documentclass[10pt, twoside]{book}
usepackage[demo]{graphicx}   %%% remove demo in your file
usepackage{multicol}
usepackage{caption}

begin{document}

 begin{multicols}{2}
 a test file for picture inclusion along with the captions and labeling
begin{center}
 fbox{includegraphics[scale=0.2]{Cauchy_sequence_illustration-png}}
 captionof{figure}{Cauchy Seq1}label{Cauchy1}
 fbox{includegraphics[scale=0.2]{Cauchy_sequence_illustration-png}}
 captionof{figure}{Cauchy Seq2}label{Cauchy2}
 end{center}
 end{multicols}

 end{document}

documentclass[10pt, twoside]{book}
usepackage[demo]{graphicx}   %%% remove demo in your file
usepackage{multicol}
usepackage{caption}
usepackage{kantlipsum}

begin{document}

 begin{multicols}{2}
 kant[1]
 end{multicols}

noindent
begin{minipage}{0.5textwidth}
centering
 fbox{includegraphics[width=dimexprtextwidth-2fboxsep-2fboxrulerelax]{Cauchy_sequence_illustration-png}}
 captionof{figure}{Cauchy Seq1}label{Cauchy1}
end{minipage}%
begin{minipage}{0.5textwidth}
centering
 fbox{includegraphics[width=dimexprtextwidth-2fboxsep-2fboxrulerelax]{Cauchy_sequence_illustration-png}}
 captionof{figure}{Cauchy Seq2}label{Cauchy2}
 end{minipage}

 begin{multicols}{2}
 kant[1]
 end{multicols}
 end{document}