Wednesday, December 29, 2004

The new math syllabus (3)

So, let's look at what's disappeared from the new math curriculum:

1. Differential equations. This is expected, and reasonable, since AFAIK no university curriculum assumes knowledge of applied maths and this has to be taught again anyway. (Except that I remember when I took a course in solid-state physics in year 1, students were supposed to solve PDEs when they didn't even know what an ODE is...)

2. Complex numbers. This is widely considered to be a difficult topic and is often given up altogther, but should we really just let students go away without knowing that a square root can be taken off from -1? So they know pi, e, but not i... and hence will not know e^{i pi} = ??

3. Harder coordinate geometry including conic sections (parabola, ellipse and hyperbola) and 3-D lines and planes.

4. Numerical methods. Even the "method of bisection" in maths seem disappeared. The stuff about Newton's method etc. get removed reasonably, I think. But strangely enough they teach trapezoidal rule.

5. The majority of the rest of Pure Maths. This includes, for a few examples,
i. logic (which I complained here before)
ii. arithmetic-geometric inequality and Cauchy-Schwarz inequality
iii. limits, covergence of sequences, L'Hospital's rule, Taylor expansion, etc.

The deletion of the majority of pure maths is inevitable, but still I'm not quite happy with this. The most important thing is not about a particular topic not being covered, but that students do not get a chance to see what mathematics really is, without the exposure to the complexity of "pure" maths.

I like pure maths.

No comments: