When I taught http://www.usna.edu/Users/math/wdj/teach/sm450.html
(python and some fairly advanced discrete math),
<<
Thanx, Dr. Joyner, for your notes from sm450! I have been pouring over
them for the last few months since you shared them with me. Your
course is way over the heads of my intro programming class, but may be
useful for my calculus research lab.
As you can see below, I have been keeping a blog on all things related
to teaching and learning math with technology. Some of my ordeal for
getting approval for my calculus research class is in there. I only
recently starting migrating my blog to blogspot. For older posts
please see http://calcpage.tripod.com/shadowfax
HTH,
A. Jorge Garcia
http://shadowfaxrant.blogspot.com
Teacher & Professor
Applied Mathematics, Physics & Computer Science
Baldwin Senior High School & Nassau Community College
-----Original Message-----
From: David Joyner <[email protected]>
To: [email protected]
Sent: Mon, Jun 7, 2010 8:48 pm
Subject: Re: [sage-edu] what should be taught?
Okay, interesting. I hope you start a blog or something on it to track
your
progress for the benefit of others.
At the end of the course, what will they be tested on? Does this course
replace a precalc course? This will determine to an extent what you can
do.
When I taught http://www.usna.edu/Users/math/wdj/teach/sm450.html
(python and some fairly advanced discrete math), I found that
the Python was almost completely orthogonal to the math. Before teaching
the course, I thought I could teach them both math and Python
by doing math examples in Python. That worked for some
very good students. For others, I had to teach them Python
and teach them the math, and then carefully explain the example in
Python.
You asked for ideas, so here is one.
Take the Fibonacci sequence, f0=1, f1=1,f2=2, f3=3, f4=5, .... It
is easy to show (using binary trees) that the "stupid" way to compute
fn using the most naive algorithm is extremely inefficient. However,
if you use a trick with matrices and repeated squaring, fn
can be computed in linear time! For your class this might take a week or
two but you would have to go through lots of cool and useful ideas.
The big payoff is that at the end, you get an algorithm which is very
short
and elegant but fast, and you have taught them a ton of useful tools.
Some details are (among many other places) in the lecture notes
posted to the 450 website above.
On Mon, Jun 7, 2010 at 8:13 PM, michel paul <[email protected]> wrote:
On Mon, Jun 7, 2010 at 6:27 AM, David Joyner <[email protected]>
wrote:
>Are you going to teach programming (eg, Python) in this course?
Exactly. We'll be using the Litvins' Math for the Digital Age and
Programming in Python, and I think we can work through that text in a
semester. Though it does touch on some precalc topics, it is not
specifically a precalc text, so we'll also draw from our regular text
to
fill in the gaps. Then second semester we'll focus on the remaining
precalc
topics not addressed in Digital Age. The kids should be proficient
enough
at that point in using Sage to be able to write little papers about
the math
we're studying. Each student will have an online Sage notebook
account that
will serve as a portfolio of their work.
Seems like you are leaning towards discrete math+precalc topics.
Is that correct?
Our current precalc text, Demana Waits, does contain a chapter on
discrete
math - basic combinatorics, sequences, series, binomial theorem, math
induction, etc., but again, it's towards the end of the text and is
normally
done 2nd semester. I think a lot of those topics could easily be
done first
semester and would have more relevance for learning programming. So
I'm
going to change some things around and save the trig stuff and the
analytic
geometry for 2nd semester.
Eventually a computational discrete math course would also be a great
thing
to create. There actually used to be a ProbStat/Finite math course
at our
school, but it was tracked for the 'lower' math students, the ones
'not
headed for calculus', and I really disliked the illusion it created
that
'Finite was for dummies' or 'not real math'.
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