Month: December 2018

Why I Became a Math Doctor

While I was setting up The Math Doctors site a year ago, I ran across the following email I received in 1998 inviting people to become Math Doctors. It illustrates well the ethos of the team: In the fall of 1994 the Math Forum at Swarthmore College (then the Geometry Forum) started an email program …

Why I Became a Math Doctor Read More »

Finding the Range of a Tricky Rational Function

I previously wrote about finding the range of various kinds of functions. The examples there were relatively easy. A recent question raised the level of difficulty, bringing up some interesting issues.

Tangents Without Calculus

I always like solving advanced problems with basic methods. For example, many problems that we usually think of as “algebra problems” can be solved by creative thinking without algebra; and some “calculus problems” can be solved using only algebra or geometry. Using simple tools for a big job requires more thought than using “the right …

Tangents Without Calculus Read More »

A Bad System of Nonlinear Equations

(A new question of the week) Sometimes a problem that looks complicated turns out to have a simple answer. And sometimes that simple answer turns out to be too simple for its own good. Today’s problem is an example of this.

Division by Zero and the Derivative

(An archive question of the week) The indeterminate nature of 0/0, which we looked at last time, is an essential part of the derivative (in calculus): every derivative that exists is a limit of that form! So it is a good idea to think about how these ideas relate.

Zero Divided By Zero: Undefined and Indeterminate

Back in January, I discussed the issue of division by zero. There is a special case of that that causes even more trouble, in every field from arithmetic to calculus: zero divided by zero. I’ll look at several typical questions that we answered at different levels.