It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.
Last week’s question led to a number of previous questions, which would have made it too long. Here we’ll look at the last couple references we gave, dealing with percentages of a negative base. This time, the problems will be mostly about money.
Continuing to look at past questions that didn’t make it into the blog, I find a question about percentage change in temperature, which nicely ties together a couple older topics that have long been on my list to cover. Let’s do that now.
Looking back at interesting questions I had to skip over when there were too many to choose, I found this interesting discussion of a functional equation.
A recent question dealt with how to write the general solution to a trigonometric equation. I want to combine that with an older question that will set the stage for the issue. This topic was touched on in Trigonometric Equations: An Overview.
We have looked at how we add, subtract, and multiply decimals. Now we’ll conclude with division: what we do, why we do it, and how we don’t really need to do it that way.
We’ve looked at how to add or subtract decimals. Now let’s move on to multiplication; we’ll look at three answers to the same sort of question.
Recently a teacher (Hi, Edite!) asked for help teaching how to divide decimals; in particular, she wanted to be able to provide a deeper understanding of the process, giving a good reason for what we do. Here I want to start a long-delayed series on operations with decimals, doing exactly this for all four basic …
Here is a short problem with several levels of difficulty. The problem itself is poorly designed, as we’ll see, but still provides several useful lessons, dealing with measurement, rounding, and ratios.
Last time, we saw how Newton’s method works. Here, we’ll look at a question about why it might not work, which will lead to a deep examination of how iterative methods work in general, from which we will discover why Newton’s method is as good as it is. I have to say, as I read …
When Newton’s Method Fails – and Why It’s So Good When It Doesn’t! Read More »