Lecture Notes

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\documentclass{article}


\title{HW7 for 214}
\author{John Doe}

\usepackage{mathrsfs, amssymb,amsmath,amsthm,amsfonts, mathtools, tikz-cd, tikz}

\def\R{\mathbb R}
\def\C{\mathbb C}
\def\acal{\mathcal A}
\def\gfrak{\mathfrak g}


\newtheorem{theo}{Theorem}[section]
\newtheorem{lemma}[theo]{Lemma}
\newtheorem{problem}[theo]{Problem}
\newtheorem{corollary}[theo]{Corollary}
\newtheorem{proposition}[theo]{Proposition}



\begin{document}

\maketitle

Let $\R$ be the field of real numbers. 

\begin{proposition}
For any right triangle, we have 
\[ a^2 + b^2 = c^2 \]
\end{proposition}
\begin{proof}
Let me ask Pythagoras.
\end{proof}


\begin{problem}
Let $G$ be a Lie group, show that $T_e G$ can be equipped with a Lie algebra structure. 
\end{problem}
\begin{proof}[Solution]
We did this in class. 
\end{proof}

$\gfrak$ is a common symbol for Lie algebra. 
\end{document}