1. I used to be both! My take: it depends extensively on what you intend for people to do with their math knowledge.
2. In fact, the worst blunder I've seen (i.e. UBC) was when the curriculum tried to split the difference between uniformity and tailoring.
3. The rub is this: the standard math curriculum in every country I've lived in mixes and matches a lot of different fields of math.
4. This mixing is not bad. It works if the intention is to expose students to lots of different aspects to see what they're interested in.
5. There might even be thematic unity: US calc 2 has integration techniques & series convergence, both of which rely on heuristic thinking.
6. The problem is, other than math geeks (hi), nobody really likes all of this. And then the question of what to do depends on application.
7. "Teach stats not algebra" works for applications to economics and business, e.g. to salaried workers looking at spreadsheets.
8. Economists also really like Lagrange multipliers for some reason... and insist on cramming it into math-for-econs classes.
9. The UBC disaster is, they crammed Lagrange multipliers and probability into an otherwise-standard calc 2 class w/o cutting anything.
10. The reason they didn't cut (say) series is that they wanted to make the various math streams (physics, biology, econs) interchangeable.
11. In contrast with the math that's useful for people poring over spreadsheets, today's curriculum works better for other professionals.
12. Engineers benefit from status quo: some algebra, some euclidean geometry and trig, some calculus, lots and lots of computational crap.
13. In comp sci, the value of analysis (like calculus) is lower, while that of algebra (number theory, linear algebra) is higher.
14. If I designed a curriculum for tech, I'd skip calc and stats and teach linear algebra, some number theory, and maybe abstract algebra.
15. In this math-for-CS curriculum I'd also emphasize proofs - the logic of proofs seems similar to what I deal with when I try coding.
16. (But then, the sort of number theory that's taught in high school and uni is already proof-heavy, and abstract algebra even more so.)
17. Limits are a week of calc 1, maybe two weeks if you want to explain why lim_{x \to \infty} x^n/a^x = 0.
18. There are 2 ways to make all of this work. First, dethrone engineering as the implicit application of math and teach something else.
19. Second, get comfortable with making the math curriculum less uniform. Offer stats and probability. Offer number theory. Offer calc.
20. Modular uni courses as in the US or Canada (or SG) are in theory good at this, but in practice they make people take calc first.
21. NUS has ways out of that prereq chain but it involves math classes that are offered at other departments, like CS or engineering.
22. UBC's splitting calc by stream is in theory good, too, but it wrecks the idea by cramming 1.5 semesters' material into calc-for-econs 2.
23. Ultimately, math is a tool. It's like writing. You can treat it like mind-numbing General Paper or freshman composition classes...
24. ...or instead you can let people choose more interesting options, giving a menu, just as you might do with writing-intensive courses.
25. People who want can take a stats class. Or number theory, or calc, or euclidean geometry, or w/e. Let a hundred flowers bloom. /end
