From 686d2d45541925a498de8baf57a386ee90848769 Mon Sep 17 00:00:00 2001
From: rnhmjoj <rnhmjoj@inventati.org>
Date: Sun, 31 May 2020 11:25:04 +0200
Subject: [PATCH] notes: add useful operators

---
 notes/sections/0.md | 30 +++++++++++++++++++++---------
 1 file changed, 21 insertions(+), 9 deletions(-)

diff --git a/notes/sections/0.md b/notes/sections/0.md
index 40efbf9..034c0e4 100644
--- a/notes/sections/0.md
+++ b/notes/sections/0.md
@@ -29,24 +29,36 @@ header-includes: |
   \usepackage{float}
   \floatplacement{figure}{H}
 
-  % customer macros
-  %% "with" in formulas
-  \DeclareMathOperator*{\with}{%
+
+  %% customer macros
+  % "with" in formulas
+  \DeclareMathOperator{\with}{%
     \hspace{30pt} \text{with} \hspace{30pt}  
   }
-  %% "thus" in formulas
-  \DeclareMathOperator*{\thus}{%
+
+  % "thus" in formulas
+  \DeclareMathOperator{\thus}{%
     \hspace{30pt} \Longrightarrow \hspace{30pt}  
   }
-  %% "et" in formulas
-  \DeclareMathOperator*{\et}{%
+
+  % "et" in formulas
+  \DeclareMathOperator{\et}{%
   \hspace{30pt} \wedge \hspace{30pt}
   }
-  %% "if" in formulas
-  \DeclareMathOperator*{\incase}{%
+
+  % "if" in formulas
+  \DeclareMathOperator{\incase}{%
   \hspace{20pt} \text{if} \hspace{20pt}
   }
 
+  % expectation and variance operators
+  \DeclareMathOperator{\Exp}{\mathbb{E}}
+  \DeclareMathOperator{\Var}{Var}
+
+  % average value with angle brakets
+  \newcommand{\avg}[1]{\langle#1\rangle}
+
+  % book cover
   \makeatletter         
   \renewcommand\maketitle{
     \begin{titlepage}