misc

documents/math-fonts/Makefile

@@ -0,0 +1,7 @@
+SOURCE = math-fonts
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.out

documents/math-fonts/math-fonts.tex

@@ -0,0 +1,55 @@
+\documentclass{scrartcl}
+\usepackage{amssymb, amsmath} % needed for math
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage[margin=2.5cm]{geometry} %layout
+\usepackage{hyperref}   % links im text
+\usepackage{parskip}
+\usepackage{multicol}
+
+\title{Minimal distance to a cubic function}
+\author{Martin Thoma}
+
+\hypersetup{ 
+  pdfauthor   = {Martin Thoma}, 
+  pdfkeywords = {}, 
+  pdftitle    = {} 
+} 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Begin document                                                    %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+\section{mathcal}
+\begin{multicols}{3}
+\begin{itemize}
+    \item $\mathcal{A}$
+    \item $\mathcal{B}$
+    \item $\mathcal{C}$
+    \item $\mathcal{D}$
+    \item $\mathcal{E}$
+    \item $\mathcal{F}$
+    \item $\mathcal{G}$
+    \item $\mathcal{H}$
+    \item $\mathcal{I}$
+    \item $\mathcal{J}$
+    \item $\mathcal{K}$
+    \item $\mathcal{L}$
+    \item $\mathcal{M}$
+    \item $\mathcal{N}$
+    \item $\mathcal{O}$
+    \item $\mathcal{P}$
+    \item $\mathcal{Q}$
+    \item $\mathcal{R}$
+    \item $\mathcal{S}$
+    \item $\mathcal{T}$
+    \item $\mathcal{U}$
+    \item $\mathcal{V}$
+    \item $\mathcal{W}$
+    \item $\mathcal{X}$
+    \item $\mathcal{Y}$
+    \item $\mathcal{Z}$
+\end{itemize}
+\end{multicols}
+\end{document}

tikz/topology-continuous-mapping/topology-continuous-mapping.tex

@@ -24,12 +24,15 @@
         \draw (\x,0.1) -- (\x,-0.1) node [below] {\x};
 
 
-    \draw[red] (0.07,0.1) -- (0,0.1) -- (0,-0.1) -- (0.07,-0.1) node [below] {};
-    \draw[red] plot [smooth] coordinates{(0.47,0.1) (0.5,0) (0.47,-0.1)};
+    \draw[thick,red] (0.07,0.1) -- (0,0.1) -- (0,-0.1) -- (0.07,-0.1) node [below] {};
+    \draw[thick,red] plot [smooth] coordinates{(0.47,0.1) (0.5,0) (0.47,-0.1)};
+    \draw[thick,red] (0,0) -- (0.5,0);
+    \draw[dotted,red] (0,-0.03) -- (0.5,-0.03);
 
     \begin{scope}[shift={(4,0)}]
         \draw[thick] (0cm,0cm) circle(1cm);
         \draw[thick, red] ([shift={(180:1cm)}]-0.0,0) arc (180:0:1cm);
+        \draw[red, dotted] ([shift={(180:0.97cm)}]-0.0,0) arc (180:0:0.97cm);
         \draw (0:1cm) node[point, label=right:{$0$}] {};
     \end{scope}
 

tikz/topology-kartenwechsel/topology-kartenwechsel.tex

@@ -1,4 +1,5 @@
 \documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{amsmath,amssymb}% math symbols / fonts
 \usepackage{tikz}
 \usepackage{tqft}
 \usetikzlibrary{patterns}
@@ -6,6 +7,7 @@
 \begin{document}
     \begin{tikzpicture}[tqft/flow=east]
         \draw (0,0) ellipse (2cm and 1cm);
+        \draw (0,-2) ellipse (3cm and 0.8cm);
         \def\ringa{(-0.3,0) circle (0.5cm)}
         \def\ringb{(+0.3,0) circle (0.5cm)}
 
@@ -30,6 +32,8 @@
         \node at (+1,0.3) {$U_j$};
         \node at (-1.9,-2) {$V_i$};
         \node at (+1.9,-2) {$V_j$};
+        \node at (+2.0,0.7) {$X$};
+        \node at (+2.4,-1.3) {$\mathbb{R}^n$};
 
 
         \path[->] (-0.35,0)  edge [bend angle=10,bend right] node[label={[label distance=0.1cm]210:$\varphi_i$}] {} (-1,-1.5);