September 14 lecture notes

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 I) go over homework

 II) questions ?

 III) this week :  programs

 --- Modules -----------------------------------

 myProgram::usage="This is the documentation.  So there.";

 myProgram[stuff_] := Module[{a,b},               (* temporary variables *)
                             doThis[stuff];
			     a=10;                (* a comment about "a" *)  
			     b=20;                (* a comment about "b" *)
                             doThat[a,b];
                             doSomethingElse[];
                            ];                  

    :=        delayed execution
    stuff_    match a single thing
    Module    a sequence of things to do
    (*  *)    internal comment, "how it works"  documentation
    ::usage   external API,     "how to use it" documentation
    ;         put a semi-colon between consecutive things to do
    {a,b},    put local variable names at the beginning of the module

 --- Loops  & Conditionals ------------------------------------

 Do[ this[i];  (* do this with i=1, i=2, ..., i=n *)
     that[],
     {i,1,n}]

                (* or just *)

 Do[ this[];    (* do this stuff n times *)
     that[];
     other[],
     {n}]
 
 If[ booleanExpression, stuffToDoIfTrue[], stuffToDoIfFalse[] ];

 While[ booleanExpression, stuffToRepeat[] ];


 --- in class practice ----------------------------------------

 i. the turtle world
    * find a recipe to draw 
       * a triangle
       * a square
       * a hexagon
    * write a program to draw an arbitrary n-gon
       * what arguments do you want to pass to it?
    * write a program to draw a collage of 
      randomly chosen shapes, with random colors
       * what arguments might you pass to it?

    * turtle homework for this week

 ii. perfect number n : sum of factors < n == n
     example:   6 is perfect: 1 + 2 + 3 = 6
     * write a program that finds the n'th perfect number
     * ... but first write one that tests whether a number is perfect
     * ... but first write one that returns a list of the factors of a number

 iii. back up a bit : 
     * How to we create these recipes (i.e. algorithms) ?
        * Isn't any simple answer.  But there are hints.
	* Hints:
	    * break problem into smaller pieces
	    * an art that can be developed with practice
	    * state recipe with words and/or pictures before code
	    * be as explicit as you can
     * How do we know that they work ?
            * TESTING and DEBUGGING   (more on this later)
	    * assume nothing; Print[] often; evaluate small bits and watch it.
     * How do we keep from re-inventing the wheel ?
            * DOCUMENTATION
	    * SMALL RE-USABLE PIECES



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