From fe600d3146ec04b2beb61ad4ce94f08615d0b7d8 Mon Sep 17 00:00:00 2001 From: Jonas_Jones Date: Fri, 20 Jun 2025 22:52:20 +0200 Subject: [PATCH] added epr rep files --- .../beamerthemeoxfordmaths.sty | 98 ++ .../azyklisch_nichtzusammenhaengend.png | Bin 0 -> 5587 bytes .../images/azyklisch_zusammenhaengend.png | Bin 0 -> 6635 bytes .../images/code_adjazenzliste.png | Bin 0 -> 29207 bytes .../images/code_fallbackparameterfunction.png | Bin 0 -> 36623 bytes .../images/code_helloworldfunction.png | Bin 0 -> 27901 bytes .../images/code_inputandreturnfunction.png | Bin 0 -> 22334 bytes .../images/code_iterationexamplesimple.png | Bin 0 -> 30153 bytes .../images/code_iterationsumnumbers.png | Bin 0 -> 37544 bytes .../images/code_lambdafunction.png | Bin 0 -> 18237 bytes .../images/code_matplotlibexample.png | Bin 0 -> 79949 bytes .../images/code_matplotlibpandas.png | Bin 0 -> 91753 bytes .../images/code_numpyelementwiseoperation.png | Bin 0 -> 45669 bytes 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.../images/graph_matplotlibpandas.png | Bin 0 -> 10025 bytes .../images/graph_ungerichtet.png | Bin 0 -> 6333 bytes .../images/zyklisch_nichtzusammenhaengend.png | Bin 0 -> 6756 bytes .../images/zyklisch_zusammenhaengend.png | Bin 0 -> 8158 bytes epr/epr_rep_folien_jonas/main.tex | 1470 +++++++++++++++++ epr/epr_rep_folien_jonas/mathematics-logo.png | Bin 0 -> 11481 bytes epr/epr_rep_folien_jonas/oxford-logo.png | Bin 0 -> 22769 bytes .../title-slide-background-wide.png | Bin 0 -> 450343 bytes .../title-slide-background.png | Bin 0 -> 405873 bytes epr/epr_rep_uebungen_jonas/main.tex | 108 ++ 39 files changed, 1676 insertions(+) create mode 100644 epr/epr_rep_folien_jonas/beamerthemeoxfordmaths.sty create mode 100644 epr/epr_rep_folien_jonas/images/azyklisch_nichtzusammenhaengend.png create mode 100644 epr/epr_rep_folien_jonas/images/azyklisch_zusammenhaengend.png create mode 100644 epr/epr_rep_folien_jonas/images/code_adjazenzliste.png create mode 100644 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+1,98 @@ +%% Mathematical Institute, University of Oxford +%% LaTeX Beamer Presentation Theme +%% +%% v1.0 Original theme: Tim Hosgood 2015 (based on department PowerPoint Template) +%% v2.0 Reimplementation: Karl Welzel May 2024 (reimplementation from a standard theme) +%% v2.1 Further adjustments and tweaks: Keith Gillow May 2024 + +% Use infolines as base +\useoutertheme{infolines} + +% tweak colours for Oxford Blue +\definecolor{oxfordblue}{RGB}{0,33,71} +\usecolortheme[named=oxfordblue]{structure} + +%turn off the navigation symbols +\setbeamertemplate{navigation symbols}{} + +% define useful layout lengths +\newlength{\textmargin} +\setlength{\textmargin}{10mm} % Left and right margin for main content +\setbeamersize{text margin left=\textmargin,text margin right=\textmargin} +\newlength{\titlehmargin} +\setlength{\titlehmargin}{5mm} % Left and right margin for title and footline +\newlength{\titlevmargin} +\setlength{\titlevmargin}{1mm} % Top and bottom margin for title and footline +\newlength{\fullpagewidth} +\setlength{\fullpagewidth}{\dimexpr\textwidth+\textmargin+\textmargin\relax} + +% Calculate widths from heights for the logos +\newlength{\oxfordlogowidth} +\setlength{\oxfordlogowidth}{\dimexpr 10mm * 214 / 311 \relax} +\newlength{\mathslogowidth} +\setlength{\mathslogowidth}{\dimexpr 3mm * 347 / 105 \relax} + +%% Title slide formatting %% +\setbeamertemplate{title page}{ + \begin{picture}(0,0) + \put(-\textmargin, \dimexpr -\paperheight*6/10 \relax){% + \ifdim\paperwidth>400pt + \includegraphics[width=\paperwidth]{title-slide-background-wide.png} + \else + \includegraphics[width=\paperwidth]{title-slide-background.png} + \fi + } + \put(-\textmargin +7mm, -55pt){% + \begin{minipage}[b][4.5cm][t]{0.7\textwidth} + \raggedright + \color{white} + \usebeamerfont{title} + {\inserttitle\\[0.9cm]} + \usebeamerfont{subtitle} + {\sc\insertauthor\\[0.1cm]} + {\it\insertinstitute\\[0.3cm]} + {\insertdate} + \end{minipage} + } + \end{picture} +} + +%% General 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Februar} %main date for title page, + %can overload it to show say 'Conference X, Date Y' + + + + +%% Now for the actual slides %% +\begin{document} + +\begin{frame}[plain] + \titlepage +\end{frame} + +\begin{frame} + \frametitle{Themen} + \begin{itemize} + \item Graphen und Bäume + \item Funktionen in Python + \item Iteration und Rekursion + \item Numpy und Pandas + \end{itemize} +\end{frame} + +\begin{frame}{Graphentheorie} + \begin{columns} + \hspace*{1cm}\begin{column}{0.64\textwidth} + \begin{itemize} + \item Definiert über ein Tupel an Mengen als G = (V,E) + \begin{itemize} + \item V: Menge an Knoten (\textit{Vertices}) + \item E: Menge an Kanten (\textit{Edges}) + \end{itemize} + \end{itemize} + \pause + + Knoten: + \begin{itemize} + \item Elemente/Zustände + \end{itemize} + + Kanten: + \begin{itemize} + \item Verbindungen/Übergänge + \end{itemize} + \end{column} + + \begin{column}{0.25\textwidth} + \centering + \scalebox{0.7}{ + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [below of=C] {D}; + + \path[--] + (A) edge (B) + (B) edge (C) + (C) edge [bend left] (A) + edge (D); + + \end{tikzpicture} + } + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Zyklisch (Nicht Kreisfrei) + \vspace{0.5} + \begin{figure}[h] + \centering + \scalebox{0.9}{ + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [below of=C] {D}; + + \path[--] + (A) edge (B) + (B) edge (C) + (C) edge [bend left] (A) + edge (D); + + \end{tikzpicture} + } + \end{figure} + \end{column} + \pause + \vline + \begin{column}{0.5\textwidth} + \centering \Large Azyklisch (Kreisfrei) + \vspace{0.75cm} + \begin{figure}[h] + \centering + \scalebox{0.9}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [right of=C] {D}; + + \path[--] + (A) edge (B) + (B) edge (C) + (C) edge (D); + + \end{tikzpicture} + } + \end{figure} + \vspace{0.75cm} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Zusammenhängend + \vspace{0.75cm} + \begin{figure}[h] + \centering + \scalebox{0.9}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [right of=C] {D}; + + \path[--] + (A) edge (B) + (B) edge (C) + (C) edge (D); + + \end{tikzpicture} + } + \end{figure} + \vspace{0.75cm} + \end{column} + \pause + \vline + \begin{column}{0.5\textwidth} + \centering \Large Nicht Zusammenhängend + \begin{figure}[h] + \centering + \scalebox{0.9}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [below of=B, xshift=2cm] {D}; % Place D separately + + \path[--] + (A) edge (B) + (B) edge (C); + + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Ungerichtet \normalsize + \begin{figure}[h] + \centering + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [right of=C] {D}; + \node (E) [right of=D] {E}; + + \path[--] + (A) edge (B) + (B) edge (C) + (C) edge (D) + (D) edge (E) + (E) edge [bend left] (A) + + \end{tikzpicture} + } + \end{figure} + \end{column} + \vline + \begin{column}{0.5\textwidth} + \centering \Large Gerichtet \normalsize + \begin{figure}[h] + \centering + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [right of=B] {C}; + \node (D) [right of=C] {D}; + \node (E) [right of=D] {E}; + + \path[->] + (A) edge (B) + (B) edge (C) + (C) edge (D) + (D) edge (E) + (E) edge [bend left] (A) + + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzliste \normalsize + \begin{itemize} + \item Liste aller Adjazenzknoten eines Knotens + \end{itemize} + \begin{table}[] + \centering + \begin{tabular}{c|c} + A & \{A, C\} \\ + B & \{A, B\} \\ + C & $\emptyset$ + \end{tabular} + \end{table} + \end{column} + \pause + \vline + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzmatrix \normalsize + \begin{itemize} + \item $n \times n$ - Matrix + \end{itemize} + \begin{table}[] + \centering + \begin{tabular}{c|c c c} + & A & B & C \\ + \hline + A & 1 & 0 & 1 \\ + B & 1 & 1 & 0 \\ + C & 0 & 0 & 0 \\ + \end{tabular} + \end{table} + \end{column} + \end{columns} + \vspace{0.5cm} + \pause + \centering Beide Darstellungen repräsentieren den gleichen Graphen +\end{frame} +% Azyklisch oder nicht? +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzliste \normalsize + \begin{table}[] + \centering + \begin{tabular}{c|c} + A & \{A, C\} \\ + B & \{A, B\} \\ + C & $\emptyset$ + \end{tabular} + \end{table} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{1.2}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [below of=A] {C}; + + \path[->] + (A) edge [loop above] (A) % Loop at A + (A) edge (C) % Edge from A to C + (B) edge (A) % Edge from B to A + (B) edge [loop right] (B); % Loop at B + + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzmatrix \normalsize + \begin{table}[] + \centering + \begin{tabular}{c|c c c} + & A & B & C \\ + \hline + A & 1 & 0 & 1 \\ + B & 1 & 1 & 0 \\ + C & 0 & 0 & 0 \\ + \end{tabular} + \end{table} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{1.2}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [below of=A] {C}; + + \path[->] + (A) edge [loop above] (A) % Loop at A + (A) edge (C) % Edge from A to C + (B) edge (A) % Edge from B to A + (B) edge [loop right] (B); % Loop at B + + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzliste \normalsize + \begin{table}[] + \centering + \begin{tabular}{c|c} + A & \{A, C\} \\ + B & \{A, B\} \\ + C & $\emptyset$ + \end{tabular} + \end{table} + \end{column} + \begin{column}{0.5\textwidth} + \centering \Large Programmatische Umsetzung \normalsize + \pause + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_adjazenzliste.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \centering \Large Adjazenzmatrix \normalsize + \begin{table}[] + \centering + \begin{tabular}{c|c c c} + & A & B & C \\ + \hline + A & 1 & 0 & 1 \\ + B & 1 & 1 & 0 \\ + C & 0 & 0 & 0 \\ + \end{tabular} + \end{table} + \end{column} + \begin{column}{0.5\textwidth} + \centering \Large Programmatische Umsetzung \normalsize + \begin{itemize} + \item Zweidimensionale verschachtelte Liste oder \textit{nested list} + \item Speicherplatz ist \textit{quaddratisch} im Vergleich zu \textit{linear} bei Adjazenzlisten, daher unüblich + \end{itemize} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \Large Komplexeres Beispiel \normalsize + \vspace{0.5cm} + \begin{columns} + \begin{column}{0.4\textwidth} + \begin{itemize} + \item Adjazenzmatrix + \begin{table}[] + \centering + \begin{tabular}{c|c c c c c c} + & A & B & C & D & E & F \\ + \hline + A & 0 & 0 & 1 & 0 & 0 & 0 \\ + B & 0 & 0 & 1 & 0 & 1 & 0 \\ + C & 1 & 1 & 0 & 1 & 1 & 0 \\ + D & 0 & 0 & 1 & 0 & 0 & 0 \\ + E & 0 & 1 & 1 & 0 & 0 & 0 \\ + F & 0 & 0 & 0 & 0 & 0 & 0 \\ + \end{tabular} + \end{table} + \end{itemize} + \end{column} + \pause + \begin{column}{0.3\textwidth} + \begin{itemize} + \item Adjazenzliste + \begin{table}[] + \centering + \begin{tabular}{c|c} + A & \{C\} \\ + B & \{C, E\} \\ + C & \{A, B, D, E\} \\ + D & \{C\} \\ + E & \{B, C\} \\ + F & $\emptyset$ \\ + \end{tabular} + \end{table} + \end{itemize} + \vspace{0.25cm} + \end{column} + \pause + \begin{column}{0.3\textwidth} + \begin{figure}[h] + \centering + \scalebox{1.0}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + \node[shape=circle,draw=black] (A) at (-1,1) {A}; + \node[shape=circle,draw=black] (B) at (1,1) {B}; + \node[shape=circle,draw=black] (C) at (0,0) {C}; + \node[shape=circle,draw=black] (D) at (-1,-1) {D}; + \node[shape=circle,draw=black] (E) at (1,-1) {E}; + \node[shape=circle,draw=black] (F) at (2,0) {F} ; + + \path [<->](A) edge (C); + \path [<->](B) edge (C); + \path [<->](B) edge (E); + \path [<->](C) edge (E); + \path [<->](D) edge (C); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + Grundbegriffe \textit{(Recap)} + \begin{itemize} + \item Knoten: Element/Zustand + \pause + \item Kante: Verbindung/Übergang + \pause + \item Grad: Anzahl an Kanten die den Knoten verbinden (nur wenn ungerichtet) + \pause + \item Eingangsgrad: Anzahl an Kanten die in den Knoten zeigen (nur wenn gerichtet) + \pause + \item Ausgangsgrad: Anzahl an Kanten die aus dem Knoten zeigen (nur wenn gerichtet) + \pause + \item Adjazenzliste: Liste an Knoten die durch den Knoten erreicht werden + \pause + \item Adjazenzmatrix: Matrix mit \texttt{boolean}-Wert für jede Knoten-Verbindung + \pause + \item Zusammenhängend: Jeder Knoten kann von kedem Knoten erreicht werden (nur wenn ungerichtet) + \pause + \item Schwach zusammenhängend: alle Knoten sind über mindestens eine Kante verbunden (nur wenn gerichtet) + \item Stark zusammenhängend: man kann von allen zu allen Knoten und zurück (nur wenn gerichtet) + \end{itemize} +\end{frame} + +\begin{frame}{Graphentheorie} + \textbf{Baum} - Spezialfall von Graphen + \begin{columns} + \begin{column}{0.7\textwidth} + \begin{itemize} + \item azyklisch + \pause + \item $n - 1$ Kanten bei $n$ Knoten + \pause + \item Innerer Knoten: Knoten der weder Wurzel noch Blatt ist + \pause + \item Tiefe: Pfadlänge (Anzahl an Kanten) von der Wurzel zum Knoten + \pause + \item Höhe: Pfadlänge (Anzahl an Kanten) vom Knoten zum nächsten Blatt + \pause + \item Eltern: Vorgänger + \pause + \item Kinder: Nachfahren + \pause + \item Geschwister: Knoten mit gleichem Elternknoten + \end{itemize} + \end{column} + \begin{column}{0.3\textwidth} + \begin{figure}[h] + \centering + \onslide + \scalebox{0.5}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,2) {A}; % Root node + \node[shape=circle,draw=black] (B) at (-2,1) {B}; % Child of A + \node[shape=circle,draw=black] (C) at (2,1) {C}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,0) {D}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,0) {E}; % Child of B + \node[shape=circle,draw=black] (F) at (1,0) {F}; % Child of C + + % Define edges + \path [--](A) edge (B); + \path [--](A) edge (C); + \path [--](B) edge (D); + \path [--](B) edge (E); + \path [--](C) edge (F); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + + +\begin{frame}{Graphentheorie} + \textbf{Ungerichteter Baum} + \begin{columns} + \begin{column}{0.7\textwidth} + \begin{itemize} + \pause + \item zusammenhängend + \pause + \item Wurzel: "Hauptknoten" (kann beliebig ausgewählt werden) + \pause + \item Blatt: Knoten ohne Nachfolger + \pause + \item Ordnung: maximaler Grad - 1 + \end{itemize} + \end{column} + \begin{column}{0.3\textwidth} + \begin{figure}[h] + \centering + \onslide + \scalebox{0.5}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,2) {A}; % Root node + \node[shape=circle,draw=black] (B) at (-2,1) {B}; % Child of A + \node[shape=circle,draw=black] (C) at (2,1) {C}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,0) {D}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,0) {E}; % Child of B + \node[shape=circle,draw=black] (F) at (1,0) {F}; % Child of C + \node[shape=circle,draw=black] (G) at (3,0) {G}; % Child of C + + % Define edges + \path [--](A) edge (B); + \path [--](A) edge (C); + \path [--](B) edge (D); + \path [--](B) edge (E); + \path [--](C) edge (F); + \path [--](C) edge (G); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \textbf{Gerichteter Baum} + \begin{columns} + \begin{column}{0.7\textwidth} + \begin{itemize} + \pause + \item nicht zusammenhängend + \pause + \item Wurzel: Knoten mit Eingangsgrad 0 + \pause + \item Blatt: Knoten mit Ausgangsgrad 0 + \pause + \item Ordnung: maximaler Ausgangsgrad + \end{itemize} + \end{column} + \begin{column}{0.3\textwidth} + \begin{figure}[h] + \centering + \onslide + \scalebox{0.5}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,2) {A}; % Root node + \node[shape=circle,draw=black] (B) at (-2,1) {B}; % Child of A + \node[shape=circle,draw=black] (C) at (2,1) {C}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,0) {D}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,0) {E}; % Child of B + \node[shape=circle,draw=black] (F) at (1,0) {F}; % Child of C + \node[shape=circle,draw=black] (G) at (3,0) {G}; % Child of C + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \path [->](C) edge (G); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \textbf{Spezielle Bäume I} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Binärbaum + \begin{itemize} + \item 0 - 2 Kinder + \item Eindeutiger Unterschied zwischen linkem und rechten Kind + \end{itemize} + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \onslide + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (1) at (0,2) {1}; % Root node + \node[shape=circle,draw=black] (2) at (-2,1) {2}; % Child of A + \node[shape=circle,draw=black] (3) at (2,1) {3}; % Child of A + \node[shape=circle,draw=black] (4) at (-3,0) {4}; % Child of B + \node[shape=circle,draw=black] (5) at (-1,0) {5}; % Child of B + \node[shape=circle,draw=black] (6) at (1,0) {6}; % Child of C + + % Define edges + \path [->](1) edge (2); + \path [->](1) edge (3); + \path [->](2) edge (4); + \path [->](2) edge (E); + \path [->](3) edge (F); + \end{tikzpicture} + } + \end{figure} + \centering \LARGE $\neq$ \normalsize + \begin{figure}[h] + \centering + \onslide + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,2) {1}; % Root node + \node[shape=circle,draw=black] (B) at (-2,1) {2}; % Child of A + \node[shape=circle,draw=black] (C) at (2,1) {3}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,0) {4}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,0) {5}; % Child of B + \node[shape=circle,draw=black] (F) at (3,0) {6}; % Child of C + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \textbf{Spezielle Bäume II} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Balancierter Baum + \begin{itemize} + \item die Länge der Pfade von der Wurzel zu allen Blättern darf sich um höchstens 1 unterscheiden + \end{itemize} + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \centering \large balanciert \normalsize + \begin{figure}[h] + \centering + \onslide + \scalebox{0.6}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (1) at (0,2) {1}; % Root node + \node[shape=circle,draw=black] (2) at (-2,1) {2}; % Child of A + \node[shape=circle,draw=black] (3) at (2,1) {3}; % Child of A + \node[shape=circle,draw=black] (4) at (-3,0) {4}; % Child of B + \node[shape=circle,draw=black] (5) at (-1,0) {5}; % Child of B + + % Define edges + \path [->](1) edge (2); + \path [->](1) edge (3); + \path [->](2) edge (4); + \path [->](2) edge (E); + \end{tikzpicture} + } + \end{figure} + \begin{figure}[h] + \centering + \scalebox{0.6}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,3) {1}; % Root node + \node[shape=circle,draw=black] (B) at (-2,2) {2}; % Child of A + \node[shape=circle,draw=black] (C) at (2,2) {3}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,1) {4}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,1) {5}; % Child of B + \node[shape=circle,draw=black] (F) at (-4,0) {6}; % Child of C + \node[shape=circle,draw=black] (G) at (-2,0) {7}; % Child of F + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](D) edge (F); + \path [->](D) edge (G); + \end{tikzpicture} + } + \end{figure} + \centering \large nicht balanciert \normalsize + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{-1.7cm} + \textbf{Spezielle Bäume III} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Suchbaum + \begin{itemize} + \item geordnete Knoten zum schnelleren Finden von Elementen + \end{itemize} + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{0.8}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes (changed to fit the binary search tree property) + \node[shape=circle,draw=black] (A) at (0,3) {10}; % Root node + \node[shape=circle,draw=black] (B) at (-2,2) {5}; % Child of A + \node[shape=circle,draw=black] (C) at (2,2) {15}; % Child of A + \node[shape=circle,draw=black] (D) at (-2.5,1) {3}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,1) {7}; % Child of B + \node[shape=circle,draw=black] (F) at (2.5,1) {20}; % Child of C + \node[shape=circle,draw=black] (G) at (2,0) {17}; % Child of F + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \path [->](F) edge (G); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \begin{columns} + \begin{column}{0.5\textwidth} + \textbf{Spezielle Bäume IV} + \begin{itemize} + \item HEAP (Heap-Eigenschaft) + \begin{itemize} + \item Die traversierten Knoten jedes Pfades von der Wurzel zu den Blättern ist auf-/ oder absteigend + \end{itemize} + \begin{itemize} + \item Min-Heap: in aufsteigender Reihenfolge (Wurzel $\rightarrow$ Blatt) + \item Max-Heap: in absteigender Reihenfolge (Wurzel $\rightarrow$ Blatt) + \end{itemize} + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Min-Heap + \node[shape=circle,draw=black] (A) at (0,3) {1}; % Root node + \node[shape=circle,draw=black] (B) at (-2,2) {3}; % Child of A + \node[shape=circle,draw=black] (C) at (2,2) {6}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,1) {5}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,1) {7}; % Child of B + \node[shape=circle,draw=black] (F) at (1,1) {8}; % Child of C + \node[shape=circle,draw=black] (G) at (3,1) {9}; % Child of C + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \path [->](C) edge (G); + \end{tikzpicture} + } + \end{figure} + \centering Min-Heap Eigenschafft erfüllt + \begin{figure}[h] + \centering + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=red!20, font=\sffamily}, + every edge/.style={draw, thick, red}] + + % Max-Heap + \node[shape=circle,draw=black] (A) at (0,3) {9}; % Root node + \node[shape=circle,draw=black] (B) at (-2,2) {7}; % Child of A + \node[shape=circle,draw=black] (C) at (2,2) {6}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,1) {5}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,1) {3}; % Child of B + \node[shape=circle,draw=black] (F) at (1,1) {2}; % Child of C + \node[shape=circle,draw=black] (G) at (3,1) {1}; % Child of C + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \path [->](C) edge (G); + \end{tikzpicture} + } + \end{figure} + \centering Max-Heap Eigenschafft erfüllt + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \vspace{-1.7cm} + \textbf{Traversierung} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Es gibt 3 Arten einen Baum zu traversieren: + \begin{itemize} + \item Pre-Order + \item In-Order + \item Post-Order + \end{itemize} + \pause + \item Bei der Traversierung werden alle Knoten in der erreichten Reihenfolge aufgeschrieben + \end{itemize} + \end{column} + \onslide + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{1}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define a single node with no label + \node[shape=circle,draw=black] (A) at (0,0) {Knoten}; % Center node + + % Dots around the node (manually placing them) + \node[shape=circle,fill=black,inner sep=0.5mm] at (-0.8, 0) {}; % Left dot + \node[shape=circle,fill=black,inner sep=0.5mm] at (0.8, 0) {}; % Right dot + \node[shape=circle,fill=black,inner sep=0.5mm] at (0, -0.8) {}; % Bottom dot + + % Text labels without circles + \node[shape=rectangle, fill=white, inner sep=1mm] at (-1.5, 0) {pre}; % Left text label + \node[shape=rectangle, fill=white, inner sep=1mm] at (0, -1.35) {in}; % Bottom text label + \node[shape=rectangle, fill=white, inner sep=1mm] at (1.6, 0) {post}; % Right text label + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Graphentheorie} + \textbf{Traversierungen} + \begin{columns} + \begin{column}{0.5\textwidth} + \pause + \begin{itemize} + \item Pre-Order (W-L-R) + \begin{itemize} + \item 1, 2, 4, 5, 3, 6, 7, 8, 9 + \end{itemize} + \end{itemize} + \pause + \begin{itemize} + \item In-Order (L-W-R) + \begin{itemize} + \item 4, 2, 5, 1, 6, 3, 8, 7, 9 + \end{itemize} + \end{itemize} + \pause + \begin{itemize} + \item Post-Order (L-R-W) + \begin{itemize} + \item 4, 5, 2, 6, 8, 9, 7, 3, 1 + \end{itemize} + \end{itemize} + \end{column} + \onslide + \begin{column}{0.5\textwidth} + \begin{figure}[h] + \centering + \scalebox{0.7}{ % Adjust scale here + \begin{tikzpicture}[shorten >=1pt, node distance=2cm, auto, + every node/.style={circle, draw, fill=blue!20, font=\sffamily}, + every edge/.style={draw, thick, blue}] + + % Define nodes + \node[shape=circle,draw=black] (A) at (0,4) {1}; % Root node + \node[shape=circle,draw=black] (B) at (-2,3) {2}; % Child of A + \node[shape=circle,draw=black] (C) at (2,3) {3}; % Child of A + \node[shape=circle,draw=black] (D) at (-3,2) {4}; % Child of B + \node[shape=circle,draw=black] (E) at (-1,2) {5}; % Child of B + \node[shape=circle,draw=black] (F) at (1,2) {6}; % Child of C + \node[shape=circle,draw=black] (G) at (3,2) {7}; % Child of C + \node[shape=circle,draw=black] (H) at (2.5,1) {8}; % Child of G + \node[shape=circle,draw=black] (I) at (3.5,1) {9}; % Child of G + + % Define edges + \path [->](A) edge (B); + \path [->](A) edge (C); + \path [->](B) edge (D); + \path [->](B) edge (E); + \path [->](C) edge (F); + \path [->](C) edge (G); + \path [->](G) edge (H); + \path [->](G) edge (I); + \end{tikzpicture} + } + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Funktionen in Python} + \pause + \textbf{Was ist eine Funktion?} + \pause + \begin{itemize} + \item Block an Code der eine bestimmte Aufgabe erfüllt + \pause + \item kann Eingabewerte annehmen und einen Ausgabewerte zurückgegeben + \end{itemize} + \pause + \textbf{Vorteile} + \begin{itemize} + \pause + \item Wiederholbarkeit: Codeblock wird \textit{einmal} geschrieben und kann \textit{beliebig} oft aufgerufen werden + \pause + \item Lesbarkeit: strukturierter und lesbarer (auch mit sinngemäßen \textit{Funktionsnamen}) + \pause + \item Modularität: Zerlegen von Logiken eines Programms in leichtere verständlichere Teile + \end{itemize} +\end{frame} + +\begin{frame}{Funktionen in Python} + \textbf{Kurzes Recap: Die Wichtigeste Typen in Python} + \begin{itemize} + \item Text: + \begin{itemize} + \item \texttt{str} + \end{itemize} + \item Numerisch: + \begin{itemize} + \item \texttt{int}, \texttt{float} + \end{itemize} + \item Sequenzen: + \begin{itemize} + \item \texttt{list}, \texttt{tuple} + \end{itemize} + \item Diverse: + \begin{itemize} + \item \texttt{dict}, \texttt{set}, \texttt{bool}, \texttt{NoneType} + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Funktionen in Python} + \begin{columns} + \begin{column}{0.5\textwidth} + \textbf{Hello-World Funktion} + \begin{itemize} + \item einfache Funktion ohne Parameterübergabe oder -rückgabe + \item Gibt "Hallo Welt!" in der Konsole aus + \item definiert mit dem \textbf{def} Schlüsselwort + \pause + \item aufgerufen wird diese mit \textbf{hello\_world\_func()} + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_helloworldfunction.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Funktionen in Python} + \begin{columns} + \begin{column}{0.5\textwidth} + \textbf{Parameterübergabe} + \begin{itemize} + \item Variablennamen in den Klammern. mit Komma getrennt, wenn mehrere + \item \textbf{return} gibt einen Wert zurück + \item (\textbf{Wichtig: zurückgeben $\neq$ ausgeben}) + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_inputandreturnfunction.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Funktionen in Python} + \begin{columns} + \begin{column}{0.5\textwidth} + \textbf{Standardwerte} + \begin{itemize} + \item Fall-Back, falls der geforderte Parameter nicht übergeben wurde + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_fallbackparameterfunction.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Funktionen in Python} + \begin{columns} + \begin{column}{0.5\textwidth} + \textbf{Lambda Funktionen} + \begin{itemize} + \item Annonyme kurze Funktionen mit \textbf{lambda} Schlüsselwort + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_lambdafunction.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Was ist Iteration?} + \begin{itemize} + \item einen bestimmten Codeabschnitt mehrfach ausführen, etwa über eine Schleife (in Python \textbf{for} und \textbf{while} + \item Häufig um eine iterierbare Datenstruktur zu durchlaufen + \end{itemize} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Vorteile der Iteration} + \begin{itemize} + \item klar und verständlich + \item gut geeignet wenn Anzahl der Iterationen bekannt + \item Speichereffizient. wird Schritt für Schritt ausgeführt + \end{itemize} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Beispiele zur Iteration} + \vspace{1cm} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_iterationexamplesimple.png} + \end{tcolorbox} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_iterationsumnumbers.png} + \end{tcolorbox} + \end{column} + \end{columns} + \vspace{1cm} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Was ist Rekursion?} + \begin{itemize} + \item eine Funktion ruft sich selbst solange auf, bis eine Abbruchbedingung erfüllt ist. + \pause + \item Das Problem wird in kleinere Teilprobleme unterteilt, die einfacher zu lösen sind + \pause + \item Nach dem Erfüllen der Abbruchbedingung ist das Problem gelöst und der erziehlte Wert kann zurückgegeben werden + \pause + \item Besteht aus: + \begin{itemize} + \item Mindestens einem Basisfall: beendet den Rekursionszweig + \item Rekursionsfälle: führt zu weiteren rekursiven Aufrufen mit modifizierten Argumenten + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Vorteile der Rekursion} + \begin{itemize} + \item kann Probleme eleganter und kürzer lösen (generell nur bei Rekursiven Problemen wie z.B. \textit{Fibonacci}, \textit{Baumdurchläufe}, etc...) + \end{itemize} + \pause + \textbf{Nachteile der Rekursion} + \begin{itemize} + \item kann zu hoher Speicherauslastung führen, vor allem wenn edge cases zu lasch definiert oder Eingabewerte zu groß sind + \item Rekursive Lösungen sind in einigen Fällen weniger effizient als iterative + \end{itemize} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Rekursionsarten} + \begin{itemize} + \item Lineare Rekursion + \item Baumrekursion + \item Wechselseitige Rekursion + \item Endrekursion \textit{(Spezialfall der linearen Rekursion)} + \end{itemize} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Lineare Rekursion} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Im Rekursionsfall wird die Funktion genau ein Mal aufgerufen + \end{itemize} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_recursionfacultyexample.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Baumrekursion} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Im Rekursionsfall wird die Funktion \textbf{mehr} als ein Mal aufgerufen + \end{itemize} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_recursionfibonacci.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Wechselseitige Rekursion} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Mindestens zwei Funktionen sind im Rekursionsfall jeweils über die andere Funktion definiert + \end{itemize} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_wechselrecursion.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Iteration und Rekursion} + \textbf{Endrekursion} + \begin{itemize} + \item Spezialfall der linearen Rekursion + \item Beim Aufruf der nächsten Rekursion sind alle Berechnungen der aktuellen Funktions-Instanz abgeschlossen + \item Verbraucht in den meisten Fällen weniger Speicher + \end{itemize} +\end{frame} + +\begin{frame}{Numpy und Pandas} +\textbf{Was ist NumPy?} + \begin{itemize} + \item eine Bibliothek für effiziente numerische Berechnungen in Python. + \item Ermöglicht Arbeiten mit mehrdimensionalen Arrays und Matrizen. + \item Bietet viele mathematische Funktionen. + \end{itemize} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \textbf{Erstellen eines Arrays} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Ein NumPy-Array kann aus einer Liste erstellt werden + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpylistcreation.png} + \end{tcolorbox} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Mehrdimensionale Arrays sind ebenfalls möglich + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpylistmultidimgeneration.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \textbf{Grundlegende Operationen} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Elementweise Addition + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpyelementwiseoperation.png} + \end{tcolorbox} + \end{column} + \pause + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Skalarmultiplikation + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpyscalarproduct.png} + \end{tcolorbox} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \textbf{Weitere nützliche Funktionen I} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpyusefulfunctions.png} +\end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \textbf{Weitere nützliche Funktionen II} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_numpyothercommands.png} + \end{tcolorbox} + \end{column} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item \textbf{ndim}: Anzahl an Dimensionen + \item \textbf{shape}: Dimensionen z.b. (n,m) + \item \textbf{size}: Anzahl an Elementen + \item \textbf{dtype}: Typ der Elemente im Array + \end{itemize} + \end{column} + \end{columns} + +\end{frame} + +\begin{frame}{Numpy und Pandas} + Das war jetzt nur eine Übersicht der wichtigesten Befehle, zur Klausurvorbereitung sind folgende wichtig: + \begin{itemize} + \item EPR Blatt 09 + \item \href{https://realpython.com/numpy-tutorial/}{https://realpython.com/numpy-tutorial/} (sehr ausführlich aber bis zur hälfte etwa Klausurrelevant + \end{itemize} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \textbf{Was ist Pandas?} + \begin{itemize} + \item Pandas ist eine Bibliothek für Datenanalyse und -manipulation. + \item Bietet Datenstrukturen wie DataFrame und Series. + \item Erleichtert das Laden, Bearbeiten und Analysieren von Daten. + \pause + \item Daten werden in sogenannten \textit{Dataframes} gespeichert, in denen sie mit der library leicht analysiert und manipuliert werden können. + \end{itemize} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Ein DataFrame kann aus einem Dictionary erstellt werden: + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=0.7\textwidth]{images/code_pandascreatedataframes.png} + \end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item ...oder durch das laden einer CSV-Datei: + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=\textwidth]{images/code_pandasdatasetcsv.png} + \end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Zugriff auf Spalten: + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=0.7\textwidth]{images/code_pandasfiltercolumn.png} + \end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Filtern von Daten: + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=0.65\textwidth]{images/code_pandasfilterdata.png} + \end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Gruppieren von Daten: + \end{itemize} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=0.6\textwidth]{images/code_pandasgroupadata.png} + \end{tcolorbox} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Matplotlib ist eine Bibliothek zur Datenvisualisierung. + \item Beispiel: Erstellen eines einfachen Diagramms: + \end{itemize} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=0.9\textwidth]{images/code_matplotlibexample.png} + \end{tcolorbox} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure} + \centering + \includegraphics[width=1\linewidth]{images/graph_matplotlibexample.png} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Numpy und Pandas} + \begin{itemize} + \item Erstellung eines Balkendiagramms aus einem DataFrame: + \end{itemize} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{tcolorbox}[colframe=oxfordblue, colback=blue!10, coltitle=white, title=Python] + \includegraphics[width=1\textwidth]{images/code_matplotlibpandas.png} + \end{tcolorbox} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure} + \centering + \includegraphics[width=1\linewidth]{images/graph_matplotlibpandas.png} + \end{figure} + \end{column} + \end{columns} + +\end{frame} + +\end{document} diff --git a/epr/epr_rep_folien_jonas/mathematics-logo.png b/epr/epr_rep_folien_jonas/mathematics-logo.png new file mode 100644 index 0000000000000000000000000000000000000000..79b5f7f7cb1c531ba09f678bc6607260c347bb19 GIT binary patch literal 11481 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