1

This code is building from the solution posted by Ronny found here.

I wanted to know how to remove the chapter number "0" from the front matter pages (like the TOC, list of figures etc.) and the back matter pages that do not have a chapter number associated with them (like the appendix and index).

Here is his code:

\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{lipsum}
\usepackage{xcolor,etoolbox,fancyhdr}
\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{fancy}}{}{}
\usepackage{fourier}
\usepackage{titlesec}
\definecolor{lightblue}{RGB}{199,232,250}
\definecolor{darkblue}{RGB}{59,134,215}
\usetikzlibrary{calc}
% Define just chapter start pages

\pagestyle{fancy}
\fancyhf[LE]{Author's Name}\fancyhead[LE,RO]{}

\fancyhead[LO]{%\textcolor{mybluei} \rightmark%
\begin{tikzpicture}[overlay,remember picture]
    % Box
    \draw[fill=lightblue,draw=none] ($(current page.north east) - (1cm,0)$) -- (current page.north east) -- (current page.south east) -- ++ (-1cm,0) -- cycle;
    % Chapter Number
    \node[scale=3,darkblue] at ($(current page.north east) + (-1cm,-4cm)$)  {\thechapter};
    % Chapter
    \node[rotate=90, anchor=east] at ($(current page.north east) + (-.5cm,-4cm)$) {\leftmark{}};
    % Circle for page number
    \draw[fill=darkblue,draw=none] ($(current page.south east) + (-1cm,3cm)$) circle (3mm);
    % Page number
    \node at ($(current page.south east) + (-1cm,3cm)$)  {\textcolor{white}\thepage};
  \end{tikzpicture}}
\fancyhead[RE]{
\begin{tikzpicture}[overlay,remember picture]
    \draw[fill=lightblue,draw=none] ($(current page.north west) + (1cm,0)$) -- (current page.north west) -- (current page.south west) -- ++ (1cm,0) -- cycle;
    \node[rotate=90,anchor=east] at ($(current page.north west) + (.5cm,-4cm)$) {\rightmark};
    \node[scale=3,darkblue] at ($(current page.north west) + (1cm,-4cm)$) {\thechapter};
    \draw[fill=darkblue,draw=none] ($(current page.south west) + (1cm,3cm)$) circle (3mm);
    \node at ($(current page.south west) + (1cm,3cm)$)  {\textcolor{white}\thepage};
  \end{tikzpicture}}


\renewcommand{\chaptermark}[1]{%
\markboth{#1}{}}

\begin{document}

%========================================================================================
%   TABLE OF CONTENTS
%========================================================================================
\frontmatter
\tableofcontents

\listoffigures

%\lstlistoflistings

\mainmatter
\chapter{My first Chapter: Problems}

\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\subsection{Solution 1}
\lipsum[1-7]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1-4]

\chapter{A second Chapter Title}
\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\newpage
\subsection{Solution 1}
\lipsum[1]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1]

\end{document} 
2

The chapter number is inserted into the margin as the label of a tikz node using \thechapter. As you want to only print the chapter number in the "main matter" parts of the document the best way to control this is to use the \@mainmatter if-flag that is set to true by \mainmatter. The code below replaces the two uses of \thechapter, for the left and right margins, with \TheChapter, which is defined by:

\makeatletter% print \the chapter in main matter components of the document
\newcommand\TheChapter{\if@mainmatter\thechapter\fi}
\makeatother

This has the desired effect (the left-hand margins are similar):

enter image description here enter image description here

As I have used \if@mainmatter, the numbers will stop appearing in the margins after a\backmatter command, which is what I think you wanted.

Here is the full code:

\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{lipsum}
\usepackage{xcolor,etoolbox,fancyhdr}
\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{fancy}}{}{}
\usepackage{fourier}
\usepackage{titlesec}
\definecolor{lightblue}{RGB}{199,232,250}
\definecolor{darkblue}{RGB}{59,134,215}
\usetikzlibrary{calc}
% Define just chapter start pages

\pagestyle{fancy}
\fancyhf[LE]{Author's Name}\fancyhead[LE,RO]{}
\makeatletter% print \the chapter in main matter components of the document
\newcommand\TheChapter{\if@mainmatter\thechapter\fi}
\makeatother
\fancyhead[LO]{%\textcolor{mybluei} \rightmark%
\begin{tikzpicture}[overlay,remember picture]
    % Box
    \draw[fill=lightblue,draw=none] ($(current page.north east) - (1cm,0)$) -- (current page.north east) -- (current page.south east) -- ++ (-1cm,0) -- cycle;
    % Chapter Number
    \node[scale=3,darkblue] at ($(current page.north east) + (-1cm,-4cm)$)  {\TheChapter};% selectively print chapter number
    % Chapter
    \node[rotate=90, anchor=east] at ($(current page.north east) + (-.5cm,-4cm)$) {\leftmark{}};
    % Circle for page number
    \draw[fill=darkblue,draw=none] ($(current page.south east) + (-1cm,3cm)$) circle (3mm);
    % Page number
    \node at ($(current page.south east) + (-1cm,3cm)$)  {\textcolor{white}\thepage};
  \end{tikzpicture}}
\fancyhead[RE]{
\begin{tikzpicture}[overlay,remember picture]
    \draw[fill=lightblue,draw=none] ($(current page.north west) + (1cm,0)$) -- (current page.north west) -- (current page.south west) -- ++ (1cm,0) -- cycle;
    \node[rotate=90,anchor=east] at ($(current page.north west) + (.5cm,-4cm)$) {\rightmark};
    \node[scale=3,darkblue] at ($(current page.north west) + (1cm,-4cm)$) {\TheChapter};% selectively print chapter number
    \draw[fill=darkblue,draw=none] ($(current page.south west) + (1cm,3cm)$) circle (3mm);
    \node at ($(current page.south west) + (1cm,3cm)$)  {\textcolor{white}\thepage};
  \end{tikzpicture}}


\renewcommand{\chaptermark}[1]{%
\markboth{#1}{}}

\begin{document}

%========================================================================================
%   TABLE OF CONTENTS
%========================================================================================
\frontmatter
\tableofcontents

\listoffigures

%\lstlistoflistings
\mainmatter
\chapter{My first Chapter: Problems}

\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\subsection{Solution 1}
\lipsum[1-7]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1-4]

\chapter{A second Chapter Title}
\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\newpage
\subsection{Solution 1}
\lipsum[1]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1]

\end{document}

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