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.

### Wednesdays, 7:00 PM, MAT P-131.

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.

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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. 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 AMS Homepage. Join our email list. 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. This is appropriate because of the prevalence of numbers in modern society and the need to have a numerate population. In particular, we often need to negotiate percentages and it is here that public understanding frequently falters.

We begin with a few examples. See All Customer Reviews. Shop Textbooks. Add to Wishlist. USD Ship This Item — This item is available online through Marketplace sellers. Temporarily Out of Stock Online Please check back later for updated availability. Overview 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.

Read an Excerpt Chapter 1 Numbers Arithmetic is one of the first topics taught to elementary pupils. How to get drunk and rich at the same time The column Money angles: where else to invest? Consider a family that buys one bottle of wine each week. Fifty per cent more for fifty per cent less The Summer, issue of Adobe Magazine Volume 8, Number 5 , includes an advertisement for Apple Macintosh. In describing its Power Max, the company makes this statement. Photoshop processes, say objects in the time that it would take to process such objects on a PC.

But this is more correctly characterized as twice as fast. Whose real world? Samantha has a total of points so far in her algebra class. What is the lowest score she can earn on the point final to get a B in the class?

Comment by EBA: When I taught college courses, students frequently asked me to do this kind of calculation. For example, if you get a D on each of three tests, what must you make on the final to get a B for the course?

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## PELL'S EQUATION by BARBEAU EDWARD J.

Finally, I realized the question is frivolous and stopped doing these calculation. For example, if you get a D on each of three tests, what must you make on the final to get a B for the course? Finally, I realized the question is frivolous and stopped doing these calculation. If you get a D on three tests, you will get a D or F on the final.

## Mathematical Fallacies, Flaws, and Flimflam

Scores on a test are a random variable that regresses to the mean. Your mean at a certain time is a good prediction for a subsequent test. I believe that students usually do a little worse on the final than on previous tests. In this example, Samantha's current average is If she really wanted a B, she should have worked harder earlier on.

Comment by EBA? He did this kind of problem in mathematics class, but on the job nobody does it this way. They test the antifreeze in the car for the temperature at which it provides protection. Then they add enough antifreeze to get to the desired temperature. You can keep on adding salt, but you will not increase the volume, because the salt dissolves. While many people use some mathematics in their jobs, Dr.

Appelbaum feels that mathematics should nonetheless be taught primarily for its own sake. Applications are fine if they are simple and appealing; otherwise they should be left to an applied course.

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She sees the current emphasis on applications as a response to anti-intellectualism among students. When students ask what good the mathematics is, she suspects that the students are really saying that they cannot understand the subject and so hope that it is no good. She has often met people who are glad that they studied mathematics, or wish that they had studied more, but never anyone who said that they were sorry to have learned mathematics.

Show More. Table of Contents 1. Numbers; 2.

## Mathematical Fallacies, Flaws and Flimflam – Science Book a Day

Algebra and trigonometry; 3. Geometry; 4. Finite mathematics; 5.