diff --git a/README.md b/README.md
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--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # Solutions for Modern Quantum Chemistry, Szabo & Ostlund
 
-Compiled with XeLaTeX. TeXLive 2020 is recommended.
+Compiled with XeLaTeX. TeXLive 2020 or 2021 is recommended.
 
 References
 * [gensoukyo.me/Modern-Quantum-Chemistry-习题解答](https://gensoukyo.me/Modern-Quantum-Chemistry-%E4%B9%A0%E9%A2%98%E8%A7%A3%E7%AD%94/)
diff --git a/notes/notes_S&O.pdf b/notes/notes_S&O.pdf
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Binary files a/notes/notes_S&O.pdf and b/notes/notes_S&O.pdf differ
diff --git a/notes/notes_S&O.tex b/notes/notes_S&O.tex
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 \newpage
 
 \setcounter{section}{-1}
-\section{}
+\section{Preface}
 spatial mol orb -- $ \psi $ -- $ i,j,k,... $\\
 spatial basis fxn -- $ \phi $ -- $ \mu,\nu,\lambda,... $\\
 spin orb -- $ \chi $\\
@@ -30,7 +30,7 @@ \section{}
 exact energy -- $ \mathscr{E} $\\
 approx energy -- $ E $
 
-\section{}
+\section{Mathematical Review}
 \subsection{}
 \subsection{}
 \subsection{}
@@ -68,7 +68,7 @@ \subsubsection{Change of Basis}
 \end{equation}
 
 
-\section{}
+\section{Many-electron Wave Functions and Operators}
 \subsection{The Electronic Problem}
 \subsubsection{Atomic Units}
 \subsubsection{The B-O Approximation}