1 Numbers
2 Algebra and trigonometry
3 Geometry
4 Finite mathematics
5 Probability
6 Calculus: limits and derivatives
7 Calculus: integration and differential equations
8 Calculus: multivariate and applications
9 Linear and modern algebra
10 Advanced undergraduate mathematics
11 Parting shots