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\handout{meyer objectives}{Course Objectives and Outcomes}{September 19, 2000}

\section*{Objectives}

On completion of 6.042, students will be able to explain and apply the
basic methods of discrete (noncontinuous) mathematics to Computer Science
problems.  They will be able to use these concepts in subsequent courses
in the design and analysis of algorithms, computability theory, software
engineering, and computer systems.

In particular, students will be able to
\begin{enumerate}
\item
\label{Basic Discrete Mathematics Concepts}
\textbf{reason mathematically about basic data types and structures}
used in computer algorithms and systems; distinguish rigorous definitions
and conclusions from merely plausible ones; synthesize elementary proofs,
especially proofs by induction.

\item
\label{Computational Processes} 
\textbf{model and analyze computational processes} (algorithms and systems) using
analytic and combinatorial methods.

\item \label{Discrete Probability} \textbf{apply principles of discrete
probability} to model and solve elementary problems of reliability and
estimation.

\item 
\label{teams} 
\textbf{work in small teams} to accomplish all the objectives above.
\end{enumerate}


\section*{Learning Outcomes}
Students will be able to:
\begin{enumerate}

\item \label{soundness} \textbf{evaluate elementary mathematical
arguments} and identify fallacious reasoning (not just fallacious
conclusions).

\item \label{proofs} \textbf{synthesize induction hypotheses and simple
proofs} in discrete mathematics using the terminology of elementary
mathematical logic.

\item \label{graphs} \textbf{apply graph theory models} of data structures
and state machines to solve elementary problems of scheduling and
connectivity.

\item \label{numbers} \textbf{prove basic properties of numbers};
calculate GCD's and evaluate arithmetic expressions in modular arithmetic.

\item \label{invariants} apply the method of invariants and well-founded
ordering to \textbf{prove correctness and termination of algorithms} and
state machines.

\item \label{closed forms} \textbf{derive closed-form and asymptotic
expressions} from series and recurrences for growth rates of processes.

\item \label{counting} \textbf{calculate numbers of possible outcomes} of
elementary combinatorial processes such as permutations and combinations.

\item \label{probability} \textbf{calculate probabilities} and discrete
distributions for simple combinatorial processes; calculate means and
variances.

\item \label{estimation} solve problems of estimation and error tolerance
by \textbf{applying theorems on deviation from the mean}.

\item \label{student teams} problem solve and \textbf{study in a small
team} with fellow students.

\end{enumerate}

\iffalse

\begin{center}
Objectives
\end{center}

\ref{defs and proofs} Proofs, \ref{optimization} Combinatorics,
\ref{data and algorithms} Data and algorithms, \ref{probability}
Probability, \ref{teams} Teams.


\begin{center}
Outcomes: reflected Objectives
\end{center}

\ref{soundness} Recognize proofs: \ref{defs and proofs}

\ref{proofs} Synthesize proofs: \ref{defs and proofs}

\ref{graph models}: \ref{defs and proofs}, \ref{optimization}, \ref{data and algorithms}

\ref{solve graphs}: \ref{optimization}, \ref{data and algorithms}

\ref{arithmetic}: \ref{defs and proofs}, \ref{data and algorithms}

\ref{closed forms}: \ref{data and algorithms}, \ref{optimization}

\ref{counting}: \ref{optimization}, \ref{probability}, \ref{data and algorithms}

\ref{invariants}: \ref{defs and proofs}, \ref{data and algorithms}

\ref{Big-O}: \ref{data and algorithms}, \ref{optimization}

\ref{calculate probability}: \ref{probability}

\ref{student teams}: \ref{teams}
\fi


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