SAGE tutorial for highschool students?

[Phillip M. Feldman]

The existing SAGE tutorial by Bill Stein has a lot of good
information, but is hard to assimilate. It would be really great to
have a tutorial written
with highschool students in mind. (This would also be useful for
others who are not professional mathematicians).

Also, I'd like to suggest that the discussion of polynomials should
not start with polynomial rings. The average highschool student (or
working engineer) has no idea what a polynomial ring is. I'd really
like to see some examples that show how to define polynomials with
rational or decimal coefficients, multiply two such polynomials
together, factor a polynomial to find the roots (using
numerical methods if necessary), divide one polynomial by another to
yield the quotient and remainder, and so on.

[William Stein]

On Fri, Jul 16, 2010 at 8:15 AM, Minh Nguyen <nguye...@gmail.com> wrote:
> Hi Phillip,

>
> On Fri, Jul 16, 2010 at 8:06 AM, Phillip M. Feldman
> <phillip....@gmail.com> wrote:
>> The existing SAGE tutorial by Bill Stein has a lot of good
>> information, but is hard to assimilate.  It would be really great to
>> have a tutorial written
>> with highschool students in mind.  (This would also be useful for
>> others who are not professional mathematicians).
>

> Agreed. What sort of topics would such a tutorial cover? I have a
> short list [1] of topics that could be included in a tutorial aimed at
> high school students.

>
>
>> Also, I'd like to suggest that the discussion of polynomials should
>> not start with polynomial rings. The average highschool student (or
>> working engineer) has no idea what a polynomial ring is.
>

> And I would have thought that a ring is what you get when you're married :-)

>
>
>> I'd really
>> like to see some examples that show how to define polynomials with
>> rational or decimal coefficients, multiply two such polynomials
>> together, factor a polynomial to find the roots (using
>> numerical methods if necessary), divide one polynomial by another to
>> yield the quotient and remainder, and so on.
>

> Can you put together a list of topics to cover? Or we could do this
> together. The idea is to produce a skeleton of the tutorial in
> question. The skeleton should have chapters, each devoted to a topic
> of high school maths. For each chapter, provide an outline (in bullet
> points if necessary) of topics to cover for that chapter. With such a
> skeleton ready, it would be easier to delegate each chapter to an
> author who would then flesh out the designated chapter.
>
> A team in France recently put together a maths book [2] written in
> French, with numerous Sage usage examples scattered throughout the
> book. I would guess that each person in the team wrote one chapter,
> then aggregated all the writings from the team members into a complete
> book. Somewhere in that project was to be found an editor who
> coordinated the whole enterprise.

Paul Zimmerman; he's very, very serious and good at this sort of coordination.

I personally didn't go to high school or ever teach it or have kids,
so I don't have much of a clue what people learn in mathematics
there...

> It's possible that we are living in different parts of the world. What
> is covered in high school maths in one country could very well be
> different from that in another country. To make the skeleton of the
> proposed tutorial more concrete, consider my skeleton [1] for the
> tutorial covering maths at the year 10 level in Victoria, Australia.

Thanks...

>
>
> [1] http://mvngu.wordpress.com/2008/08/11/year-10-mathematics-in-victoria/
>
> [2] http://sagebook.gforge.inria.fr/
>
> --
> Regards
> Minh Van Nguyen
>
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>
>

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[calc...@aol.com]

Well, I did a few YouTube screencasts to introduce the use of SAGE. I had my High School students in mind as the target audience. So, you may find my SAGE playlist on http://www.youtube.com/calcpage2009 channel of some use.

----------
Sent from my Verizon Wireless mobile phone

[Mike OS]

On Jul 15, 3:06 pm, "Phillip M. Feldman" <phillip.m.feld...@gmail.com>
wrote:

> The existing SAGE tutorial by Bill Stein has a lot of good
> information, but is hard to assimilate.  It would be really great to
> have a tutorial written
> with highschool students in mind.  (This would also be useful for
> others who are not professional mathematicians).
>

Agreed!

I've been working with a student, Ryan Rosenbaum, on a tutorial for
our undergraduates, but with an eye
to making the introductory parts very accessible to high school
students.
Coincidentally, we (well, Ryan) are just about to finish a first
draft, which we will post
someplace for comments, and I will notify this newsgroup.

As to Williams comment:

> I personally didn't go to high school or ever teach it or have kids,
> so I don't have much of a clue what people learn in mathematics
> there.

I've done em all, and there's a lot to be said in favor of each such
experience!
I plan to test and get comments from them, their friends and teachers.

Mike

[Bruce Cohen]

Great! This topic is timely for me as well.

I would like to begin having my students use Sage this year in my high
school calculus class. (The class is roughly equivalent to the first
two semester of a college class. Students will take the AP BC exam
in May and so I have long included the use of a TI-8x calculator.) I
need to assume that students have never programmed and have not heard
of any math software, let alone used something -- even a spreadsheet.
I'd like to have a documentation to take these students from where
they are to having enough Sage at any time in the year to augment
their work in class -- maybe JESTEC
Just Enough Sage To Enhance Calculus

I've set up an experimental Sage server in my basement and have met
with a few students this summer to try out some ideas. Here are
(notes about a possible opening session. I have intentionally stayed
away from the plot command as I want students to build a little
appreciation of what goes into making (and meaning) of a function
graph.

I'm closed with a few lines of (my first effort at) ReStructuredText
which might help. It has occured to me that I might take some Python
and Sage documentation which is in Sphinx and build a set of
documentation of first year calculus students.

Comments and help will be greatly appreciated.

-Bruce

.. Begin ReST
.. _Notes of Introduction to JESTEC:

====
Notes of Introduction to JESTAC (Just Enough Sage To Enhance Calculus):
====
I'd like to get them up and running by looking at lists, math functions, and
list_plots. As these students have taken precalculus, I assume they have
seen sigma notation.

Math Notation to Sage
----
The first step is to go from the math notation of:
$$\sum_{i = 0}^7 i^2$$
to the Sage/Python notation of::

sage: L = [i^2 for i in range(8)]
sage: L
sage: sum(L)

Function Domain, Range and Ordered Pairs
----
Now focus of math functions with a discrete domain and corresponding range::

# introduce a math function
sage: f(x) = x^2
# setup a domain
sage: D = [x for x in range(-4,5)]
# setup a list of ordered pairs
sage: P = [(x,f(x)) for x in D]
sage: P
# plot the ordered pairs
sage: plot1 = list_plot(P);plot1
# setup a domain and range lists
sage: D = [x for x in range(-4,5)]
sage: R = [f(x) for x in D]
# introduce grabbing elements of a list, e.g. the 4th element of R
sage: R[3]
# combine the lists to get the ordered pairs
sage: P1 = [(D[i],R[i]) for i in range(len(D))]
sage: list_plot(P1)

Introduce list where numbers need not be integers
----
(I don't want to get into QQ vs RR.) This also starts students on idea
of named parameters. ::

# Getting more points using non-integer $\Delta x$.
sage: deltax = 0.5
sage: start = -4
sage: stop = 4 + deltax
sage: f(x) = x^2
sage: D2 = [x for x in srange(start,stop,deltax)]
sage: P2 = [(x,f(x)) for x in D2]
sage: plot2 = list_plot(P2)

Use lists to plot parametric functions
----
The need for the *aspect_ratio* parameter comes up naturally::

# lists and parametric functions
sage: x(t) = cos(t) ; y(t) = sin(t)
sage: C = [(x(t),y(t)) for t in srange(0,2*pi,pi/8)]
sage: list_plot(C)
# fix the aspect ratio to get a better circle
sage: list_plot(C,aspect_ratio=1)

.. end ReST

[A. Jorge Garcia]

Well, I'm starting a new "Calculus Research Lab" next year that meets
every other day in addition to my BC Calculus class to do Calculus on
SAGE! Take a look at the link on the right side of my blog entitled
"Calculus Research Lab" for more info on what I am including in this
course.

These kids are way over scheduled, so I couldn't require all my BC
students take the Lab. As a result, I had low enrollment until I
opened it up to AB Calculus students as well. So, its going to cover
mostly AB material, but I will try to throw in some BC topics as well!

HTH,
A. Jorge Garcia
http://shadowfaxrant.blogspot.com
http://www.youtube.com/calcpage2009

Teacher & Professor
Applied Mathematics, Physics & Computer Science
Baldwin Senior High School & Nassau Community College