[Edu-sig] Cut and paste from Moodle (apologies if formatting messed up)

[kirby urner]

1Introduction to
CS201<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=78>


What this course is about: learning enough Python to make your explorations
of algebra concepts more enjoyable and self-informative.


Getting Started<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=79>


Some brief remarks about getting going in Python

How to Think Like a Computer
Scientist<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=80>

The Python version of Allen Downey's open source book, with Jeff Elkner.

Introducing Sequences<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=81>

A first look at sequences as a stepping stone into various algebra topics.

On-Line Encyclopedia of Integer
Sequences<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=82>

Enter the beginning terms of your sequence and see if there's a
corresponding sequence in the database.

Pythonic Mathematics<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=84>

I wrote this PDF for Europython 2005, held in Gothenberg, Sweden.  This PDF
summarizes a lot of my thinking at the time, and likely reflects a lot of my
thinking to this day.  I also have an accompanying PowerPoint
version<http://www.4dsolutions.net/presentations/pythonicmath.ppt>(shared
with my audience in Sweden).

This course needs DVD
clips<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=98>


I think a lot of this material would be much more accessible if we had an
easy way to pull up relevant short clips, such as we find on Sesame Street
about the letter A or number 5, except about other topics (the ones studied
here). The emergence of video.google.com is an exciting development in this
regard.

Classroom Infrastructure<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=99>

A posting to the Math Forum about new technology I'd like to see in the
classroom.

2Prime and Composite
Numbers<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=100>


Let's review what we know about the positive integers: they break down into
roughly two sets: the prime and the composite. The numbers 1 and 0 don't
really belong to either group.

Basic Operations in
Python<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=101>

In this curriculum segment, we investigate primitive numeric operations,
plus we import some functions from the math module.

Euclid's Algorithm for the
GCD<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=87>

Euclid's algorithm is one of the oldest on record.  We don't think Euclid
invented it, any more than we suppose Plato first discovered the five
Platonic solids.  However, Euclid, like Plato, helped ensure this valuable
method remained available to subsequent scholars.

Functions and Looping<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=102>

Here we look at control structures within the body of a Python function.  We
also take a look at how to set default arguments.

Generators and Pascal's
Triangle<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=120>

The concept of a generator is not unique to Python -- I believe it was
inspired by a feature in Icon, another language, just like list
comprehension syntax was inspired by Haskell.  A generator is like a looping
function with state, i.e. it remembers local variables from one cycle to the
next.

Dot Notation<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=121>

Common to many object oriented languages is dot notation, a way of using the
period to gain access to an object's properties and methods.

3Triangular and Square
Numbers<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=89>


Let's write Python functions to return the Nth term in the Triangular and
Square number sequences.

Tetrahedral and Cubic
Numbers<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=90>

Now let's use Python to generate these polyhedral number sequences.

Cuboctahedral and Icosahedral
Numbers<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=91>

Finally, let's explore this important number sequence, and where it takes us
in molecular biology, crystallography, chemistry, and architecture.

Python and Mathematics (PyCon
2004)<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=96>

Note: I was unable to actually present this paper owing to sudden news of
family illness. I was in DC for a symposium on Buckminster Fuller, on a
panel with E.J. Applewhite and others.  Then I helped Blaine D'Amico with a
science workshop for kids (we built at octet truss out of toothpicks).
After that, I flew home.

Microarchitecture of the
Virus<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=114>

The icosahedral numbers thread turns into the geodesic spheres thread,
leading to microbiology (virology), architecture (Tacoma Dome etc.), and
chemistry (buckyballs, nanotubes).

Prototyping Shelters<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=115>


This is a sidebar on pioneering work in the world of shelter design. Fuller
called them "environment controls" in an effort to counter our prejudicial
imaginations, which a very biased towards a particular concept of "home".
Perhaps these prototypes are for vacation or resort villages, or for
disaster relief.

4Types of Object<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=105>

Now that we've learned about controlling flow using functions, it's time to
package our functions, as methods, into objects.  Objects maintain state and
allow us to organize our thinking using metaphors that remind us of our real
world experience, of objects with properties (e.g. color) and behavior (e.g.
wags tail).

Playing with Robots<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=110>

Ideally, this curriculum segment will benefit from marketplace innovations
in the "programmable robot pet" genre.  This course would especially benefit
if the control language were Python.

5The Rational Number
Type<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=106>

Let's develop a Rat class (or name it something else if you're afraid of
rats).



The Polynomial Type<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=107>

Polynomials have degree and coefficients.  In this module we develop a
compact way of expressing polynomial objects, such that we may multiply them
together.  Dividing one polynomial by another is not guaranteed to give you
a new polynomial however.  Polynomials form a Ring (see future module).

Vector Type<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=108>

We're going through these in fairly quick progression.  This is a preview
course.  We go back and dissect and embellish in more detail in follow-up
courses.  This is all about whetting the appetite and providing overview.

A Quick Dive into
Fractals<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=113>

When two complex numbers multiply, the Argand Diagram shows a rotation and
magnitude effect.  An iterative approach (start with any complex number on
the plane and keep plugging back in) will give a divergent or convergent
result, with the rate of divergence driving a color wheel mapping.

Fractals with Python and
PIL<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=116>

PIL is Python's Imaging Library.  Using PIL, we're able to control the
individual pixels on a canvas object, allowing us to publish the visual
representation of a fractal, once we've chosen a color scheme.

Python Code for a Vector
Class<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=117>

No need to reinvent the wheel.  Start with working code, tweak to taste.

Python Code for Talking to
POV-Ray<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=118>

Python is a good glue language.  What does that mean?  In this module, we
translate "vector talk" (is in coords.py) into "scene description language,"
the native language of POV-Ray <http://www.povray.org/>.  Replace "html"
with "py" in the URL for a plaintext version.

A Shapes class<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=119>

This may be more source code than you want or need.  Many will call my
approach idiosyncratic, in that I make use of quadrays, a type of simplicial
coordinate system, plus calibrate my volumes to match those of the
concentric hierarchy in synergetics.  These are somewhat esoteric features
that only a few teachers will probably care for, at least initially.

6Modulo Number Type<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=109>

This class allows us to set a class variable (new concept in this context),
namely the Modulus N for all the objects.  These objects, basically
integers, will then perform arithmetic operations modulo N.

GCD and Relative
Primality<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=86>

If two integers have no factors in common other than one, we say their
relatively prime, or coprime.  Some people call them "strangers."  They have
no common denomintor.  Our GCD function will therefore tell us about the
relative primehood of any two integers.

Euler's Totient
Concept<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=88>

The totient of a positive integer N is the number of smaller positive
integers that are relatively prime to N.  For example, the numbers less than
12 with 1 as the only common factor are: 1, 5, 7, 11.  Therefore, the
totient of 12 is 4.

7Properties of a
Group<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=85>

A review of Group Theory concepts covered so far.

Vegetable Group
Soup<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=97>

This demo uses vegetables in place of integers in Z(6).  The supplementary
reading is somewhat technical for early algebra students, but the demo
itself should prove fairly digestible.

Properties of a
Ring<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=92>

The algebraic structure known as a Ring introduces and second operation, in
relationship to the first.  We have full group properties for the first
operation, but not the second.

Properties of a
Field<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=93>

Fields have two operations, both with full group properities, plus the
distributive relationship between them.

8Polyhedra and Symmetry
Groups<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=94>

Polyhedra may be categorized according to what kinds of rotational symmetry
they support and their various axes.  For example, the icosahedron is 5-fold
symmetric around its vertex-to-opposite-vertex axes:  if you rotate it 1/5th
of a complete rotation around such an axis (72 degrees), it ends up looking
unchanged.

Symmetry: A Unifying
Concept<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=95>

by Istvan and Magdolna Hargittai

9Fermat's Little
Theorem<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=103>

Fermat's Little Theorem defines a condition that's always true for prime
numbers, but is also true for some composites.  By tweaking the condition,
we're albe to filter out almost all composites, but not all of them.

Euler's Theorem<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=104>


Euler's Theorem is actually more general than Fermat's Little Theorem, i.e.
once we prove Euler's is true, we get Fermat's as a consequence.

Crypto 101<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=112>


A short introduction to the history of cryptography, with special attention
to the symmetric secret key system versus the public key system. This is how
we pay them back for slogging through some of those number theory segments:
RSA will be somewhat comprehensible.

10Topical Review and Class
Party<http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=111>

This might be some multi-media blow-out, where we recap a lot of content
visually, with allusions to future possibilities, but let the students have
fun, let off steam, stage a dance, invite a band, whatever.
  ------------------------------

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