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.

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.

Comparing Logarithms With Different Bases

Logarithms are not hard to work with when only one base is involved (as in most real-life problems); but they can be challenging when each log has a different base. Here, we’ll look at a few problems in which we have to compare logarithms with different bases, showing various strategies.

Is Zero Positive or Negative? Even or Odd?

Last week we looked at some basics about zero; now let’s look at whether zero is positive or negative, and then at the topic of the recent comment that triggered this series: whether zero is even or odd.