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These notes are companion notes for several courses, for example:
- Precalculus: sets, mappings, induction principle (without Peano's axioms), etc.
- Discrete Mathematics: mathematical logic, sets, binary relations, mappings, graphs.

At the beginning, e used the Archimedean Notes entitled ``Discrete
Mathematics'' with numerous modifications and additions. In particular, we addedmany diagrams and drawings; among them
- Venn diagrams for sets and operations on sets.
- Diagrams for binary relations, including the Hasse diagram of a poset.
- Arrow diagrams for mappings.

Moreover, many topics have been expanded (properties of oredrings,
Hasse diagrams, properties of mappings, etc.) and many topics have
been moved from their original place to another one (For example the
Inclusion-Exclusion principle has been postponed).
Last but not least: these lecture notes are not supposed to be used
linearly. We often use later notions at an earlier step. Cross
references are given in the text.
The variety of topics lead us to the following choice: the definition
of a notion can appear more than once in the text (for example, the
definition of an algebraic number appears in Chapter and in Chapter 7).
We wish to thank the authors of the Archimedean Note in reference for
their nice work.
Disclaimer: these notes are intended to be an auxiliary material for
my students, without any commercial purpose. Nobody is entitled to use
them for a commercial purpose (©).

** Next:** Elementary mathematical logic
** Up:** Discrete Mathematics
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2002-06-10