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Probability and statistics without calculus?  Well, yes, many problems are small and finite.  And the basic concepts can certainly be illustrated by examples that are small and finite.  

But:  

Bell curve, Poisson distribution, probability density, all calculus.  

Every time you replace an intractible situation involving very large (but finite) numbers with a continuous model you are doing calculus.  

The Fates are kind.

by Gaianne on Fri May 25th, 2007 at 10:22:07 AM EST
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You don't need calculus to teach what you need to teach for good citizenship. Proving the finite cases and presenting the infinite cases where necessary should suffice.
by Colman (colman at eurotrib.com) on Fri May 25th, 2007 at 10:32:24 AM EST
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With Nelson's Radically Elementary Probability Theory, everything including stochastic processes is countable, even finite. But that's a facetious answer.

A better answer is volume 1 of Feller's "Introduction to Probability Theory and its Applications", which uses entirely elementary techniques.

Epistemologically, all statistics is finite, and infinites and continuity only appear in the limit (via a process of closure useful because completeness simplifies many proofs, but not essential as sophisticated but straighforward proofs by closure can be turned into involved proofs using elementary techniques). Also, stochastic processes are equivalent iff all their finite-dimensional distributions are equivalent, so even there things can be a lot smaller than they are made to be by professional mathematicians.

My actual point is that the fixation with Calculus as the gateway to higher mathematics is misplaced. There is nothing more useless that what Americans call "AP Calculus" or "Freshman Calculus", especially for people in the humanities and social sciences (who, often, take a single term of Calculus as their only exposure to 'higher math'). I would much rather teach people "finite mathematics".

Bush is a symptom, not the disease.

by Migeru (migeru at eurotrib dot com) on Fri May 25th, 2007 at 10:34:46 AM EST
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Radically Elementary Probability Theory

Which I must finish reading. When I find it again ...

by Colman (colman at eurotrib.com) on Fri May 25th, 2007 at 12:34:17 PM EST
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Every time you replace an intractible situation involving very large (but finite) numbers with a continuous model you are doing calculus.

Yes, but you don't have to teach calculus on its own first, you can just do it, in context.

Bush is a symptom, not the disease.

by Migeru (migeru at eurotrib dot com) on Fri May 25th, 2007 at 11:12:22 AM EST
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I think it might be more useful to teach people to recognise when their leaders, the media, and the ad companies are all talking crap and trying to eat their brains.

Some elementary stats might be useful ('the increase in cancer risk is a shocking 100% greater! - from p = 0.0000001 to p =  0.0000002...') but perhaps best left as an optional extra for those who want the advanced course.  

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri May 25th, 2007 at 11:44:21 AM EST
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I think it might be more useful to teach people to recognise when their leaders, the media, and the ad companies are all talking crap and trying to eat their brains.

Which part of math is that? The point of the subthread was that, if you're going to teach people "advanced math", it should be prob/stat.

Although making "How to lie with statistics" compulsory reading in secondary school wouldn't be all that bad an idea.

Bush is a symptom, not the disease.

by Migeru (migeru at eurotrib dot com) on Fri May 25th, 2007 at 11:48:17 AM EST
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It's not math. It's education.
by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri May 25th, 2007 at 03:13:30 PM EST
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