Last time, we looked at the scalar, or dot, product of vectors, focusing on proving the equivalence of two ways to define it. This time, we’ll look at the vector, or cross, product in the same way. The distinction between dot and cross product reflects the symbol used, u · v vs. u × v, …
Having covered the basics of defining and adding vectors, multiplying by scalars and finding unit vectors, it’s time to look at multiplying vectors together. What makes this entirely unlike working with numbers is that there are two ways (in fact, more than two!) to multiply two vectors. We’ll look at one of those today, the …
(A new question of the week) Since we looked at a question about economics last week, let’s examine another, which is very different, relating the supply and demand curves to the concept of variation or proportion. We are not economists, so we can’t go deeply into that subject, but it makes us think about some …
(A new question of the week) As we approach a new year, I want to start cleaning up a backlog of recent questions, and start posting more typical interactions, rather than waiting for the most momentous. Many of these will therefore be relatively short! This one goes back to last July, but it connects to …
The concept of independent events can be both very simple and easily misunderstood. We’ll be looking at several explanations of the idea, starting with the basics and then digging into some deeper questions that are often overlooked.
(An archive question of the week) We’ve been looking at some issues involving frequency distributions and the classes used in them. Let’s look at a related concept with some similar issues, namely the cumulative distribution function (CDF), also called an ogive (more on that name at the end of the post!).
(An archive question of the week) While I’m showing some recent explanations of basic trigonometry techniques, this is a good time to look at an even more basic explanation of the essentials of the subject for a beginner.
(An archive question of the week) Recently we have had a number of series digging into multiple aspects of an idea like area or percentages. But I am always running into miscellaneous questions that can’t fit into such a series because of their length or uniqueness. I want to spend the summer focusing on random …
Having looked at two common questions in probability that are often challenged, let’s turn to the realm of numbers. Non-terminating decimals are inherently problematic, and one particular example causes difficulty for many, even after they fully accept the mathematics of it. Our FAQ page on this topic, at 0.9999… = 1, is very brief, and …
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.