\emph{Functional Dependencies (FDs)} 
      \item are a \emph{generalization of keys}
      \item central part of \emph{relational database design theory}
  \item This theory defines when a relation is in \emph{normal form}.\\
    \remark{(with respect to a given set of functional dependencies)}
  \item It is usually a sign of \emph{bad database design} 
    if a schema contains relations that \emph{violate the normal form}.\\
    %\remark{There are exceptions and trade-offs, however.}

  \item If a normal form is violated
      \item data is stored \emph{redundantly} and
      \item information about different concepts is \emph{intermixed}
          \multicolumn{4}{c}{COURSES} \\ \hline
          \hd{\underline{CRN}} & \hd{TITLE} & \hd{INAME} & \hd{PHONE} \\
          22268 & Databases I            & Grust & 7111 \\
          42232 & Functional Programming & Grust & 7111 \\
          31822 & Graph Theory           & Klotz & 2418 \\
    The phone number for each instructor is stored multiple times!