From 414cf36bfb56a6e237e09968f01981abd8ecd40c Mon Sep 17 00:00:00 2001 From: Elias Fierke Date: Sun, 24 May 2026 10:41:30 +0200 Subject: [PATCH] initialized template --- Matheclub.sty | 383 +++++++++++++++++++++++++ bibliography.bib | 22 ++ content/Anhang.tex | 8 + content/Arbeitsmaterialien.tex | 17 ++ content/Einleitung.tex | 23 ++ content/Einordnung_Lehrplan.tex | 3 + content/Kernideen.tex | 7 + content/Mathematischer_Hintergrund.tex | 84 ++++++ content/Stichworte.tex | 8 + content/Weiterfuehrende_Ideen.tex | 1 + content/Zeitplan.tex | 3 + galton.tex | 67 +++++ images/KleinBottle.png | Bin 0 -> 185606 bytes images/mlogo.pdf | Bin 0 -> 12090 bytes images/ulogo.pdf | Bin 0 -> 6202 bytes 15 files changed, 626 insertions(+) create mode 100644 Matheclub.sty create mode 100644 bibliography.bib create mode 100644 content/Anhang.tex create mode 100644 content/Arbeitsmaterialien.tex create mode 100644 content/Einleitung.tex create mode 100644 content/Einordnung_Lehrplan.tex create mode 100644 content/Kernideen.tex create mode 100644 content/Mathematischer_Hintergrund.tex create mode 100644 content/Stichworte.tex create mode 100644 content/Weiterfuehrende_Ideen.tex create mode 100644 content/Zeitplan.tex create mode 100644 galton.tex create mode 100644 images/KleinBottle.png create mode 100644 images/mlogo.pdf create mode 100644 images/ulogo.pdf diff --git a/Matheclub.sty b/Matheclub.sty new file mode 100644 index 0000000..f987746 --- /dev/null +++ b/Matheclub.sty @@ -0,0 +1,383 @@ +%------- Matheclub.sty ------- +\ProvidesPackage{Matheclub} +\renewcommand{\familydefault}{\sfdefault} %FONT + +%------- Math Commands ------- +\RequirePackage{lipsum} +\RequirePackage{epsfig} +\RequirePackage{amsmath} +\RequirePackage{amsthm} +\RequirePackage{amssymb} +\RequirePackage{multicol} +\RequirePackage{graphicx,url} +\RequirePackage[absolute,overlay]{textpos} +\RequirePackage{tikz} +\RequirePackage{enumitem} +\RequirePackage{xparse} +\RequirePackage{wrapfig} + + + + +%------- Formatting Commands ------- +\RequirePackage{mleftright}\mleftright +\RequirePackage[strict, style=german]{csquotes} \MakeOuterQuote{"} + +\RequirePackage{parskip} % für Abstand zwischen Absätzen +\setlength{\parindent}{0cm} % no indent on new line +\setlength{\parskip}{1mm} +\addtolength{\footskip}{5mm} % move page number/footer down by 5mm +\allowdisplaybreaks % allow page breaks in equation environments +\RequirePackage{float} + +\RequirePackage[scaled=.95]{inconsolata} %monospace font and size +\renewcommand{\UrlFont}{\footnotesize\ttfamily} + +%------- Bibliography Commands ------- +\RequirePackage[ + backend=biber, + style=alphabetic, % gives [..] brackets and works well with shorthands +]{biblatex} +\DeclareFieldFormat{postnote}{#1} +\DeclareFieldFormat{multipostnote}{#1} +\renewcommand*{\nameyeardelim}{\addcomma\space} +\DeclareFieldFormat[article]{volume}{Vol.\space #1} +\DeclareFieldFormat[article]{number}{Nr.\space #1} + +\renewbibmacro*{volume+number+eid}{% + \printfield{volume}% + \setunit{\addspace}% + \printfield{number}% + \setunit{\addcomma\space}% + \printfield{eid}} + +\RequirePackage{xurl} % allow line breaks in URL strings at arbitrary locations + +%------- Reference Commands ------- +\RequirePackage{hyperref} +\hypersetup{ + colorlinks=true, + linkcolor=blue, + citecolor=blue, + urlcolor=cyan + } +% cleveref must be loaded after hyperref +\RequirePackage[ngerman]{cleveref} + +\crefname{equation}{Gleichung}{Gleichungen} +\crefname{figure}{Abbildung}{Abbildungen} +\crefname{table}{Tabelle}{Tabellen} +\crefname{section}{Abschnitt}{Abschnitte} + + +%------- Theorem Boxes ------- +\RequirePackage{tcolorbox} +\tcbuselibrary{theorems,breakable, skins} +\RequirePackage{xcolor} +\RequirePackage{titlesec} + + +\definecolor{Satz}{RGB}{66,133,244} +\definecolor{Definition}{RGB}{255,204,0} % lighter blue +\definecolor{Korollar}{RGB}{10, 100, 120} % light blue +\definecolor{Beispiel}{HTML}{339551} % yellow +\definecolor{Lemma}{RGB}{75, 50, 130} % light blue +\definecolor{Proposition}{HTML}{c7dbe2} % apricot +\definecolor{Background}{HTML}{fffbf0} + +\newcommand{\mc@theoremnote}[1]{\par\hfill{\footnotesize #1}} + + +\iffalse +Wir haben die Umgebungen Satz, Lemma, Proposition, Korollar, Definition, Beispiel und Bemerkung definiert. Sie können diese Umgebungen verwenden, um Sätze, Lemmata, Propositionen, Korollare, Definitionen, Beispiele und Bemerkungen zu erstellen. Die Umgebungen sind nummeriert und können mit \cref{satz:SatzLabel}, \cref{lem:LemmaLabel}, \cref{prop:PropositionLabel}, \cref{kor:KorollarLabel}, \cref{def:DefinitionLabel}, \cref{bsp:BeispielLabel} und \cref{bem:BemerkungLabel} referenziert werden. Die Umgebungen sind farblich hervorgehoben, um sie leicht von anderen Texten zu unterscheiden. + +Die Umgebungen können wie folgt verwendet werden: +\begin{satz}[Optionaler Satzname]{SatzLabel}{Optional: Quellenangabe} + Hier steht der Inhalt des Satzes. +\end{satz} + +Der optionale Satzname wird in eckigen Klammern angegeben, diese können einfach weggelassen werden, wenn kein Name angegeben werden soll. +In den geschweiften Klammern wird das Label angegeben, mit dem der Satz später referenziert werden kann. Das Label muss eindeutig sein, damit es nicht zu Verwechslungen kommt. +Die geschweiften Klammern müssen immer angegeben werden, auch wenn kein Label angegeben werden soll. In diesem Fall kann man einfach leere geschweifte Klammern angeben, also {}. + +Um ein Satz zu referenzieren verwenden Sie den Befehl \cref{satz:SatzLabel}. In dem geschriebenen Text erscheint dann automatisch Satz 1.1 oder so ähnlich. + +Die anderen Umgebungen funktionieren analog. +Die cref Bezeichnungen lauten: + \cref{satz:SatzLabel} für Sätze + \cref{lem:LemmaLabel} für Lemmata + \cref{prop:PropositionLabel} für Propositionen + \cref{kor:KorollarLabel} für Korollare + \cref{def:DefinitionLabel} für Definitionen + \cref{bsp:BeispielLabel} für Beispiele + \cref{bem:BemerkungLabel} für Bemerkungen + \cref{tab:TabelleLabel} für Tabellen + \cref{fig:AbbildungLabel} für Abbildungen + \cref{eq:GleichungLabel} für Gleichungen + +Wenn der Inhalt der Ungebungen aus einer Quelle stammt, kann diese mit der dritten geschweiften Klammer angegeben werden. In diesem Fall müssen die geschweiften Klammern in denen das Label angegeben wird geschrieben werden! Falls Sie dennoch kein Label vergeben wolen, lassen Sie den Inhalt der geschweiften Klammern einfach leer, also {}. Die Quellenangabe wird dann in kleiner Schrift am Ende der Umgebung angezeigt. +\fi + + +\newtcbtheorem[auto counter, number within=subsection, crefname={Satz}{Sätze}]{satzbox}{Satz}{ + breakable, + enhanced, + colback=Satz!5, + colframe=Satz, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Satz!40, + colframe=Satz, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{satz} +\NewDocumentEnvironment{satz}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{satzbox}{#1}{#2}} + {\begin{satzbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{satzbox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Lemma}{Lemmata}]{lemmabox}{Lemma}{ + breakable, + enhanced, + colback=Lemma!5, + colframe=Lemma, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Lemma!40, + colframe=Lemma, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{lem} +\NewDocumentEnvironment{lemma}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{lemmabox}{#1}{#2}} + {\begin{lemmabox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{lemmabox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Proposition}{Propositionen}]{propositionbox}{Proposition}{ + breakable, + enhanced, + colback=Proposition!5, + colframe=Proposition, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Proposition!40, + colframe=Proposition, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{prop} +\NewDocumentEnvironment{proposition}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{propositionbox}{#1}{#2}} + {\begin{propositionbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{propositionbox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Korollar}{Korollare}]{korollarbox}{Korollar}{ + breakable, + enhanced, + colback=Korollar!5, + colframe=Korollar, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Korollar!40, + colframe=Korollar, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{kor} +\NewDocumentEnvironment{korollar}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{korollarbox}{#1}{#2}} + {\begin{korollarbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{korollarbox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Definition}{Definitionen}]{definitionbox}{Definition}{ + breakable, + enhanced, + colback=Definition!5, + colframe=Definition, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Definition!40, + colframe=Definition, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{def} +\NewDocumentEnvironment{definition}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{definitionbox}{#1}{#2}} + {\begin{definitionbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{definitionbox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Beispiel}{Beispiele}]{beispielbox}{Beispiel}{ + breakable, + enhanced, + colback=Beispiel!5, + colframe=Beispiel, + arc=0.25mm, + boxrule=1pt, + top=4mm, + attach boxed title to top left={yshift=-3mm, xshift=2mm}, + boxed title style={ + enhanced, + colback=Beispiel!40, + colframe=Beispiel, + arc=1mm, + boxrule=0pt, + left=4pt, + right=4pt, + top=3pt, + bottom=3pt, + }, + coltitle=black, + fonttitle=\bfseries, +}{bsp} + +\NewDocumentEnvironment{beispiel}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{beispielbox}{#1}{#2}} + {\begin{beispielbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{beispielbox}% +}{} + +\newtcbtheorem[use counter from=satzbox, crefname={Bemerkung}{Bemerkungen}]{bemerkungbox}{Bemerkung}{ + breakable, + colback=white, + colframe=white, + boxrule=0pt, + left=0pt, + right=0pt, + top=0pt, + bottom=0pt, + before skip=\baselineskip, + after skip=\baselineskip, + coltitle=black, + fonttitle=\itshape, + fontupper=\normalfont, + separator sign={.} +}{bem} + +\NewDocumentEnvironment{bemerkung}{ O{} g g +b }{% + \IfNoValueTF{#3} + {\begin{bemerkungbox}{#1}{#2}} + {\begin{bemerkungbox}[after upper={\mc@theoremnote{#3}}]{#1}{#2}} + #4 + \end{bemerkungbox}% +}{} + + +%--------- Fix Cleverref for Appendix --------- +\makeatletter +\let\mc@oldappendix\appendix +\renewcommand{\appendix}{% + \mc@oldappendix + \crefname{appendix}{Anhang}{Anhänge}% + \Crefname{appendix}{Anhang}{Anhänge}% + \crefalias{section}{appendix}% +} +\makeatother + + + + +% ------- Inhaltsverzeichnis ------- +\RequirePackage{tocloft} + +\renewcommand{\cftsecfont}{\normalfont} +\renewcommand{\cftsecpagefont}{\normalfont} +\renewcommand{\cftsubsecfont}{\normalfont} +\renewcommand{\cftsubsecpagefont}{\normalfont} +\renewcommand{\cftsubsubsecfont}{\normalfont} +\renewcommand{\cftsubsubsecpagefont}{\normalfont} +\setlength{\cftbeforesecskip}{0pt} +\setlength{\cftbeforesubsecskip}{0pt} +\setlength{\cftbeforesubsubsecskip}{0pt} + +\makeatletter +\renewcommand{\tableofcontents}{% + \section*{\contentsname}% + \@starttoc{toc}% +} +\makeatother + + + + + +\RequirePackage{minted} % allows for writing nice code +\usemintedstyle{solarized-light} % a nice, colorful theme +\setminted{ + bgcolor=Background, + breaklines=true, + breakanywhere=true, + linenos=true, + %fontsize=\footnotesize +} +\renewcommand{\theFancyVerbLine}{% + \ttfamily\scriptsize\arabic{FancyVerbLine}} \ No newline at end of file diff --git a/bibliography.bib b/bibliography.bib new file mode 100644 index 0000000..58795fb --- /dev/null +++ b/bibliography.bib @@ -0,0 +1,22 @@ + +% Ein Eintrag in der Bibliographie könnte so aussehen: +@book{Beutelspacher2009, + shorthand = {Beu09}, + author = {Beutelspacher, Albrecht}, + editor = {}, + publisher = {Vieweg+Teubner Verlag}, + title = {"Das ist o.B.d.A. trivial!"}, + subtitle = {Tipps und Tricks zur Formulierung mathematischer Gedanken}, + year = {2009}, + edition = {9. Auflage}, + url = {https://doi.org/10.1007/978-3-8348-9599-8}, + note = {Zugriff am 31. Mai 2026} +} +% Beutelspacher2009 ist der Zitationsschlüssel, der in \cite{Beutelspacher2009} verwendet wird. Er sollte eindeutig sein und kann nach Belieben gewählt werden, z.B. durch Kombination von Autorennamen und Jahr. +% Shorthand gibt vor, wie der Eintrag in der Bibliographie angezeigt wird. +% Bei einem Autor sollten die ersten drei Buchstaben des Nachnamens und die letzten zwei Ziffern des Jahres verwendet werden, z.B. Beu09 für Beutelspacher 2009. +% Bei mehreren Autoren sollten die Initialien der Nachnamen der ersten drei Autoren und die letzten zwei Ziffern des Jahres verwendet werden, z.B. ABM20 für einen Eintrag von Autoren A, B und M aus dem Jahr 2020. +% Die anderen Einträge (author, editor, publisher, title, year, edition, url) sollten entsprechend den Informationen des zitierten Werks ausgefüllt werden. +% Es ist hilfreich, die URL anzugeben, wenn das Werk online verfügbar ist, damit Leser leicht darauf zugreifen können. +% Wenn die URL angegeben wird, sollte auch das Zugriffsdatum hinzugefügt werden, um anzugeben, wann die Quelle zuletzt überprüft wurde. + diff --git a/content/Anhang.tex b/content/Anhang.tex new file mode 100644 index 0000000..ec6d44c --- /dev/null +++ b/content/Anhang.tex @@ -0,0 +1,8 @@ +\section{Anhang 1} % Der Anhangstitel sollte natürlich passend zum Inhalt gewählt werden. Hier könnte z.B. "Arbeitsmaterialien" oder "Weiterführende Ideen" stehen. + +Hier können Sie weitere Materialien, die für die Bearbeitung des Themas relevant sind, bereitstellen. Das können zum Beispiel Arbeitsblätter, Übungsaufgaben, Lösungen, weiterführende Literatur oder auch Links zu Online-Ressourcen sein. + + +\section{Anhang 2} + +Wenn Sie verschiedene Materialien bereitstellen möchten, können Sie auch mehrere Anhänge erstellen. Achten Sie darauf, dass die Materialien gut strukturiert und leicht zugänglich sind, damit sie später gut nutzbar sind. \ No newline at end of file diff --git a/content/Arbeitsmaterialien.tex b/content/Arbeitsmaterialien.tex new file mode 100644 index 0000000..92276c7 --- /dev/null +++ b/content/Arbeitsmaterialien.tex @@ -0,0 +1,17 @@ +Stellen Sie Ihre Arbeitsmaterialien hier dar. + +Dies ist der zweitwichtigste Teil des Dokuments und soll (inhaltlich) auch den zweitgrößten Teil des Dokuments ausmachen. Da Arbeitsmatierialien inhaltlich sehr unterschiedlich sind, ist es schwierig, hier genaue Vorgaben zu machen. Eine Bastelanleitung mit Bastelbögen hätte ja z.B. eine ganz andere Struktur als eine Sammlung von Aufgaben und kann schnell ein paar Seiten umfassen... + + Falls Sie Arbeitsmaterialien in separaten Dokumenten haben, erstellen Sie hier zumindest eine kurze Beschreibung der entsprechenden Materialien. + + +Ein paar Anregungen für die Arbeitsmaterialien (kommt natürlich auf das Thema an): +\begin{itemize} + \item Aufgaben + \item Musterlösungen bzw. Lösungsskizzen + \item Knobeleien + \item Basteleien +\end{itemize} + + +Bitte bedenken Sie, zumindest Lösungsskizzen zu den Aufgaben zu geben! Besser noch vollständige Musterlösungen. Als Lehrkraft ist es nicht immer einfach, die Lösungen schnell zu finden und das Dokument soll ja den Lehrkräften die Arbeit erleichtern. \ No newline at end of file diff --git a/content/Einleitung.tex b/content/Einleitung.tex new file mode 100644 index 0000000..aa755a2 --- /dev/null +++ b/content/Einleitung.tex @@ -0,0 +1,23 @@ +\textbf{Wichtig:} Dieses Dokument hier soll nicht mehr als 30 Seiten umfassen (mehr bitte nur nach Absprache). +\\[1em] +% großer Abstand +Ziel des Seminars ist die Ausarbeitung eines \glqq rundum-sorglos-Pakets\grqq \ für eine Einheit in einem Matheclub, einer Mathe-AG oder einer ähnlichen Veranstaltung an einem Gymnasium. Unter einer Einheit ist nicht zwingend eine Doppelstunde zu verstehen, aber eine Doppelstunde soll mindestens mit Inhalt gefüllt werden. + + +Besonders wichtig ist es die folgenden Punkte zu beachten: + +\begin{enumerate} + \item Es handelt sich um ein Zusatzangebot (Freizeit!) für die Schülerinnen und Schüler. Der Spaß an der Mathematik darf also auf keinen Fall zu kurz kommen. + \item Mathclubs sind in der Regel nach Jahrgängen aufgeteilt. Bei uns sollen als Zielgruppe die Klassenstufen 9-12 angenommen werden. Wählen Sie sinnvoll eine Klassenstufe aus, für die sich ihr Thema eignet. Welche Voraussetzungen bringen die Schülerinnen und Schüler mit? + \item Gehen Sie davon aus, dass Sie es mit motivierten Schülerinnen und Schülern zu tun haben. Die Kinder erwarten klare Argumente, Beweise, etc., die auch über den Lehrplan (deutlich) hinaus gehen. + \item Überlegen Sie, woran Sie Spaß hätten. Seien Sie kreativ! +\end{enumerate} + + +Wir wollen eine Datenbank für Mathe-Clubs aufbauen. Daher ist eine einheitliche Struktur aller Datensätze zwingend erforderlich. Es sind somit einige technische Punkte zu beachten: + +\begin{itemize} + \item Halten Sie sich bitte streng an die vorgegebene Latex-Vorlage (inklusive Ordner- und Dateistruktur). +\end{itemize} + +Die Einleitung soll einen kurzen Überblick über den Inhalt des Dokuments geben. Sie soll den Leser neugierig machen und ihn dazu bringen, weiterzulesen. Hier gehören gegebenenfalls (nicht zwingend notwendig!) auch eine geschichtliche Einordnung und Anekdoten hinein (als Unterkapitel). diff --git a/content/Einordnung_Lehrplan.tex b/content/Einordnung_Lehrplan.tex new file mode 100644 index 0000000..3d4ef20 --- /dev/null +++ b/content/Einordnung_Lehrplan.tex @@ -0,0 +1,3 @@ +Orden Sie bitte Ihr Material kurz und prägnant in den Lehrplan ein. Das ist wichtig, damit die Lehrkräfte, die Ihr Material verwenden, auch wissen, wo sie es im Lehrplan finden können. + +Wichtig: Nicht mehr als eine halbe Seite! Das ist nur eine kurze Einordnung, keine vollständige Darstellung des Lehrplans. \ No newline at end of file diff --git a/content/Kernideen.tex b/content/Kernideen.tex new file mode 100644 index 0000000..3ebc8bf --- /dev/null +++ b/content/Kernideen.tex @@ -0,0 +1,7 @@ +Ziel des Kapitels ist es, der Leserschaft auf einen Blick die zentralen Ideen zu präsentieren. + +Beschreiben Sie hier also knapp die mathematische Fragestellung. Es soll klar der mathematische Rahmen umrissen werden und die Fragestellung in den größeren Kontext eingeordnet werden. + +Falls es einen zentralen Satz gibt, der die Fragestellung beantwortet, dann kann dieser hier auch genannt werden (auch wenn er später nochmal auftaucht und bewiesen wird). + +Ansonsten soll die Fragestellung zwar klar umrissen werden, aber eher informell beschrieben werden. \ No newline at end of file diff --git a/content/Mathematischer_Hintergrund.tex b/content/Mathematischer_Hintergrund.tex new file mode 100644 index 0000000..cfaaf50 --- /dev/null +++ b/content/Mathematischer_Hintergrund.tex @@ -0,0 +1,84 @@ +%"ltex.language": "de-DE" +Dies ist der zentrale Teil des Dokuments und soll (inhaltlich) den größten Teil des Dokuments ausmachen. + +\subsection{Mathematischer Teil auf Hochsuchschulniveau} + +Es ist essenziell, dass der mathematische Teil auf Hochschulniveau den Standards für wissenschaftliches Arbeiten in der Fachmathematik entspricht. Dazu gehört die Verwendung von Definitionen, Sätzen, Beweisen und Beispielen. Diese Struktur hilft dabei, die Argumentation klar und nachvollziehbar zu gestalten. + +\begin{satz}[Satz Name]{satz1} + Hier steht ein Satz, der in einem Buch steht. Der Satz ist wichtig, weil er eine wichtige Eigenschaft beschreibt. +\end{satz} + +\begin{proof} + Hier steht der Beweis des Satzes. Der Beweis ist wichtig, weil er zeigt, dass der Satz wahr ist. Der Beweis kann aus mehreren Schritten bestehen, die logisch aufeinander aufbauen. +\end{proof} + +\begin{beispiel}{beispiel1} + Hier steht ein Beispiel, das den Satz veranschaulicht. Das Beispiel ist wichtig, weil es zeigt, wie der Satz in der Praxis angewendet werden kann. +\end{beispiel} + +Sätze, Lemmata, Korollare und Beispiele sowie Beweise können einfach mit den entsprechenden Befehlen erstellt werden. Hier haben wir z.B. \cref{satz:satz1} und \cref{bsp:beispiel1} erstellt. Der Befehl \verb|\begin{proof}| erzeugt den Beweis. Der Befehl \verb|\end{proof}| beendet den Beweis. Der Befehl \verb|\begin{beispiel}| erzeugt das Beispiel. Der Befehl \verb|\end{beispiel}| beendet das Beispiel. Für Sätze, Lemmata und Korollare gelten die analogen Befehle. + +Um auf die Beweise und Beispiele zu verweisen zu können, verwenden Sie den Befehl \verb|\label{bsp:beispiel1}|. Damit wird das Beispiel mit dem Label \verb|bsp:beispiel1| versehen. Um auf das Beispiel zu verweisen, verwenden Sie \verb|\cref{bsp:beispiel1}|. Damit wird auf das Beispiel verwiesen. Das funktioniert auch für Sätze, Lemmata und Korollare sowie nummerierte Gleichungen, Grafiken, Tabellen und auch für Kapitel. + +\subsection{Mathematischer Teil auf Mathe-Club-Niveau} + +Halten Sie sich auch beim mathematischen Teil auf Mathe-Club-Niveau so weit wie möglich an die Standards für wissenschaftliches Arbeiten. Verwenden Sie Definitionen, Sätze, Beweise und Beispiele. Die Struktur hilft auch SuS dabei, die Argumentation nachzuvollziehen. + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{images/KleinBottle.png} + \caption{So sieht eine Klein'sche Flasche aus.} + \label{fig:logo} +\end{figure} + +Und natürlich gilt immer (ob hier oder auf Hochschulniveau): Ein Bild sagt mehr als 1000 Worte. Verwenden Sie Bilder, Grafiken, Diagramme, ... um Ihre Argumentation zu unterstützen. Außerdem sieht die Klein'sche Flasche in Abbildung \ref{fig:logo} sehr schön aus. Sie ist ein Beispiel für eine Fläche, die nicht orientierbar ist. Das bedeutet, dass es keine konsistente Möglichkeit gibt, die Normalenvektoren an jedem Punkt der Fläche zu definieren. Dies ist ein wichtiges Konzept in der Differentialgeometrie. + +Und als kleines Beispiel für Formeln in \LaTeX~ schreiben wir mal die Cauchy-Schwarz-Ungleichung: +\begin{equation}\label{eq:cauchy-schwarz} +\left| \sum_{i=1}^n a_i b_i \right| +\leq +\left( \sum_{i=1}^n a_i^2 \right)^{1/2} +\left( \sum_{i=1}^n b_i^2 \right)^{1/2} +\end{equation} + +Die \cref{eq:cauchy-schwarz} wird z.\,B. in Beweisen zur Orthogonalität verwendet. + +Mit etwas Aufwand und Übung kann man mit tikz auch sehr schöne Grafiken erstellen. +% +\begin{figure}[H] + \centering + \begin{tikzpicture} + \draw[thick,->] (-1,0) -- (1,0) node[right] {$x$}; + \draw[thick,->] (0,-1) -- (0,1) node[above] {$y$}; + \draw[thick,blue] plot[domain=-1:1] (\x,\x*\x) node[right] {$f(x)=x^2$}; + \end{tikzpicture} + \caption{Eine einfache Grafik mit tikz.} + \label{fig:tikz} +\end{figure} +% +Auf die Grafik kann man dann natürlich auch verweisen. Zum Beispiel in \cref{fig:tikz} sehen Sie eine einfache Grafik, die mit tikz erstellt wurde. Tikz ist ein sehr mächtiges Werkzeug, um Grafiken in \LaTeX~ zu erstellen. Es gibt viele Möglichkeiten, Grafiken zu erstellen und zu gestalten. Außerdem bietet tikz einfache mathematische Rechenfähigkeiten. + + +Weiter stehen Ihnen die folgenden Umgebungen zur Verfügung: + +\begin{definition}[]{definition1} + Eine Definition ist eine präzise Beschreibung eines Begriffs oder Konzepts. Sie hilft dabei, Missverständnisse zu vermeiden und Klarheit zu schaffen. +\end{definition} + +\begin{korollar}[]{korollar1}{\cite[S. 12]{Beutelspacher2009}} + Korollar heißt Folgerung. Ein Korollar ist also ein Satz, der ganz einfach (manchmal sogar trivial) aus dem vorhergehenden Satz oder seinem Beweis folgt. Bei einem Korollar muss man immer angeben können, wovon diese Aussage ein Korollar sein soll. +\end{korollar} + +\begin{bemerkung}[]{bemerkung1}{} + Eine Bemerkung ist eine Anmerkung oder ein Kommentar zu einem Satz, einer Proposition oder einem Korollar. Sie kann zusätzliche Informationen oder Erklärungen enthalten. +\end{bemerkung} + +\begin{lemma}[]{lemma1}{\cite[S. 12]{Beutelspacher2009}} + Lemma stammt aus dem Griechischen und bedeutet "Stichwort" oder "Hauptgedanke". Bei einem Lemma handelt es sich also um einen besonders wichtigen Schlüsselgedanken, der in vielen verschiedenen Situationen nützlich ist. +\end{lemma} + +Auf all diese kann man wieder verweisen: \cref{def:definition1}, \cref{kor:korollar1}, \cref{bem:bemerkung1}, \cref{lem:lemma1}. + + + diff --git a/content/Stichworte.tex b/content/Stichworte.tex new file mode 100644 index 0000000..323b3d4 --- /dev/null +++ b/content/Stichworte.tex @@ -0,0 +1,8 @@ +Hier kommt eine Liste der relevanten \textbf{Stichworte} hin. Die Stichworte sollen mindestens die folgenden Inhalte abdecken: + +\begin{itemize} + \item Stichworte zur Fragestellung + \item Mathematische Themen- bzw. Fachgebiete + \item Ungefähr passende Klassenstufen + \item Welche fundamentalen Ideen werden behandelt? +\end{itemize} \ No newline at end of file diff --git a/content/Weiterfuehrende_Ideen.tex b/content/Weiterfuehrende_Ideen.tex new file mode 100644 index 0000000..fbacc58 --- /dev/null +++ b/content/Weiterfuehrende_Ideen.tex @@ -0,0 +1 @@ +Da Sie ja umfangreich recherchiert haben, werden Sie deutlich mehr Material haben, als Sie in diesem Dokument unterbringen können. Hier können Sie Ihre weiterführenden Ideen kurz darstellen. Vergessen Sie nicht, auch hier die Quellen anzugeben! \ No newline at end of file diff --git a/content/Zeitplan.tex b/content/Zeitplan.tex new file mode 100644 index 0000000..4e2b38f --- /dev/null +++ b/content/Zeitplan.tex @@ -0,0 +1,3 @@ +Hier ist kein minutengenauer Zeitplan nötig, aber eine grobe Übersicht über den Zeitplan ist sinnvoll. Insbesondere, wie viel Zeit Sie für die einzelnen Themen bzw. Arbeitsmaterialien veranschlagen. + +Das ganze muss nicht in eine Doppelstunde passen, aber es ist sinnvoll, wenn Sie die normalen Doppelstunden als grobe Richtlinie verwenden. Der Zeitplan kann z.B. gerne als eine Tabelle dargestellt werden. \ No newline at end of file diff --git a/galton.tex b/galton.tex new file mode 100644 index 0000000..c34faed --- /dev/null +++ b/galton.tex @@ -0,0 +1,67 @@ +\documentclass[11pt]{article} +\usepackage[a4paper]{geometry} +\geometry{top=3cm,bottom=3cm,left=3cm,right=3.5cm} +\usepackage[ngerman]{babel} + +\usepackage{Matheclub} + +\addbibresource{bibliography.bib} + + + + +\title{Beispiel Titel} + +\author{Fierke, E. \& Janik, T. \& Weidlich, L. + \\ Seminar Erweitertes Fachwissen - Mathe Club} + +\date{Sommersemester \the\year} + +\begin{document} +\begin{textblock*}{3cm}(1cm,1.5cm) + \includegraphics[width=3cm]{images/mlogo.pdf} + \end{textblock*} + + \begin{textblock*}{3cm}(\dimexpr\paperwidth-3.5cm\relax,1.2cm) + \includegraphics[width=2.5cm]{images/ulogo.pdf} + \end{textblock*} + + \maketitle + +\tableofcontents + +\section{Einleitung} +\input{content/Einleitung.tex} + +\section{Kernideen} +\input{content/Kernideen.tex} + +\section{Stichworte} +\input{content/Stichworte.tex} + +\section{Mathematischer Hintergrund} +\input{content/Mathematischer_Hintergrund.tex} + +\section{Arbeitsmaterialien} +\input{content/Arbeitsmaterialien.tex} + +\section{Zeitplan} +\input{content/Zeitplan.tex} + +\section{Weiterführende Ideen} +\input{content/Weiterfuehrende_Ideen.tex} + +\section{Einordnung in den Lehrplan} +\input{content/Einordnung_Lehrplan.tex} + + +\printbibliography + +\appendix +\input{content/Anhang.tex} + + + + + +\end{document} \ No newline at end of file diff --git a/images/KleinBottle.png b/images/KleinBottle.png new file mode 100644 index 0000000000000000000000000000000000000000..961c1ba971130dc2b4493ad08c52af2aa89dff52 GIT binary patch literal 185606 zcmd3NgLfqT^L4bbZQIVowr$&XHa0i5ZJQh0wv&xE*le7>q%K+aXEQRHTK|mT4;NFeD z0Y4L)N~y?$fcQ{?fCPqufV={C1)hU|xHE%*To{3X@MM61U^(SYFqd*v61LfaJ{Bj^4 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