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                    Mathematica-Compatible Notebook

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Notebook[{

Cell[CellGroupData[{
Cell["Getting Started", "Title"],

Cell["Some Basics", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \(4\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ lists, \ append\ and\ join\ *) \nmylist = {3, 4, 5}\)\)], "Input"],

Cell[BoxData[
    \({3, 4, 5}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \(12\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ built\ in\ functions\ *) \nSin[Pi/2]\)\)], "Input"],

Cell[BoxData[
    \(1\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Rational vs. Floating Poing numbers", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ rational\ number\ calculation\ *) \n3/Sqrt[5.0]\)\)], "Input"],

Cell[BoxData[
    \(1.34164078649987383`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ floating\ point\ calculation\ *) \n3.0/4\)\)], "Input"],

Cell[BoxData[
    \(0.75`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ floating\ point\ result\ of\ rational\ calculation\ *) \n
    N[3*Sqrt[4/5]]\)\)], "Input"],

Cell[BoxData[
    \(2.68328157299974767`\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Mathematical Worksheet", "Title"],

Cell["Matrices", "Subtitle"],

Cell[BoxData[
    \(\(ClearAll[]; \)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(Clear[a, b, c, d]; \nsampleMatrix\  = \ {{a, \ b}, \ {c, \ d}}\), 
    \(sampleMatrix // MatrixForm\), 
    \(\(sampleMatrix[\([2]\)]\)[\([2]\)]\)}], "Input"],

Cell[BoxData[
    \({{a, b}, {c, d}}\)], "Output"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", GridBox[{
            {"a", "b"},
            {"c", "d"}
            }], ")"}],
      (MatrixForm[ #]&)]], "Output"],

Cell[BoxData[
    \(d\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sampleMatrix[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({a, b}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(MatrixForm[{{x}, {y}}]\), 
    \(MatrixForm[sampleMatrix.{{x}, {y}}]\)}], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", GridBox[{
            {"x"},
            {"y"}
            }], ")"}],
      (MatrixForm[ #]&)]], "Output"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", GridBox[{
            {\(a\ x + b\ y\)},
            {\(c\ x + d\ y\)}
            }], ")"}],
      (MatrixForm[ #]&)]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Det[sampleMatrix]\)], "Input"],

Cell[BoxData[
    \(\(-b\)\ c + a\ d\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(IdentityMatrix[4] // MatrixForm\)], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", GridBox[{
            {"1", "0", "0", "0"},
            {"0", "1", "0", "0"},
            {"0", "0", "1", "0"},
            {"0", "0", "0", "1"}
            }], ")"}],
      (MatrixForm[ #]&)]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Inverse[sampleMatrix] // MatrixForm\)], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", GridBox[{
            {\(d\/\(\(-b\)\ c + a\ d\)\), \(-\(b\/\(\(-b\)\ c + a\ d\)\)\)},
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      (MatrixForm[ #]&)]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Symbolic Computation", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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  "Input"],

Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Builtin Functions", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \(3\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]]
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Cell[CellGroupData[{

Cell["Programming Language", "Title"],

Cell["Function Definition", "Subtitle"],

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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell["File operations and data manipulation", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell["\<\
run1\t0\t1
run2\t1000\t3
run3\t40000\t10
run4\t90000\t22
run5\t160000\t36
run6\t1000000\t227
run7\t4000000\t890
run8\t9000000\t2042
run9\t16000000\t3617\
\>", "Print"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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    data = ReadList[infile, {Word, Number, Number}]\)\)], "Input"],

Cell[BoxData[
    \({{"run1", 0, 1}, {"run2", 1000, 3}, {"run3", 40000, 10}, {"run4", 
        90000, 22}, {"run5", 160000, 36}, {"run6", 1000000, 227}, {"run7", 
        4000000, 890}, {"run8", 9000000, 2042}, {"run9", 16000000, 3617}}\)], 
  "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ select\ specific\ records\ *) \n
    Select[data, #[\([2]\)] < 50000\ &]\)\)], "Input"],

Cell[BoxData[
    \({{"run1", 0, 1}, {"run2", 1000, 3}, {"run3", 40000, 10}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
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      Statistics`DataManipulation`\), 
    \(\t\txydata = Column[data, {2, 3}]\)}], "Input"],

Cell[BoxData[
    \({{0, 1}, {1000, 3}, {40000, 10}, {90000, 22}, {160000, 36}, {1000000, 
        227}, {4000000, 890}, {9000000, 2042}, {16000000, 3617}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Clear[x]; \nfunc = Fit[xydata, {1, x}, x]\)], "Input"],

Cell[BoxData[
    \(\(-0.0941854307867600226`\) + 0.000226101735461922981`\ x\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Imperative Programming", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*if\ stmt, \ For\ stmt, \ block\ for\ multilines*) \n
    Block[{x = 1, y = 3}, \n\tz = x + y; \n\tp = 2*z\n\t]\)\)], "Input"],

Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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  "Input"],

Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ for\ loop\ *) \n
    For[j = 0; i = 0, i < 3, \(j++\); \(i++\), Print[i, j + 1]]\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[\(0\[InvisibleSpace]1\),
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Cell[BoxData[
    InterpretationBox[\(1\[InvisibleSpace]2\),
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Cell[BoxData[
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      SequenceForm[ 2, 3],
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ groups\ of\ statements\ *) \n
    Do[Print[i]; \ Print[j]\n\t, {i, 5, 6}, {j, 1, 2}]\)\)], "Input"],

Cell[BoxData[
    \(5\)], "Print"],

Cell[BoxData[
    \(1\)], "Print"],

Cell[BoxData[
    \(5\)], "Print"],

Cell[BoxData[
    \(2\)], "Print"],

Cell[BoxData[
    \(6\)], "Print"],

Cell[BoxData[
    \(1\)], "Print"],

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]]
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Cell[CellGroupData[{

Cell["Functional Programming", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ map\ a\ function\ to\ a\ list\ of\ items\ *) \n
    Map[Sin, {Pi/2, Pi, Pi/4}]\)\)], "Input"],

Cell[BoxData[
    \({1, 0, 1\/\@2}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*\ apply\ function\ to\ list\ of\ params\ *) \n
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Output to other Languages", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell["4 + Power(Pi,2)", "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell["12*(3 + g)", "Output"]
}, Open  ]]
}, Open  ]]
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Cell[CellGroupData[{

Cell["Visualization/Graphing", "Title"],

Cell["Graphing Equations", "Subtitle"],

Cell[CellGroupData[{

Cell[BoxData[
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