[nSLUG] APL (was: On programming)

Jason Kenney jason at ohm.ath.cx
Wed Oct 22 16:47:22 ADT 2003


> This gives me a perfect opening for my standard complaint on math and
> math education.
> Calculus, at least at the first year level, is a requirement for
> graduation from just about any 'higher education' in
> science/engineering. The only modern reason for this that I can see that
> it continues to be taught is a 'test of streangth' / 'if I did it, you
> should do it'. And because of that, math education in high school is all
> pre-calculus; math earlier then that is all pre-pre....

I don't think first year calculus is a 'test of strength' by any means. 
More a test of competency. First calculus is pretty easy compared to most 
other maths you do in later university classes. So maybe not everyone gets 
an A+, but if you can't pass first-year calculus (they offer the first 
term extended over both semesters if you really have trouble) in a couple 
tries, then science probably isn't the discipline for you.

I don't know much about chemistry, but in other scientific domains:

Engineering and Physics: pretty much everything that moves or changes are 
described through differential equations. 
Without a sound background in calculus: ie, how to differentiate, how to 
integrate, you're out of luck. 

Biology and Pyschology: everything has to do with statistics. There is 
very little that has to do with probability here, it is all statistics. I 
make the distinction because stats are very heavily dependant on calculus 

> Through both my brother (who has a BSC/math from Dal), and my high
> school Calculus tutor (whos specific job I never knew but was a
> profesional 'real world' mathamatician (as opposed to an accademic); he
> worked on hard math problem for the US defence industry for a while), it
> is my understanding that in second and third year courses students are
> taught shortcuts and tricks that generaly make solving calculus problems
> easier. But of course your not allowed to use any of those tricks in
> first year courses.

In my experiences, you are always taught the underlying concepts. You can 
use whatever method you want to solve the problem, unless you are being 
one specific method. Sometimes the method being taught is the computer 
method - you're required to use a computer to solve the problem, even if 
you could do it quicker on paper.

> The reason that Im sure woluld be given by anyone in authority for this
> is that you need to learn how it works before you can learn the
> shortcuts. Which is petty bulshit for the other %99.9 of the people who
> wont be going on to upper level calculus education; even excluding CS,
> not all upper math is calculus. For the %99.9 of the people calculus
> should be taught because it is a convient way of sloving a certin set of
> problem types with paper and pencil.

The "learn how it works" before you use the "shortcuts" is so that you can 
learn which situations you can and cannot apply the "shortcuts" 
appropriately. There are almost always contraints on any methods that 
aren't completely comprehensive.

> Of course, in 2003, and for that matter in 1945, sufficently complex
> problems (and these days 'trivial' problems too...) arn't solved with
> paper and pencil, there solved with machines desigined for computation.
> Don't even try to give me the 'but calculus is infinitly percise'
> argument: we live in a finite universe, with measuring equiptement only
> capable of finite percision. If the 15th digit of pi is out, it will
> only matter to people who are building something on the scale of a Dyson
> Spehere.

It's not about precision, it's about understanding. Maple and my 
calculator will both do indefinite integrals for me no problem! But how do 
I know if they're right? And if the problem is too big for them, how would 
I break it down to smaller problems to help me? The computer is always 
used as a tool, but you have to understand what it's doing to use it 

> So what we have today is a math education system desigined in the 19th
> century; for when anyone doing sufficently hard math problem used
> calculus. It once made sence to educate university students with
> calculus; they might need it at some point. Comparativily, Discrete math
> isnt taught, typically, untill second year university, and then only to
> CS students.
> Its interesting to wonder what would happen if Jr and Sr High math
> wasent taught with the unstated goal of 'calculus in first year uni',
> but with 'programming in first year uni'.. I think, with the possible
> exception of recursion, all the concepts taught in firsr year university
> progamming courses could be grasped as easily by jr high students then
> whatever there getting now. Infinitly more usefull; obviously more
> usefull to the students; and therfor more engaging to them.

I think the "unstated goal" of Jr and Sr High math is closer to "teach 
them to do math well enough to work cash at McDonald's." Since the math 
system is even failing at that, I don't see how you can pretend it's trying to 
prepare students for higher level calculus.

Even assuming it is working, "Calculus in first year university" applies to 
more people then "programming in first year university". I don't see how 
programming is more useful than calculus. There's no need to have everyone 
working as a programmer. People who want to study plants can study plants. 
If they have problems they need computers to help them solve, they can 
hire programmers! 

Schools now are teaching programming of sorts, and other computer skills 
in school. At my old junior high, there was a drafting class, a 
woodworking class, a sewing class and a cooking class. Now *all* of that 
has been replaced by a class on using flash. I think that's horrible! 

I also doubt you'll be able to interest junior high students in 
programming anymore than you can interest them in simple geometry, algebra or 

> But my opinions are uninportant; Im not a member of the cult of
> university graduates.

I agree there is a cult of sorts, but it's not clear you have to be 
a member to succeed. It looks like the trade schools are a better a place to 
be if you want to make money at the moment. I know people I graduated with 
who are already licensed electricians, who have been working for a year, who 
are probably making more money than I will if I go into the workforce when I 


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