preamble.tex

% Shared preamble — included by all course main.tex files

% --- Layout ---
\usepackage[margin=1in]{geometry}

% --- Math ---
\usepackage{amsmath, amssymb, amsthm}

% --- Graphs ---
\usepackage{pgfplots}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc}

% --- Boxes ---
\usepackage{tcolorbox}
\tcbuselibrary{theorems, breakable}

% --- Misc ---
\usepackage{enumitem}
\usepackage{hyperref}
\usepackage{pifont}

% --- Theorem-like environments ---

% Definition — green box, own counter
\newtcbtheorem[number within=section]{definition}{Definition}{%
  colback=red!3, colframe=red!40,
  fonttitle=\bfseries, breakable
}{def}

% --- Example box ---
\NewTColorBox{example}{ o }{%
  colback=gray!5,
  colframe=gray!60,
  fonttitle=\bfseries,
  title={Example\IfValueTF{#1}{: #1}{}},
  breakable
}

% Theorem — blue box, uses shared counter
\newtcbtheorem[number within=section]{theorem}{Theorem}{%
  colback=blue!3, colframe=blue!40,
  fonttitle=\bfseries, breakable
}{thm}

\theoremstyle{plain}

\theoremstyle{remark}
\newtheorem*{remark}{Remark}
\newtheorem*{note}{Note}

% --- Common shortcuts ---
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\ve}[1]{\langle #1 \rangle}   % vector brackets
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\dd}[1]{\,\mathrm{d}#1}       % differential
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}  % partial derivative
\newcommand{\xmark}{\ding{55}}