Back to Basics

The last time I taught basic physics and mathematics stuff was when I was asked to teach Diploma students in Bintulu campus, right after I reported duty in Serdang campus. At the time (in 1991), internet access is mainly for emails and there were no mobile or smart phones then; to call home (mum), I used a payphone. Earlier I did teach Diploma students in the main campus (1981-ish) for lab classes, and even designed an experiment or two based on my undergraduate experience. When I was back in the main campus, the department gave me quantum mechanics to teach and did that for many years, and later advanced theoretical subjects. So my experience with teaching basic physics/mathematics was rather limited.

Right now, in Xiamen University Malaysia (XMUM), I'm back to teaching basics, namely Applied Calculus (for business and finance students) and Linear Algebra (for data science and engineering students). While these are essentially basic and are taught to first year students of respective programmes, there are 'new' things that I get to learn while teaching these subjects. For instance, the vertical line test for functions (disallowing many-valued functions) and the horizontal line test for one-to-one functions, which I thought was quite neat thing to be taught for beginning calculus students. Note however these are meant for single-variable functions; unsure if they can be generalized neatly for many-variable functions. Right now, I have started to teach integration (after differentiation) to the students. In a way, it seems integration is harder to teach and was wondering if there is a more natural way to think about integration besides the usual 'area under the curve' approach. Searching the internet, I was surprised to see a school of thought that prefers integration to be taught first before differentiation. In fact, the classic book by Apostol, does it that way (see its table of contents below). Historically, it seems that integration comes earlier than differentiation - see the book "Calculus Reordered" by Bressoud. Will read both books with interest.

Some may very well thought it was strange that I do not know this but it is just one never really bothered to think about these questions until one has to teach them.

For Linear Algebra, I have finished teaching determinants and was asked to skipped the material on areas and volumes. I guess, the idea is that they will pick these up later since the textbook didn't introduce interior and exterior products of vectors to start with. I told the class, associated to these products are geometrical constructs like Kronecker delta tensor and the alternating tensor (which I do introduce in other courses before). There was a question in my head about how to introduce Laplace cofactor expansion of determinant beyond its computational us. I do remember Prof. Herbert Green taught us quite early in his course and I went to look for his notes (see below).

I found more gems as I looked through his notes; I certainly did not catch the depth of the ideas when I learned them. I have already mentioned in an earlier post how Prof. Green has influenced the way I think. For a write-up showing how original Prof. Green, I found this article. I'm thankful that I was blessed for being taught by him.