
Course unit
ALGEBRA AND DISCRETE MATHEMATICS
SCP4063958, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/02 
Algebra 
6.0 
Basic courses 
MAT/03 
Geometry 
4.0 
Basic courses 
MAT/09 
Operational Research 
2.0 
Mode of delivery (when and how)
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Practice 
5.0 
40 
85.0 
No turn 
Lecture 
7.0 
58 
117.0 
No turn 
Start of activities 
26/02/2018 
End of activities 
01/06/2018 
Prerequisites:

Analytical skills (logical reasoning), knowledge and skills as specified in the syllabus of the page of the degree course in computer science. In particular:
 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, linear systems);
 sets and functions (language of settheory, the notion of function, graphs of fundamental functions, concept of sufficient and necessary condition);
geometry (Euclidean plane geometry, angles, radians, areas and similar figures, notion of geometric place, properties of triangles, parallelograms, circles, symmetry and similarity, transformations in the plane, Cartesian coordinates and equations of simple geometric places, elements of trigonometry, elements of spatial Euclidean geometry, volumes). 
Target skills and knowledge:

The aim of the course is: to recall basic properties of natural numbers and of polynomials; to introduce methods and some
applications of linear algebra and discrete mathematics. 
Examination methods:

Written examination. 
Assessment criteria:

The written test includes a set of questions and exercises designed to assess the level of acquisition of the concepts taught during the course and the ability of autonomosly applying them. 
Course unit contents:

GCD and Euclid's algorithm; rings of integers modulo m.
Reminder on polynomials: division, roots, factorization into irreducibles (over the real and complex numbers).
Linear equations and matrices: matrix operations, systems of linear equations, Gauss's elimination process, homogeneous systems,
inverse matrix, elementary operations.
Vector spaces, subspaces, bases. Linear functions, kernel and image. Eigenvalues, eigenvectors, diagonalizing matrices. Scalar
product, orthogonality, GramSchmidt procedure.
Introduction to quadratic forms.
Graph theory: Definitions and basic properties, connectivity, paths, cuts, trees, planar graphs, eulerian cycles and hamiltonian circuits.
Combinatorics: simple arrangements and selections, arrangements and selections with repetitions, distributions, binomial identities and Pascal triangle, recurrence relations. 
Planned learning activities and teaching methods:

Classroom lessons and exercises. 
Additional notes about suggested reading:

Instructor's teaching material. 
Textbooks (and optional supplementary readings) 

Marco Abate e Chiara de Fabritiis, Geometria analitica con elementi di algebra lineare. : McGrawHill, .

Alan Tucker, Applied Combinatorics. : Wiley and Sons, 2007.


