Discrete math demonstration ideas...

RICHARD BOTTING rbotting at csusb.edu
Tue Jan 31 16:42:40 EST 2006

I often use my key ring as an example of tree structured
data: There is a ring of car keys that has two rings
on it: one for each car, for example.  To demonstrate the need
to store a pointer to the root of a tree I pretend to hook
the keys back on the belt and in fact drop them.   They
land with a satisfying crash...
(except for the one time when they got hooked on a trouser pocket
 as they fell)

You could illustrate graph theory by referring back to
Dudeney's "Button and String method" of solving puzzles
and mazes.  Introduce a puzzle -- eg boat+goat+cabbage+....
And then producing a collection of balls
connected by string so that they fit the  puzzle

Hold up the start position and the finish and pull
tight.... and there is your solution: the shortest
path through the maze.

Note: I read this analogy in a book of recreational
math to motivate graph theory 30 or 40 years ago.

Hope this helps...

Comp Sci, CSUSB.

----- Original Message -----
From: math-thinking-l-request at geneseo.edu
Date: Tuesday, January 31, 2006 0:02 am
Subject: Math-thinking-l Digest, Vol 5, Issue 14
To: math-thinking-l at geneseo.edu
> Message: 1
> Date: Mon, 30 Jan 2006 19:46:46 -0500
> From: Aaron Bloomfield <asb at cs.virginia.edu>
> Subject: Discrete math demonstration ideas...
> To: math-thinking-l at geneseo.edu
> Message-ID: <43DEB376.1010109 at cs.virginia.edu>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> Hi, all,
>    I'm trying to form a collection of demonstrations for discrete 
> math 
> topics, and thought I'd solicit suggestions from this list.
>    I'm looking for ways to demonstrate concepts to students in a 
> discrete math course (and CS1 / CS2 courses as well) using 
> physical 
> objects.  For example, using a phone book to illustrate a binary 
> search 
> (I rip it up in the process), or using a conch shell for 
> illustrating 
> the growth of the Fibonacci sequence.  I envision these as 
> different 
> from KLAs (http://sequoia.cs.berkeley.edu/kla/index.php), which 
> generally require class participation.  And I see them as 
> different than 
> the nifty examples as well (as those tend to be interesting 
> problems 
> that require solving).  My thought is to use all three of these 
> (nifty 
> examples, KLAs, and the demonstrations) together to help form a 
> more 
> compelling lecture.  Essentially, I'm looking for ways to 
> demonstrate a 
> concept to a class using physical, real-world objects, but without 
> having to directly involve them in the demo.  And something that, 
> with a 
> bit of showmanship, can really "wake up" the class -- such as 
> blowing a 
> conch shell or dramatically tearing a phone book to shreds.
>    Any thoughts or suggestions?  Do such lists exist anywhere?  I 
> couldn't seem to find any.  Of course, I'll make the ensuing list 
> publicly available.
>    Thanks!
> -Aaron
> -- 
> Aaron Bloomfield, Assistant Professor
> Department of Computer Science, University of Virginia
> asb (at) cs (dot) virginia (dot) edu
> http://www.cs.virginia.edu/~asb

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