First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063958, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC1167, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Number of ECTS credits allocated 12.0
Type of assessment Mark
Course unit English denomination ALGEBRA AND DISCRETE MATHEMATICS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge GEMMA PARMEGGIANI MAT/02

ECTS: details
Type Scientific-Disciplinary 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
Hours of
Individual study
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 second-degree 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, Gram-Schmidt 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. --: McGraw-Hill, --. Cerca nel catalogo
  • Alan Tucker, Applied Combinatorics. --: Wiley and Sons, 2007. Cerca nel catalogo