eBook ISBN:  9781614445180 
Product Code:  SPEC/25.E 
List Price:  $30.00 
MAA Member Price:  $22.50 
AMS Member Price:  $22.50 
eBook ISBN:  9781614445180 
Product Code:  SPEC/25.E 
List Price:  $30.00 
MAA Member Price:  $22.50 
AMS Member Price:  $22.50 

Book DetailsSpectrumVolume: 25; 2000; 167 pp
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.

Table of Contents

Chapters

1. Numbers

2. Algebra and Trignometry

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


Reviews

For several years now, Ed Barbeau has been editing a regular column in the CMJ called 'Fallacies, Flaws, and Flimflam.' The column collects interesting examples of mistakes, fallacies, and other mathematical howlers. Some come from students, some from publications, others from contributors who have invented their own swindles and fallacies. This book (which acquired a 'Mathematical' in the title to accomodate readers unfamiliar with the column) is a kind of 'Best of FFF.' It collects over 150 articles from the column, organized by topic into sections ranging from 'Numbers' to 'Advanced Undergraduate Mathematics,' with some 'Parting Shots' thrown in for good measure. There are some wild errors and some quite subtle ones; some things we recognize from many past student productions, others that are quite original...Collected together, they make a book of the sort one reads compulsively from cover to cover. I suspect it can be very useful in our teaching, since some of these creative mistakes would make great discussion starters...'Mathematical Fallacies, Flaws, and Flimflam' is definitely worth your time.
Fernando Q. Gouvéa, MAA Reviews


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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.

Chapters

1. Numbers

2. Algebra and Trignometry

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

For several years now, Ed Barbeau has been editing a regular column in the CMJ called 'Fallacies, Flaws, and Flimflam.' The column collects interesting examples of mistakes, fallacies, and other mathematical howlers. Some come from students, some from publications, others from contributors who have invented their own swindles and fallacies. This book (which acquired a 'Mathematical' in the title to accomodate readers unfamiliar with the column) is a kind of 'Best of FFF.' It collects over 150 articles from the column, organized by topic into sections ranging from 'Numbers' to 'Advanced Undergraduate Mathematics,' with some 'Parting Shots' thrown in for good measure. There are some wild errors and some quite subtle ones; some things we recognize from many past student productions, others that are quite original...Collected together, they make a book of the sort one reads compulsively from cover to cover. I suspect it can be very useful in our teaching, since some of these creative mistakes would make great discussion starters...'Mathematical Fallacies, Flaws, and Flimflam' is definitely worth your time.
Fernando Q. Gouvéa, MAA Reviews