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\begin{document}

\title{Algebraic Structures and Discrete Mathematics\\
Class notes for course MACS 358 \\
Colorado School of Mines}


\author{Nicolas M. Thiéry}


\email{nthiery@users.sf.net \url{mailto:nthiery@users.sf.net}}


\urladdr{\url{http://www.lapcs.univ-lyon1.fr/~nthiery/}}


\curraddr{LaPCS, Université Claude Bernard Lyon I, Bâtiment recherche {[}B{]}\\
50, avenue Tony-Garnier, Domaine de Gerland, \\
69366 Lyon Cedex 07, FRANCE}


\thanks{Those notes grew up from the class MACS 358 that I taught during
three semesters at the Colorado School of Mines, using the textbook
\emph{Mathematical Structures for Computer Sciences} (4th edition)
by Judith L. Gersting\cite{Gersting.MSCS}.\\
Copyright Nicolas M. Thiéry 1999-2000\\
They are released, with the approbation of the publisher of the textbook,
under the GNU Free Documentation License (see \url{http://www.gnu.org/copyleft/fdl.html}):
in short, copying, redistribution in any form, modification or reuse
is permitted, and even encouraged, as long as I get credit for the
original version, and don't get blamed for other's modifications.
Moreover, any suggestions for improvements are warmly welcomed.\\
I use LyX \url{http://www.lyx.org} to typeset them, as well as to
display them in class on a LCD-projector plugged in my laptop. The
dvi, PDF, ps, HTML and pure text versions are then created using \LaTeX,
Hevea \url{http://para.inria.fr/~maranget/hevea/}, Htmlpp \url{http://htmlpp.sourceforge.net},
and some Makefile magic. I highly recommend the PDF of ps versions,
since the HTML and pure text versions are far from perfect due to
the limitations of those formats.}

\maketitle
\tableofcontents{}

\input{Introduction.tex}


\part{Formal Logic}

\graphicspath{{1_FormalLogic/}}

\input{1_FormalLogic/PropositionalLogic.tex}

\input{1_FormalLogic/PredicateLogic.tex}


\part{Proofs}

\graphicspath{{2_Proofs/}}

\input{2_Proofs/ProofTechniques.tex}

\input{2_Proofs/Induction.tex}

\input{2_Proofs/ProofOfCorrectness.tex}

\input{2_Proofs/AnalysisOfAlgorithms.tex}


\part{Sets and Combinatorics}

\graphicspath{{3_SetsAndCombinatorics/}}

\input{3_SetsAndCombinatorics/Sets.tex}

\input{3_SetsAndCombinatorics/Combinatorics.tex}


\part{Relations Functions and Matrices}

\graphicspath{{4_RelationsFunctionsAndMatrices/}}

\input{4_RelationsFunctionsAndMatrices/Relations.tex}

\input{4_RelationsFunctionsAndMatrices/Functions.tex}


\part{Modeling, Arithmetic, Computations and Languages}

\graphicspath{{8_ModelingArithmeticComputationsAndLanguages/}}

\input{8_ModelingArithmeticComputationsAndLanguages/Groups.tex}

\bibliographystyle{plain}
\bibliography{combinatoire}

\end{document}
