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flyleaf.tex
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flyleaf.tex
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\begin{center}
\renewcommand{\arraystretch}{1.07}
{\large\textsc{Notation}} \\[3ex]
\begin{tabular}{r|l}
$\N$ &natural numbers $\set{0,1,2,\ldots}$ \\
$\Z$, $\Z^+$ &integers $\set{\ldots, -2,-1,0,1,2,\ldots}$,
positive integers $\set{1,2,\ldots}$ \\
% $\Z^+$ &positive integers; $\set{1,2,\ldots}$ \\
$\R$ &real numbers \\
$\Q$ &rational numbers \\
$a\divides b$ &$a$ divides~$b$ \\
$a\bmod b$ &the remainder when $a$ is divided by $b$ \\
$a\equiv c\pmod b$ &$a$ and $c$ have the same remainder when divided by $b$ \\
$\gcd(a,b)$, $\lcm(a,b)$ &greatest common divisor, least common multiple \\
$a\in A$ &$a$ is an element of the set $A$ \\
$\emptyset$ &empty set $\set{}$ \\
$A\subseteq B$ &$A$ is a subset of~$B$ \\
$\charfcn{A}$ &characteristic function of the set~$A$ \\
$\setcomp{A}$ &complement of the set~$A$ \\
$A\union B$, $A\intersection B$ &union, intersection of the sets \\
$A- B$, $A\symdiff B$ &difference, symmetric difference of the sets \\
$|A|$ &order of the set $A$; the number of elements \\
$\powerset(A)$ &power set of $A$; the set of all of $A$'s subsets \\
$\seq{x_0,x_1,\ldots}$, $(x_0,x_1)$ &sequence, ordered pair \\
$\lh(\seq{x_0,x_1,\ldots})$ &length of the sequence \\
$A_0\times A_1\times \cdots \times A_{n-1}$, $A^n$ &Cartesian product of sets, product of a set with itself \\
$\map{f}{D}{C}$ &function with domain~$D$ and codomain~$C$ \\
$\map{\identity}{D}{D}$ &identity map; $\identity(d)=d$ \\
$\restrictionmap{f}{B}$ &restriction of $f$ to a subset of the domain \\
$f^{-1}(c)$, $f^{-1}(A)$ &inverse image of an element or subset of the codomain \\
$\composed{g}{f}$ &function composition \\
$f^{-1}$ &function inverse to~$f$ \\
$x\equiv y\pmod R$ &$(x,y)\in R$ where $R$ is an equivalence relation \\
$\eqclass{x}$ &equivalence class containing~$x$ \\
$\partition{P}$ &partition of a set \\
$A\sim B$ &two sets with the same cardinality
\end{tabular}
\end{center}
\vspace*{\fill}
\begin{center}
{\large\textsc{Greek letters with pronounciation}}
\\[3ex]
\newcommand{\pronounced}[1]{\hspace*{.2em}\small\textit{#1}}
\begin{tabular}{cl@{\hspace*{3em}}cl}
character &\multicolumn{1}{c}{\makebox[-3.5em][r]{name}}
&character &\multicolumn{1}{c}{\makebox[-3.5em][r]{name}} \\
\hline
\makebox[1em][l]{\( \alpha \)} &alpha \pronounced{AL-fuh}
&\makebox[1em][l]{\( \nu \)} &nu \pronounced{NEW} \\
\makebox[1em][l]{\( \beta \)} &beta \pronounced{BAY-tuh}
&\makebox[1em][l]{\( \xi \), \( \Xi \)} &xi \pronounced{KSIGH} \\
\makebox[1em][l]{\( \gamma \), \( \Gamma \)} &gamma \pronounced{GAM-muh}
&\makebox[1em][l]{\( o \)} &omicron \pronounced{OM-uh-CRON} \\
\makebox[1em][l]{\( \delta \), \( \Delta \)} &delta \pronounced{DEL-tuh}
&\makebox[1em][l]{\( \pi \), \( \Pi \)} &pi \pronounced{PIE} \\
\makebox[1em][l]{\( \epsilon\)} &epsilon \pronounced{EP-suh-lon}
&\makebox[1em][l]{\( \rho \)} &rho \pronounced{ROW} \\
\makebox[1em][l]{\( \zeta \)} &zeta \pronounced{ZAY-tuh}
&\makebox[1em][l]{\( \sigma \), \( \Sigma \)} &sigma \pronounced{SIG-muh} \\
\makebox[1em][l]{\( \eta \)} &eta \pronounced{AY-tuh}
&\makebox[1em][l]{\( \tau \)} &tau \pronounced{TOW (as in cow)} \\
\makebox[1em][l]{\( \theta \), \( \Theta \)} &theta \pronounced{THAY-tuh}
&\makebox[1em][l]{\( \upsilon\), \( \Upsilon \)} &upsilon \pronounced{OOP-suh-LON} \\
\makebox[1em][l]{\( \iota \)} &iota \pronounced{eye-OH-tuh}
&\makebox[1em][l]{\( \phi \), \( \Phi \)} &phi \pronounced{FEE, or FI (as in hi)} \\
\makebox[1em][l]{\( \kappa \)} &kappa \pronounced{KAP-uh}
&\makebox[1em][l]{\( \chi \)} &chi \pronounced{KI (as in hi)} \\
\makebox[1em][l]{\( \lambda \), \( \Lambda \)} &lambda \pronounced{LAM-duh}
&\makebox[1em][l]{\( \psi \), \( \Psi \)} &psi \pronounced{SIGH, or PSIGH} \\
\makebox[1em][l]{\( \mu \)} &mu \pronounced{MEW}
&\makebox[1em][l]{\( \omega \), \( \Omega \)} &omega \pronounced{oh-MAY-guh}
\end{tabular} \\[3ex]
The capitals shown are the ones that differ from Roman capitals.
\end{center}