<table valign="top" class="generaltable" align="center" border="0" cellpadding="5" cellspacing="1" width="100%"><tbody><tr valign="top"><td class="generaltablecell" align="center">1</td><td class="generaltablecell" align="left">
<a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=78">Introduction to CS201</a></td><td class="generaltablecell" align="left"><p><br>
What this course is about: learning enough Python to make your
explorations of algebra concepts more enjoyable and self-informative.<br> <br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=79">Getting Started</a></td><td class="generaltablecell" align="left">
<p><br>
Some brief remarks about getting going in Python<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=80">How to Think Like a Computer Scientist
</a></td><td class="generaltablecell" align="left"><p>The Python version of Allen Downey's open source book, with Jeff Elkner.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=81">Introducing Sequences</a>
</td><td class="generaltablecell" align="left"><p>A first look at sequences as a stepping stone into various algebra topics.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=82">On-Line Encyclopedia of Integer Sequences
</a></td><td class="generaltablecell" align="left"><p>Enter the beginning terms of your sequence and see if there's a corresponding sequence in the database.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=84">Pythonic Mathematics</a></td>
<td class="generaltablecell" align="left"><p>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 <a href="http://www.4dsolutions.net/presentations/pythonicmath.ppt">PowerPoint version</a> (shared with my audience in Sweden).<br></p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=98">This course needs DVD clips
</a></td><td class="generaltablecell" align="left"><p><br>
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 <a href="http://video.google.com/">video.google.com</a> is an exciting development in this regard.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=99">Classroom Infrastructure</a>
</td><td class="generaltablecell" align="left"><p>A posting to the Math Forum about new technology I'd like to see in the classroom.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">2</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=100">Prime and Composite Numbers
</a></td><td class="generaltablecell" align="left"><p><br>
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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=101">Basic Operations in Python
</a></td><td class="generaltablecell" align="left"><p>In this curriculum segment, we investigate primitive numeric operations, plus we import some functions from the math module. <br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=87">Euclid's Algorithm for the GCD
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=102">Functions and Looping</a>
</td><td class="generaltablecell" align="left"><p>Here we look at control structures within the body of a Python function. We also take a look at how to set default arguments.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=120">Generators and Pascal's Triangle
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=121">Dot Notation</a></td><td class="generaltablecell" align="left">
<p>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.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">3</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=89">Triangular and Square Numbers
</a></td><td class="generaltablecell" align="left"><p><br>
Let's write Python functions to return the Nth term in the Triangular and Square number sequences.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=90">Tetrahedral and Cubic Numbers
</a></td><td class="generaltablecell" align="left"><p>Now let's use Python to generate these polyhedral number sequences.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=91">Cuboctahedral and Icosahedral Numbers
</a></td><td class="generaltablecell" align="left"><p>Finally,
let's explore this important number sequence, and where it takes us in
molecular biology, crystallography, chemistry, and architecture.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=96">Python and Mathematics (PyCon 2004)
</a></td><td class="generaltablecell" align="left"><p>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.<br></p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=114">Microarchitecture of the Virus
</a></td><td class="generaltablecell" align="left"><p>The
icosahedral numbers thread turns into the geodesic spheres thread,
leading to microbiology (virology), architecture (Tacoma Dome etc.),
and chemistry (buckyballs, nanotubes).<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=115">Prototyping Shelters</a>
</td><td class="generaltablecell" align="left"><p><br>
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.<br></p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">4</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=105">Types of Object</a></td><td class="generaltablecell" align="left">
<p>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).<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=110">Playing with Robots</a></td>
<td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">5</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=106">The Rational Number Type</a>
</td><td class="generaltablecell" align="left"><p>Let's develop a Rat class (or name it something else if you're afraid of rats).<br><br> <br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=107">The Polynomial Type</a></td>
<td class="generaltablecell" align="left"><p>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).<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=108">Vector Type</a></td><td class="generaltablecell" align="left">
<p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=113">A Quick Dive into Fractals
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=116">Fractals with Python and PIL
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=117">Python Code for a Vector Class
</a></td><td class="generaltablecell" align="left"><p>No need to reinvent the wheel. Start with working code, tweak to taste.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=118">Python Code for Talking to POV-Ray
</a></td><td class="generaltablecell" align="left"><p>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 <a href="http://www.povray.org/">POV-Ray</a>. Replace "html" with "py" in the URL for a plaintext version.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=119">A Shapes class</a></td><td class="generaltablecell" align="left">
<p>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.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">6</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=109">Modulo Number Type</a></td>
<td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=86">GCD and Relative Primality
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=88">Euler's Totient Concept</a>
</td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">7</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=85">Properties of a Group</a></td>
<td class="generaltablecell" align="left"><p>A review of Group Theory concepts covered so far.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=97">Vegetable Group Soup</a></td>
<td class="generaltablecell" align="left"><p>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.<br></p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=92">Properties of a Ring</a></td>
<td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=93">Properties of a Field</a>
</td><td class="generaltablecell" align="left"><p>Fields have two operations, both with full group properities, plus the distributive relationship between them.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">8</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=94">Polyhedra and Symmetry Groups
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=95">Symmetry: A Unifying Concept
</a></td><td class="generaltablecell" align="left"><p>by Istvan and Magdolna Hargittai<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">9</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=103">Fermat's Little Theorem</a>
</td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=104">Euler's Theorem</a></td>
<td class="generaltablecell" align="left"><p><br>
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.<br>
</p></td></tr>
<tr valign="top"><td class="generaltablecell" align="center"><br></td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=112">Crypto 101</a></td><td class="generaltablecell" align="left">
<p><br>
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.<br>
</p></td></tr>
<tr valign="top"><td colspan="3"><br></td></tr>
<tr valign="top"><td class="generaltablecell" align="center">10</td><td class="generaltablecell" align="left"><a href="http://winterhaven.teacherhosting.com/moodle/mod/resource/view.php?id=111">Topical Review and Class Party
</a></td><td class="generaltablecell" align="left"><p>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.<br>
</p></td></tr>
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