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

[Joseph Traub]

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: [phone]    Messages: [phone]    Fax: [phone]

Columbia University
Computer Science Department
1214 Amsterdam Avenue, MC0401
New York, NY 10027
USA

Administrative Assistant: Sophie Majewski
sophie@... [phone]


**************************************************************

  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
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Discuss mailing list
Discuss@...
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[backspaces]

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: [phone]    Messages: [phone]    Fax: (212)  
> 666-0140
>
> Columbia University
> Computer Science Department
> 1214 Amsterdam Avenue, MC0401
> New York, NY 10027
> USA
>
> Administrative Assistant: Sophie Majewski
> sophie@... [phone]
>
>
> **************************************************************
>
> 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

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Discuss mailing list
Discuss@...
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[ERIC P. CHARLES]

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: [phone]    Messages: [phone]   
Fax: (212)  
> 666-0140
>
> Columbia University
> Computer Science Department
> 1214 Amsterdam Avenue, MC0401
> New York, NY 10027
> USA
>
> Administrative Assistant: Sophie Majewski
> sophie@... [phone]
>
>
> **************************************************************
>
> 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

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Discuss@...
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[backspaces]

Agreed.

There is an interesting shared concept that I hope does not get lost,  
a sort of "join" between the continuous and discrete.  That is the  
limit, and the epsilon/delta argument.

It is generally placed in the Continuous realm and thus most students  
do not see how it is used in the Discrete.  But the limit of a  
sequence is just one example of its use in the discrete.
   http://en.wikipedia.org/wiki/Limit_of_a_sequence
   http://en.wikipedia.org/wiki/Cauchy_sequence

     -- Owen


On Jun 30, 2009, at 7:19 AM, ERIC P. CHARLES wrote:

> 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: [phone]    Messages: [phone]
> Fax: (212)
> > 666-0140
> >
> > Columbia University
> > Computer Science Department
> > 1214 Amsterdam Avenue, MC0401
> > New York, NY 10027
> > USA
> >
> > Administrative Assistant: Sophie Majewski
> > sophie@... [phone]
> >
> >
> > **************************************************************
> >
> > 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

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[FrankW3]

I am reading Spivak's book(s) on differential geometry (there are 5
volumes).  This includes topics like vector bundles, tensors, Lie groups,
Riemannian metrics and de Rahm cohomology.  I find the notation to be
beautiful and succinct and I think it would be very difficult to treat those
topics with only the symbols on a standard keyboard.  Obviously TeX or other
tools can convert such symbols to the elegant notation but...

Frank

-----Original Message-----
From: discuss-bounces@...
[mailto:discuss-bounces@...] On Behalf Of Joseph Traub
Sent: Monday, June 29, 2009 8:20 PM
To: Owen Densmore; friam@...
Cc: Joseph Traub; discuss@...
Subject: [sfx: Discuss] [FRIAM] Arthur Benjamin's formula for changing math
education | Video on TED.com

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: [phone]    Messages: [phone]    Fax: [phone]

Columbia University
Computer Science Department
1214 Amsterdam Avenue, MC0401
New York, NY 10027
USA

Administrative Assistant: Sophie Majewski
sophie@... [phone]


**************************************************************

  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_educati
on.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
_______________________________________________
Discuss mailing list
Discuss@...
http://lists.sfcomplex.org/mailman/listinfo/discuss
http://www.nabble.com/sfComplex-Discuss-f33403.html

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Discuss mailing list
Discuss@...
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[backspaces]

Agreed: a special keyboard would not work, but how about TeX producing  
the mathematical notation you'd like?

You'd type the TeX, and it could replace the TeX with the MN.  Then,  
if you needed to edit the MN, you'd double click on it to add/remove  
the TeX script.  Having an edit/view mode has worked find in other  
contexts.

I'm not a TeX expert, but judging from all the books that use it  
successfully, I think you could create the beautiful and succinct  
notation you see in the books.

AND, you could send it to me (email, web page, blog, wiki, ..) so that  
I could enjoy it too!

     -- Owen


On Jul 1, 2009, at 4:50 PM, Frank Wimberly wrote:

> I am reading Spivak's book(s) on differential geometry (there are 5
> volumes).  This includes topics like vector bundles, tensors, Lie  
> groups,
> Riemannian metrics and de Rahm cohomology.  I find the notation to be
> beautiful and succinct and I think it would be very difficult to  
> treat those
> topics with only the symbols on a standard keyboard.  Obviously TeX  
> or other
> tools can convert such symbols to the elegant notation but...
>
> Frank
>
> -----Original Message-----
> From: discuss-bounces@...
> [mailto:discuss-bounces@...] On Behalf Of Joseph Traub
> Sent: Monday, June 29, 2009 8:20 PM
> To: Owen Densmore; friam@...
> Cc: Joseph Traub; discuss@...
> Subject: [sfx: Discuss] [FRIAM] Arthur Benjamin's formula for  
> changing math
> education | Video on TED.com
>
> 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: [phone]    Messages: [phone]    Fax: (212)  
> 666-0140
>
> Columbia University
> Computer Science Department
> 1214 Amsterdam Avenue, MC0401
> New York, NY 10027
> USA
>
> Administrative Assistant: Sophie Majewski
> sophie@... [phone]
>
>
> **************************************************************
>
>  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_educati
> on.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
>
>
>  ============================================================
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