Discrete Mathematics

The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the $\mathit{\text{Rota}}\mathit{\text{way}}$. The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of \textit{combinatorial coefficients} are just by their $\mathit{\text{combinatorial}}\mathit{\text{meaning}}$. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods:

• The $\mathit{\text{bad}}\mathit{\text{element}}$ method (for $\mathit{\text{recursive}}$ formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of $\mathit{\text{conditional}}\mathit{\text{probability}}$.
• The $\mathit{\text{overcounting}}$ principle (for $\mathit{\text{close}}\mathit{\text{form}}$ formulae). Therefore, $\mathit{\text{no}}\mathit{\text{computation}}$ is required in $\mathit{\text{proofs}}$: $\mathit{\text{computation}}\mathit{\text{formulae}}\mathit{\text{are}}\mathit{\text{byproducts}}\mathit{\text{of}}\mathit{\text{combinatorial}}\mathit{\text{constructions}}$. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the $\mathit{\text{combinatorial}}\mathit{\text{point}}\mathit{\text{of}}\mathit{\text{view}}$: we invite the reader to draw the (obvious) $\mathit{\text{probabilistic}}\mathit{\text{interpretations}}$.