Exercises |

**Orthogonal trajectories**

In the spring of 1998, a student solving a problem about orthogonal trajectories wrote the following sentence.

Since the two equations are negative inverses of each other, then the slopes are perpendicular.

If you were this student's instructor in a class on differential equations, what advice would you give the student? (You may assume that the student is a native speaker of English who has above average mathematical ability.)

**Modify me**

Criticize and rewrite the following sentences.

There are many times in science and mathematics when a list of data is found by a researcher which, when plotted, looks almost like a line.

[From a student essay about the method of least squares approximation, fall 1996.]First described in the 1940s, scientists were amazed at how the juvenile cottonmouth uses its tail.

[From a display case at Easterwood Airport, College Station, May 1999.]

**Sign of our times**

Comment on this sign seen at the entrance to a campus building in the fall of 1997:

**Daylight Saving Time**

Find and correct the errors in the following sentence, which appeared on the front page of the Bryan / College Station Eagle on Saturday, October 25, 1997.

**Truth in advertising**

On December 30, 1997, Karen J.
Cravens posted a report to the
newsgroup `rec.humor.funny`

of receiving a promotional
diskette from an online service advertising "immediate
response-less waiting." Why is this funny?

Hint: there is
a difference between a hyphen and a dash.

In December 2000, an advertisement for telephone services stated, "Service not available in all areas." Why is this funny?

**Normal families**

Find in the library two books on the subject of normal families: one book about mathematics and the other book about psychotherapy. Photocopy the first page of the first chapter of each book. Which page is easier for an outsider to the field to understand, and why?

**Are symbols better than words?**

For each of the following six properties, describe in words
the class of real-valued functions *f* on the real line
satisfying the property. (For example, your description might
use words like "continuous", "bounded", and "constant".)

- For every positive
*eps*there exists a positive*delta*such that*|f(x)-f(0)| < eps*whenever*|x| < delta*. - For some positive
*eps*there exists a positive*delta*such that*|f(x)-f(0)| < eps*whenever*|x| < delta*. - For every positive
*eps*and for every positive*delta*we have*|f(x)-f(0)| < eps*whenever*|x| < delta*. - For some positive
*eps*and for every positive*delta*we have*|f(x)-f(0)| < eps*whenever*|x| < delta*. - For some positive
*delta*and for every positive*eps*we have*|f(x)-f(0)| < eps*whenever*|x| < delta*. - For every positive
*delta*there exists a positive*eps*such that*|f(x)-f(0)| < eps*whenever*|x| < delta*.

**Kids: don't try this at home**

Here are two examples of egregious violations of principles of good mathematical exposition. These examples were created by a professional stunt man, so you should not try to emulate them.

List all the things you can think of that are wrong with these two paragraphs.

Rewrite the examples intelligently and with good style.

The Math 696 course pages were last modified April 5, 2005.

These pages are copyright © 1995-2005 by Harold P. Boas. All rights reserved.

Exercises |