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(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 "Intro to ",
 StyleBox["Mathematica",
  FontSlant->"Italic"]
}], "Title",
 CellMargins->{{Inherited, 30.75}, {Inherited, Inherited}},
 TextAlignment->Center,
 TextJustification->0],

Cell["Fall 2003 ", "Text",
 CellMargins->{{Inherited, 30.75}, {Inherited, Inherited}},
 TextAlignment->Center,
 FontSize->16],

Cell["Victor Adamchik", "Text",
 CellMargins->{{Inherited, 30.75}, {Inherited, Inherited}},
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Cell[CellGroupData[{

Cell[TextData[{
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Cell["\<\
A fully integrated environment for scientific computing. It includes\
\>", "Text"],

Cell[TextData[{
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Cell[TextData[{
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}], "2ColumnBox"],

Cell[TextData[{
 "\t",
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  FontWeight->"Bold"]
}], "3ColumnBox"],

Cell[TextData[{
 "Do not treat ",
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  FontSlant->"Italic"],
 " as a programming language. It is not. Do not bother with a language \
symantic. It does not have neither types, nor exceptions, nor inheritance. It \
does not have a compiler, data structures. You do not worry about memory \
allocation and garbage collection. It is very much like the Basic language, \
that was developed 25 years ago. "
}], "Text"],

Cell[TextData[{
 StyleBox["Mathematica",
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 " is a tool for ",
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Cell[CellGroupData[{

Cell[" The Architecture", "Section"],

Cell["Mathematica consists of three parts: ", "Text"],

Cell[TextData[{
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Cell[TextData[{
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kernel",
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Cell[TextData[{
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Cell[TextData[{
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Cell["Example 1.", "Example",
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Cell[BoxData[
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Cell[TextData[{
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Cell[TextData[{
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Cell["\<\
The front end took the output and drew a smooth surface over those points.\
\>", "Text"],

Cell[TextData[{
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  FontWeight->"Plain",
  FontSlant->"Italic"],
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Cell[TextData[{
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Cell[CellGroupData[{

Cell[TextData[{
 " What is a ",
 StyleBox["Notebook",
  FontSlant->"Italic"],
 "?"
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Cell[TextData[{
 "A ",
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  FontSlant->"Italic"],
 " notebook is what you see! It is an electronic document that may contain \
text,  graphics, and actual ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " output. If you want to save the result of todays work, you will save it in \
a form of Notebook. You can work simultaneously with as many notebooks as you \
wish. To open a notebook, go to \"File\" and click on either \"New\" or \
\"Open\". To save it, click \"Save\" or \"Save as\"."
}], "Text"],

Cell["\<\
If you want to save the result of todays work, you will save it in a form of \
Notebook. You can work simultaneously with as many notebooks as you wish. To \
open a notebook, go to \"File\" and click on either \"New\" or \"Open\". To \
save it, click \"Save\" or \"Save as\".\
\>", "Text"],

Cell[TextData[{
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 " notebook consists of a list of ",
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  FontSlant->"Italic"],
 " Cells are indicated along the right edge of the notebook by various \
brackets. Clicking and double-clicking on these brackets allows one to open, \
close and format the cells. For example, to change the background color of \
_this_ cell, you do the following: click on cell bracket, go to \"Format\" \
menu and choose \"Background Color\", and then click on \"Blue\"."
}], "Text",
 Background->None],

Cell[TextData[{
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Evaluatable means that a given cell can be used as an input to the ",
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Cell["2^10", "Input"],

Cell[TextData[{
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bracket in the input cell, then click on \"Cell\" menu, and then \"Cell \
Properties\". Do the same for the output cell. The input cell is evaluatable, \
the output is not."
}], "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell[" Getting Help", "Section"],

Cell["\<\
Mathematica has a number of on-line help facilities. Click on \"Help\" and \
choose \"Help Browser\". In a small window \"Go To\" type \"plus\" and hit \
enter.\
\>", "Text"],

Cell["\<\
F1 is an useful shortcut. Type \"times\" anywhere in your notebook and hit \
F1.\
\>", "Text"],

Cell["Another way to get a little bit of help is to use ? or ??", "Text"],

Cell[BoxData[
 RowBox[{"?", "Plus"}]], "Input"],

Cell["\<\
If you don't exactly remember the name of what you are looking for, use the \
wildcard\
\>", "Text"],

Cell[BoxData[
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Cell[TextData[{
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " is case sensistive"
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 FontSize->13],

Cell[BoxData[
 RowBox[{"??", "*lo*"}]], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell[" File System", "Section"],

Cell["\<\
That is very important to know (especially under Win/NT) in what directory \
you are\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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 CellLabel->"In[6]:="],

Cell[BoxData["\<\"C:\\\\Program Files\\\\Wolfram \
Research\\\\Mathematica\\\\5.0\"\>"], "Output",
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}, Open  ]],

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Cell[BoxData[
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Cell[BoxData["$Failed"], "Output",
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}, Open  ]],

Cell["how to get the list of files", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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 CellLabel->"In[9]:="],

Cell[BoxData[
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Cell["how to change the current directory", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData["\<\"C:\\\\Temp\"\>"], "Output",
 CellLabel->"Out[11]="]
}, Open  ]],

Cell["how to write to the file", "Text"],

Cell[BoxData[
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  RowBox[{"IntegerDigits", "[", 
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Cell["how to read from the file", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell["Let's write it again", "Text"],

Cell[BoxData[
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Cell["Check the content of the file", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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 CellLabel->"In[15]:="],

Cell["\"What is >>>?\"", "Print",
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}, Open  ]],

Cell[TextData[{
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system to another. Nevertheless, ",
 StyleBox["Mathematica",
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}], "Text"],

Cell[TextData[{
 "I refer you the ",
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  BaseStyle->"RefGuideLink",
  ButtonData:>{"Directory"}],
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  FontColor->RGBColor[0, 0, 1],
  Background->None],
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Cell[CellGroupData[{

Cell["Numerical Computations", "Section"],

Cell[TextData[{
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\[CloseCurlyDoubleQuote]. ",
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Cell["\<\
We compute this number to machine accuracy. Six digits are usually displayed. \
\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell["Here are 50 digits in the result. ", "Text"],

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Cell[BoxData["0.\
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Cell[TextData[{
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}], "Text"],

Cell[TextData[{
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  FontWeight->"Bold"],
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Cell[BoxData[
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Cell[TextData[StyleBox["There are much more extreme cases of numbers which \
are almost integers. They are called Pisot numbers",
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Cell["Definition of Functions", "Section"],

Cell[TextData[{
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Cell["", "Text"],

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Cell[TextData[{
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Cell[TextData[{
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Let us make an experiment. First, we define the function f(x):\
\>", "Text",
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Cell[TextData[{
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valid input. The rhs is an actual function definition in unevaluated form. To \
protect evaluation of rhs we use ",
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 Cell[BoxData["SetDelayed"]],
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Cell[CellGroupData[{

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Cell["\<\
Since the argument in lhs can be any expression, let's see what happen if we \
run\
\>", "Text",
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Cell["Perhaps we want to avoid any symbolic inputs:", "Text",
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Cell[TextData[{
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Cell[CellGroupData[{

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Cell["On the next step we need to iterate the function f:", "Text",
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Cell[TextData[{
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The sequence oscillates between -1 and 0, so it remains bounded (but it does \
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You may ask, what's so special about this iteration. Much of the fascination \
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Cell[CellGroupData[{

Cell["Julia Set ", "Section"],

Cell[TextData[{
 "Consider a rational function ",
 Cell[BoxData[
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   RowBox[{"R", "(", "z", ")"}], TraditionalForm]]],
 ". The \"filled-in\" Julia set  is the set of points z which is bounded \
after ",
 Cell[BoxData[
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   RowBox[{"R", "(", "z", ")"}], TraditionalForm]]],
 " is repeatedly applied. There are two types of Julia sets: connected sets \
(for example, Mandelbrot set) and Cantor sets (Fatou dust). "
}], "Text"],

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