%=====================================================%
%                                                     %
%   Course Notes Template v1.3                        %
%   created 2014-02-09                                %
%                                                     %
%   Copyright (C) 2014 Zev Chonoles                   %
%   zevchonoles@gmail.com                             %
%   http://math.uchicago.edu/~chonoles/               %
%                                                     %
%   Please leave this information in the source       %
%   code as attribution if you choose to edit or      %
%   redistribute this file.                           %
%                                                     %
%   This work is licensed under the Creative          %
%   Commons BY-SA 3.0 Unported License. See           %
%   http://creativecommons.org/licenses/by-sa/3.0/.   %
%                                                     %
%=====================================================%




%======================%
%       METADATA       %
%======================%

%  Put information about the course in these macros. Some of these are passed to
%  the hyperref package later, so if you use math or non-ASCII characters, see
%  http://tex.stackexchange.com/q/53513 or http://tex.stackexchange.com/q/12981.
\newcommand{\coursetitle}{Course Notes Template v1.3}
\newcommand{\lecturer}{Prof. Fields Medal}
\newcommand{\notetaker}{Confused Student}
\newcommand{\notetakersemail}{confused@math.uawesome.edu}
\newcommand{\courseterm}{Winter \the\year}
\newcommand{\institution}{University of Awesome}




%====================%
%       BASICS       %
%====================%

%  Sets document class and font size.
\documentclass[11pt]{article}

%  Sets dimensions of the document.
\usepackage[margin=1in]{geometry}

%  Sets headers and footers.
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{14pt}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0.4pt}
\lfoot{\parbox[t]{1in}{\centering Last edited\\ \today}}
\cfoot{\parbox[t]{3in}{\centering \coursetitle}}
\rfoot{\parbox[t]{0.9in}{\centering Page \thepage\\ Lecture \arabic{lecture}}}

%  Sets date formatting to the ISO 8601 standard, YYYY-MM-DD.
\usepackage{datetime}
\renewcommand{\dateseparator}{-}
\yyyymmdddate




%=========================%
%       MATHEMATICS       %
%=========================%

%  Loads standard AMS packages. See http://tex.stackexchange.com/q/32100.
\usepackage{amsmath,amssymb,amsthm}

%  Defines \eucal for Euler script.
\usepackage{eucal}
\let\eucal\mathcal
\let\mathcal\CMcal

%  Defines \mathscr for Ralph Smith's Formal Script.
\usepackage{mathrsfs}

%  Provides a lot of all-around useful stuff.
\usepackage{mathtools}

%  Provides for easy creation of commutative diagrams.
\usepackage{tikz-cd}

%  Fixes spacing around \left and \right. See http://tex.stackexchange.com/a/2610.
\let\originalleft\left
\let\originalright\right
\renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft}
\renewcommand{\right}{\aftergroup\egroup\originalright}

%  Allows equation, align, gather, etc. environments to split across pages.
\allowdisplaybreaks




%========================%
%       TYPOGRAPHY       %
%========================%

%  Turns off indentation in favor of block paragraphs.
\usepackage{parskip}

%  Provides better kerning, hyphenation, etc. for words with accents.
%  See http://tex.stackexchange.com/q/664.
\usepackage[T1]{fontenc}

%  An updated version of Knuth's original Computer Modern font.
%  See http://tex.stackexchange.com/q/1390, http://tex.stackexchange.com/q/79319.
\usepackage{lmodern}

%  Improves the document's microtypography.
%  See http://tex.stackexchange.com/q/66052.
\usepackage{microtype}

%  Removes extra space after periods. See tex.stackexchange.com/q/4715.
\frenchspacing




%==================================%
%       THEOREM ENVIRONMENTS       %
%==================================%

%  Defines some theorem environments for commonly-encountered elements of a
%  lecture, in numbered and non-numbered versions. The numbering for each
%  environment is reset for each lecture.
\newcounter{lecture}
\newcounter{thmN}[lecture]              \newcounter{defN}[lecture]
\newcounter{lemmaN}[lecture]            \newcounter{remN}[lecture]
\newcounter{corN}[lecture]              \newcounter{exmN}[lecture]
\newcounter{propN}[lecture]             \newcounter{exrN}[lecture]
\newcounter{claimN}[lecture]

\newtheorem*{theorem}{Theorem}          \newtheorem{theorem-N}[thmN]{Theorem}
\newtheorem*{lemma}{Lemma}              \newtheorem{lemma-N}[lemmaN]{Lemma}
\newtheorem*{corollary}{Corollary}      \newtheorem{corollary-N}[corN]{Corollary}
\newtheorem*{proposition}{Proposition}  \newtheorem{proposition-N}[propN]{Proposition}
\newtheorem*{claim}{Claim}              \newtheorem{claim-N}[claimN]{Claim}

\theoremstyle{definition}
\newtheorem*{definition}{Definition}    \newtheorem{definition-N}[defN]{Definition}
\newtheorem*{remark}{Remark}            \newtheorem{remark-N}[remN]{Remark}
\newtheorem*{remarks}{Remarks}
\newtheorem*{example}{Example}          \newtheorem{example-N}[exmN]{Example}
\newtheorem*{examples}{Examples}
\newtheorem*{exercise}{Exercise}        \newtheorem{exercise-N}[exrN]{Exercise}
\newtheorem*{exercises}{Exercises}

%  Fixes the spacing above theorem environments, which is messed up when
%  using the parskip package. See http://tex.stackexchange.com/q/22119.
\makeatletter
\def\thm@space@setup{\thm@preskip=\parskip \thm@postskip=0pt}
\makeatother

%  Fixes spacing above proof environments. See http://tex.stackexchange.com/q/49801.
\makeatletter
\renewenvironment{proof}[1][\proofname]{\pushQED{\qed}\normalfont
\partopsep=\z@skip \topsep=\z@skip \trivlist \item[\hskip\labelsep\itshape #1\@addpunct{.}]
\ignorespaces}{\popQED\endtrivlist\@endpefalse}
\makeatother




%======================%
%       GRAPHICS       %
%======================%

%  Provides better support for graphics.
\usepackage{graphicx}

%  Defines some custom colors. See http://tex.stackexchange.com/q/51488.
\usepackage{xcolor}
\definecolor{myred}{rgb}{0.9,0.2,0.2}
\definecolor{mygreen}{rgb}{0.2,0.6,0.2}
\definecolor{myblue}{rgb}{0.2,0.2,1}




%===============================%
%       TABLE OF CONTENTS       %
%===============================%

%  Defines a command to be placed at the top each day's notes. It makes a heading
%  as well as a corresponding entry in the table of contents. You should give
%  each lecture a title and specify the date, and you can modify this command to
%  decide how (or whether) such information appears in the table of contents and
%  in the heading.
\newcommand{\startlecture}[2]{%
\newpage\stepcounter{lecture}           % New page, and increments the counter.
\phantomsection\addcontentsline{toc}{section}%
{Lecture \arabic{lecture}: #2 (#1)}     % Inserts a line in the table of contents.
\section*{Lecture \arabic{lecture}: #2} % Puts header at the start of the lecture.
}

%  Sets the space below the "Contents" heading.
\usepackage{tocloft}
\setlength\cftaftertoctitleskip{16pt}




%===========================%
%       MISCELLANEOUS       %
%===========================%

%  So that the preamble stays organized, I recommend keeping all of your personal
%  macros and commands here (examples below). If you are using any additional
%  packages, put them in the relevant section of the preamble if there is one,
%  otherwise keep it here. This is also smart because most packages should be
%  loaded before hyperref - see http://tex.stackexchange.com/q/1863.
\newcommand{\directsum}{\oplus}
\newcommand{\weaklyto}{\rightharpoonup}




%=====================================%
%       HYPERLINKS AND METADATA       %
%=====================================%

\newcommand{\email}[1]{\href{mailto:#1}{\texttt{#1}}}
\newcommand{\site}[1]{\href{#1}{\texttt{#1}}}

%  Lets you create hyperlinks, and specifies the metadata of the output pdf.
%  See http://tex.stackexchange.com/q/1863, http://tex.stackexchange.com/q/41461,
%  http://tex.stackexchange.com/q/12981, and http://tex.stackexchange.com/q/140892.
\usepackage[bookmarks = false]{hyperref}
\usepackage{hyperxmp}
\hypersetup{%
pdftitle      = {\coursetitle},
pdfauthor     = {\notetaker},
pdfproducer   = {LaTeX},
pdflang       = {en},
pdfcopyright  = {Copyright (C) \the\year\ \notetaker. This work is licensed under
                 a Creative Commons BY-SA 3.0 Unported License. All attribution
                 should be to \lecturer\ as the lecturer, and to \notetaker\ as
                 the person taking these notes.},
pdflicenseurl = {http://creativecommons.org/licenses/by-sa/3.0/},
pdfinfo       = {Copyright={(C) \the\year\ \notetaker. This work is licensed under
                 a Creative Commons BY-SA 3.0 Unported License. All attribution
                 should be to \lecturer\ as the lecturer, and to \notetaker\ as
                 the person taking these notes.}},
colorlinks    = true,
linkcolor     = myred,
citecolor     = mygreen,
urlcolor      = myblue,
linktoc       = all,
pdfstartview  = FitH
}




%===================================%
%       ATTACHING SOURCE CODE       %
%===================================%

%  Lets you attach files to the output pdf. See http://tex.stackexchange.com/q/13187.
\usepackage{attachfile2}
\attachfilesetup{color = myred}




%======================%
%       DOCUMENT       %
%======================%

\begin{document}




%------------------------%
%       Title Page       %
%------------------------%

\author{Lectures by \lecturer\\ Notes by \notetaker}
\title{\bf \coursetitle}
\date{\institution, \courseterm}

%  See http://tex.stackexchange.com/q/1736.
\maketitle
\thispagestyle{empty}

%  See http://tex.stackexchange.com/q/85558.
\setcounter{page}{-2}
\thispdfpagelabel{Title Page}




%---------------------------------------------------------------------------%
\newpage
\thispagestyle{empty}
\thispdfpagelabel{Front Matter}

%--------------------------%
%       Introduction       %
%--------------------------%

\section*{Introduction}


%  Put some information about the course here. For example,

These are notes from \lecturer's semester-long course giving an
elementary introduction to the theory of completely incomplete
$\ell$-adic ultrapluripsuedosymplectic $(\infty,1)$-categories.


%  It's good to be polite.

I am responsible for all faults in this document, mathematical or otherwise;
any merits of the material here should be credited to the lecturer, not to me.

Please email any corrections or suggestions to \email{\notetakersemail}.


%-----------------------%
%       Copyright       %
%-----------------------%

%  Specify a copyright and license for your notes, if you want.
%  You should first ask the lecturer whether they consent.
%
%  Note that this copyright and license is also in the preamble of this file,
%  to be included in the metadata of the output PDF. Thus, if you want to change
%  it, be sure to change it in both locations.

\section*{Copyright}

Copyright \textcopyright\ \the\year\ \notetaker.

This work is licensed under a Creative Commons BY-SA
3.0 Unported License. This means you are welcome to do essentially 
anything with this work, including editing, adapting, distributing, 
and making commercial use of it, as long as you

\begin{itemize}
\item include an attribution of \lecturer\ as the lecturer of the course
these notes are based on, and \notetaker\ as the person taking the notes,
\item do so in a way that does not suggest either of us endorses you or
your use of this work, and
\item if you alter, transform, or build upon this work, you must apply to
your work the same, or similar, license to this one.
\end{itemize}

More details are available at
\site{http://creativecommons.org/licenses/by-sa/3.0/}.


%-------------------------%
%       Attribution       %
%-------------------------%

%  Please leave this section in the document as attribution. Of course, if there
%  are other attributions you need to make, you may add to this section as needed.

\section*{Attribution}

This document is based on Course Notes Template v1.3, which was created by Zev
Chonoles and is licensed under a Creative Commons BY-SA 3.0 Unported License.


%---------------------------------%
%       Link to Source Code       %
%---------------------------------%

\section*{Source Code}

The \LaTeX\ source code for this document is embedded within it. Depending on your PDF
viewer, you can click the link below to access it.\vspace{0.1in}

%  In order for this to work
%
%    YOU MUST TYPE OUT THE CURRENT FILE NAME!
%
%  See http://tex.stackexchange.com/q/125813, http://tex.stackexchange.com/a/23172.

\begin{center}
\textattachfile{course_notes_template_v1.3.tex}{\fbox{\texttt{view source code}}}
\end{center}




%---------------------------------------------------------------------------%
\newpage
\thispdfpagelabel{Contents}

%-------------------------------%
%       Table of Contents       %
%-------------------------------%

%  See http://tex.stackexchange.com/q/2995.
\tableofcontents
\thispagestyle{empty}



%---------------------------------------------------------------------------%
\newpage

%--------------------------%
%       Course Notes       %
%--------------------------%

%  Each lecture's notes should have at the top
%
%      \startlecture{date}{title}
%
%  You could take two different approaches for organizing the notes:
%
%      1: Take all notes within this file.
%      2: Make a new file for each lecture, and include them into this file.
%
%  In approach 1, just start writing below,
%
%      \startlecture{date1}{title1}
%
%      stuff
%
%      \startlecture{date2}{title2}
%
%      more stuff
%
%      ...
% 
%  In approach 2, it's best to use a naming scheme like
%
%      lecture1.tex, lecture2.tex, ...
%
%  keeping them in the same folder as this file, and each starting with its
%  own \startlecture. Then just write below
%
%      \include{lecture1}
%      \include{lecture2}
%      ...
%
%  The advantage of approach 2 is that, when you're only working on the
%  notes for one lecture, you can easily comment out the lines corresponding
%  to the other lectures, making the document compile much faster.
%


\startlecture{2014-02-03}{The Hodge Conjecture}

Today we will prove the Hodge Conjecture.


\startlecture{2014-02-05}{An Amazing Equation}

Today we will discuss the implications of the equation $1+1=2$.



\end{document}