# proposed extenstions to content MathML

From: <RobertM@dessci.com>
Date: Fri, 6 May 2005 14:15:53 -0500
Message-Id: <200505061915.j46JFrs04686@intuition.geomtech.com>

```

Hello All.

Kyle Siegrist, who created the Virtual Laboratories in Probability and
Statistics web site <http://www.math.uah.edu/stat/>, recently
suggested the following extensions to me, as good candidates for a
MathML 3 update.  Prof. Siegrist writes:

"Here is what I would love to see added to Content MathML:

1. Binomial coefficient

2. Permutation coefficient:  n(n -1)...(n - k + 1), usually
rendered P(n, k) or nPk or (n)k.

3. A probability operator with an optional "given" construction
(for conditional probability).  Typical rendering would be
P(A, B, ...) (without conditioning) or  P(A, B, ... | C, D, ...)
(with conditioning).

4. An expected value operator with an optional "given" construction
(for conditional expected value).  Typical rendering would be E(A,
B, ...) (without conditioning) or  E(A, B, ... | C, D, ...) (with
conditioning).

5. General union, to form the union of Ai over i = a to b, or the
union of Ai where i is in an index set I.  This would work just
like the sum construction, with a bound variable and with lower and
upper limits, or with a bound variable and with a condition.

6. Exactly like 5, but with intersection.

If I had these extensions, I think that I could do just about
everything that I wanted without going over to Presentation MathML.

Items 3 and 4 (with the "given" construction) are really important in
probability, statistics, and stochastic processes; conditional
probability and expected value are central notions.  Ordinary
probability and expected value can be done with the usual function
("apply") construction, but there is no way to do the conditioning
without adding Presentation MathML as a kludge.

I am really surprised that items 5 and 6 are not already present;
they seem very natural and necessary for lots of areas of math."

Anyone want to second these proposals?  Or take issue with them?

--Robert

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Dr. Robert Miner                                RobertM@dessci.com
W3C Math Interest Group co-chair                      651-223-2883
Design Science, Inc.   "How Science Communicates"   www.dessci.com
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Received on Friday, 6 May 2005 19:16:01 GMT

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