Course Details for A.Y. 2014/2015
Name:
Matematica Discreta I / Discrete Mathematics I
Basic information
Credits:
: Bachelor Degree in Computer Science 6 CFU (a)
Degree(s):
Bachelor Degree in Computer Science 1^{st} anno curriculum General Compulsory
Language:
Italian
Course Objectives
The goal of this course is to provide the motivations, definitions and techniques in support of the usefulness of algrbra and linear algebra in the effective and efficient modeling of data and knowledge.
On successful completion of this module, the student should understand the fundamental concepts of algebra and linear algebra.
Course Content
 Sets: functions, equivalence relations, products, elementary combinatorics.
 Permutations.
 Groups: subgroups, quotients, isomporphism theorems, factor groups, permutation groups, cyclic groups.
 Arithmetic: divisibility theory in the ring of integers and of polinomials over a field.
 Congruences. Chinese remainder theorem.
 Rings: subrings, ideals, quotients, isomorphism theorem, ring of polynomials, domains, euclidean rings, PID, UFD.
 Fields: simple field extensions, finite fields.
 Matrices and systems of linear equations: Gauss reduction, determinants.
 Vectors, vector spaces, independence, bases.
 inner product, cross product.
 Eigenvalues, eigenvectors. Diagonalization and canonical forms of matrices.
 Application: systems of differential equations.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should

have profound knowledge of basic techniques in set theory, have knowledge and understanding of logical and deductive arguments, understand the fundamental concepts of mathematical logic and should be aware of potential applications in computing, have profound knowledge of basic techniques in Linear Algebra, have knowledge and understanding of geometric relationships within the axiomatic structure of Euclidean geometry;

understand and apply geometric properties and relationships

understand and explain the meaning of complex statements using mathematical notation and language, understand and explain the relation of geometry to algebra and trigonometry by using the Cartesian coordinate and recognize geometric relationships in the world;

demonstrate skill in mathematical reasoning, manipulation and calculation, demonstrate capacity for finding rigorous proofs of small problems; demonstrate skill in mathematical reasoning, manipulation and calculation by synthesizing geometric concepts into algebraic, functional, and problemsolving activities; demonstrate capacity to deduce properties of, and relationships between, figures from given assumptions and from using transformations.
Prerequisites and Learning Activities
Set Theory (language of set theory, the notion of function, graphs of fundamental functions, concept of sufficient and necessary condition), Numerical Structures (natural numbers, prime numbers, numerical fractions, rational numbers, basics of real numbers, inequalities, absolute value, powers and roots);
Elementary algebra ( polynomials and operations on polynomials, identity, first and seconddegree equations); Algebraic Structures (Groups, homeomorphisms, rings); Linear Algebra: Linear systems, matrices, matrix operations, vectors and vector spaces, elementary operations on vectors, linear independence, bases, rank of a matrix linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors.
Assessment Methods and Criteria
Written and oral exam.
Textbooks
 A. Asperti, A. Ciabattoni, Logica a informatica , McGraw Hill. 1997.
 Paola Favro, Andreana Zucco, Appunti di Geometria Analitica , Quaderni Didattici del Dipartimento di MatematicaUniversità di Torino. 2004. Disponibili online tra il materiale del corso
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 26 febbraio 2014, 12:43