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MATH299M Lesson 1 - Introduction and Basics - with notes.nb
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MATH299M Lesson 1 - Introduction and Basics - with notes.nb
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"\nUse the escape key to create a \[AliasDelimiter] symbol,",
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StyleBox["then type the letters corre",
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"sponding to the symbol you want and press escape (\[AliasDelimiter]) again \
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special character on the right.\n\n",
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StyleBox["and Set Theory ",
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\nand\t\t\[And]\nor\t\t\[Or]\nnot\t\t\[Not]\nfa\t\t\[ForAll]\nex\t\t\[Exists]\
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\[GreaterEqual]\t\[NotLessEqual]\nsub\t\t\[Subset]\t\[NotSubset]\nsup\t\t\
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\t\[SupersetEqual]\t\[NotSupersetEqual]\n\n",
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letter\na\t\[Alpha]\tA\t\[CapitalAlpha]\talpha\t\[Alpha]\tAlpha\t\
\[CapitalAlpha]\nb\t\[Beta]\tB\t\[CapitalBeta]\tbeta\t\t\[Beta]\tBeta\t\t\
\[CapitalBeta]\nc\t\[Chi]\tC\t\[CapitalChi]\tchi\t\t\[Chi]\tChi\t\t\
\[CapitalChi]\nd\t\[Delta]\tD\t\[CapitalDelta]\tdelta\t\[Delta]\tDelta\t\
\[CapitalDelta]\ne\t\[Epsilon]\tE\t\[CapitalEpsilon]\tepsilon\t\[Epsilon]\t\
Epsilon\t\[CapitalEpsilon]\nf\t\[Phi]\tF\t\[CapitalPhi]\tphi\t\t\[Phi]\tPhi\t\
\t\[CapitalPhi]\ng\t\[Gamma]\tG\t\[CapitalGamma]\tgamma\t\[Gamma]\tGamma\t\
\[CapitalGamma]\nh\t\[Eta]\tH\t\[CapitalEta]\teta\t\t\[Eta]\tEta\t\t\
\[CapitalEta]\ni\t\[Iota]\tI\t\[CapitalIota]\tiota\t\t\[Iota]\tIota\t\t\
\[CapitalIota]\nj\t\[CurlyPhi]\nk\t\[Kappa]\tK\t\[CapitalKappa]\tkappa\t\
\[Kappa]\tKappa\t\[CapitalKappa]\nl\t\[Lambda]\tL\t\[CapitalLambda]\tlambda\t\
\[Lambda]\tLambda\t\[CapitalLambda]\nm\t\[Mu]\tM\t\[CapitalMu]\tmu\t\t\[Mu]\t\
Mu\t\t\[CapitalMu]\nn\t\[Nu]\tN\t\[CapitalNu]\tnu\t\t\[Nu]\tNu\t\t\
\[CapitalNu]\no\t\[Omega]\tO\t\[CapitalOmega]\tomega\t\[Omega]\tOmega\t\
\[CapitalOmega]\np\t\[Pi]\tP\t\[CapitalPi]\tpi\t\t\[Pi]\tPi\t\t\[CapitalPi]\n\
q\t\[Theta]\tQ\t\[CapitalTheta]\ttheta\t\[Theta]\tTheta\t\[CapitalTheta]\nr\t\
\[Rho]\tR\t\[CapitalRho]\trho\t\t\[Rho]\tRho\t\t\[CapitalRho]\ns\t\[Sigma]\tS\
\t\[CapitalSigma]\tsigma\t\[Sigma]\tSigma\t\[CapitalSigma]\nt\t\[Tau]\tT\t\
\[CapitalTau]\ttau\t\t\[Tau]\tTau\t\t\[CapitalTau]\nu\t\[Upsilon]\tU\t\
\[CapitalUpsilon]\tupsilon\t\[Upsilon]\tUpsilon\t\[CapitalUpsilon]\nv\t\[Vee]\
\nw\t\[Omega]\tW\t\[CapitalOmega]\tomega\t\[Omega]\tOmega\t\[CapitalOmega]\nx\
\t\[Xi]\tX\t\[CapitalXi]\txi\t\t\[Xi]\tXi\t\t\[CapitalXi]\ny\t\[Psi]\tY\t\
\[CapitalPsi]\tpsi\t\t\[Psi]\tPsi\t\t\[CapitalPsi]\nz\t\[Zeta]\tZ\t\
\[CapitalZeta]\tzeta\t\t\[Zeta]\tZeta\t\t\[CapitalZeta]\n\n",
StyleBox["Double Struck and Script Letters ",
FontWeight->"Bold"],
"-",
StyleBox[" ",
FontWeight->"Bold"],
"Type escape ds and then a letter to get a double-struck version of it, and \
sc for a script version",
StyleBox["\n",
FontWeight->"Bold"],
"dsR\t\[DoubleStruckCapitalR]\ndsQ\t\[DoubleStruckCapitalQ]\ndsZ\t\
\[DoubleStruckCapitalZ]\ndsN\t\[DoubleStruckCapitalN]\nscS\t\[ScriptCapitalS]\
\nscA\t\[ScriptCapitalA]\nscm\t\[ScriptM]"
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Cell[TextData[StyleBox["f[x,y] - function argument are placed in square \
brackets\nx = val - set a value\nx == val - test equality\nleftHandSide := \
rightHandSide - function \na-> b - rule for transformations\na b c - spaces \
mean multiplication\n\n\nOn the left of operation you can see a \
\[OpenCurlyDoubleQuote]In[x]\[CloseCurlyDoubleQuote] and \
\[OpenCurlyDoubleQuote]Out[x]\[CloseCurlyDoubleQuote] label to differentiate \
between input and output, will be nice when your programs get much more \
complex!",
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Cell["nn *^ee - scientific notation", "Text",
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/@ symbol is shorthand for map notation (which we will get into)\
\>", "Text",
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? symbol to get information on a function or symbol (demonstrated later in \
lesson)\
\>", "Text",
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"Congrats! You did a computation. Notice how it says In[1]:= next to the \
input cell and Out[1]:= next to the output cell? We\[CloseCurlyQuote]re going \
to want to leave those output cells alone, and just mess with the input \
cells. You can change the values in \[OpenCurlyDoubleQuote]2+2\
\[CloseCurlyDoubleQuote] to something else, maybe \
\[OpenCurlyDoubleQuote]2+2+3\[CloseCurlyDoubleQuote], then evaluate the input \
cell again, and it will override the previous output in the output cell. \
Think of each input cell as having its own output cell corresponding to it, \
in which the results of all of your calculations will reside. Mathematica\
\[CloseCurlyQuote]s style is ",
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" dependent on this input-output structure, that is, everything you do with \
Mathematica will be to generate something in an output cell, whether that be \
a number, plot, etc. Oh, and if it wasn\[CloseCurlyQuote]t obvious, that\
\[CloseCurlyQuote]s how you comment out code!"
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Cell["\<\
We can output multiple things by pressing return between lines of input, that \
is, separating input by a new line will give us a new output for the input on \
that line. Here we get three separate output blocks generated from one input \
block.\
\>", "Text",
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When we evaluate a cell where we assign a variable a value, the output that \
Mathematica gives is that value. This often isn\[CloseCurlyQuote]t useful to \
us, we know what we just put in that variable. Below is an example where we \
define two variables and then suppress the output by using a semicolon, \
however notice I left the third line of input without a semicolon so that it \
would evaluate.\
\>", "Text",
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We can also put new commands right after something with a semicolon without a \
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Now let us say that you want to get a numerical approximation, no worries: \
use N[]\
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But now you have decided that you would like to instead be able to get more \
decimals spots...\
\>", "Text",
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But 10 is not enough you in Mathematica it is go big or go home....\
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Some of your operations should be in scientific form because otherwise we do \
not want to look at it\
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Okay, now let\[CloseCurlyQuote]s start doing things. Functions are called by \
writing the name of the function and then putting the arguments of the \
function in square braces, delimited by commas. All of the functions I use \
below as examples are built in to Mathematica.\
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General form of a function Name[argument, more argument, more more \
argument...] (Case sensitive, starts with capital letter and the full word is \
written)\
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