Re: [FRIAM] Arthur Benjamin's formula for changing math education | Video on TED.com

> While much of the conversation below is steeped in issues I only  
> peripherally understand, from a pedagogical perspective I am in  
> complete agreement with Benjamin. A basic understanding of  
> probability and statistics is more likely to be achieved by  
> students, and would be more useful in most of their lives than a  
> basic understanding of calculus. Calculus is a big stumbling block  
> even for many students who enjoyed the math before that. I'm not  
> sure how the high school curriculum would change to accommodate the  
> new agenda, but I'd be really interested in finding out.
>
> Eric
>
> On Mon, Jun 29, 2009 11:19 PM, Owen Densmore <owen@...>  
> wrote:
> Hi joe.
>
> > However, I don't understand your comment that math notation is the
> > roman
> > numerals of our times. Which branch of math do you have in mind?
> > Certainly
> > not calculus, where, as you know, we use Leibniz's elegant notation.
>
> The core problem is the clash between two cultures: not the humanities
> vs the sciences, but that between mathematics and computing.  Or more
> precisely, between mathematics and algorithms.
>
> This is a large topic: it includes the lack of good mathematical
> languages (like APL of old, and J today)
>    http://www.jsoftware.com/
>    http://www.jsoftware.com/jwiki/Guides/Getting%20Started
> ..which bridge the gap between symbolic computing and MN. It also
> refers to the impossibility of parsing mathematics .. it is ill-
> defined as a language.  I.e. AB may mean A * B or the single variable
> named AB.
>
> It extends to the "Asymptotic Assumption" made by many mathematicians
>
> when a discrete problem is more easily solved by converting to
> continuous. (Reminds one of ABM vs Math modeling)  Knuth has a good
> discussion on this in his book Concrete Mathematics (CON=Continuous,
> Crete=Discrete).  Basically he makes the case that, although the leap
> is reasonable at some point, it generally is taken too quickly.
>
> So Roman Numerals == notational roadblock.  MN is not only is
> impossible to parse (and apply semantics to), it does not include any
>
> notion of "scripting" .. i.e. pseudo-code.
>
> > I also don't follow your comment about discrete versus continuous.
> > Among theoretical computer scientists, people who want to understand
> > the power of the computer and questions such as P vs NP study  
> discrete
> > problems whereas people like me who want to solve problems
> > coming from, say, physics or computational finance think about
> > solving continuous problems such as path integration.
>
> See above on Asymptotic Assumption and MN vs scripting.  Certainly
> computing, intrinsically discrete, provides wonderful approximations
> to continuous problems.
>
> Interestingly enough, the Sage system:
>    http://www.sagemath.org/
> .. was originated by mathematicians who *required* open source so that
> their theorems could be solved knowing the system on which they were
> built.  Sage is the first system I know of that has variable
> declarations of Ring, Field, and so on.  What would happen if Euclid
> were propriatorey and only the results, not proofs were public
> knowledge?
>
> Computer use by mathematicians remind me of Statistics use by social
> scientists.  Often the techniques are used without understanding the
> domain within which they are valid.  If nothing else, the power law
> distribution made many of us run back to see if our assumptions were
> reasonable.  Economics has fallen prey to this, the Black–Scholes
> model apparently assumed a Gaussian where a fatter tail was needed.
>
> This rant is a long one, but the summary is simple enough: Mathematics
> and Computing/Algorithms need to be reconciled.  Modern MN needs
> (minor) changes to be at least machine readable.  Computing languages
>
> for mathematics need to bridge the gap between pseudo-code and
> symbolics.  APL/J are close.
>
> How about a beer or glass of wine over this fascinating topic!
>
>      -- Owen
>
>
> On Jun 29, 2009, at 8:19 PM, Joseph Traub wrote:
>
> > Owen,
> >
> > I find nothing to argue with in Benjamin's talk. He says that  
> students
> > studying economics, science, engineering, or math should learn
> > calculus
> > but that it may not be needed by other students who should study
> > probability and statistics.
> >
> > However, I don't understand your comment that math notation is the
> > roman
> > numerals of our times. Which branch of math do you have in mind?
> > Certainly
> > not calculus, where, as you know, we use Leibniz's elegant notation.
> >
> > I also don't follow your comment about discrete versus continuous.
> > Among theoretical computer scientists, people who want to understand
> > the power of the computer and questions such as P vs NP study  
> discrete
> > problems whereas people like me who want to solve problems
> > coming from, say, physics or computational finance think about
> > solving continuous problems such as path integration.
> >
> > Best, Joe
> > <>
> >
> > Joseph F. Traub,   Edwin Howard Armstrong Professor of Computer
> > Science
> >                   and External Professor, Santa Fe Institute
> >
> > traub@...          http://www.cs.columbia.edu/~traub
> >
> > Phone: (212) 939-7013    Messages: (212) 939-7000
> Fax: (212)
> > 666-0140
> >
> > Columbia University
> > Computer Science Department
> > 1214 Amsterdam Avenue, MC0401
> > New York, NY 10027
> > USA
> >
> > Administrative Assistant: Sophie Majewski
> > sophie@... (212)939-7023
> >
> >
> > **************************************************************
> >
> > From: Owen Densmore <owen@...>
> > Date: June 29, 2009 12:07:14 PM MDT
> > To: The Friday Morning Applied Complexity Coffee Group
> <friam@...
> > >,
> > General topics & issues <discuss@...>
> > Subject: [FRIAM] Arthur Benjamin's formula for changing math
> > education |
> > Video on TED.com
> > Reply-To: The Friday Morning Applied Complexity Coffee Group
> > <friam@...>
> >
> > This is kinda cool and less than 3 minutes long!
> >
> http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.h
> > tml
> >
> > The thesis is a different spin on my claim that modern Math Notation
> > (MN) is
> > the roman numerals of our times.  Arthur Benjamin clearly explains
> > that  statistics and probability should be the "pinnacle" of our
> > basic math
> > education, not calculus.  His reasoning includes the discrete vs
> > continuous
> > argument that resonates with my MN vs Algorithm (or MN vs script)
> > concern,
> > which I'd love to see resolved in a parsable reworking of MN.
> >
> >    -- Owen
> >
> >
> > ============================================================
> > FRIAM Applied Complexity Group listserv
> > Meets Fridays 9a-11:30 at cafe at St. John's College
> > lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> Eric Charles
>
> Professional Student and
> Assistant Professor of Psychology
> Penn State University
> Altoona, PA 16601
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org