notation.tex

\Extrachap{Notations}\label{sec:Notation}

\section*{General Math Notations}

\begin{longtable}{cl}
\hline\noalign{\smallskip}
\textbf{Symbol} & \textbf{Meaning} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\lfloor x \rfloor$ & Floor of $x$, i.e. round down to nearest integer\\
$\lceil x \rceil$ & Ceiling of $x$, i.e. round up to nearest integer\\
% floor(key) & The largest key $\leq$ the given key \\
% ceil(key) & The smallest key $\geq$ the given key \\
$\log x$ & The base of logarithm is 2 unless otherwise stated\\
$a \wedge b$ & Logical AND\\
$a \vee b$ & Logical OR\\
$\neg a $ & Logical NOT\\
$a\AND b$ & Bit AND\\
$a \OR b$ & Bit OR\\
$a \XOR  b$ & Bit XOR\\
$\NOT a$ & Bit NOT\\
$\SHIFTL a$ & Bit shift left\\
$\SHIFTR a$ & Bit shift right\\
$\infty$ & Infinity\\
$\rightarrow$ & Tends towards, e.g., $n \rightarrow \infty$\\
$\propto$ &Proportional to; $y = ax$ can be written as $y \propto x$\\
$\abs{x}$ & Absolute value\\
$||\vec{a}||$ & $L_2$ distance (Euclidean distance) of a vector; norm-2 \\
$\abs{\mathcal{S}}$ & Size (cardinality) of a set\\
$n!$ & Factorial function\\
$\triangleq$ & Defined as\\
$O(\cdot)$ & Big-O notation, complexity upper bound\\
$\mathbb{R}$ & The real numbers\\
$0:n$ & Range (Python convention): $0:n = {0, 1, 2,...,n-1}$\\
$\approx$ & Approximately equal to\\
$\sim$ & Tilde, the leading term of mathematical expressions \\
$\arg\max\limits_x f(x)$ & Argmax: the value $x$ that maximizes $f$\\
$\binom{n}{k}$ & $n$ choose $k$ , equal to $\frac{n!}{k!(n-k)!}$\\
$\text{range}(i,j)$ & Range of number from i (inclusive) to j (exclusive) \\
$A[i:j]$ & Subarray consist of $A_i, A_{i+1}, ..., A_{j-1}$.
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{longtable}


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