Scientific Disciplinary Sector (SSD)
INF/01 - INFORMATICS
II sem. dal Mar 2, 2015 al Jun 12, 2015.
The course intends to introduce the fundamental discrete structure by emphasizing their use in the definition of mathematical models of biological relevance. In the first part, after an introduction to the basic discrete structures, the number systems are analyzed, with the number representation systems, and the principle of structural induction. Then, the main concepts of formal language theory are presented, by concluding with the study of the principal combinatorial schemata.
Discrete structures: sets, multisets, sequences, strings, operations, relations, functions, variables, parentheses and expressions. Numbers and induction: number systems, number representations, proofs by induction, definitions by induction of important number sequences. Structural induction over strings, trees e graphs. Outlines of first order logical languages (terms, formulas, interpretations). Formal languages, grammars and automata. Patterns and regular expressions, Chomsky hierarchy, finite state automata. Computing automata and Turing macjine. Decidability, semidecidability ed undecidability. Elements of combinatorics: allocations and partitions, binomial and multinomial coefficients. Enumeration of partitions and multisets. Numbers of Stirling, Bell, Catalan. Magnitude orders and asymptotic orders. Outlines of discrete probability.
Written and oral examination.