Wow, that's a good outline! There's a lot of work left to do,
however, namely how to best introduce SAGE concepts along with math
concepts.
One silly question, what the heck is a "surd?"
A couple of suggestions, maybe you could add the cross product in the
chapter on vectors and matrices. I know my High School students,
especially those taking AP Physics C Mechanics, are always asking me
to explain this! Also, in the Statistics chapter, perhaps you could
introduce the SAGE interface to R?
I thought of including the SAGE interface to Octave in the vectors and
matrices chapter, but the SAGE vector() and matrix() classes are
suffiient for this. Anyway, R "ships" with SAGE and Octave doesn't
correct?
Regards,
A. Jorge Garcia
Applied Math & CS
Baldwin SHS & Nassau CC
http://shadowfaxrant.blogspot.com
http://www.youtube.com/calcpage2009
Sent from my iPod
On Jul 17, 2010, at 12:41 AM, Minh Nguyen <nguyenmi...@gmail.com> wrote:
Hi Phillip,
On Sat, Jul 17, 2010 at 8:51 AM, Phillip Feldman
<phillip.m.feld...@gmail.com> wrote:
Hello Minh,
I have put together an outline of a tutorial book. The goal of this
tutorial is to present high school mathematics accompanied by numerous
examples on how to use Sage to study the said mathematics. The full
outline can be found at
http://code.google.com/p/high-school-sage/
where you could get both a PDF version of the tutorial, and a
compressed file containing all the relevant TeX files and programs for
managing the tutorial.
I think that your list [1] is an excellent start. Here are a few
comments:
(1) Your examples under the heading "Factorization" look like
algebraic
expansion rather than factorization.
Here is the current outline. The chapter "Algebraic Simplification"
should present common techniques for simplifying algebraic
expressions. Such comon techniques include application of:
* the distributive laws
* difference of two squares identity
* perfect squares identity
* perfect cubes identity
* sum and difference of two cubes identities
When we come to the chapter "Polynomials and Their Factorization", we
also use the above techniques for factorizing polynomials. A main
point is that the above five rules can be applied whenever you want to
(expand and then) simplify an expression, or when you want to
factorize an expression.
(2) Perhaps there should be a topic on number theory, to include
prime
numbers, greatest common divisor, least common multiple, prime
factorization, relative primeness, and the like? (Most children in
the U.S.
get this material before the 10th grade, but some don't).
Done. See the outline of the chapter "Number Theory".
(3) I'd like to see a unit on polynomials, including expanding a
product of
two polynomials, evaluation of polynomials (for specific values of
the
independent variable), and factorization.
Done. For the time being, I lumped polynomials and factorization into
one chapter: "Polynomials and Their Factorization".
(4) It would be good to have something on trigonometry, including
graphs of
trigonometric functions, and trigonometric simplification using
standard
identities.
Done. See the outline of the chapter "Trigonometric Functions".
What do you think?
An outline of the tutorial is pretty much there. What we need now is
volunteers to flesh out the contents.
--
Regards
Minh Van Nguyen
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