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\footnotesize \sf
Computer Science and Engineering
\\
Ferguson Hall -- 0115
\\
472-2402
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\LARGE \bf
Course Specification\vspace*{3mm}
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{\Large \bf \begin{center} CSCE-235 \\
Introduction to Discrete Structures \\
\end{center} }

\paragraph{Catalogue Description:}~ \newline
235. Introduction to Discrete Structures (3 cr) Prereq: CSCE 155
and Math 106. A survey of elementary discrete mathematics for the
computer science student.  The topics include: set theory including relations
and functions; elementary graph theory including coloring, paths and cycles,
trees;  recursion, induction, recurrence relations, and generating functions;
complexity of algorithms and growth rates; propositional logic; methods of
proof; elementary combinatorics including permutations and combinations.


\paragraph{Textbook(s) and/or Other Required Materials:}~ \newline
Goodaire and Parmenter, {\em Discrete Mathematics with Graph Theory} or \\
Rosen, {\em Discrete Mathematics and its Applications}

\paragraph{Prerequisites by Topic:}~ 
\begin{enumerate}
\item {\bf Mastery} of college algebra.
\item {\bf Familiarity} with a higher level programming language including
  arrays and sorting; calculus.
\item {\bf Exposure} to recursion in programming languages.
\end{enumerate}

\paragraph{Course Objectives:}~ 
\begin{enumerate}
\item {\bf Familiarity} with induction and recursion; sets and relations; functions;
  propositional logic; methods of proof; integers; counting; permutations,
  combinations, derangements, and binomial theorem; graphs and digraphs including 
  isomorphism, paths and circuits, trees; linear recurrences and recursive techniques;
  algorithmic complexity, growth rates;
  generating functions, power series; partial orders.
\item {\bf Exposure} to Stirling numbers, algebraic systems with one
  binary operator.
\end{enumerate}

\vfill
{\small ~ \hfill  \today}
\newpage
\paragraph{Topics Covered:}~ 
\begin{enumerate}
\item Propositional logic. (1 week)
\item Methods of proof. (1 week)
\item Sets and relations: operations, equivalence relations, partial
  orders. (2 weeks)
\item Functions: introduction, inverses and composition. (1 week)
\item Integers: division, GCDs, primes, Euler's $\phi$ function,
  Fermat's little theorem. (1 1/2 weeks)
\item Induction and recursion: mathematical induction, recursively
  defined sequences, solving recurrence relations, generating functions,
  power series. (2 weeks)
\item Counting: inclusion-exclusion, pigeon-hole. (1 week)
\item Permutations and combinations: with derangements, binomial theorem.
  (2 weeks)
\item Complexity: growth rates. (1 week)
\item Graphs: definiton, properties, isomorphism. (1 week)
\item Paths and circuits: Eulerian, Hamiltonian. (1/2 week)
\item Trees: definition, properties. (1 week)
\end{enumerate}

\paragraph{Relationship of Course to Program Objectives:}~ \newline


\paragraph{Contribution of Course to Meeting the Professional Component:}~ \newline


\paragraph{Class/Laboratory Schedule:}~ \newline
Lecture: 45 hours \\
Recitation: 15 hours 

\paragraph{Prepared by:}~ \newline
Charles Riedesel, Senior Lecturer

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