September 7 lecture notes - intro programming w/ mathematica

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 I) initial business
   1) bookstore and textbooks
   2) experience so far with running and exploring the software
   3) this week
        a) overview of computers and how they work
	b) general "how to use" mathemtica, especially the "front end"
	c) logic basics : not, and, or, truth tables

 II) overview of computers
   1) hardware
        cpu
        memory (fast, transient)
        disk/filesystem (slower, bigger)
   2) cpu
        gazillions of "transistors" 
        each a hardware logic "gate"
	(two different metals, 2 input wires, 1 output wires)
	very, very primitive operations
   3) turing machine
        a few simple things it can do (read/write/move/change state)
	any digital computer has same (though faster) capability
   4) general computer
        inputs:  (keyboard, mouse clicks, ...)
	outputs: (screen, speakers, printer, ...)
   5) computer science
        all about getting simple pieces to do complex things
   6) how to manage complexity ?
        *** layers ***
	break problem into pieces, and those pieces into smaller pieces, ...
	each piece has an API : how to invoke it and what it can do
	testing
	documentation
   7) algorithms and data structures
   8) programming languages, operating systems
        low level        - close to machine hardware            ( assembly )
	intermediate     - better, but still machine specific   ( C, C++ )
	system services  - disk, memory, multi-tasking, ...     ( unix, ... )
	high             - abstract representation of problem   ( Java, ... )
   9) applications with a GUI (Graphical User Interface)
        point'n'click - cartoons
	command line  - words
   10) typical steps computer programming
        (a) create source code file with editor
	(b) compile code (i.e. translate to assembly) to an executable file
	(c) run executable
   11) IDE - interactive development environment
        application to combine these three together
	example: Mathematica application


 III) using Mathematica
   1) Kernel vs Front End
   2) Notebook (.nb) files
   3) Cells and their types : text, input, output, ...
   4) Preferences and the Option Inspector
   5) Help
        help browser
        typing ?*foo* 
   6) Traditional Form vs Standard Form (under "Cell" menu)
   7) Palettes and typing tricks
        control-^
	control-space
	esc a esc for alpha
   8) Function[arguments]  -  huge number of them
   9) strings ("This is a string"), integer (3/5), float (3./5.)
   10) assignments:   a=10;
   11) semi-colon: do it without showing me
   12) {"This", "is", "a", "list", 1, 2, 3}
   13) symbolic vs integer vs numeric results:
   14) postfix (Pi//N) , prefix  ( Sin @ Pi ),  infix ( 10 ~Mod~ 3 )
   15) rules ( a+b/.{a->2,b->3} ) and Options (  Options[Plot] )

 IV) programming logic
    1) we'll need it for writing algorithms:  if (...) then (...)
    2) primitives         Mathematica versions
        and               &&
        or                ||
        not               !
        true, false       True, False  
      Note: also set-like math notations     
    3) examples
        x = 10;  y = 7;
	x<10 && y>5
	x<10 || y>10      true or false?
	
    4) more of formal logic
        * Implies[p,q], also written as "p => q"
	* ForAll, Exists