DISCRETE MATHEMATICS

The course is one of the basic activities of the Bachelor's Degree in Informatics and its aim is to present the basic ideas and computational techniques of discrete mathematics, as opposed to the mathematics of continuum. The student will gently be introduced to the abstract concepts of the discrete mathematics.
The abstract ideas of discrete mathematics are introduced through a wide variety of applications with particular emphasis on formal, algebraic and computational aspects.

Knowledge and understanding:
- knowledge and understanding of the fundamental concepts of discrete mathematics;
- understanding the feasibility and complexity of solving problems of discrete mathematics;
- knowledge of methodologies to compute with integers, integers modulo, and the cardinality of finite sets.

Ability to apply knowledge and understanding:
- to solve concrete problems;
- to apply the induction principle;
- ability of computing in the finite arithmetics of integers, and the usual arithmetics.

Knowledge of the fundamental notions of discrete mathematics: set theory, arithmetics, induction, combinatory.

Any high school diploma to give access to the University.

Boolean algebra and logic.
Introduction to set theory: union, intersection and complementation of sets.
Functions and relations. Posets. Equivalence relations and partitions.
Natural numbers. Order on nat. Induction. Definition and proofs by induction.
Integers. The theory of congruences.
Greatest common divisor and least common multiple . Euclidean algorithm.
Prime factorization and fundamental theorem of arithmetic.
Combinatorics: the principle of addition and multiplication. Permutations and combinations.
Binomial coefficients: their properties.
Fibonacci sequence.
The principle of inclusion-exclusion.

Elementi di matematica discreta. Interi. Calcolo Combinatorio e Grafi.
Giuseppe Lancia
Independently Published, 2018

The exam consists of a written test.
The exercises aimed at verifying:
1) the capability to compute with integers and integers modulo;
2) the ability to compute the cardinality of finite sets;
3) the knowledge and the capability to apply the induction principle;
4) the ability to formalize in the mathematical and set-theoretical language.

During the written test is not allowed the use of books, notes, electronic media.

Lessons with the digital and traditional blackboard.
Written home work and exercises in the classroom will gently introduce the student to discrete mathematics:
sets and Boolean algebras, Arithmetic of integers and modular arithmetic. Combinatorics.

Italian

written