Skip to main content\(\newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}}
\newcommand{\lb}{\mathrm{lb}} \newcommand{\ub}{\mathrm{ub}}
\newcommand{\vx}{\mathbf{x}} \newcommand{\va}{\mathbf{a}}
\newcommand{\vb}{\mathbf{b}} \newcommand{\vc}{\mathbf{c}}
\newcommand{\vy}{\mathbf{y}} \newcommand{\vz}{\mathbf{z}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Analysis for Beginners
September 25, 2026
