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\(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newcommand{\F}{\mathbb F}
\newcommand{\ev}{{\mathrm ev}}
\newcommand{\Inn}[1]{\operatorname{Inn}\left(#1\right)}
\newcommand{\Gal}[2]{\operatorname{Gal}\left(#1/#2\right)}
\newcommand{\Aut}[2]{\operatorname{Aut}\left(#1/#2\right)}
\newcommand{\unit}{1\!\!1}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
The following notes are intended as a supplement/companion to the textbook. Some remarks/notes that are not directly given in the Fields and Galois theory chapters are included here.