September 9 lecture notes - intro programming w/ mathematica

 -------------------------------------------------------------

 I) questions
   1) Mathematica notebooks
   2) entry of symbols (Traditional Form)
   3) functions lists  (Standard Form)

II) a bit more logic
   1)   x<10 && y>5
	x<10 || y>10      true or false?
   2)	if (a) then (b)         Implies[a,b]      a => b
   3)   For All, Exists 
   4) See silly example of logic puzzle (from Rev. Dodgeson) in code/

   5) Class exercise:  
      a) do truth table for a=>b
      b) find a way to write a=>b using !,&&,||

III) more on lists
    a = {1,2,3,4}
    first element is a[[1]]
    or is it...  check out a[[0]] and FullForm[a]
   
    For a really good time, try FullForm[a/b], (a/b)[[0]]
    Also see Part[]

    *** everything in mathematica is really a list ***

    Also see Hold[]   (stops something from being evaluated)
    Also see NumberMarks, 1.2`    for approximate results

IV) functions in mathematica

  f[x]=...;     has TWO PROBLEMS :
                1st, this matches only "x" exactly.
                     Mathematica allows multiple definitions;
		     it uses the most specific.
		     example:
		     f[1]=1;
		     f[0]=1;
		     f[x]=f[x-1]+f[x-2];
                2nd, this evaluates the RHS right away, and stores result.
                     example: f[x]=StringJoin["**",ToString[x],"**"];
                            

 To fix both problems, use

  f[x_]:= (put definition here);


             1)    x_ means "match any single thing"
	     2)    := means "delay evaluation until later"

  example:  
  f[]:= Print["Hi there!\n"];       (* This line defines a subroutine/program, *)
  f[] enter                         (* and this runs it *)


 Note that comments in Mathematica go within (*  *) marks.

V) "Hello world" subroutine in other languages

--- C -------------------------                one of the classics
  void f(){
    printf("Hi there!\n");
  }

--- perl ----------------------                often Jim's choice
  sub f {
    print "Hi there!\n";
  }

--- Java ----------------------                popular in typical college classes
  class Hello{
    public static void main(String[] args){
      System.out.println("Hi there!\n");
    }
  }
  
--- javascript ------------------              what you'll see in a web page
 <!-- in a web page -->
 <script language="JavaScript">
    function hi { document.write("Hi there!\n"); };
 </script>

--- lisp ----------------------                popular for AI research
  
 (defun hi ()
        (format t "Hi there!"))