In our bridging course (and indeed in Maths 1M and Maths 1A and several other courses) there is a section on differentiating logarithmic functions. One of the classic questions that we ask in such a section is to differentiate the log of some horrifying function, with the intention that the students use the log laws […]
I had a long chat with one of the students the other day about rotation matrices. They had come up in the Engineering Physics course called Dynamics as a way of finding the components of vectors relative to rotated axes. He had some notes scrawled on a piece of paper from one of my MLC […]
Once upon a time, I lectured Maths 1A calculus, and when I got to teaching hyperbolic trig functions I put a great deal of effort into making sure they were well-connected to other ideas the students knew. So I listed the properties of ordinary trig functions and alongside I listed the matching properties of hyperbolic […]
Students make a lot of mistakes when doing their maths, but sometimes they will make two mistakes in such a way that their final answer is still correct. This happened last week with one student quite spectacularly, because his doubly wrong method of doing a particular problem always produces the correct answer.
Let me explain: the […]
Students in Maths 1M are learning the cross product at the moment. This is a way to multiply two vectors in 3D space — let’s call them v1 and v2 — to produce a new vector, which is called v1 × v2. The length of this new vector is related to the lengths of the two […]
As I said recently, quadrics hold a special place in my heart and I get excited every time the topic comes around in Maths 1B. Quadrics have so many cool things you can say about them, and are such a great opportunity to talk about the deep connection between algebra and geometry. I personally could […]
There is a particularly annoying puzzle that goes something like this:
“A rooster sits on the apex of a barn roof. The roof pitches at an angle of 43 degrees above the horizontal and is made of wood painted red. On the northern side of the roof, there is a large tree which casts a shadow […]
If someone asked you what your favourite 3D shape was, what would you say? A cube? A sphere? A dodecahedron?
Well, my favourite 3D shape is the frustrated cone. A frustrated cone is a cone with the pointy bit cut off (some people call it a “conical frustum” or a “truncated cone”, but “frustrated cone” sounds […]
Last week a student visited the Drop-In Centre to talk about the different sizes of infinity. His lecturer had been talking about the sizes of sets and had made an off-hand comment that there were different sizes of infinite sets, and he wanted to know what the hell that meant.
So I explained it. It’s not […]
The number pi is very cool. Many people say that pi is cool because of all the unexpected places it appears. In fact, they don’t just say it’s cool, they even go so far as to say that there is some sort of mystical significance in the fact that it appears all over the place.