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dka316 committed Jun 1, 2019
1 parent 16e0ba4 commit eb76324
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6 changes: 1 addition & 5 deletions front.tex
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@@ -1,21 +1,17 @@
% Title page

\maketitle

\cover

\vfill

\begin{abstract}
\noindent\syllabus
\end{abstract}

\pagebreak

% Contents page

\tableofcontents

\pagebreak

% Document page
\setcounter{section}{-1}
207 changes: 107 additions & 100 deletions header.tex
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Expand Up @@ -10,6 +10,7 @@
\usepackage{fancyhdr}
\usepackage[margin=1in]{geometry}
\usepackage{graphicx}
\usepackage[hidelinks]{hyperref}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\usepackage{mathtools}
Expand All @@ -19,18 +20,15 @@

% Formatting

\setlength{\parindent}{0cm}
\addto\captionsUKenglish{\renewcommand{\abstractname}{Syllabus}}
\delimitershortfall5pt
\ifx\thm\undefined\newtheorem{n}{}\else\newtheorem{n}{}[\thm]\fi
\let\g\gg
\let\l\ll
\setlength{\parindent}{0cm}

% Environments

\ifx \thm\undefined
\newtheorem{n}{}
\else
\newtheorem{n}{}[\thm]
\fi

\theoremstyle{plain}
\newtheorem{algorithm}[n]{Algorithm}
\newtheorem{conjecture}[n]{Conjecture}
Expand All @@ -57,86 +55,21 @@

% Commands

\renewcommand{\eval}[1]{\left. #1 \right|} % Evaluation
\newcommand{\br}{\del} % Brackets

\newcommand{\abr}[1]{\left\langle #1 \right\rangle} % Angle brackets
\newcommand{\fbr}[1]{\left\lfloor #1 \right\rfloor} % Floor brackets

\newcommand{\F}{\mathbb{F}} % Finite fields
\newcommand{\N}{\mathbb{N}} % Natural numbers
\newcommand{\Z}{\mathbb{Z}} % Integral numbers
\newcommand{\Q}{\mathbb{Q}} % Rational numbers
\newcommand{\R}{\mathbb{R}} % Real numbers
\newcommand{\C}{\mathbb{C}} % Complex numbers
\renewcommand{\H}{\mathbb{H}} % Quaternion numbers
\newcommand{\A}{\mathbb{A}} % Affine space
\renewcommand{\P}{\mathbb{P}} % Projective space

\renewcommand{\aa}{\mathfrak{a}} % Ideal 1
\newcommand{\bb}{\mathfrak{b}} % Ideal 2
\newcommand{\mm}{\mathfrak{m}} % Maximal ideal 1
\newcommand{\nn}{\mathfrak{n}} % Maximal ideal 2
\newcommand{\pp}{\mathfrak{p}} % Prime ideal 1
\newcommand{\qq}{\mathfrak{q}} % Prime ideal 2

\renewcommand{\AA}{\mathcal{A}} % Calligraphic A
\newcommand{\BB}{\mathcal{B}} % Calligraphic B
\newcommand{\CC}{\mathcal{C}} % Calligraphic C
\newcommand{\DD}{\mathcal{D}} % Calligraphic D
\newcommand{\EE}{\mathcal{E}} % Calligraphic E
\newcommand{\FF}{\mathcal{F}} % Calligraphic F
\newcommand{\GG}{\mathcal{G}} % Calligraphic G
\newcommand{\HH}{\mathcal{H}} % Calligraphic H
\newcommand{\II}{\mathcal{I}} % Calligraphic I
\newcommand{\JJ}{\mathcal{J}} % Calligraphic J
\newcommand{\KK}{\mathcal{K}} % Calligraphic K
\newcommand{\LL}{\mathcal{L}} % Calligraphic L
\newcommand{\MM}{\mathcal{M}} % Calligraphic M
\newcommand{\NN}{\mathcal{N}} % Calligraphic N
\newcommand{\OO}{\mathcal{O}} % Calligraphic O
\newcommand{\PP}{\mathcal{P}} % Calligraphic P
\newcommand{\QQ}{\mathcal{Q}} % Calligraphic Q
\newcommand{\RR}{\mathcal{R}} % Calligraphic R
\renewcommand{\SS}{\mathcal{S}} % Calligraphic S
\newcommand{\TT}{\mathcal{T}} % Calligraphic T
\newcommand{\UU}{\mathcal{U}} % Calligraphic U
\newcommand{\VV}{\mathcal{V}} % Calligraphic V
\newcommand{\WW}{\mathcal{W}} % Calligraphic W
\newcommand{\XX}{\mathcal{X}} % Calligraphic X
\newcommand{\YY}{\mathcal{Y}} % Calligraphic Y
\newcommand{\ZZ}{\mathcal{Z}} % Calligraphic Z

\newcommand{\notb}[1]{\br{\neg #1}} % Negation
\newcommand{\orb}[2]{\br{#1 \lor #2}} % Disjunction
\newcommand{\andb}[2]{\br{#1 \land #2}} % Conjunction
\newcommand{\impb}[2]{\br{#1 \rightarrow #2}} % Implication
\newcommand{\iffb}[2]{\br{#1 \leftrightarrow #2}} % Biconditional
\newcommand{\fab}[1]{\br{\forall #1}} % Universal quantifier
\newcommand{\teb}[1]{\br{\exists #1}} % Existential quantifier
\newcommand{\eqb}[2]{\br{#1 = #2}} % Equal to
\newcommand{\ltb}[2]{\br{#1 < #2}} % Less than
\newcommand{\leb}[2]{\br{#1 \le #2}} % Less than or equal to
\newcommand{\neb}[2]{\br{#1 \ne #2}} % Not equal to
\newcommand{\inb}[2]{\br{#1 \in #2}} % An element of
\newcommand{\nib}[2]{\br{#1 \notin #2}} % Not an element of
\newcommand{\subb}[2]{\br{#1 \subseteq #2}} % Subset of

\newcommand{\jacobi}[2]{\br{\tfrac{#1}{#2}}} % Jacobi symbol
\newcommand{\Unit}[1]{\br{\dfrac{\Z}{#1\Z}}^\times} % Unit group vertical
\newcommand{\unit}[1]{\br{\Z / #1\Z}^\times} % Unit group horizontal

% Macros

\newcommand{\lecture}[3]{
\newcommand{\lecture}[3]{ % Lecture
\marginpar{
Lecture #1 \\
#2
#2 \\
#3
}
}

\newcommand{\function}[5][]{
\renewcommand{\eval}[1]{\left. #1 \right|} % Evaluation
\newcommand{\br}{\del} % Brackets
\newcommand{\abr}[1]{\left\langle #1 \right\rangle} % Angle brackets
\newcommand{\fbr}[1]{\left\lfloor #1 \right\rfloor} % Floor brackets
\newcommand{\lbr}[1]{\left\lfloor #1 \right\rfloor} % Ceiling brackets

\newcommand{\function}[5][]{ % Function
\ifx &#1&
\begin{array}{rcl}
#2 & \longrightarrow & #3 \\
Expand All @@ -147,7 +80,17 @@
\fi
}

\newcommand{\correspondence}[2]{
\newcommand{\F}{\mathbb{F}} % Finite fields
\newcommand{\N}{\mathbb{N}} % Natural numbers
\newcommand{\Z}{\mathbb{Z}} % Integral numbers
\newcommand{\Q}{\mathbb{Q}} % Rational numbers
\newcommand{\R}{\mathbb{R}} % Real numbers
\newcommand{\C}{\mathbb{C}} % Complex numbers
\renewcommand{\H}{\mathbb{H}} % Quaternion numbers
\newcommand{\A}{\mathbb{A}} % Affine spaces
\renewcommand{\P}{\mathbb{P}} % Projective spaces

\newcommand{\correspondence}[2]{ % Correspondence
\cbr{
\begin{array}{c}
#1
Expand All @@ -163,56 +106,120 @@
}
}

\newcommand{\intd}[4]{
\int_{#1}^{#2} \, #3 \, \dif #4
}

\newcommand{\iintd}[4]{
\iint_{#1} \, #2 \, \dif #3 \, \dif #4
}
\newcommand{\intd}[4]{\int_{#1}^{#2} \, #3 \, \dif #4} % Single integral
\newcommand{\iintd}[4]{\iint_{#1} \, #2 \, \dif #3 \, \dif #4} % Double integral
\newcommand{\iiintd}[5]{\iint_{#1} \, #2 \, \dif #3 \, \dif #4 \, \dif #5} % Triple integral

\newcommand{\onebytwo}[2]{
\newcommand{\onebytwo}[2]{ % One by two matrix
\begin{pmatrix}
#1 & #2
\end{pmatrix}
}

\newcommand{\onebythree}[3]{
\newcommand{\onebythree}[3]{ % One by three matrix
\begin{pmatrix}
#1 & #2 & #3
\end{pmatrix}
}

\newcommand{\twobyone}[2]{
\newcommand{\twobyone}[2]{ % Two by one matrix
\begin{pmatrix}
#1 \\
#2
\end{pmatrix}
}

\newcommand{\twobytwo}[4]{
\newcommand{\twobytwo}[4]{ % Two by two matrix
\begin{pmatrix}
#1 & #2 \\
#3 & #4
\end{pmatrix}
}

\newcommand{\threebyone}[3]{
\newcommand{\threebyone}[3]{ % Three by one matrix
\begin{pmatrix}
#1 \\
#2 \\
#3
\end{pmatrix}
}

\newcommand{\threebythree}[9]{
\newcommand{\threebythree}[9]{ % Three by three matrix
\begin{pmatrix}
#1 & #2 & #3 \\
#4 & #5 & #6 \\
#7 & #8 & #9
\end{pmatrix}
}

\renewcommand{\aa}{\mathfrak{a}} % Fraktur a
\newcommand{\bb}{\mathfrak{b}} % Fraktur b
\newcommand{\cc}{\mathfrak{c}} % Fraktur c
\newcommand{\dd}{\mathfrak{d}} % Fraktur d
\newcommand{\ee}{\mathfrak{e}} % Fraktur e
\newcommand{\ff}{\mathfrak{f}} % Fraktur f
\renewcommand{\gg}{\mathfrak{g}} % Fraktur g
\newcommand{\hh}{\mathfrak{h}} % Fraktur h
\newcommand{\ii}{\mathfrak{i}} % Fraktur i
\newcommand{\jj}{\mathfrak{j}} % Fraktur j
\newcommand{\kk}{\mathfrak{k}} % Fraktur k
\renewcommand{\ll}{\mathfrak{l}} % Fraktur l
\newcommand{\mm}{\mathfrak{m}} % Fraktur m
\newcommand{\nn}{\mathfrak{n}} % Fraktur n
\newcommand{\oo}{\mathfrak{o}} % Fraktur o
\newcommand{\pp}{\mathfrak{p}} % Fraktur p
\newcommand{\qq}{\mathfrak{q}} % Fraktur q
\newcommand{\rr}{\mathfrak{r}} % Fraktur r
\renewcommand{\ss}{\mathfrak{s}} % Fraktur s
\renewcommand{\tt}{\mathfrak{t}} % Fraktur t
\newcommand{\uu}{\mathfrak{u}} % Fraktur u
\newcommand{\vv}{\mathfrak{v}} % Fraktur v
\newcommand{\ww}{\mathfrak{w}} % Fraktur w
\newcommand{\xx}{\mathfrak{x}} % Fraktur x
\newcommand{\yy}{\mathfrak{y}} % Fraktur y
\newcommand{\zz}{\mathfrak{z}} % Fraktur z

\renewcommand{\AA}{\mathcal{A}} % Calligraphic A
\newcommand{\BB}{\mathcal{B}} % Calligraphic B
\newcommand{\CC}{\mathcal{C}} % Calligraphic C
\newcommand{\DD}{\mathcal{D}} % Calligraphic D
\newcommand{\EE}{\mathcal{E}} % Calligraphic E
\newcommand{\FF}{\mathcal{F}} % Calligraphic F
\newcommand{\GG}{\mathcal{G}} % Calligraphic G
\newcommand{\HH}{\mathcal{H}} % Calligraphic H
\newcommand{\II}{\mathcal{I}} % Calligraphic I
\newcommand{\JJ}{\mathcal{J}} % Calligraphic J
\newcommand{\KK}{\mathcal{K}} % Calligraphic K
\newcommand{\LL}{\mathcal{L}} % Calligraphic L
\newcommand{\MM}{\mathcal{M}} % Calligraphic M
\newcommand{\NN}{\mathcal{N}} % Calligraphic N
\newcommand{\OO}{\mathcal{O}} % Calligraphic O
\newcommand{\PP}{\mathcal{P}} % Calligraphic P
\newcommand{\QQ}{\mathcal{Q}} % Calligraphic Q
\newcommand{\RR}{\mathcal{R}} % Calligraphic R
\renewcommand{\SS}{\mathcal{S}} % Calligraphic S
\newcommand{\TT}{\mathcal{T}} % Calligraphic T
\newcommand{\UU}{\mathcal{U}} % Calligraphic U
\newcommand{\VV}{\mathcal{V}} % Calligraphic V
\newcommand{\WW}{\mathcal{W}} % Calligraphic W
\newcommand{\XX}{\mathcal{X}} % Calligraphic X
\newcommand{\YY}{\mathcal{Y}} % Calligraphic Y
\newcommand{\ZZ}{\mathcal{Z}} % Calligraphic Z

\newcommand{\notb}[1]{\br{\neg #1}} % Negation
\newcommand{\orb}[2]{\br{#1 \lor #2}} % Disjunction
\newcommand{\andb}[2]{\br{#1 \land #2}} % Conjunction
\newcommand{\impb}[2]{\br{#1 \rightarrow #2}} % Implication
\newcommand{\iffb}[2]{\br{#1 \leftrightarrow #2}} % Biconditional
\newcommand{\fab}[1]{\br{\forall #1}} % Universal quantifier
\newcommand{\teb}[1]{\br{\exists #1}} % Existential quantifier
\newcommand{\eqb}[2]{\br{#1 = #2}} % Equal to
\newcommand{\ltb}[2]{\br{#1 < #2}} % Less than
\newcommand{\leb}[2]{\br{#1 \le #2}} % Less than or equal to
\newcommand{\neb}[2]{\br{#1 \ne #2}} % Not equal to
\newcommand{\inb}[2]{\br{#1 \in #2}} % An element of
\newcommand{\nib}[2]{\br{#1 \notin #2}} % Not an element of
\newcommand{\subb}[2]{\br{#1 \subseteq #2}} % Subset of

\newcommand{\jacobi}[2]{\br{\tfrac{#1}{#2}}} % Jacobi symbol
\newcommand{\Unit}[1]{\br{\dfrac{\Z}{#1\Z}}^\times} % Unit group vertical
\newcommand{\unit}[1]{\br{\Z / #1\Z}^\times} % Unit group horizontal

% Tikz

\tikzset{
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