Dave Peterson

(Doctor Peterson) A former software engineer with degrees in math, I found my experience as a Math Doctor starting in 1998 so stimulating that in 2004 I took a new job teaching math at a community college in order to help the same sorts of people face to face. I have three adult children, and live near Rochester, N.Y. I am the author and instigator of anything on the site that is not attributed to someone else.

… And The Oldest Has Red Hair

It’s been a while since we’ve done a puzzle, just for fun. Here we’ll look at two versions of a riddle, about finding children’s ages from a known product, a partially known sum, and a bizarre fact about the oldest. Then we’ll close with an interesting variation.

Monotonic Functions, Inequalities, and Optimization

Looking for a cluster of questions on similar topics, I found several from this year in which monotonic functions (functions that either always increase, or always decrease) provide shortcuts for various types of problems (optimization with or without calculus, and also algebraic inequalities). We’ll look at a few of these.

Inverse Trig Notation: What Do sin^-1 and arcsin Mean?

Since we’ve been looking at an example of ambiguity in notation, let’s look at a very different one. There is a lot to be confused by in inverse trigonometry! We’ll try to untangle the notations of \(\sin^{-1}\) and \(\arcsin\).

Implied Multiplication 2: Is There a Standard?

This is part 2 of a series of extracts from discussions we have had on whether multiplication implied by juxtaposition is to be done before division (which I call IMF, for Implied Multiplication First). Some people write to us claiming that there is one official correct answer. Are they right?

Anything to the Zero Power: Why 1?

We’ve been looking at oddities of zero. Because “nothing” behaves differently than “something”, operations with it can be surprising. Although students learn that \(x^0=1\) for any non-zero number x, they often wonder, why?? I’ve selected a few out of at least a dozen such questions in our archive.