M.G. Piacentini Cattaneo:
Matematica Discreta e Applicazioni - Zanichelli
Learning Objectives
Acquiring the fundamentals in arithmetic, combinatorics, graph theory and logic. Capacity of build rigorous arguments and proofs.
Prerequisites
Basic arithmetic and logic skills
Teaching Methods
Lectures
Further information
Students should enroll to the moodle course:
https://e-l.unifi.it/
Type of Assessment
Written and oral exam.
Written exam: it tests the ability to use the acquired knowledge in order to solve problems and exercises.
Oral exam: it tests the knowledge of the arguments object of the course and the ability of the student of giving a formal and precise exposition.
Course program
Elements of set theory. Relations and maps. Induction. Recurrence. Integers; gcd, Euclidean algorithm, Bezout formula. Prime numbers. Diofantine equations. Combinatorics.
Modular arithmetics. Eulero-Fermat theorem.
Polynomials; irreducibility criteria.
Algebraic structures: monoids, groups, rings.
Partially ordered sets. Lattices. Boolean algebras. Graphs theory.
Elements of first order logic.