Learning outcomes

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 and the principal combinatorial schemata. Then, the main concepts of formal language theory are presented, by concluding with the study of main classes of automata and the notions of decidability, computability, and semidecidability.

Knowledge and comprehension ability. Students will acquire knowledge about the essentials of discrete mathematics;
formal notions and methods for studying problems by means of computers, and representations of biological information.

Skills to apply knowledge and comprehendion. Students will be ableto analyze biological data of different types (genome seqwuences, biological processes, networks of biological interactions) by means of theoretical informational conceots.

Program

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. Recurrent schemata. Outlines of first order logical languages (terms, formulas, interpretations). Elements of combinatorics: allocations and partitions, binomial and multinomial coefficients. Multisets, Partitions of sets and integers. Formal languages, grammars and automata. Patterns and regular expressions, Chomsky hierarchy, finite state automata. Computing automata and Turing macjine. Decidability, semidecidability ed undecidability.

Examination Methods

Written and oral examination.

The written exam requires that the student is able to use correctly the formalism taught in the course for expressing synthetically and correctly the solutions to the problems asked in the exam text.

The oral examination starts by checking the answers given by the student in the written exam, possibly by asking specific clarifications and motivations to specific passages and statements. During this verification the student is also asked to refer about specific points of the course, with the intention of checking the understanding of the main concepts that the course intends to teach.

Teaching Material
Manca, V. - Infobiotics. Springer, 2013 (Chapters 5, 6, 7).
Manca V. - Vademecum all'Esame di Metodi Informazionali (with a list of definitions and theorems plus 100 exercises with the corresponding solutions).