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Spectrum
More Fallacies, Flaws & Flimflam (Spectrum) by Edward Barbeau
Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau's previous book, Mathematical Fallacies, Flaws and Flimflam, material is drawn from a variety of sources including the work of students, textbooks, the media, and even professional mathematicians. The errors presented here serve both to entertain, and to emphasise the need to subject even the most obvious assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. Each item is carefully analysed and the source of the error is exposed. All students and teachers of mathematics, from school to university level, will find this book both enlightening and entertaining.
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First published October 1, 2013
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December 19, 2014
This is the second of two books on errors that have been made in mathematics. Some of them were made by students where they made major errors that somehow led to the correct answers (referred to as howlers) and others are errors in proofs that are at times deep and difficult to spot even though the conclusion is obviously false.
The howlers are generally for entertainment purposes while the others can and should be used to provide deeper insight into the structure of a theorem as well as the extent of the conclusion. Some of the examples point out common flaws in proof techniques such as induction, my favorites are in the first chapter that contains mathematical flaws, some of which have appeared in mass media. One of the examples is a questioning of the effectiveness of proposition 8 in California that there be heavier sentences for repeat offenders. The issue examined is whether the change in sentencing had the desired deterrent effect.
The problems are split into the categories:
*) Arithmetic
*) School algebra
*) Geometry
*) Limits, sequences and series
*) Differential calculus
*) Integral calculus
*) Combinatorics
*) Probability and statistics
*) Complex analysis
*) Linear and modern algebra
*) Miscellaneous
It is a fact of human existence that we learn more from our mistakes than we do from our successes. When applied to mathematics this principle allows us to gain insight from the mistakes of others. Some of these examples are amusing but most are educational, worthy of being used in math classes to explain potential pitfalls.
Published in Journal of Recreational Mathematics, reprinted with permission
The howlers are generally for entertainment purposes while the others can and should be used to provide deeper insight into the structure of a theorem as well as the extent of the conclusion. Some of the examples point out common flaws in proof techniques such as induction, my favorites are in the first chapter that contains mathematical flaws, some of which have appeared in mass media. One of the examples is a questioning of the effectiveness of proposition 8 in California that there be heavier sentences for repeat offenders. The issue examined is whether the change in sentencing had the desired deterrent effect.
The problems are split into the categories:
*) Arithmetic
*) School algebra
*) Geometry
*) Limits, sequences and series
*) Differential calculus
*) Integral calculus
*) Combinatorics
*) Probability and statistics
*) Complex analysis
*) Linear and modern algebra
*) Miscellaneous
It is a fact of human existence that we learn more from our mistakes than we do from our successes. When applied to mathematics this principle allows us to gain insight from the mistakes of others. Some of these examples are amusing but most are educational, worthy of being used in math classes to explain potential pitfalls.
Published in Journal of Recreational Mathematics, reprinted with permission
Displaying 1 of 1 review
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