diff --git a/.gitignore b/.gitignore index 9babe23b4919362401c08da7958e578972b2348a..eafcdef43c176fb872e4f5bb48f49c617d23670b 100755 --- a/.gitignore +++ b/.gitignore @@ -32,3 +32,4 @@ mat *.html */ltxpng/* vc.tex +*.thm diff --git a/Makefile b/Makefile new file mode 100644 index 0000000000000000000000000000000000000000..8bfc412f3f345467cb622abefcda4eaf6cea322f --- /dev/null +++ b/Makefile @@ -0,0 +1,39 @@ +# LaTeX Makefile + +latexmain = skript-rtg-lectures-ws1617 +content = *.tex + +bibtexfiles = literature.bib +vcfile = vc.tex + +makeindexstyle = index.ist + +all: $(latexmain).pdf + +$(latexmain).pdf: $(latexmain).tex $(content) $(vcfile) $(bibtexfiles) + pdflatex $(latexmain).tex + bibtex $(latexmain).aux + makeindex -s $(makeindexstyle) "$(latexmain)" + pdflatex $(latexmain).tex + pdflatex $(latexmain).tex + + +$(vcfile): .git/logs/HEAD + echo "%%% This file is generated by Makefile." > vc.tex + echo "%%% Do not edit this file!\n%%%" >> vc.tex + git log -1 --format="format:\ + \\gdef\\GITAbrHash{%h}\ + \\gdef\\GITAuthorDate{%ad}\ + \\gdef\\GITAuthorName{%an}" >> vc.tex + echo -n "\gdef\GITVersionTag{" >> vc.tex + git describe --abbrev=0 --tags | xargs echo -n >> vc.tex + echo -n "}" >> vc.tex + + +clean: + rm -f *.aux *.idx *.ilg *.ind *.log *.toc *.log *.bbl *.blg *_region_.tex + rm -f *.glo *.gls *.glg *.slg *.syg *.syi bachelor-thesis.ist + rm -f *~ *.out + rm -r -f *.prv + rm -f .tex *.thm + diff --git a/contents.tex b/contents.tex new file mode 100644 index 0000000000000000000000000000000000000000..c7a5c4c9f9d50fa7504d17ab591dfb97a26e4632 --- /dev/null +++ b/contents.tex @@ -0,0 +1,13 @@ + +% !TEX root = skript-group-actions-in-riemannian-geometry.tex + +\tableofcontents + +\section*{} + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "skript-rtg-lectures-ws1617" +%%% End: diff --git a/frontmatter.tex b/frontmatter.tex new file mode 100644 index 0000000000000000000000000000000000000000..d73c2bd56c7665111b5e20f86bda91f27264442e --- /dev/null +++ b/frontmatter.tex @@ -0,0 +1,24 @@ +\begin{titlepage} + \begin{center}\Large + + % \includegraphics[scale=0.45]{kit-logo.jpg} + % \hfill + % \includegraphics[scale=0.15]{mathe-logo.jpg} + + \vspace*{3cm} + {\Large \textsc{Notes}}\\[0.8cm] + {\huge \textsc{RTG Lectures}}\\[0.8cm] + \textsc{Prof. Dr. R. Sauer and Dr. A. Sanders} + + \vfill + + \textsc{Winter 2016/17}\\[0.5cm] + \textsc{Torsion Invariants | Harmonic maps}\\[0.7cm] + \vspace{2cm} + \end{center} +\end{titlepage} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "skript-rtg-lectures-ws1617" +%%% End: diff --git a/index.ist b/index.ist new file mode 100755 index 0000000000000000000000000000000000000000..dd6f9e68cc9598b8374fa5197c7441929b6ab84d --- /dev/null +++ b/index.ist @@ -0,0 +1,2 @@ +preamble "\\thispagestyle{fancy}\n\n\\begin{theindex}\\thispagestyle{fancy}\n" +postamble "\n\n\\end{theindex}\n" diff --git a/lecture-notes.sty b/lecture-notes.sty new file mode 100644 index 0000000000000000000000000000000000000000..3bf82618bc718afe5ba60c35120fef49a055b44b --- /dev/null +++ b/lecture-notes.sty @@ -0,0 +1,277 @@ +%% +%% Lecture Notes +%% +%% Collection of macros for lecture notes +%% + +\ProvidesPackage{lecture-notes} + +%% +%% Inclusions +%% + +\RequirePackage{babel} + +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage[amsmath,amsthm,thmmarks]{ntheorem} + +\RequirePackage{enumitem} +\RequirePackage{xifthen} + +\RequirePackage{index} + +\RequirePackage{xspace} + +\RequirePackage{fancyhdr} + +%% +%% Standard Settings and declarations +%% + +\setlength{\parindent}{0cm} + +\makeindex + +%% Fancyhdr settings + +\fancyhead{} +\renewcommand{\headrulewidth}{0cm} +\usepackage{hyperref} + +%% Common mathematical operators and sets +\newcommand{\blank}{{-}} % blank argument + +\DeclareMathOperator{\grad}{grad} % Gradient +\DeclareMathOperator{\sgn}{sgn} % Signum +\DeclareMathOperator{\res}{res} % Residuum +\DeclareMathOperator{\ind}{ind} % Umlaufzahl +\DeclareMathOperator{\n}{n} % Umlaufzahl +\DeclareMathOperator{\diag}{diag} % diagonal matrix +\DeclareMathOperator{\codim}{codim} % codimension + +\DeclareMathOperator{\Charakt}{char} +\DeclareMathOperator{\Charakteristik}{char} +\DeclareMathOperator{\Characteristic}{char} +\DeclareMathOperator{\aff}{aff} % affine Hülle + +% Lie Theory +\DeclareMathOperator{\Ad}{Ad} % Ad +\DeclareMathOperator{\ad}{ad} % ad +\DeclareMathOperator{\Der}{Der} % Derivationen + +% abstract simplicial complexes +\DeclareMathOperator{\st}{st} % star +\DeclareMathOperator{\cl}{cl} % closure +\DeclareMathOperator{\lk}{lk} % link + +\DeclareMathOperator{\rg}{rank} +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\tr}{tr} +\DeclareMathOperator{\spur}{tr} +\DeclareMathOperator{\Abb}{Map} +\DeclareMathOperator{\Map}{Map} +\DeclareMathOperator{\Kern}{Ker} % refering to the set +\DeclareMathOperator{\kernel}{ker} % refering to the map +\DeclareMathOperator{\Bild}{Im} +\DeclareMathOperator{\Rang}{Rank} +\DeclareMathOperator{\Ker}{Ker} + +\DeclareMathOperator{\Hom}{Hom} % homomorphisms +\DeclareMathOperator{\Diff}{Diff} % diffeomorphisms +\DeclareMathOperator{\Aut}{Aut} % automorphisms +\DeclareMathOperator{\Sym}{Sym} % symmetric group +\DeclareMathOperator{\End}{End} % endomorphisms +\DeclareMathOperator{\Isom}{Isom} % isometries + +\DeclareMathOperator{\Ext}{Ext} % Ext term +\DeclareMathOperator{\Tor}{Tor} % Tor term +\DeclareMathOperator{\Gl}{GL} % general linear group +\DeclareMathOperator{\GL}{GL} +\DeclareMathOperator{\GeneralLinear}{GL} +\DeclareMathOperator{\SL}{SL} % specific linear group +\DeclareMathOperator{\SpecialLinear}{SL} +\DeclareMathOperator{\Orthogonal}{O} +\DeclareMathOperator{\SO}{SO} +\DeclareMathOperator{\SpecialOrthogonal}{SO} +\DeclareMathOperator{\Unitary}{U} +\DeclareMathOperator{\SU}{SU} +\DeclareMathOperator{\SpecialUnitary}{SU} +\DeclareMathOperator{\GTwo}{G_2} +\DeclareMathOperator{\Spin}{Spin} + +% Curvature +\DeclareMathOperator{\ric}{ric} % Ricci Tensor +\DeclareMathOperator{\Ric}{Ric} % Ricci Tensor field +\DeclareMathOperator{\scal}{scal} % scalar curvature + +\renewcommand{\Re}{\ensuremath{\operatorname{Re}}} +\renewcommand{\Im}{\ensuremath{\operatorname{Im}}} + +\DeclareMathOperator{\diam}{diam} % diameter +\DeclareMathOperator{\dist}{dist} % distance +\DeclareMathOperator{\Fix}{Fix} % fixpoint set + +\DeclareMathOperator{\supp}{supp} % support +\DeclareMathOperator{\Graph}{Graph} + +\DeclareMathOperator{\R}{\mathbb{R}} +\DeclareMathOperator{\N}{\mathbb{N}} +\DeclareMathOperator{\Q}{\mathbb{Q}} +\DeclareMathOperator{\Z}{\mathbb{Z}} +\DeclareMathOperator{\C}{\mathbb{C}} +\DeclareMathOperator{\K}{\mathbb{K}} +\DeclareMathOperator{\F}{\mathbb{F}} +\DeclareMathOperator{\A}{\mathbb{A}} +% Redeclare \P (Prim or Propability) and put the old, reversed "breakline P" in \BreakLineP +\let\BreakLineP\P +\renewcommand{\P}{\ensuremath{\mathbb{P}}} + +\newcommand{\RP}{\mathbb{R}\mathrm{P}} +\newcommand{\CP}{\mathbb{C}\mathrm{P}} +\newcommand{\HP}{\mathbb{H}\mathrm{P}} + +% differentiation, +\DeclareMathOperator{\T}{T} % tangent bundle +\DeclareMathOperator{\D}{D} % Jacobi matrix or derivative +\DeclareMathOperator{\Jacobian}{Jac} % Jacobi matrix +\makeatletter +\providecommand*{\dop}% +{\@ifnextchar^{\@diffOperator}{\@diffOperator^{}}} +\def\@diffOperator^#1{% + \mathop{\mathrm{\mathstrut d}}% + \nolimits^{#1}\gobblespace} + +\providecommand*{\Dop}% +{\@ifnextchar^{\@DiffOperator}{\@DiffOperator^{}}} +\def\@DiffOperator^#1{% + \mathop{\mathrm{\mathstrut D}}% + \nolimits^{#1}\gobblespace} + +\def\gobblespace{% + \futurelet\diffarg\opspace} +\def\opspace{% + \let\DiffSpace\!% + \ifx\diffarg(% + \let\DiffSpace\relax + \else + \ifx\diffarg[% + \let\DiffSpace\relax + \else + \ifx\diffarg\{% + \let\DiffSpace\relax + \fi\fi\fi\DiffSpace} +\makeatother + +\newcommand{\modulo}[1]{\ensuremath{/_{\displaystyle #1}}} + + +%% Theorems +\newcounter{thmglobal} +% \swapnumbers +\theoremstyle{plain} + +\newtheorem{thm}[thmglobal]{Theorem} +\newtheorem{lemma}[thmglobal]{Lemma} +\newtheorem{cor}[thmglobal]{Corollary} +\newtheorem{prop}[thmglobal]{Proposition} + +\theoremstyle{definition} + +\newtheorem{dfn}[thmglobal]{Definition} +\newtheorem{expl}[thmglobal]{Example} + +\theoremstyle{remark} + +\newtheorem{rem}[thmglobal]{Remark} +\newtheorem{exc}[thmglobal]{Exercise} + +% Add unnumbered Theorems, use amsthm style in both style modes +\theoremstyle{plain} +\theorembodyfont{\itshape} + +\renewtheorem*{thm*}{Theorem} +\renewtheorem*{lemma*}{Lemma} +\renewtheorem*{cor*}{Corollary} +\renewtheorem*{prop*}{Proposition} + +\theoremstyle{definition} +\theorembodyfont{\normalfont} + +\renewtheorem*{dfn*}{Definition} +\renewtheorem*{expl*}{Example} + +\theoremstyle{remark} +\renewtheorem*{rem*}{Remark} +\renewtheorem*{exc*}{Exercise} + +\RequirePackage{thmtools} +\RequirePackage{nameref,cleveref} + +\crefname{thm}{theorem}{theorems} +\Crefname{thm}{Theorem}{Theorems} +\crefname{lemma}{lemma}{lemmata} +\Crefname{lemma}{Lemma}{Lemmata} +\crefname{prop}{proposition}{propositions} +\Crefname{prop}{Proposition}{Propositions} +\crefname{cor}{corollary}{corollaries} +\Crefname{cor}{Corollary}{Corollaries} +\crefname{rem}{remark}{remarks} +\Crefname{rem}{Remark}{Remarks} +\crefname{dfn}{definition}{definitions} +\Crefname{dfn}{Definition}{Definitions} +\crefname{expl}{example}{examples} +\Crefname{expl}{Example}{Examples} + +\numberwithin{equation}{section} +\numberwithin{thmglobal}{section} + + +%% +%% Functionality +%% + +% List of stuff one is currently working on +% This is considered additional content +\newcommand{\WorkingOn}[1]{% + \ifthenelse{\boolean{showAdditionalContent}}{% + \bufferfootnotes + \begin{framed} + #1 + \end{framed} + \stopbufferingfootnotes + }{} +} + +% Editor note +\newcommand{\EditorNote}[1]{% + \ifthenelse{\boolean{showAdditionalContent}}{% + \textcolor{darkred}{#1} + }{} +} + +% Mark additional stuff gray +\newcommand{\AdditionalInfo}[1]{% + \ifthenelse{\boolean{showAdditionalContent}}{% + \marginnote{\textcolor{gray}{#1}} + }{} +} + + +% Add a command put sth. in quotes +\newcommand{\CmQ}[1]{\iflanguage{ngerman}{\CmGermanQuotes{#1}}{\CmEnglishQuotes{#1}}} + +\newcommand{\CmGermanQuotes}[1]{\glqq #1\grqq} +\newcommand{\CmEnglishQuotes}[1]{``#1''} + + +% indexing support + +% Print and index given text +% usage: \CmIndex{[(optionally put another text for the index in here)]{(text to print and add to index)} +\newcommand{\CmIndex}[2][]{\ifthenelse{\isempty{#1}}{\index{#2}}{\index{#1}}#2} + +% Highlight(bold) and index the given text +% usage: \CmMark[(optionally put another text for the index in here)]{(text to highlight and add to index)} +\newcommand{\CmMark}[2][]{\textit{\CmIndex[#1]{#2}}} + diff --git a/literature.bib b/literature.bib new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/skript-rtg-lectures-ws1617.tex b/skript-rtg-lectures-ws1617.tex index 652c3a5b2854f56496479325bbe37f4537ceb1c7..c87ad97aa57993ca1dad491ddb6d13c02c727232 100755 --- a/skript-rtg-lectures-ws1617.tex +++ b/skript-rtg-lectures-ws1617.tex @@ -1,15 +1,60 @@ - -\documentclass[a4paper, 11pt]{report} +\documentclass[a4paper, 12pt, twoside]{article} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc} -\usepackage{lmodern} +\usepackage{stix} + +\usepackage{fixltx2e} +\usepackage{ellipsis} +\usepackage{ragged2e} +\usepackage[tracking=true]{microtype} + +\usepackage[english]{babel} +\usepackage[left=3cm,right=3cm,top=3cm,bottom=3cm]{geometry} + +\usepackage{marginnote} +\usepackage{graphicx} +\usepackage{xcolor} + +\usepackage{tikz} + +\usepackage{setspace} +\renewcommand{\baselinestretch}{1.1} + + +\usepackage{lecture-notes} + + +% boolean value to indicate if WorkingOn, EditorNote and AdditionalInfo produce visible output +\newboolean{showAdditionalContent} +% \setboolean{showAdditionalContent}{false} +\setboolean{showAdditionalContent}{true} + + +% Setup headlines +\usepackage[explicit]{titlesec} +\titleformat{\section}{\normalfont\Large\filcenter}{Lecture \thesection.\hspace*{0.2cm}}{0cm}{#1} +\titleformat{name=\section,numberless}{\normalfont\Large\filcenter}{}{0cm}{#1} +\titlespacing{\section}{0cm}{0.6cm}{0.4cm} + +% Setup table of contents +\usepackage[titles]{tocloft} +\cftsetindents{section}{0cm}{2cm} +\renewcommand\cftsecpresnum{Lecture } +\crefname{section}{Lecture}{Lectures} -\usepackage[ngerman]{babel} -\usepackage[left=2.5cm,right=2cm,top=2cm,bottom=3cm]{geometry} \begin{document} +% cover page +\input{frontmatter} + +\input{contents} + +\nocite{*} +\bibliographystyle{amsalpha} +\bibliography{literature} +\printindex \end{document}