Course Details for A.Y. 2014/2015

The information on this page refer to the academic year 2014/2015. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2014/2015

Name:

Matematica Discreta I / Discrete Mathematics I

Type:

Module

Main course:

Matematica Discreta / Discrete Mathematics

Basic information

Code:

Sector:

MAT/02

Credits:

: Bachelor Degree in Computer Science 6 CFU (a)

Term:

2^nd semester

Degree(s):

Bachelor Degree in Computer Science 1^st anno curriculum General Compulsory

Language:

Italian

Teacher(s):

Carlo Scoppola

Same as:

Matematica Discreta I

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 problem-solving 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 second-degree 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 Matematica-Università 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