(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 21804, 810]*) (*NotebookOutlinePosition[ 52092, 1930]*) (* CellTagsIndexPosition[ 52048, 1926]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Discovering Number Theory", "Subtitle"], Cell["\<\ Jeffrey J. Holt University of Virginia John W. Jones Arizona State University\ \>", "Text", TextAlignment->Center, TextJustification->0], Cell["Copyright \[Copyright] 2001 by W. H. Freeman and Company", "Text", TextAlignment->Center, TextJustification->0, FontSize->10] }, Closed]], Cell["Introduction to Using Mathematica", "Title", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Initializations", "Subsection", Evaluatable->False, TextAlignment->Left, AspectRatioFixed->True], Cell[BoxData[ \(Off[General::"\"]; \nOff[General::"\"]; \)], "Input", InitializationCell->True, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Mathematica Basics\n", StyleBox["Click twice on the outer bracket at the right to open the cell.", FontFamily->"Courier", FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }], "Section", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ If you're reading this cell now, then you've mastered the second \ hardest thing about Mathematica -- figuring out how to open a closed \ collection of cells. \ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ The hardest thing about Mathematica is figuring out how to have \ Mathematica execute a computation. For example, to have Mathematica evaluate \ 17 + 34, we type\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(17 + 34\)], "Input", AspectRatioFixed->True], Cell[TextData[{ "To perform a computation, click the mouse on the command you want to \ execute, hold down the ", StyleBox["Shift", FontWeight->"Bold"], " key, and press the normal carriage return key, labeled ", StyleBox["Enter", FontWeight->"Bold"], " or ", StyleBox["Return", FontWeight->"Bold"], ". (Hitting only the ", StyleBox["Enter", FontWeight->"Bold"], " key in the numeric keypad portion of your keyboard will also work, \ although we do not openly advocate hitting computers.) Try it out on the \ above command. The first time that you execute a command in a Mathematica \ session, you will be asked \"Do you want to automatically evaluate all of the \ initialization cells in this notebook?\" Your response to this question \ should always be \"Yes\"." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ If everything works the way it should, then you will get the answer \ 51. If you don't, ask for help. \ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["Try having Mathematica evaluate the following:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(3 + 4\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(13 - 47\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(12\ 23\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(12*23\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(284/16\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(2^143\)], "Input", AspectRatioFixed->True], Cell[TextData[{ "Notice that ", StyleBox["12 23", "Input"], " and ", StyleBox["12*23", "Input"], " have the same effect. Multiplication can be indicated either with the \ symbol ", StyleBox["*", "Input"], " or by leaving a space between the two quantities that are to be \ multiplied together." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Now that you have made some modifications to this notebook, you should \ save your work. Doing so is easy: Click on ", StyleBox["Save", FontWeight->"Bold"], " in the ", StyleBox["File", FontWeight->"Bold"], " menu. There is also a keyboard \"shortcut\" that you can use. On a \ Windows machine, hold down the ", StyleBox["Ctrl", FontWeight->"Bold"], " key and type ", StyleBox["s", FontWeight->"Bold"], ". On a Macintosh, hold down the \"cloverleaf\" key adjacent to the ", StyleBox["Space", FontWeight->"Bold"], " bar and type ", StyleBox["s", FontWeight->"Bold"], ". (In the future, we shall use the word ", StyleBox["control", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], " to refer to the ", StyleBox["Ctrl", FontWeight->"Bold"], " key on a Windows machine and the \"cloverleaf\" key on a Macintosh. If \ you are using something other than a Windows machine or a Macintosh, check \ with your instructor to determine your \"control\" key.) You should save \ frequently to avoid losing your work if the machine malfunctions." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Everything in a Mathematica notebook is contained in \"cells\". \ The scope of a given cell is indicated by the square bracket at the right. \ There are a variety of different kinds of cells. This one is called a \"text\ \" cell, and (you guessed it) is used for text. There are other kinds of \ cells, such as those shown below:\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(This\ is\ an\ input\ cell . \ \((Do\ not\ \(execute . \))\)\)], "Input",\ AspectRatioFixed->True], Cell["This is a text cell.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["This is a subsection cell.", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "You can change the type of cell by clicking on the cell bracket (it will \ become shaded) and then by clicking on the ", StyleBox["Format", FontWeight->"Bold"], " menu and selecting ", StyleBox["Style", FontWeight->"Bold"], ". The different types of cells allow great freedom in customizing \ notebooks. " }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "To create a new cell, move the cursor until it is between cells (the \ cursor will change from vertical to horizontal) and then click. A horizontal \ line should appear. Then start typing; you will get an ", StyleBox["input", FontWeight->"Bold"], " cell, which can be changed to a different type of cell using the ", StyleBox["Style", FontWeight->"Bold"], " menu within the ", StyleBox["Format", FontWeight->"Bold"], " menu." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Create a cell below this one to compute 123!. (The \"!\" is not at \ the end of the sentence for emphasis, it's there to indicate the factorial \ operation. Factorials are entered just as shown).\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "You can obtain decimal approximations using the command \"", StyleBox["N", "Input"], "\". For instance, when you executed the command to compute ", StyleBox["284/16", "Input"], ", Mathematica reduced the fraction but returned a fraction as output. To \ get a decimal approximation, run the command below:" }], "Text"], Cell[BoxData[ \(N[284/16]\)], "Input", AspectRatioFixed->True], Cell[TextData[ "You can get more decimal places. For instance, here are 100 digits of \ \[Pi]:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(N[Pi, 100]\)], "Input", AspectRatioFixed->True], Cell["\<\ To close this collection of cells, click twice on the outer cell \ bracket.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ " Adept Algebra with Mathematica\n", StyleBox["Click twice on the outer bracket at the right to open the cell.", FontFamily->"Courier", FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Here is ", Cell[BoxData[ \(TraditionalForm\`\((x\ + \ 2\ y)\)\^\(25\ \)\)]], "multiplied out:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(Clear[x, y]\), \(Expand[\((x + 2 y)\)^25]\)}], "Input", AspectRatioFixed->True], Cell[TextData[{ "If you don't hang the command ", StyleBox["Expand", "Input"], " with the square brackets ", StyleBox["[ ]", "Input"], " around the product, Mathematica will not multiply out the terms because \ it was not told to do so. 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To Mathematica, \"", StyleBox["ab", "Input"], "\" is not a product but a two\[Hyphen]letter variable name." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(a\ b\), \(ab\)}], "Input", AspectRatioFixed->True], Cell[TextData[{ "Note that Mathematica remembers the values of ", StyleBox["a", "Input"], " and ", StyleBox["b", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell["Exercise 1", "Subsubsection", CellDingbat->"\[GraySquare]", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ The following calculations suggest a pattern. What is the general \ formula suggested by these calculations? \ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(Clear[x]\), \(Expand[\((1 - x)\)\ \((1 + x)\)]\), \(Expand[\((1 - x)\)\ \((1 + x + x^2)\)]\), \(Expand[\((1 - x)\)\ \((1 + x + x^2 + x^3)\)]\), \(Expand[\((1 - x)\)\ \((1 + x + x^2 + x^3 + x^4)\)]\)}], "Input", AspectRatioFixed->True] }, Closed]], Cell["Save your work!", "Text", CellDingbat->None, CellMargins->{{10, Inherited}, {Inherited, Inherited}}, Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True, FontSize->14, FontColor->RGBColor[1, 0, 0]], Cell["\<\ To close this collection of cells, click twice on the outer cell \ bracket.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Defining Functions and Constants\n", StyleBox["Click twice on the outer bracket at the right to open the cell.", FontFamily->"Courier", FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }], "Section", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Defining functions in Mathematica is easy. Here's an example:\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(f[x_] := Cos[x]; \)\)], "Input", AspectRatioFixed->True], Cell[TextData[{ "By executing the above command (which you should do now if you haven't \ already), you tell Mathematica that the function ", StyleBox["f", "Input"], " is defined to be ", StyleBox["Cos[x]", "Input"], ". There are three important points that you need to remember when \ defining functions:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "1. You must use the underscore \"", StyleBox["_", "Input"], "\" on the left side of the definition." }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "2. You must use square brackets \"", StyleBox["[ ]", "Input"], "\" rather then parentheses \"", StyleBox["( )", "Input"], "\"." }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "3. You should use \"", StyleBox[":=", "Input"], "\" in the definition. (In most cases, \"", StyleBox["=", FontWeight->"Bold"], "\" will also work.)" }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "To evaluate a function, you just \"plug in\" a value. For instance, if we \ want to know ", StyleBox["f[7\[Pi]/12]", "Input"], ", we just type it in:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(f[7 Pi/12]\)], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["Note", FontWeight->"Bold"], ": For this command to evaluate properly, you must first have executed the \ definition for ", StyleBox["f", "Input"], " above. All definitions must be executed prior to their use during ", StyleBox["each", FontWeight->"Bold"], " Mathematica session." }], "Text"], Cell[TextData[{ "Here's ", StyleBox["f[1]", "Input"], ":" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(f[1]\)], "Input", AspectRatioFixed->True], Cell[TextData[{ "Remember that Mathematica gives exact answers unless told to do otherwise. \ Here's a decimal approximation to ", StyleBox["f[1]", "Input"], ":" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(N[f[1]]\)], "Input", AspectRatioFixed->True], Cell[TextData[{ "Defining constants is even easier than defining functions. Suppose that \ you wish to set the constant ", StyleBox["a", "Input"], " to be equal to 1.4142135624, which happens to be the first ten decimal \ places of the square root of 2. All you do is the following:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(a = 1.4142135624\)], "Input", AspectRatioFixed->True], Cell["\<\ To close this collection of cells, click twice on the outer cell \ bracket.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Two Useful Commands\n", StyleBox["Click twice on the outer b....., well, you know the drill!", FontFamily->"Courier", FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }], "Section", Evaluatable->False, AspectRatioFixed->True], Cell["Two commands that you will use constantly are ", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ 1. Copy 2. Paste.\ \>", "Listing"], Cell["Here is an example of how to use these commands.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(N[3432902008176640000/121645100408832000]\)], "Input"], Cell["\<\ 1. Select the cell above by clicking on the bracket at the right.\ \ \>", "Listing", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "2. Hold down the \"control\" key and hit ", StyleBox["c", FontWeight->"Bold"], ". This copies the cell to the computer's memory. (This is the copy \ part.)" }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ 3. Move the cursor down below this cell. Put the cursor in a space \ between two of the brackets on the right. The cursor will switch from \ vertical to horizontal. Click the mouse once. A horizontal line will appear \ on the screen.\ \>", "Listing", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "4. Hold down the \"control\" key, and hit ", StyleBox["v", FontWeight->"Bold"], ". A copy of the cell you chose should now appear on the screen. (This is \ the pasting part.)" }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ 5. Use the mouse to select the first digit in the numerator. Use \ the keyboard to change it from 3 to 2. Run your new command. The answer \ should be 20.\ \>", "Listing", Evaluatable->False, AspectRatioFixed->True], Cell["Some other things about copy\[Hyphen]and\[Hyphen]paste:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "6. You can use copy\[Hyphen]and\[Hyphen]paste on whole cells. Click on the \ bracket defining the cell, hit \"control\"-", StyleBox["c", FontWeight->"Bold"], " to copy. Later, use \"control\"-", StyleBox["v", FontWeight->"Bold"], " to paste." }], "Listing", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ 7. You can use copy\[Hyphen]and\[Hyphen]paste to copy materials \ from one part of a notebook to another. You can also use copy\[Hyphen]and\ \[Hyphen]paste between notebooks. This can be very useful when you have an \ elaborate set of instructions in one notebook that you want to copy to \ another notebook.\ \>", "Listing", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["Getting Help in Mathematica", "Section", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Mathematica is a big program with lots of parts. However, it's not \ necessary to learn everything about Mathematica in order to use it. Feel \ free to experiment -- look at the menus, try out different things, play with \ the program. Don't be afraid of breaking anything. You can't break the \ machine just by pushing keys!\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "You can get help from the Mathematica program itself. If you want to find \ out what a certain function does, you can type ?\"", StyleBox["FunctionName", "Input"], "\". For example, to find out what the functions ", StyleBox["Divisors", "Input"], " and ", StyleBox["FactorInteger", "Input"], " do, you would type:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(?Divisors\)\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(?FactorInteger\)\)], "Input", AspectRatioFixed->True], Cell["You get more information by using two question marks:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(?? Divisors\)], "Input", AspectRatioFixed->True], Cell[BoxData[ \(?? FactorInteger\)], "Input", AspectRatioFixed->True], Cell["\<\ Selecting \"Help . . .\" in the \"Help\" menu provides a means of \ searching for commands.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ As you go along, you may find that something doesn't work the way \ you expect it to, or that there is something you would like Mathematica to \ do, but you don't know how to make it work. In those cases, you should seek \ help from the following sources:\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "1. Your fellow students.\n2. The lab assistant (if there is one).\n3. Your \ teacher.\n4. The ? command.\n4", Cell[BoxData[ FormBox[ StyleBox[ FractionBox[ StyleBox["1", FontWeight->"Bold"], StyleBox["2", FontWeight->"Bold"]], FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], TraditionalForm]]], ". The ?? command.\n5. The function browser in the Help menu.\n6. The \ Mathematica manual. 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Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Text", FontFamily->"Times", FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, TextJustification->1, LineSpacing->{1, 5}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, TextJustification->1, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, TextJustification->1] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellFrame->True, CellMargins->{{12, 10}, {7, 7}}, CellGroupingRules->"OutputGrouping", TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"SmallText", FontFamily->"Times", FontSize->12, FontSlant->"Plain"], Cell[StyleData["SmallText", "Presentation"], CellFrame->True, CellMargins->{{14, 24}, {8, 8}}, TextJustification->1, LineSpacing->{1, 5}, FontSize->12, FontSlant->"Plain"], Cell[StyleData["SmallText", "Condensed"], CellFrame->True, CellMargins->{{14, 24}, {5, 5}}, TextJustification->1, LineSpacing->{1, 2}, FontSize->12, Background->GrayLevel[1]], Cell[StyleData["SmallText", "Printout"], CellFrame->True, CellMargins->{{14, 24}, {5, 5}}, TextJustification->1, FontSize->12, Background->GrayLevel[1]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the kernel. Be careful when modifying, renaming, or removing these styles, because the front end associates special meanings with these style names. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output", FontSize->12], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontSize->12, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None, FontSize->12], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontSize->12], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->12], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->12, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, etc. They automatically give the cell a FrameLabel containing a reference to a particular counter, and also increment that counter. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, TextAlignment->Center, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False, FontSize->12], Cell[StyleData["NumberedEquation", "Presentation"]], Cell[StyleData["NumberedEquation", "Condensed"]], Cell[StyleData["NumberedEquation", "Printout"]] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "NumberedFigure"]}]], None}}, CounterIncrements->"NumberedFigure", ImageMargins->{{43, Inherited}, {Inherited, 0}}, FormatTypeAutoConvert->False], Cell[StyleData["NumberedFigure", "Presentation"]], Cell[StyleData["NumberedFigure", "Condensed"]], Cell[StyleData["NumberedFigure", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{44, Inherited}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Table ", CounterBox[ "NumberedTable"]}]], None}}, TextAlignment->Center, CounterIncrements->"NumberedTable", FormatTypeAutoConvert->False], Cell[StyleData["NumberedTable", "Presentation"]], Cell[StyleData["NumberedTable", "Condensed"]], Cell[StyleData["NumberedTable", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], ShowCellBracket->False, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True, StyleMenuListing->None, FontSize->12, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{0, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Research Question"], CellDingbat->"\[GraySquare]", CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->"InputGrouping", PageBreakBelow->False, CellFrameLabelMargins->6, LineSpacing->{1, 3}, CounterIncrements->"Text", FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Research Question", "Presentation"], CellDingbat->"\[GraySquare]", CellMargins->{{36, 10}, {11, 32}}, CellGroupingRules->"InputGrouping", LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Research Question", "Condensed"], CellDingbat->"\[GraySquare]", CellMargins->{{16, Inherited}, {6, 12}}, CellGroupingRules->"InputGrouping", FontSize->14], Cell[StyleData["Research Question", "Printout"], CellDingbat->"\[GraySquare]", CellMargins->{{9, 0}, {7, 22}}, CellGroupingRules->"InputGrouping", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Listing"], CellMargins->{{63, 10}, {7, 7}}, TextJustification->1, LineSpacing->{1, 3}, CounterIncrements->"Text", FontFamily->"Times", FontSize->12], Cell[StyleData["Listing", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, TextJustification->1, LineSpacing->{1, 5}], Cell[StyleData["Listing", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, TextJustification->1, LineSpacing->{1, 1}], Cell[StyleData["Listing", "Printout"], CellMargins->{{2, 2}, {6, 6}}, TextJustification->1] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], ShowCellBracket->False, CellMargins->{{10, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, TextAlignment->Center, ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, FontSize->18, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["DisplayFormula", "Presentation"], TextAlignment->Center, LineSpacing->{1, 5}, FontSize->18], Cell[StyleData["DisplayFormula", "Condensed"], TextAlignment->Center, LineSpacing->{1, 1}, FontSize->18], Cell[StyleData["DisplayFormula", "Printout"], TextAlignment->Center, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], ShowCellBracket->False, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->15], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->10.5], Cell[StyleData["Program", "Printout"], CellMargins->{{0, 0}, {6, 6}}, FontSize->9.5] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", 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StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, or between Notebooks. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help system. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in palette templates. \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most cells. If a cell's FormatType matches the name of one of the styles defined below, then that style is applied between the cell's style and its own options. \ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell within another. \ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 45, 0, 46, "Subtitle"], Cell[1779, 53, 151, 8, 109, "Text"], Cell[1933, 63, 137, 3, 30, "Text"] }, Closed]], Cell[2085, 69, 98, 2, 55, "Title", Evaluatable->False], Cell[CellGroupData[{ Cell[2208, 75, 108, 3, 49, "Subsection", Evaluatable->False], Cell[2319, 80, 144, 3, 70, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[2500, 88, 281, 9, 49, "Section", Evaluatable->False], Cell[2784, 99, 231, 6, 52, "Text", Evaluatable->False], Cell[3018, 107, 234, 6, 52, "Text", Evaluatable->False], Cell[3255, 115, 66, 2, 30, "Input"], Cell[3324, 119, 863, 22, 128, "Text", Evaluatable->False], Cell[4190, 143, 174, 5, 33, "Text", Evaluatable->False], Cell[4367, 150, 110, 2, 33, "Text", Evaluatable->False], Cell[4480, 154, 64, 2, 30, "Input"], Cell[4547, 158, 66, 2, 30, "Input"], Cell[4616, 162, 65, 2, 30, "Input"], Cell[4684, 166, 64, 2, 30, "Input"], Cell[4751, 170, 65, 2, 30, "Input"], Cell[4819, 174, 64, 2, 30, "Input"], Cell[4886, 178, 369, 12, 54, "Text", Evaluatable->False], Cell[5258, 192, 1201, 34, 147, "Text", Evaluatable->False], Cell[6462, 228, 405, 8, 71, "Text", Evaluatable->False], Cell[6870, 238, 120, 3, 30, "Input"], Cell[6993, 243, 84, 2, 33, "Text", Evaluatable->False], Cell[7080, 247, 96, 2, 49, "Subsection", Evaluatable->False], Cell[7179, 251, 402, 12, 71, "Text", Evaluatable->False], Cell[7584, 265, 530, 15, 71, "Text", Evaluatable->False], Cell[8117, 282, 268, 6, 52, "Text", Evaluatable->False], Cell[8388, 290, 346, 7, 73, "Text"], Cell[8737, 299, 68, 2, 30, "Input"], Cell[8808, 303, 154, 4, 33, "Text", Evaluatable->False], Cell[8965, 309, 69, 2, 30, "Input"], Cell[9037, 313, 188, 7, 30, "Text", Evaluatable->False] }, Closed]], 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