From f5edbabd8e4a9b3992035afa7bd3107ffa74a639 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 19 May 2022 13:46:51 +0200
Subject: [PATCH] Vortragsfolien 19.5.2022

---
 20220519/Zeichen_123.pdf                      |   1 +
 20220519/ad-20220519.pdf                      | Bin 0 -> 140807 bytes
 20220519/ad-20220519.tex                      | 218 ++++++++++++++++++
 .../{ad-202200519.txt => ad-20220519.txt}     |   0
 20220519/logo-hochschule-bochum-cvh-text.pdf  |   1 +
 20220519/logo-hochschule-bochum.pdf           |   1 +
 20220519/pgslides.sty                         |   1 +
 7 files changed, 222 insertions(+)
 create mode 120000 20220519/Zeichen_123.pdf
 create mode 100644 20220519/ad-20220519.pdf
 create mode 100644 20220519/ad-20220519.tex
 rename 20220519/{ad-202200519.txt => ad-20220519.txt} (100%)
 create mode 120000 20220519/logo-hochschule-bochum-cvh-text.pdf
 create mode 120000 20220519/logo-hochschule-bochum.pdf
 create mode 120000 20220519/pgslides.sty

diff --git a/20220519/Zeichen_123.pdf b/20220519/Zeichen_123.pdf
new file mode 120000
index 0000000..fdbc897
--- /dev/null
+++ b/20220519/Zeichen_123.pdf
@@ -0,0 +1 @@
+../common/Zeichen_123.pdf
\ No newline at end of file
diff --git a/20220519/ad-20220519.pdf b/20220519/ad-20220519.pdf
new file mode 100644
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diff --git a/20220519/ad-20220519.tex b/20220519/ad-20220519.tex
new file mode 100644
index 0000000..36d2244
--- /dev/null
+++ b/20220519/ad-20220519.tex
@@ -0,0 +1,218 @@
+% ad-20220519.pdf - Lecture Slides on Algorithms and Data Structures in C/C++
+% Copyright (C) 2018, 2019, 2020, 2021, 2022  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Gruppen, Ringe, Körper
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{tikz}
+\usepackage{rotating}
+
+\newcommand{\underconstruction}{%
+  \begin{picture}(0,0)
+    \color{black}
+    \put(7.5,-2.2){\makebox(0,0)[b]{\includegraphics[width=1.5cm]{Zeichen_123.pdf}}}
+    \put(7.5,-2.5){\makebox(0,0)[t]{\shortstack{Änderungen\\vorbehalten}}}
+  \end{picture}}
+
+\title{Algorithmen und Datenstrukturen in C/C++}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{19.\ Mai 2022}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \underconstruction
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/ad.git}}}
+    \item[\textbf{2}] \textbf{Einführung in C++}
+    \item[\textbf{3}] \textbf{Datenkodierung}
+%      \begin{itemize}
+%        \item Fehlererkennung und -korrektur
+%        \item Kompression
+%        \item Kryptographie
+%      \end{itemize}
+    \item[\textbf{4}] \textbf{Datenorganisation}
+%      \begin{itemize}
+%        \item Listen, Bäume, Hash-Tabellen, \dots
+%      \end{itemize}
+    \item[\textbf{5}] \textbf{Hardwarenahe Algorithmen}
+%      \begin{itemize}
+%        \item FFT, CORDIC, \dots
+%      \end{itemize}
+    \item[\textbf{6}] \textbf{Optimierung}
+%      \begin{itemize}
+%        \item Wegfindung, \dots
+%      \end{itemize}
+    \color{gray}
+    \item[\textbf{7}] \textbf{Numerik}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{2}
+\section{Datenkodierung}
+\subsectionnonumber{\boldmath 3.$(x^2 - 1)$\quad Der Herr der Ringe: Manchmal ist $1 + 1 = 0$.}
+\subsubsectionnonumber{\boldmath 3.$(x^2 - 1).x$\quad Motivation}
+
+\begin{frame}
+
+  \showsection
+  \pause
+  \showsubsectionnonumber
+  \pause
+  \showsubsubsectionnonumber
+
+  Man kann auch mit sehr merkwürdigen Objekten\\
+  wie mit "`ganz normalen"' Zahlen rechnen.
+
+  \pause
+  \bigskip
+  
+  Anwendungen:
+  \begin{itemize}
+    \item Funktionsweise von Computern (\textarrow\ Rechnertechnik)
+    \item Fehlererkennung
+    \item Fehlerkorrektur
+    \item Verschlüsselung
+    \item Digitale Signaturen
+  \end{itemize}
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 3.$(x^2 - 1).(x + 1)$\quad Gruppen}
+
+\begin{frame}
+
+  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $G$ eine Menge, $*$ eine Verknüpfung auf $G$.
+  Wenn
+  \begin{itemize}
+    \item
+      $\forall a, b, c \in G$: $(a * b) * c = a * (b * c)$ \quad (Assoziativgesetz),
+    \item
+      $\exists e \in G$: $\forall a \in G$: $a * e = e * a = a$ \quad (neutrales Element),
+    \item
+      $\forall a \in G$: $\exists a^{-1} \in G$: $a * a^{-1} = a^{-1} * a = e$ \quad (inverses Element),
+  \end{itemize}
+  dann heißt $(G,*)$ eine \newterm{Gruppe}.
+
+  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(G,*)$ eine Gruppe.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      $\forall a, b \in G$: $a * b = b * a$ \quad (Kommutativgesetz),
+  \end{itemize}
+  dann heißt $(G,*)$ eine \newterm{kommutative Gruppe}.
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 3.$(x^2 - 1).(x + 2)$\quad Ringe}
+
+\begin{frame}
+
+%  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $R$ eine Menge; seien $+$ und $\cdot$ Verknüpfungen auf $R$.
+  Wenn
+  \begin{itemize}
+    \item
+      $(R,+)$ eine kommutative Gruppe ist,
+    \item
+      $\forall a, b, c \in R$: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ \quad (Assoziativgesetz),
+    \item
+      $\forall a, b, c \in R$: $(a + b)\cdot c = a\cdot c + b\cdot c$
+      und $a\cdot(b + c) = a\cdot b + a\cdot c$ \quad (Distributivgesetze),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{Ring}.
+
+  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(R,+,\cdot)$ ein Ring.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      $\forall a, b \in R$: $a \cdot b = b \cdot a$ \quad (Kommutativgesetz),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{kommutativer Ring}.
+
+  \pause
+  \bigskip
+
+  \textbf{Definition:}
+  Sei $(R,+,\cdot)$ ein (kommutativer) Ring.
+  Wenn zusätzlich
+  \begin{itemize}
+    \item
+      ein $e \in R$ existiert, so daß für alle $a \in R$ gilt: $a \cdot e = e \cdot a = a$\\
+      (neutrales Element),
+  \end{itemize}
+  dann heißt $(R,+,\cdot)$ ein \newterm{(kommutativer) Ring mit 1}.
+
+  \vspace*{-1cm}
+
+\end{frame}
+
+\subsubsectionnonumber{\boldmath 3.$(x^2 - 1).(x + 3)$\quad Körper}
+
+\begin{frame}
+
+%  \showsection
+  \showsubsectionnonumber
+  \showsubsubsectionnonumber
+
+  \textbf{Definition:}
+  Sei $K$ eine Menge; seien $+$ und $\cdot$ Verknüpfungen auf $K$.
+  Wenn
+  \begin{itemize}
+    \item
+      $(K,+,\cdot)$ ein Ring mit 1 ist und
+    \item
+      $(K \backslash \{0\},\cdot)$ eine kommutative Gruppe ist,
+  \end{itemize}
+  dann heißt $(K,+,\cdot)$ ein \newterm{Körper}.
+
+\end{frame}
+
+\end{document}
diff --git a/20220519/ad-202200519.txt b/20220519/ad-20220519.txt
similarity index 100%
rename from 20220519/ad-202200519.txt
rename to 20220519/ad-20220519.txt
diff --git a/20220519/logo-hochschule-bochum-cvh-text.pdf b/20220519/logo-hochschule-bochum-cvh-text.pdf
new file mode 120000
index 0000000..a059461
--- /dev/null
+++ b/20220519/logo-hochschule-bochum-cvh-text.pdf
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+../common/logo-hochschule-bochum-cvh-text.pdf
\ No newline at end of file
diff --git a/20220519/logo-hochschule-bochum.pdf b/20220519/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20220519/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20220519/pgslides.sty b/20220519/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20220519/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
-- 
GitLab