anomalousdecay
Premium Member
- Joined
- Jan 26, 2013
- Messages
- 5,766
- Gender
- Male
- HSC
- 2013
Well if learning it in HSC, it would be quite an incomplete topic without knowledge of vectors imo. I was referring to it being a step up from vectors if you were to learn them properly.matrices are actually taught at the equivalent of year 10 level in many countries, not to mention that some keen students here self-learn it, it is by no means too complex for the course
And by properly, I don't mean just finding REF or solving a system of linear equations, I mean as in being able to do matrix multiplication, knowing the basic laws about matrices, etc.
Proves my point.It's not too complex but for a course like 4U it doesn't really fit in well with the rest of the content imo.
A basic understanding of matrices also would be quite superficial and would leave many students questioning "why are we doing this?"
Its not until you hit some areas of engineering (possibly science too but not sure) that you start to see some real applications of using complex numbers.The problem with matrices is that you have to learn a term of methods (multiplication, Gaussian elimination, etc.) before you can start actually doing interesting stuff with them. Also, it's difficult to motivate them. Complex numbers can be used for awesome unrelated proofs and students still complain about their perceived lack of practical applications.
Any graph theory in a high school course would be 60% definitions and 30% algorithm memorisation. However, I agree that the ability to abstract problems into graph theoretical terms is one of the most useful devices in one's mathematical bag of tricks. No joke, I encountered a problem at work today involving popping elements off queues over a network, and the solution was to model each queue as a weighted path graph with common source and run Dijkstra's algorithm on it.
I hope statistical inference includes Bayes' theorem.