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Topic: A question about straight lines
Replies: 103   Last Post: Feb 8, 2014 8:28 AM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: A question about straight lines
Posted: Feb 2, 2014 12:59 PM
 att1.html (6.1 K)

On Sun, Feb 2, 2014 at 4:46 AM, Robert Hansen <bob@rsccore.com> wrote:

> > That being said though, a 12 year can surely understand sets, subsets,
> unions, intersections, etc. Naive set theory.
>
> Yes. I have no problem with introducing that kind of set theory, even well
> before 12. I recall my son having those lessons in 2nd grade, using Venn
> diagrams and sets of "things". Unfortunately, I think the curriculums then
> drop any mention of it till algebra. But modern curriculums are like that
> with everything. Vey little in the way of systematic and continuous
> development.
>
> Bob Hansen
>

This is where a computer language with a built-in set type, that one
continues to use over the years, would come in handy.

Interactively:

>>> farm1 = {"chicken", "pig", "cow", "horse"}
>>> farm2 = {"pig", "emu", "pony", "cow"}
>>> farm1 & farm2

{'cow', 'pig'}
>>> farm1 | farm2
{'horse', 'pony', 'cow', 'pig', 'emu', 'chicken'}

Since sets only allow unique members, no double-listings, they come in handy
as dupe removers:

>>> thelist = ["dupes", "has", "double", "words", "has", "dupes", "double",
"words"]
>>> thelist = list (set (thelist ))
>>> thelist

['double', 'dupes', 'has', 'words']

An early pioneering language for interactively exploring set concepts:
ISETL.

http://bit.ly/1eiw2k7

Python's set object API includes: union(), intersection(), difference(),
and symmetric_difference(), issubset(), and issuperset().

In a curriculum that introduces sets as one more type of object among many,
they might lose some of their mystique and that could be a problem and an
explanation for the bottleneck (resistance). Bertrand Russell & Co. were
eager to establish math's "foundations" and sets seemed to be the ticket.
They had exalted status as foundational.

After Sputnik, when US Americans panicked about the relative quality of
their educations, set theory was fast-tracked to the forefront on the New
Math front, in part because it had the hallmarks of the latest most cutting
edge thinking, at least in Anglo-American circles.

Putting New Math on top of sets, with the notation that goes with 'em,
would allow future generations of US American to keep up with those
Russians etc.

Fast forward to the 21st century and you have proponents of "Gnu Math" such
as myself, also in favor of continuing the set stuff, but not with such
emphasis on "foundations" necessarily.

The motivation for having sets hasn't changed much in terms of their being
integral to both the concepts and notation of modern math books, but, in
addition, the set type has utilitarian value that might be exploited to add
more continuity to the curriculum.

Sets are "math objects" (of the set class). They have specific attributes
and methods. We teach 'em alongside lists (heterogeneous content), arrays
(all elements same type), tuples (immutable lists), dicts (key:value pairs)
and more dynamic types such as closures and co-routines.

You could also use Mathematica on a Raspberry Pi for all this. Another
interactive prompting environment. Clojure, Scheme, APL, J, Logo...
Python, Ruby... all support REPL. Java, C++, C#, C... not so much.

gives a longer list of REPL-supporting languages).

REPL is the technical name for a prompt-centric environment and I tend to
draw the line with REPL i.e. languages that don't offer it are not on my
short list for what to replace the TI calculators with.

Gnu Math is about replacing calculators with free and open source computing
devices of a more general purpose nature, such as might be used to practice
with SQL (lingua franca for table creation, data storage and retrieval) and
Regular Expressions (pattern matching mini-language).

In our planned discrete math course (a STEM offering), topics such as SQL
and Regexps are not verboten. "Computer science is the new mathematics"
according to Dr. Christos Papadimitriou, co-author of Logicomix, a book I
like to promote, the story of Bertrand Russell in manga format:

http://mathforum.org/kb/message.jspa?messageID=7067602&tstart=0

REPL means "using it like a calculator" (interactively) is very doable, so
you don't lose that experience, plus you get the bigger screen (unless
trying to do all this on your smartphone). You can also plot in 3D and
rotate the results, given the right tools, such as VPython and/or POV-Ray
and/or VRML etc. All great "hard fun" toys we should let high schoolers gain
experience with, for math credit, not just elective CS credit.

Kirby

Date Subject Author
1/26/14 Neighbor
1/26/14 kirby urner
1/27/14 Neighbor
1/27/14 Robert Hansen
1/27/14 Bishop, Wayne
1/27/14 kirby urner
1/27/14 Neighbor
1/27/14 Robert Hansen
1/27/14 Neighbor
1/27/14 Neighbor
1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Robert Hansen
1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Robert Hansen
1/28/14 Neighbor
1/28/14 Gary Tupper
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Louis Talman
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/29/14 Robert Hansen
1/29/14 Bishop, Wayne
1/29/14 GS Chandy
1/29/14 Domenico Rosa
1/29/14 Neighbor
1/29/14 Joe Niederberger
1/29/14 Neighbor
1/29/14 Domenico Rosa
1/30/14 Bishop, Wayne
1/29/14 Joe Niederberger
1/29/14 Neighbor
1/29/14 Robert Hansen
1/29/14 Joe Niederberger
1/29/14 Joe Niederberger
1/29/14 Robert Hansen
1/30/14 Neighbor
1/29/14 Robert Hansen
1/29/14 Joe Niederberger
1/30/14 Louis Talman
1/29/14 Joe Niederberger
1/30/14 Neighbor
1/30/14 Jonathan J. Crabtree
1/30/14 Joe Niederberger
1/30/14 Joe Niederberger
1/31/14 kirby urner
1/30/14 Joe Niederberger
1/31/14 Neighbor
1/30/14 Joe Niederberger
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Robert Hansen
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 GS Chandy
1/31/14 GS Chandy
1/31/14 GS Chandy
1/31/14 Joe Niederberger
2/1/14 GS Chandy
2/1/14 Robert Hansen
2/1/14 kirby urner
2/1/14 Robert Hansen
2/1/14 Joe Niederberger
2/1/14 Robert Hansen
2/1/14 Joe Niederberger
2/2/14 Robert Hansen
2/2/14 kirby urner
2/1/14 Joe Niederberger
2/2/14 Robert Hansen
2/2/14 James Elander
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 Joe Niederberger
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 GS Chandy
2/4/14 GS Chandy
2/4/14 GS Chandy
2/4/14 GS Chandy
2/8/14 GS Chandy