move all iamges to separate files

40 files changed, 670 insertions, 482 deletions

diff --git a/buch/chapters/05-zahlen/ganz.tex b/buch/chapters/05-zahlen/ganz.tex
index 4809e29..fab2dcb 100644
--- a/buch/chapters/05-zahlen/ganz.tex
+++ b/buch/chapters/05-zahlen/ganz.tex
@@ -28,6 +28,14 @@ Die Rechenoperationen sind wie folgt definiert:
 \end{aligned}
 \label{buch:zahlen:ganze-rechenregeln}
 \end{equation}
+Die Darstellung ganzer Zahlen als Paare von natürlichen Zahlen
+findet man auch in der Buchhaltung, wo man statt eines Vorzeichen
+{\em Soll} und {\em Haben} verwendet.
+Dabei kommt es nur auf die Differenz der beiden Positionen an.
+Fügt man beiden Positionen den gleichen Betrag hinzu, ändert sich
+nichts.
+Viele der Paare $(a,b)$ müssen also als äquivalent angesehen
+werden.
 
 \subsubsection{Äquivalenzrelation}
 Die Definition~\eqref{buch:zahlen:ganze-rechenregeln}
diff --git a/buch/chapters/05-zahlen/images/komplex.pdf b/buch/chapters/05-zahlen/images/komplex.pdf
new file mode 100644
index 0000000..d502e3c
--- /dev/null
+++ b/buch/chapters/05-zahlen/images/komplex.pdf
diff --git a/buch/chapters/05-zahlen/images/komplex.tex b/buch/chapters/05-zahlen/images/komplex.tex
new file mode 100644
index 0000000..8cda85b
--- /dev/null
+++ b/buch/chapters/05-zahlen/images/komplex.tex
@@ -0,0 +1,39 @@
+%
+% komplex.tex -- Betrag und Argument einer komplexen Zahl
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1.5}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\pgfmathparse{atan(2/3)}
+\xdef\winkel{\pgfmathresult}
+\fill[color=blue!20] (0,0) -- (1.5,0) arc (0:\winkel:1.5) -- cycle;
+\draw[->] (-1,0) -- (4,0) coordinate[label={$\Re z$}];
+\draw[->] (0,-1) -- (0,3) coordinate[label={right:$\Im z$}];
+\draw[line width=0.5pt] (3,0) -- (3,2);
+\node at (3,1) [right] {$\Im z=b$};
+\node at (1.5,0) [below] {$\Re z=a$};
+\draw[->,color=red,line width=1.4pt] (0,0) -- (3,2);
+\node at (3,2) [above right] {$z=a+bi$};
+\def\punkt#1{
+	\fill[color=white] #1 circle[radius=0.04];
+	\draw #1 circle[radius=0.04];
+}
+\punkt{(0,0)}
+\punkt{(3,2)}
+\node[color=red] at (1.5,1) [rotate=\winkel,above] {$r=|z|$};
+\node[color=blue] at ({\winkel/2}:1.0)
+	[rotate={\winkel/2}] {$\varphi=\operatorname{arg}z$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/05-zahlen/komplex.tex b/buch/chapters/05-zahlen/komplex.tex
index 3cbf473..2a9b4a9 100644
--- a/buch/chapters/05-zahlen/komplex.tex
+++ b/buch/chapters/05-zahlen/komplex.tex
@@ -188,27 +188,7 @@ genauer untersuchen müssen.
 
 \begin{figure}
 \centering
-\begin{tikzpicture}[>=latex,thick,scale=1.5]
-\pgfmathparse{atan(2/3)}
-\xdef\winkel{\pgfmathresult}
-\fill[color=blue!20] (0,0) -- (1.5,0) arc (0:\winkel:1.5) -- cycle;
-\draw[->] (-1,0) -- (4,0) coordinate[label={$\Re z$}];
-\draw[->] (0,-1) -- (0,3) coordinate[label={right:$\Im z$}];
-\draw[line width=0.5pt] (3,0) -- (3,2);
-\node at (3,1) [right] {$\Im z=b$};
-\node at (1.5,0) [below] {$\Re z=a$};
-\draw[->,color=red,line width=1.4pt] (0,0) -- (3,2);
-\node at (3,2) [above right] {$z=a+bi$};
-\def\punkt#1{
-	\fill[color=white] #1 circle[radius=0.04];
-	\draw #1 circle[radius=0.04];
-}
-\punkt{(0,0)}
-\punkt{(3,2)}
-\node[color=red] at (1.5,1) [rotate=\winkel,above] {$r=|z|$};
-\node[color=blue] at ({\winkel/2}:1.0)
-	[rotate={\winkel/2}] {$\varphi=\operatorname{arg}z$};
-\end{tikzpicture}
+\includegraphics{chapters/05-zahlen/images/komplex.pdf}
 \caption{Argument und Betrag einer komplexen Zahl $z=a+ib$ in der 
 Gaussschen Zahlenebene
 \label{buch:zahlen:cfig}}
diff --git a/buch/chapters/05-zahlen/natuerlich.tex b/buch/chapters/05-zahlen/natuerlich.tex
index 3863191..acad943 100644
--- a/buch/chapters/05-zahlen/natuerlich.tex
+++ b/buch/chapters/05-zahlen/natuerlich.tex
@@ -35,9 +35,20 @@ $n'\in \mathbb{N}$.
 \item Wenn zwei Zahlen $n,m\in\mathbb{N}$ den gleichen Nachfolger haben,
 $n'=m'$, dann sind sie gleich $n=m$.
 \item Enthält eine Menge $X$ die Zahl $0$ und mit jeder Zahl auch ihren
-Nachfolger, dann ist $X\subset\mathbb{N}$. %TODO: X = N?...
+Nachfolger, dann ist $\mathbb{N}\subset X$.
 \end{enumerate}
 
+\subsubsection{Vollständige Induktion}
+Es letzte Axiom formuliert das Prinzip der vollständigen Induktion.
+Um eine Aussage $P(n)$ für alle natürlichen Zahlen $n$
+mit vollständiger Induktion zu beweisen, bezeichnet man mit
+$X$ die Menge aller Zahlen, für die $P(n)$ wahr ist.
+Die Induktionsverankerung beweist, dass $P(0)$ wahr ist, dass also $0\in X$.
+Der Induktionsschritt beweist, dass mit einer Zahl $n\in X$ auch der
+Nachfolger $n'\in X$ ist.
+Nach dem letzten Axiom ist $\mathbb{N}\subset X$, oder anders ausgedrückt,
+die Aussage $P(n)$ ist wahr für jede natürliche Zahl.
+
 \subsubsection{Addition}
 Aus der Nachfolgereigenschaft lässt sich durch wiederholte Anwendung
 die vertrautere Addition konstruieren.
diff --git a/buch/chapters/10-vektorenmatrizen/ringe.tex b/buch/chapters/10-vektorenmatrizen/ringe.tex
index 42e2a7e..21b29c2 100644
--- a/buch/chapters/10-vektorenmatrizen/ringe.tex
+++ b/buch/chapters/10-vektorenmatrizen/ringe.tex
@@ -108,37 +108,6 @@ $c_0(\mathbb{Z})$ ist immer noch ein Ring, aber er hat kein Eins.
 \begin{figure}
 \centering
 \includegraphics{chapters/10-vektorenmatrizen/images/gausszahlen.pdf}
-%\begin{tikzpicture}[>=latex,thick,scale=0.8]
-%\draw[->] (-8.5,0) -- (8.5,0) coordinate[label={$\Re z$}];
-%\draw[->] (0,-4.5) -- (0,4.5) coordinate[label={right:$\Im z$}];
-%\foreach \x in {-8,...,8}{
-%	\foreach \y in {-4,...,4}{
-%		\fill (\x,\y) circle[radius=0.05];
-%	}
-%}
-%
-%
-%\coordinate (O) at (0,0);
-%\coordinate (A) at (2,2);
-%\coordinate (B) at (-3,1);
-%\coordinate (C) at (-8,-4);
-%\coordinate (D) at (-1,3);
-%\draw[line width=0.5pt] (A)--(D)--(B);
-%\draw[->,color=red] (O) -- (A);
-%\draw[->,color=red] (O) -- (B);
-%\draw[->,color=blue] (O) -- (C);
-%\draw[->,color=darkgreen] (O) -- (D);
-%\fill[color=red] (A) circle[radius=0.08];
-%\fill[color=red] (B) circle[radius=0.08];
-%\fill[color=blue] (C) circle[radius=0.08];
-%\fill[color=darkgreen] (D) circle[radius=0.08];
-%\fill[color=black] (O) circle[radius=0.08];
-%\node[color=red] at (A) [above right] {$z$};
-%\node[color=red] at (B) [above left] {$w$};
-%\node[color=darkgreen] at (D) [above] {$z+w$};
-%\node[color=blue] at (C) [below right] {$z\cdot w$};
-%
-%\end{tikzpicture}
 \caption{Der Ring der ganzen Gausschen Zahlen besteht aus den ganzahligen
 Gitterpunkten in der Gausschen Zahlenebene
 \label{buch:vektorenmatrizen:fig:ganzgauss}}
diff --git a/buch/chapters/30-endlichekoerper/chapter.tex b/buch/chapters/30-endlichekoerper/chapter.tex
index 2d16d80..150c719 100644
--- a/buch/chapters/30-endlichekoerper/chapter.tex
+++ b/buch/chapters/30-endlichekoerper/chapter.tex
@@ -37,6 +37,7 @@ lösbar werden.
 
 
 \section*{Übungsaufgaben}
+\rhead{Übungsaufgaben}
 \aufgabetoplevel{chapters/30-endlichekoerper/uebungsaufgaben}
 \begin{uebungsaufgaben}
 \uebungsaufgabe{3002}
diff --git a/buch/chapters/40-eigenwerte/chapter.tex b/buch/chapters/40-eigenwerte/chapter.tex
index e097b8d..e769b38 100644
--- a/buch/chapters/40-eigenwerte/chapter.tex
+++ b/buch/chapters/40-eigenwerte/chapter.tex
@@ -38,6 +38,7 @@ Dies wird in Abschnitt~\ref{buch:section:spektraltheorie} beschrieben.
 \input{chapters/40-eigenwerte/spektraltheorie.tex}
 
 \section*{Übungsaufgaben}
+\rhead{Übungsaufgaben}
 \aufgabetoplevel{chapters/40-eigenwerte/uebungsaufgaben}
 \begin{uebungsaufgaben}
 \uebungsaufgabe{4001}
diff --git a/buch/chapters/40-eigenwerte/grundlagen.tex b/buch/chapters/40-eigenwerte/grundlagen.tex
index 55c3344..dbc19ce 100644
--- a/buch/chapters/40-eigenwerte/grundlagen.tex
+++ b/buch/chapters/40-eigenwerte/grundlagen.tex
@@ -346,63 +346,7 @@ $b_{ij}=0$ für $i+k>j$ und $c_{ij}=0$ für $i+l>j$.
 In der folgenden graphischen Darstellung der Matrizen sind die
 Bereiche, wo die Matrixelemente verschwinden, weiss.
 \begin{center}
-
-\newtcbox{\myboxA}{blank,boxsep=0mm,
-clip upper,minipage,
-width=31.0mm,height=17.0mm,nobeforeafter,
-borderline={0.0pt}{0.0pt}{white},
-}
-
-\begin{tikzpicture}[>=latex,thick]
-
-\def\cx{1.8}
-\def\cy{1.2}
-
-\draw[line width=0.3pt] (-3,2.5) -- (6,2.5);
-
-\begin{scope}[xshift=-4cm]
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (0.5,3) -- (3,0.5) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+0.5*0.5},{\cy+0.5*0.5}) [rotate=-45] {$k$};
-\draw[color=blue,line width=1.4pt] (0,2.5) -- (1.0,2.5);
-\draw[color=red,line width=1.4pt] (1.0,2.5) -- (3,2.5);
-\node at (1,1) {$B$};
-\node at (-0.3,2.5) [left] {$i$};
-\node at (1,2.5) [above right] {$i+k$};
-\end{scope}
-
-\node at (-0.5,1.5) {$\mathstrut\cdot\mathstrut$};
-
-\begin{scope}
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (1.0,3) -- (3,1.0) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+1.0*0.5},{\cy+1.0*0.5}) [rotate=-45] {$l$};
-\draw[color=red,line width=1.4pt] (2,3)--(2,2);
-\draw[color=blue,line width=1.4pt] (2,2)--(2,0);
-\node at (1,1) {$C$};
-\node at (2,3) [above] {$j$};
-\node at (2,2) [above right] {$j-l$};
-\end{scope}
-
-\node at (3.5,1.5) {$\mathstrut=\mathstrut$};
-
-\begin{scope}[xshift=4cm]
-\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
-\fill[color=red!30] (1.5,3) -- (3,1.5) -- (3,3) -- cycle;
-\draw (0,0) rectangle (3,3);
-\draw (0,3) -- (3,0);
-\node at ({\cx+1.5*0.5},{\cy+1.5*0.5}) [rotate=-45] {$k+l$};
-\fill[color=red!50!blue] (2,2.5) circle[radius=0.1];
-\draw[line width=0.3pt] (2,3) -- (2,2.5);
-\node at (2,3) [above] {$j$};
-\node at (1,1) {$D$};
-\end{scope}
-
-\end{tikzpicture}
+\includegraphics{chapters/40-eigenwerte/images/nilpotent.pdf}
 \end{center}
 Bei der Berechnung des Elementes $d_{ij}$ wird die Zeile $i$ von $B$
 mit der Spalte $j$ von $C$ multipliziert.
diff --git a/buch/chapters/40-eigenwerte/images/Makefile b/buch/chapters/40-eigenwerte/images/Makefile
index 5915d30..db00dac 100644
--- a/buch/chapters/40-eigenwerte/images/Makefile
+++ b/buch/chapters/40-eigenwerte/images/Makefile
@@ -3,7 +3,7 @@
 #
 # (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
 #
-all:	sp.pdf 
+all:	sp.pdf   nilpotent.pdf
 
 sp.pdf:	sp.tex sppaths.tex
 	pdflatex sp.tex
@@ -11,3 +11,6 @@ sp.pdf:	sp.tex sppaths.tex
 sppaths.tex:	spbeispiel.m
 	octave spbeispiel.m
 
+nilpotent.pdf:	nilpotent.tex
+	pdflatex nilpotent.tex
+
diff --git a/buch/chapters/40-eigenwerte/images/nilpotent.pdf b/buch/chapters/40-eigenwerte/images/nilpotent.pdf
new file mode 100644
index 0000000..2106697
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/nilpotent.pdf
diff --git a/buch/chapters/40-eigenwerte/images/nilpotent.tex b/buch/chapters/40-eigenwerte/images/nilpotent.tex
new file mode 100644
index 0000000..1e6cd79
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/nilpotent.tex
@@ -0,0 +1,76 @@
+%
+% nilpotent.tex -- Produkt nilpotenter Matrizen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage[many]{tcolorbox}
+
+\begin{document}
+\def\skala{1}
+
+\newtcbox{\myboxA}{blank,boxsep=0mm,
+clip upper,minipage,
+width=31.0mm,height=17.0mm,nobeforeafter,
+borderline={0.0pt}{0.0pt}{white},
+}
+
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\cx{1.8}
+\def\cy{1.2}
+
+\draw[line width=0.3pt] (-3,2.5) -- (6,2.5);
+
+\begin{scope}[xshift=-4cm]
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (0.5,3) -- (3,0.5) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+0.5*0.5},{\cy+0.5*0.5}) [rotate=-45] {$k$};
+\draw[color=blue,line width=1.4pt] (0,2.5) -- (1.0,2.5);
+\draw[color=red,line width=1.4pt] (1.0,2.5) -- (3,2.5);
+\node at (1,1) {$B$};
+\node at (-0.3,2.5) [left] {$i$};
+\node at (1,2.5) [above right] {$i+k$};
+\end{scope}
+
+\node at (-0.5,1.5) {$\mathstrut\cdot\mathstrut$};
+
+\begin{scope}
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (1.0,3) -- (3,1.0) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+1.0*0.5},{\cy+1.0*0.5}) [rotate=-45] {$l$};
+\draw[color=red,line width=1.4pt] (2,3)--(2,2);
+\draw[color=blue,line width=1.4pt] (2,2)--(2,0);
+\node at (1,1) {$C$};
+\node at (2,3) [above] {$j$};
+\node at (2,2) [above right] {$j-l$};
+\end{scope}
+
+\node at (3.5,1.5) {$\mathstrut=\mathstrut$};
+
+\begin{scope}[xshift=4cm]
+\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
+\fill[color=red!30] (1.5,3) -- (3,1.5) -- (3,3) -- cycle;
+\draw (0,0) rectangle (3,3);
+\draw (0,3) -- (3,0);
+\node at ({\cx+1.5*0.5},{\cy+1.5*0.5}) [rotate=-45] {$k+l$};
+\fill[color=red!50!blue] (2,2.5) circle[radius=0.1];
+\draw[line width=0.3pt] (2,3) -- (2,2.5);
+\node at (2,3) [above] {$j$};
+\node at (1,1) {$D$};
+\end{scope}
+
+\end{tikzpicture}
+
+\end{document}
+
diff --git a/buch/chapters/40-eigenwerte/images/sp.pdf b/buch/chapters/40-eigenwerte/images/sp.pdf
index 5346e06..d4de984 100644
--- a/buch/chapters/40-eigenwerte/images/sp.pdf
+++ b/buch/chapters/40-eigenwerte/images/sp.pdf
diff --git a/buch/chapters/50-permutationen/endlich.tex b/buch/chapters/50-permutationen/endlich.tex
index 7669a17..700c0f2 100644
--- a/buch/chapters/50-permutationen/endlich.tex
+++ b/buch/chapters/50-permutationen/endlich.tex
@@ -21,31 +21,7 @@ Element} der Gruppe $S_n$ und wir auch mit $e$ bezeichnet.
 \subsection{Permutationen als $2\times n$-Matrizen}
 Eine Permutation kann als $2\times n$-Matrix geschrieben werden:
 \begin{center}
-\begin{tikzpicture}[>=latex,thick]
-\def\sx{0.8}
-\def\sy{1}
-\begin{scope}[xshift=-3cm]
-\foreach \x in {1,...,6}{
-	\node at ({(\x-1)*\sx},\sy) [above] {$\tiny\x$};
-	\fill ({(\x-1)*\sx},\sy) circle[radius=0.05];
-	\fill ({(\x-1)*\sx},0) circle[radius=0.05];
-}
-\draw[->] (0,\sy) to[out=-70,in=110] (\sx,0);
-\draw[<-] (0,0) to[out=70,in=-110] (\sx,\sy);
-\draw[->] ({2*\sx},\sy) -- ({2*\sx},0);
-\draw[->] ({3*\sx},\sy) to[out=-70,in=110] ({4*\sx},0);
-\draw[->] ({4*\sx},\sy) to[out=-70,in=110] ({5*\sx},0);
-\draw[->] ({5*\sx},\sy) to[out=-110,in=70] ({3*\sx},0);
-\end{scope}
-\node at (2.4,{\sy/2}) {$\mathstrut=\mathstrut$};
-\node at (5,{\sy/2}) {$\displaystyle
-\renewcommand{\arraystretch}{1.4}
-\begin{pmatrix}
-1&2&3&4&5&6\\
-2&1&3&5&6&4
-\end{pmatrix}
-$};
-\end{tikzpicture}
+\includegraphics{chapters/50-permutationen/images/permutation.pdf}
 \end{center}
 Das neutrale Element hat die Matrix
 \[
@@ -64,43 +40,7 @@ Permutation angeordnet.
 Die zusammengesetzte Permutation kann dann in der zweiten Zeile
 der zweiten Permutation abgelesen werden:
 \begin{center}
-\begin{tikzpicture}[>=latex,thick]
-\begin{scope}[xshift=-4.5cm]
-\node at (0,0) {$\displaystyle
-\sigma_1=\begin{pmatrix}
-1&2&3&4&5&6\\
-2&1&3&5&6&4
-\end{pmatrix}$};
-\node at (0,-1) {$\displaystyle
-\sigma_2=\begin{pmatrix}
-1&2&3&4&5&6\\
-3&4&5&6&1&2
-\end{pmatrix}
-$};
-\end{scope}
-\begin{scope}
-\node at (0,0) {$\displaystyle
-\begin{pmatrix}
-1&2&3&4&5&6\\
-2&1&3&5&6&4
-\end{pmatrix}$};
-\node at (0,-1) {$\displaystyle
-\begin{pmatrix}
-2&1&3&5&6&4\\
-4&3&5&1&2&6
-\end{pmatrix}
-$};
-
-\end{scope}
-\begin{scope}[xshift=4.5cm]
-\node at (0,-0.5) {$\displaystyle
-\sigma_2\sigma_1=\begin{pmatrix}
-1&2&3&4&5&6\\
-4&3&5&1&2&6
-\end{pmatrix}
-$};
-\end{scope}
-\end{tikzpicture}
+\includegraphics{chapters/50-permutationen/images/komposition.pdf}
 \end{center}
 Die Inverse einer Permutation kann erhalten werden, indem die beiden
 Zeilen vertauscht werden und dann die Spalten wieder so angeordnet werden,
@@ -130,47 +70,7 @@ Eine Permutation $\sigma\in S_n$ kann auch mit sogenanten Zyklenzerlegung
 analysiert werden.
 Zum Beispiel:
 \begin{center}
-\begin{tikzpicture}[>=latex,thick]
-\begin{scope}[xshift=-3cm]
-\node at (0,0) {$\displaystyle
-\sigma=\begin{pmatrix}
-{\color{red}1}&{\color{red}2}&{\color{darkgreen}3}&{\color{blue}4}&{\color{blue}5}&{\color{blue}6}\\
-{\color{red}2}&{\color{red}1}&{\color{darkgreen}3}&{\color{blue}5}&{\color{blue}6}&{\color{blue}4}
-\end{pmatrix}$};
-\end{scope}
-\node at (0,0) {$\mathstrut=\mathstrut$};
-\begin{scope}[xshift=1.5cm]
-\coordinate (A) at (0,0.5);
-\coordinate (B) at (0,-0.5);
-\draw[->,color=red] (A) to[out=-20,in=20] (0,-0.5);
-\draw[->,color=red] (B) to[out=160,in=-160] (0,0.5);
-\node at (A) [above] {$\tiny 1$};
-\node at (B) [below] {$\tiny 2$};
-\fill (A) circle[radius=0.05];
-\fill (B) circle[radius=0.05];
-
-\coordinate (C) at (1.5,0.25);
-\node at (C) [above] {$\tiny 3$};
-\draw[->,color=darkgreen] ({1.5+0.01},0.25) to[out=-10,in=-170] ({1.5-0.01},0.25);
-\draw[color=darkgreen] (1.5,{0.25-0.3}) circle[radius=0.3];
-\fill (C) circle[radius=0.05];
-
-\def\r{0.5}
-\coordinate (D) at ({3.5+\r*cos(90)},{0+\r*sin(90)});
-\coordinate (E) at ({3.5+\r*cos(210)},{0+\r*sin(210)});
-\coordinate (F) at ({3.5+\r*cos(330)},{0+\r*sin(330)});
-\node at (D) [above] {$\tiny 4$};
-\node at (E) [below left] {$\tiny 5$};
-\node at (F) [below right] {$\tiny 6$};
-\draw[->,color=blue] (D) to[out=180,in=120] (E);
-\draw[->,color=blue] (E) to[out=-60,in=-120] (F);
-\draw[->,color=blue] (F) to[out=60,in=0] (D);
-\fill (D) circle[radius=0.05];
-\fill (E) circle[radius=0.05];
-\fill (F) circle[radius=0.05];
-
-\end{scope}
-\end{tikzpicture}
+\includegraphics{chapters/50-permutationen/images/zyklenzerlegung.pdf}
 \end{center}
 
 \begin{definition}
diff --git a/buch/chapters/50-permutationen/images/Makefile b/buch/chapters/50-permutationen/images/Makefile
new file mode 100644
index 0000000..c2e0e9f
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/Makefile
@@ -0,0 +1,20 @@
+#
+# Makefile -- Bilder 
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	transpositionen.pdf zyklenzerlegung.pdf permutation.pdf \
+	komposition.pdf
+
+permutation.pdf:	permutation.tex
+	pdflatex permutation.tex
+
+komposition.pdf:	komposition.tex
+	pdflatex komposition.tex
+
+transpositionen.pdf:	transpositionen.tex
+	pdflatex transpositionen.tex
+
+zyklenzerlegung.pdf:	zyklenzerlegung.tex
+	pdflatex zyklenzerlegung.tex
+
diff --git a/buch/chapters/50-permutationen/images/komposition.pdf b/buch/chapters/50-permutationen/images/komposition.pdf
new file mode 100644
index 0000000..9e532bf
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/komposition.pdf
diff --git a/buch/chapters/50-permutationen/images/komposition.tex b/buch/chapters/50-permutationen/images/komposition.tex
new file mode 100644
index 0000000..ef3ec65
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/komposition.tex
@@ -0,0 +1,55 @@
+%
+% komposition.tex -- Komposition zweier Permutationen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\begin{scope}[xshift=-4.5cm]
+\node at (0,0) {$\displaystyle
+\sigma_1=\begin{pmatrix}
+1&2&3&4&5&6\\
+2&1&3&5&6&4
+\end{pmatrix}$};
+\node at (0,-1) {$\displaystyle
+\sigma_2=\begin{pmatrix}
+1&2&3&4&5&6\\
+3&4&5&6&1&2
+\end{pmatrix}
+$};
+\end{scope}
+\begin{scope}
+\node at (0,0) {$\displaystyle
+\begin{pmatrix}
+1&2&3&4&5&6\\
+2&1&3&5&6&4
+\end{pmatrix}$};
+\node at (0,-1) {$\displaystyle
+\begin{pmatrix}
+2&1&3&5&6&4\\
+4&3&5&1&2&6
+\end{pmatrix}
+$};
+
+\end{scope}
+\begin{scope}[xshift=4.5cm]
+\node at (0,-0.5) {$\displaystyle
+\sigma_2\sigma_1=\begin{pmatrix}
+1&2&3&4&5&6\\
+4&3&5&1&2&6
+\end{pmatrix}
+$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/50-permutationen/images/permutation.pdf b/buch/chapters/50-permutationen/images/permutation.pdf
new file mode 100644
index 0000000..cdfa186
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/permutation.pdf
diff --git a/buch/chapters/50-permutationen/images/permutation.tex b/buch/chapters/50-permutationen/images/permutation.tex
new file mode 100644
index 0000000..ee58d4a
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/permutation.tex
@@ -0,0 +1,43 @@
+%
+% permutation.tex -- Definition einer Permutation
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\sx{0.8}
+\def\sy{1}
+\begin{scope}[xshift=-3cm]
+\foreach \x in {1,...,6}{
+	\node at ({(\x-1)*\sx},\sy) [above] {$\tiny\x$};
+	\fill ({(\x-1)*\sx},\sy) circle[radius=0.05];
+	\fill ({(\x-1)*\sx},0) circle[radius=0.05];
+}
+\draw[->] (0,\sy) to[out=-70,in=110] (\sx,0);
+\draw[<-] (0,0) to[out=70,in=-110] (\sx,\sy);
+\draw[->] ({2*\sx},\sy) -- ({2*\sx},0);
+\draw[->] ({3*\sx},\sy) to[out=-70,in=110] ({4*\sx},0);
+\draw[->] ({4*\sx},\sy) to[out=-70,in=110] ({5*\sx},0);
+\draw[->] ({5*\sx},\sy) to[out=-110,in=70] ({3*\sx},0);
+\end{scope}
+\node at (2.4,{\sy/2}) {$\mathstrut=\mathstrut$};
+\node at (5,{\sy/2}) {$\displaystyle
+\renewcommand{\arraystretch}{1.4}
+\begin{pmatrix}
+1&2&3&4&5&6\\
+2&1&3&5&6&4
+\end{pmatrix}
+$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/50-permutationen/images/transpositionen.pdf b/buch/chapters/50-permutationen/images/transpositionen.pdf
new file mode 100644
index 0000000..ad2ea7c
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/transpositionen.pdf
diff --git a/buch/chapters/50-permutationen/images/transpositionen.tex b/buch/chapters/50-permutationen/images/transpositionen.tex
new file mode 100644
index 0000000..0670a2c
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/transpositionen.tex
@@ -0,0 +1,103 @@
+%
+% transpositionen.tex -- Darstellung eines Zyklus aus Transpositionen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+
+\def\kreuz#1#2#3{
+	\draw[->] ({(#1)-1},#2) to[out=-90,in=90] ({#1},{#2-1});
+	\draw[->] ({#1},#2) to[out=-90,in=90] ({#1-1},{#2-1});
+	\node at ({(#1)-0.5+0.2},{#2-0.5}) [right] {$#3$};
+}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+\foreach \x in {1,2,3,6,7,8,9}{
+	\fill ({\x-1},0) circle[radius=0.05];
+}
+\foreach \x in {1,2,3}{
+	\node at ({\x-1},0) [above] {$\tiny \x$};
+}
+\node at (8,0) [above] {$\tiny k$};
+\node at (7,0) [above] {$\tiny k-1$};
+\node at (6,0) [above] {$\tiny k-2$};
+\node at (5,0) [above] {$\tiny k-3$};
+\foreach \x in {1,2,3,4,7,8,9}{
+	\fill ({\x-1},-8) circle[radius=0.05];
+}
+\foreach \x in {1,2,3,4}{
+	\node at ({\x-1},-8) [below] {$\tiny \x$};
+}
+\node at (6,-8) [below] {$k-2$};
+\node at (7,-8) [below] {$k-1$};
+\node at (8,-8) [below] {$k$};
+
+\foreach \x in {3,3.2,...,5}{
+	\fill (\x,{-8+\x}) circle[radius=0.02];
+	\fill ({\x+0.5},-8) circle[radius=0.02];
+	\fill ({\x-0.5},0) circle[radius=0.02];
+}
+
+\kreuz{8}{0}{\tau_{k-1,k}}
+\kreuz{7}{-1}{\tau_{k-2,k-1}}
+\kreuz{6}{-2}{\tau_{k-3,k-2}}
+%\kreuz{5}{-3}{\tau_{56}}
+%\kreuz{4}{-4}{\tau_{45}}
+\kreuz{3}{-5}{\tau_{34}}
+\kreuz{2}{-6}{\tau_{23}}
+\kreuz{1}{-7}{\tau_{12}}
+
+\draw[->,color=gray] (0,0) -- (0,-7);
+\draw[->,color=gray] (1,0) -- (1,-6);
+\draw[->,color=gray] (2,0) -- (2,-5);
+%\draw[->,color=gray] (3,0) -- (3,-4);
+%\draw[->,color=gray] (4,0) -- (4,-3);
+\draw[->,color=gray] (5,0) -- (5,-2);
+\draw[->,color=gray] (6,0) -- (6,-1);
+
+\draw[->,color=gray] (8,-1) -- (8,-8);
+\draw[->,color=gray] (7,-2) -- (7,-8);
+\draw[->,color=gray] (6,-3) -- (6,-8);
+%\draw[->,color=gray] (5,-4) -- (5,-8);
+%\draw[->,color=gray] (4,-5) -- (4,-8);
+\draw[->,color=gray] (3,-6) -- (3,-8);
+\draw[->,color=gray] (2,-7) -- (2,-8);
+	
+\fill (6,-1) circle[radius=0.05];
+\fill (7,-1) circle[radius=0.05];
+\fill (8,-1) circle[radius=0.05];
+
+\fill (5,-2) circle[radius=0.05];
+\fill (6,-2) circle[radius=0.05];
+\fill (7,-2) circle[radius=0.05];
+
+%\fill (4,-3) circle[radius=0.05];
+\fill (5,-3) circle[radius=0.05];
+\fill (6,-3) circle[radius=0.05];
+
+%\fill (3,-4) circle[radius=0.05];
+%\fill (4,-4) circle[radius=0.05];
+%\fill (5,-4) circle[radius=0.05];
+
+\fill (2,-5) circle[radius=0.05];
+\fill (3,-5) circle[radius=0.05];
+%\fill (4,-5) circle[radius=0.05];
+
+\fill (1,-6) circle[radius=0.05];
+\fill (2,-6) circle[radius=0.05];
+\fill (3,-6) circle[radius=0.05];
+
+\fill (0,-7) circle[radius=0.05];
+\fill (1,-7) circle[radius=0.05];
+\fill (2,-7) circle[radius=0.05];
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf b/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf
new file mode 100644
index 0000000..72d9353
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/zyklenzerlegung.pdf
diff --git a/buch/chapters/50-permutationen/images/zyklenzerlegung.tex b/buch/chapters/50-permutationen/images/zyklenzerlegung.tex
new file mode 100644
index 0000000..c197579
--- /dev/null
+++ b/buch/chapters/50-permutationen/images/zyklenzerlegung.tex
@@ -0,0 +1,60 @@
+%
+% zyklenzerlegung.tex -- Zerlegung einer Permutation in Zyklen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\begin{scope}[xshift=-3cm]
+\node at (0,0) {$\displaystyle
+\sigma=\begin{pmatrix}
+{\color{red}1}&{\color{red}2}&{\color{darkgreen}3}&{\color{blue}4}&{\color{blue}5}&{\color{blue}6}\\
+{\color{red}2}&{\color{red}1}&{\color{darkgreen}3}&{\color{blue}5}&{\color{blue}6}&{\color{blue}4}
+\end{pmatrix}$};
+\end{scope}
+\node at (0,0) {$\mathstrut=\mathstrut$};
+\begin{scope}[xshift=1.5cm]
+\coordinate (A) at (0,0.5);
+\coordinate (B) at (0,-0.5);
+\draw[->,color=red] (A) to[out=-20,in=20] (0,-0.5);
+\draw[->,color=red] (B) to[out=160,in=-160] (0,0.5);
+\node at (A) [above] {$\tiny 1$};
+\node at (B) [below] {$\tiny 2$};
+\fill (A) circle[radius=0.05];
+\fill (B) circle[radius=0.05];
+
+\coordinate (C) at (1.5,0.25);
+\node at (C) [above] {$\tiny 3$};
+\draw[->,color=darkgreen] ({1.5+0.01},0.25) to[out=-10,in=-170] ({1.5-0.01},0.25);
+\draw[color=darkgreen] (1.5,{0.25-0.3}) circle[radius=0.3];
+\fill (C) circle[radius=0.05];
+
+\def\r{0.5}
+\coordinate (D) at ({3.5+\r*cos(90)},{0+\r*sin(90)});
+\coordinate (E) at ({3.5+\r*cos(210)},{0+\r*sin(210)});
+\coordinate (F) at ({3.5+\r*cos(330)},{0+\r*sin(330)});
+\node at (D) [above] {$\tiny 4$};
+\node at (E) [below left] {$\tiny 5$};
+\node at (F) [below right] {$\tiny 6$};
+\draw[->,color=blue] (D) to[out=180,in=120] (E);
+\draw[->,color=blue] (E) to[out=-60,in=-120] (F);
+\draw[->,color=blue] (F) to[out=60,in=0] (D);
+\fill (D) circle[radius=0.05];
+\fill (E) circle[radius=0.05];
+\fill (F) circle[radius=0.05];
+
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/50-permutationen/transpositionen.tex b/buch/chapters/50-permutationen/transpositionen.tex
index baed2fb..604e010 100644
--- a/buch/chapters/50-permutationen/transpositionen.tex
+++ b/buch/chapters/50-permutationen/transpositionen.tex
@@ -35,92 +35,7 @@ also die Permutation, die $1\to2\to3\to\dots\to k-2\to k-1\to k\to 1$
 abbildet.
 Dieser Zyklus lässt sich wie folgt aus Transpositionen zusammensetzen:
 \begin{center}
-\def\kreuz#1#2#3{
-	\draw[->] ({(#1)-1},#2) to[out=-90,in=90] ({#1},{#2-1});
-	\draw[->] ({#1},#2) to[out=-90,in=90] ({#1-1},{#2-1});
-	\node at ({(#1)-0.5+0.2},{#2-0.5}) [right] {$#3$};
-}
-\begin{tikzpicture}[>=latex,thick]
-\foreach \x in {1,2,3,6,7,8,9}{
-	\fill ({\x-1},0) circle[radius=0.05];
-}
-\foreach \x in {1,2,3}{
-	\node at ({\x-1},0) [above] {$\tiny \x$};
-}
-\node at (8,0) [above] {$\tiny k$};
-\node at (7,0) [above] {$\tiny k-1$};
-\node at (6,0) [above] {$\tiny k-2$};
-\node at (5,0) [above] {$\tiny k-3$};
-\foreach \x in {1,2,3,4,7,8,9}{
-	\fill ({\x-1},-8) circle[radius=0.05];
-}
-\foreach \x in {1,2,3,4}{
-	\node at ({\x-1},-8) [below] {$\tiny \x$};
-}
-\node at (6,-8) [below] {$k-2$};
-\node at (7,-8) [below] {$k-1$};
-\node at (8,-8) [below] {$k$};
-
-\foreach \x in {3,3.2,...,5}{
-	\fill (\x,{-8+\x}) circle[radius=0.02];
-	\fill ({\x+0.5},-8) circle[radius=0.02];
-	\fill ({\x-0.5},0) circle[radius=0.02];
-}
-
-\kreuz{8}{0}{\tau_{k-1,k}}
-\kreuz{7}{-1}{\tau_{k-2,k-1}}
-\kreuz{6}{-2}{\tau_{k-3,k-2}}
-%\kreuz{5}{-3}{\tau_{56}}
-%\kreuz{4}{-4}{\tau_{45}}
-\kreuz{3}{-5}{\tau_{34}}
-\kreuz{2}{-6}{\tau_{23}}
-\kreuz{1}{-7}{\tau_{12}}
-
-\draw[->,color=gray] (0,0) -- (0,-7);
-\draw[->,color=gray] (1,0) -- (1,-6);
-\draw[->,color=gray] (2,0) -- (2,-5);
-%\draw[->,color=gray] (3,0) -- (3,-4);
-%\draw[->,color=gray] (4,0) -- (4,-3);
-\draw[->,color=gray] (5,0) -- (5,-2);
-\draw[->,color=gray] (6,0) -- (6,-1);
-
-\draw[->,color=gray] (8,-1) -- (8,-8);
-\draw[->,color=gray] (7,-2) -- (7,-8);
-\draw[->,color=gray] (6,-3) -- (6,-8);
-%\draw[->,color=gray] (5,-4) -- (5,-8);
-%\draw[->,color=gray] (4,-5) -- (4,-8);
-\draw[->,color=gray] (3,-6) -- (3,-8);
-\draw[->,color=gray] (2,-7) -- (2,-8);
-	
-\fill (6,-1) circle[radius=0.05];
-\fill (7,-1) circle[radius=0.05];
-\fill (8,-1) circle[radius=0.05];
-
-\fill (5,-2) circle[radius=0.05];
-\fill (6,-2) circle[radius=0.05];
-\fill (7,-2) circle[radius=0.05];
-
-%\fill (4,-3) circle[radius=0.05];
-\fill (5,-3) circle[radius=0.05];
-\fill (6,-3) circle[radius=0.05];
-
-%\fill (3,-4) circle[radius=0.05];
-%\fill (4,-4) circle[radius=0.05];
-%\fill (5,-4) circle[radius=0.05];
-
-\fill (2,-5) circle[radius=0.05];
-\fill (3,-5) circle[radius=0.05];
-%\fill (4,-5) circle[radius=0.05];
-
-\fill (1,-6) circle[radius=0.05];
-\fill (2,-6) circle[radius=0.05];
-\fill (3,-6) circle[radius=0.05];
-
-\fill (0,-7) circle[radius=0.05];
-\fill (1,-7) circle[radius=0.05];
-\fill (2,-7) circle[radius=0.05];
-
-\end{tikzpicture}
+\includegraphics{chapters/50-permutationen/images/transpositionen.pdf}
 \end{center}
 Es ist also
 \[
diff --git a/buch/chapters/70-graphen/beschreibung.tex b/buch/chapters/70-graphen/beschreibung.tex
index 6e8e59b..2dcc78f 100644
--- a/buch/chapters/70-graphen/beschreibung.tex
+++ b/buch/chapters/70-graphen/beschreibung.tex
@@ -236,26 +236,7 @@ sind.
 \begin{beispiel}
 \begin{figure}
 \centering
-\begin{tikzpicture}[>=latex,thick]
-\def\l{0.25}
-\def\r{1}
-\def\punkt#1{({\r*sin(((#1)-1)*72)},{\r*cos(((#1)-1)*72)})}
-\def\R{2}
-\def\Punkt#1{({\R*sin(((#1)-6)*72)},{\R*cos(((#1)-6)*72)})}
-\draw \Punkt{6} -- \Punkt{7} -- \Punkt{8} -- \Punkt{9} -- \Punkt{10} -- cycle;
-\draw \punkt{1} -- \punkt{3} -- \punkt{5} -- \punkt{2} -- \punkt{4} -- cycle;
-\foreach \k in {1,...,5}{
-	\draw \punkt{\k} -- \Punkt{(\k+5)};
-	\fill[color=white] \punkt{\k} circle[radius=\l];
-	\node at \punkt{\k} {$\k$};
-	\draw \punkt{\k} circle[radius=\l];
-}
-\foreach \k in {6,...,10}{
-	\fill[color=white] \Punkt{\k} circle[radius=\l];
-	\node at \Punkt{\k} {$\k$};
-	\draw \Punkt{\k} circle[radius=\l];
-}
-\end{tikzpicture}
+\includegraphics{chapters/70-graphen/images/peterson.pdf}
 \caption{Peterson-Graph mit zehn Knoten.
 \label{buch:figure:peterson}}
 \end{figure}
diff --git a/buch/chapters/70-graphen/images/Makefile b/buch/chapters/70-graphen/images/Makefile
new file mode 100644
index 0000000..2199ddc
--- /dev/null
+++ b/buch/chapters/70-graphen/images/Makefile
@@ -0,0 +1,10 @@
+#
+# Makefile -- Bilder für Kapitel Graphen
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	peterson.pdf
+
+peterson.pdf:	peterson.tex
+	pdflatex peterson.tex
+
diff --git a/buch/chapters/70-graphen/images/peterson.pdf b/buch/chapters/70-graphen/images/peterson.pdf
new file mode 100644
index 0000000..259d808
--- /dev/null
+++ b/buch/chapters/70-graphen/images/peterson.pdf
diff --git a/buch/chapters/70-graphen/images/peterson.tex b/buch/chapters/70-graphen/images/peterson.tex
new file mode 100644
index 0000000..c0af98b
--- /dev/null
+++ b/buch/chapters/70-graphen/images/peterson.tex
@@ -0,0 +1,38 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\l{0.25}
+\def\r{1}
+\def\punkt#1{({\r*sin(((#1)-1)*72)},{\r*cos(((#1)-1)*72)})}
+\def\R{2}
+\def\Punkt#1{({\R*sin(((#1)-6)*72)},{\R*cos(((#1)-6)*72)})}
+\draw \Punkt{6} -- \Punkt{7} -- \Punkt{8} -- \Punkt{9} -- \Punkt{10} -- cycle;
+\draw \punkt{1} -- \punkt{3} -- \punkt{5} -- \punkt{2} -- \punkt{4} -- cycle;
+\foreach \k in {1,...,5}{
+	\draw \punkt{\k} -- \Punkt{(\k+5)};
+	\fill[color=white] \punkt{\k} circle[radius=\l];
+	\node at \punkt{\k} {$\k$};
+	\draw \punkt{\k} circle[radius=\l];
+}
+\foreach \k in {6,...,10}{
+	\fill[color=white] \Punkt{\k} circle[radius=\l];
+	\node at \Punkt{\k} {$\k$};
+	\draw \Punkt{\k} circle[radius=\l];
+}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/google.tex b/buch/chapters/80-wahrscheinlichkeit/google.tex
index 3616760..ca78b3d 100644
--- a/buch/chapters/80-wahrscheinlichkeit/google.tex
+++ b/buch/chapters/80-wahrscheinlichkeit/google.tex
@@ -41,46 +41,6 @@ zerstört.
 \begin{figure}
 \centering
 \includegraphics{chapters/80-wahrscheinlichkeit/images/internet.pdf}
-%\begin{tikzpicture}[>=latex,thick]
-%\foreach \x in {0,3,6,9}{
-%	\foreach \y in {0,3}{
-%		\fill[color=white] ({\x},{\y}) circle[radius=0.3];
-%		\draw ({\x},{\y}) circle[radius=0.3];
-%	}
-%}
-%\node at (0,3) {$1$};
-%\node at (0,0) {$2$};
-%\node at (3,3) {$3$};
-%\node at (3,0) {$4$};
-%\node at (6,3) {$5$};
-%\node at (6,0) {$6$};
-%\node at (9,3) {$7$};
-%\node at (9,0) {$8$};
-%% 1
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (3,3);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (0,0);
-%% 2
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,0) to[out=-20,in=-160] (3,0);
-%% 3
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (6,3);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (0,0);
-%% 4
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,3);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,0);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) to[out=160,in=20] (0,0);
-%% 5
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,3);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,0);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (6,0);
-%% 6
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,0) to[out=20,in=160] (9,0);
-%% 7
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) .. controls (7.5,4) .. (6,4) -- (3,4) .. controls (1.5,4) .. (0,3);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) to[out=-110,in=110] (9,0);
-%% 8
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=-160,in=-20] (6,0);
-%\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=70,in=-70] (9,3);
-%\end{tikzpicture}
 \caption{Modell-Internet als Beispiel für die Link-Matrix und die Google-Matrix.
 \label{buch:figure:modellinternet}}
 \end{figure}
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/Makefile b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
index b04f6ff..8d34217 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/Makefile
+++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
@@ -5,7 +5,8 @@
 #
 all:	dreieck.pdf trenn.pdf vergleich.pdf vergleich.jpg \
 	positiv.pdf positiv.jpg diffusion.png diffusion.pdf \
-	konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf
+	konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf \
+	spielB.pdf spielBtilde.pdf
 
 # Visualisierung diffusion in einer primitiven Matrix
 diffusion.pdf:	diffusion.tex diffusion.jpg
@@ -71,3 +72,8 @@ markov2.pdf:	markov2.tex
 markov3.pdf:	markov3.tex
 	pdflatex markov3.tex
 
+spielB.pdf:	spielB.tex
+	pdflatex spielB.tex
+
+spielBtilde.pdf:	spielBtilde.tex
+	pdflatex spielBtilde.tex
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf
new file mode 100644
index 0000000..466974d
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex
new file mode 100644
index 0000000..92989ed
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex
@@ -0,0 +1,59 @@
+%
+% spielB.tex -- Zutandsdiagramm für Spiel B
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\R{2}
+\def\r{0.5}
+\coordinate (A) at (0,\R);
+\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R});
+\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R});
+
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B);
+
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C);
+
+\pgfmathparse{0.93*\R}
+\xdef\Rgross{\pgfmathresult}
+
+\node at (30:\Rgross) {$\frac34$};
+\node at (150:\Rgross) {$\frac14$};
+\node at (-90:\Rgross) {$\frac14$};
+
+\pgfmathparse{0.33*\R}
+\xdef\Rklein{\pgfmathresult}
+
+\node at (-90:\Rklein) {$\frac34$};
+\node at (30:\Rklein) {$\frac9{10}$};
+\node at (150:\Rklein) {$\frac1{10}$};
+
+\fill[color=white] (A) circle[radius=\r];
+\draw (A) circle[radius=\r];
+\node at (A) {$0$};
+
+\fill[color=white] (B) circle[radius=\r];
+\draw (B) circle[radius=\r];
+\node at (B) {$2$};
+
+\fill[color=white] (C) circle[radius=\r];
+\draw (C) circle[radius=\r];
+\node at (C) {$1$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf
new file mode 100644
index 0000000..7812c9c
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex
new file mode 100644
index 0000000..b2d4b01
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex
@@ -0,0 +1,59 @@
+%
+% spielBtilde.tex -- Zustandsdiagramm des modifzierten Spiels
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\R{2.5}
+\def\r{0.5}
+\coordinate (A) at (0,\R);
+\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R});
+\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R});
+
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B);
+
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A);
+\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C);
+
+\pgfmathparse{0.93*\R}
+\xdef\Rgross{\pgfmathresult}
+
+\node at (30:\Rgross) {$\frac34-\varepsilon$};
+\node at (150:\Rgross) {$\frac14+\varepsilon$};
+\node at (-90:\Rgross) {$\frac14+\varepsilon$};
+
+\pgfmathparse{0.32*\R}
+\xdef\Rklein{\pgfmathresult}
+
+\node at (-90:\Rklein) {$\frac34-\varepsilon$};
+\node at (30:\Rklein) {$\frac9{10}+\varepsilon$};
+\node at (150:\Rklein) {$\frac1{10}-\varepsilon$};
+
+\fill[color=white] (A) circle[radius=\r];
+\draw (A) circle[radius=\r];
+\node at (A) {$0$};
+
+\fill[color=white] (B) circle[radius=\r];
+\draw (B) circle[radius=\r];
+\node at (B) {$2$};
+
+\fill[color=white] (C) circle[radius=\r];
+\draw (C) circle[radius=\r];
+\node at (C) {$1$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
index c6173ce..b7215b4 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
+++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/parrondo.tex b/buch/chapters/80-wahrscheinlichkeit/parrondo.tex
index 3bdba9a..a62d813 100644
--- a/buch/chapters/80-wahrscheinlichkeit/parrondo.tex
+++ b/buch/chapters/80-wahrscheinlichkeit/parrondo.tex
@@ -61,48 +61,7 @@ Fälle recht gross, in einem Fall aber sehr klein.
 \subsubsection{Übergangsmatrix im Spiel $B$}
 \begin{figure}
 \centering
-\begin{tikzpicture}[>=latex,thick]
-\def\R{2}
-\def\r{0.5}
-\coordinate (A) at (0,\R);
-\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R});
-\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R});
-
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B);
-
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C);
-
-\pgfmathparse{0.93*\R}
-\xdef\Rgross{\pgfmathresult}
-
-\node at (30:\Rgross) {$\frac34$};
-\node at (150:\Rgross) {$\frac14$};
-\node at (-90:\Rgross) {$\frac14$};
-
-\pgfmathparse{0.33*\R}
-\xdef\Rklein{\pgfmathresult}
-
-\node at (-90:\Rklein) {$\frac34$};
-\node at (30:\Rklein) {$\frac9{10}$};
-\node at (150:\Rklein) {$\frac1{10}$};
-
-\fill[color=white] (A) circle[radius=\r];
-\draw (A) circle[radius=\r];
-\node at (A) {$0$};
-
-\fill[color=white] (B) circle[radius=\r];
-\draw (B) circle[radius=\r];
-\node at (B) {$2$};
-
-\fill[color=white] (C) circle[radius=\r];
-\draw (C) circle[radius=\r];
-\node at (C) {$1$};
-
-\end{tikzpicture}
+\includegraphics{chapters/80-wahrscheinlichkeit/images/spielB.pdf}
 \caption{Zustandsdiagramm für das Spiel $B$, Zustände sind die
 Dreierreste des Kapitals.
 \label{buch:wahrscheinlichkeit:fig:spielB}}
@@ -454,51 +413,10 @@ U^t (G\odot B) p
 \]
 wie erwartet.
 
-\subsubsection{Das modifizierte Spiel $B$}
+\subsubsection{Das modifizierte Spiel $\tilde{B}$}
 \begin{figure}
 \centering
-\begin{tikzpicture}[>=latex,thick]
-\def\R{2.5}
-\def\r{0.5}
-\coordinate (A) at (0,\R);
-\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R});
-\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R});
-
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B);
-
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A);
-\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C);
-
-\pgfmathparse{0.93*\R}
-\xdef\Rgross{\pgfmathresult}
-
-\node at (30:\Rgross) {$\frac34-\varepsilon$};
-\node at (150:\Rgross) {$\frac14+\varepsilon$};
-\node at (-90:\Rgross) {$\frac14+\varepsilon$};
-
-\pgfmathparse{0.32*\R}
-\xdef\Rklein{\pgfmathresult}
-
-\node at (-90:\Rklein) {$\frac34-\varepsilon$};
-\node at (30:\Rklein) {$\frac9{10}+\varepsilon$};
-\node at (150:\Rklein) {$\frac1{10}-\varepsilon$};
-
-\fill[color=white] (A) circle[radius=\r];
-\draw (A) circle[radius=\r];
-\node at (A) {$0$};
-
-\fill[color=white] (B) circle[radius=\r];
-\draw (B) circle[radius=\r];
-\node at (B) {$2$};
-
-\fill[color=white] (C) circle[radius=\r];
-\draw (C) circle[radius=\r];
-\node at (C) {$1$};
-
-\end{tikzpicture}
+\includegraphics{chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf}
 \caption{Zustandsdiagramm für das modifizerte Spiel $\tilde{B}$,
 Zustände sind die Dreierreste des Kapitals.
 Gegenüber dem Spiel $B$
diff --git a/buch/chapters/95-homologie/chapter.tex b/buch/chapters/95-homologie/chapter.tex
index 95ecb79..eaa56c4 100644
--- a/buch/chapters/95-homologie/chapter.tex
+++ b/buch/chapters/95-homologie/chapter.tex
@@ -14,42 +14,7 @@ Es ist zum Beispiel nicht möglich, ein Dreieck vom Rand eines
 Dreiecks zu unterscheiden~\ref{buch:homologie:figure:zusammenziehbar}.
 \begin{figure}
 \centering
-\begin{tikzpicture}[>=latex,thick]
-\def\punkt#1{
-	\fill[color=white] #1 circle[radius=0.07];
-	\draw #1 circle[radius=0.07];
-}
-\begin{scope}[xshift=3cm]
-\draw[->] (0,0) -- (3,3);
-\draw[->] (0,0) -- (4,1);
-\draw[->] (4,1) -- (3,3);
-\node at (0,0) [below left] {$P_0$};
-\node at (4,1) [below right] {$P_1$};
-\node at (3,3) [above] {$P_2$};
-\punkt{(0,0)}
-\punkt{(4,1)}
-\punkt{(3,3)}
-\node at (2,0.5) [below] {$k_{01}$};
-\node at (1.5,1.5) [above left] {$k_{02}$};
-\node at (3.5,2) [right] {$k_{12}$};
-\end{scope}
-\begin{scope}[xshift=-3cm]
-\fill[color=gray!40] (0,0) -- (4,1) -- (3,3) -- cycle;
-\draw[->] (0,0) -- (3,3);
-\draw[->] (0,0) -- (4,1);
-\draw[->] (4,1) -- (3,3);
-\node at (0,0) [below left] {$P_0$};
-\node at (4,1) [below right] {$P_1$};
-\node at (3,3) [above] {$P_2$};
-\node at (2,0.5) [below] {$k_{01}$};
-\node at (1.5,1.5) [above left] {$k_{02}$};
-\node at (3.5,2) [right] {$k_{12}$};
-\node at (2.333,1.333) {$\triangle$};
-\punkt{(0,0)}
-\punkt{(4,1)}
-\punkt{(3,3)}
-\end{scope}
-\end{tikzpicture}
+\includegraphics{chapters/95-homologie/images/dreieck.pdf}
 \caption{Ein Dreieck $\triangle$ (rechts) und der Rand des Dreicks
 (links) sind mit den Methoden
 der Graphentheorie nicht unterschiedbar. 
diff --git a/buch/chapters/95-homologie/images/Makefile b/buch/chapters/95-homologie/images/Makefile
new file mode 100644
index 0000000..82f1285
--- /dev/null
+++ b/buch/chapters/95-homologie/images/Makefile
@@ -0,0 +1,10 @@
+#
+# Makefile
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	dreieck.pdf
+
+dreieck.pdf:	dreieck.tex
+	pdflatex dreieck.tex
+
diff --git a/buch/chapters/95-homologie/images/dreieck.pdf b/buch/chapters/95-homologie/images/dreieck.pdf
new file mode 100644
index 0000000..e5d360a
--- /dev/null
+++ b/buch/chapters/95-homologie/images/dreieck.pdf
diff --git a/buch/chapters/95-homologie/images/dreieck.tex b/buch/chapters/95-homologie/images/dreieck.tex
new file mode 100644
index 0000000..1c28bc7
--- /dev/null
+++ b/buch/chapters/95-homologie/images/dreieck.tex
@@ -0,0 +1,54 @@
+%
+% dreieck.tex -- Dreieck und Simplex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\punkt#1{
+	\fill[color=white] #1 circle[radius=0.07];
+	\draw #1 circle[radius=0.07];
+}
+\begin{scope}[xshift=3cm]
+\draw[->] (0,0) -- (3,3);
+\draw[->] (0,0) -- (4,1);
+\draw[->] (4,1) -- (3,3);
+\node at (0,0) [below left] {$P_0$};
+\node at (4,1) [below right] {$P_1$};
+\node at (3,3) [above] {$P_2$};
+\punkt{(0,0)}
+\punkt{(4,1)}
+\punkt{(3,3)}
+\node at (2,0.5) [below] {$k_{01}$};
+\node at (1.5,1.5) [above left] {$k_{02}$};
+\node at (3.5,2) [right] {$k_{12}$};
+\end{scope}
+\begin{scope}[xshift=-3cm]
+\fill[color=gray!40] (0,0) -- (4,1) -- (3,3) -- cycle;
+\draw[->] (0,0) -- (3,3);
+\draw[->] (0,0) -- (4,1);
+\draw[->] (4,1) -- (3,3);
+\node at (0,0) [below left] {$P_0$};
+\node at (4,1) [below right] {$P_1$};
+\node at (3,3) [above] {$P_2$};
+\node at (2,0.5) [below] {$k_{01}$};
+\node at (1.5,1.5) [above left] {$k_{02}$};
+\node at (3.5,2) [right] {$k_{12}$};
+\node at (2.333,1.333) {$\triangle$};
+\punkt{(0,0)}
+\punkt{(4,1)}
+\punkt{(3,3)}
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+