Update for 2024

main.tex

@@ -13,9 +13,7 @@
 \author{Tung Anh Vu}
 % TODO: Make a combined logo for KAM as on the department website.
 \titlegraphic{%
-  \includegraphics[width=0.4\textwidth]{logos/kam_logo.eps}
-  \hspace{2em}
-  \includegraphics[width=0.5\textwidth]{logos/logotyp_fakulty2.eps}
+  \includegraphics[width=\textwidth]{logos/logo_csi.png}
 }
 
 \begin{document}
@@ -24,7 +22,7 @@
   \vfill
   \titlepage
   \vfill
-  \usebeamerfont{institute} Contact: \url{tung@kam.mff.cuni.cz}
+  \usebeamerfont{institute} Contact: \url{tung@iuuk.mff.cuni.cz}
 \end{frame}
 
 \begin{frame}{Systems of equations}
@@ -247,7 +245,7 @@
     Suppose we have~\(\vec{u}, \vec{v}, \vec{w} \in \R^n\).
     The \emph{dot product\footnote{You will see during your studies that there are multiple types of dot products. This one is usually known as the \emph{standard dot product}.} of~\(\vec{u}\) and~\(\vec{v}\)} is defined as
     \[
-       \vec{u} \cdot \vec{v}  = (u_1 v_1, u_2 v_2, \ldots, u_n v_n).
+      \vec{u} \cdot \vec{v} = u_1v_1 + u_2v_2 + \cdots + u_nv_n = \sum_{i = 1}^n u_iv_i.
     \]
   \end{definition}
 
@@ -257,7 +255,7 @@
     \begin{itemize}
       \item \emph{Commutativity}: \(\vec{u} \cdot \vec{v} = \vec{v} \cdot \vec{u}\).
         \pause
-      \item \(\vec{0} \cdot \vec{v} = \vec{0}\).
+      \item \(\vec{0} \cdot \vec{v} = 0\).
         \pause
       \item \emph{Distributivity}: \(\vec{u} \cdot (\vec{v} + \vec{w}) = \vec{u} \cdot \vec{v} + \vec{u} \cdot \vec{w}\).
         \pause