Course Details for A.Y. 2015/2016
Name:
Matematica Discreta II / Discrete Mathematics II
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
LOGIC: The goal of this Module is to provide the motivations, definitions and techniques in support of the usefulness of logic in the effective and efficient modeling of data and knowledge.
This Module is an introduction to mathematical logic and covers elementary discrete mathematics for computer science.
On successful completion of this module, the student should understand the fundamental concepts of mathematical logic and should be aware of potential applications in computing, including the limitations of algorithms.
GEOMETRY: The goals of this Module are to introduce students to the terminology and theorems of plane and solid geometry, and to apply algebraic, spatial, and logical reasoning to solve geometry problems.
This Module covers the fundamental concepts of Linear Algebra and its role in describing geometric settings.
On successful completion of this module, the student will develop spatial sense, visualize and represent geometric figures , explore transformations of geometric figures, understand and apply geometric properties and relationships, synthesize geometric concepts into algebraic, functional, and problemsolving activities.
Course Content
 LOGIC
Propositional Logic: Logical formulae, valuations, truth tables, logical equivalence of formulae, satisfaction and logical implication.
Deductive Logic: Formal axiom schemes, the structure of formal proofs, Sequent Calculus, Natural Deduction, the Deduction Theorem, and connections between truth and proof (the Soundness and Completeness Theorems).
 GEOMETRY
Euclidean plane geometry, angles, radians, 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.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should

On successful completion of this module, the student should

have profound knowledge of basic techniques in set theory;

have knowledge and understanding of logical and deductive arguments;

have profound knowledge of basic techniques in Linear Algebra;

have knowledge and understanding of logical and deductive arguments;

have knowledge and understanding of geometric relationships within the axiomatic structure of Euclidean geometry;

understand and apply geometric properties and relationships;

demonstrate capacity for finding rigorous proofs of small problems;

understand and explain the meaning of complex statements using mathematical notation and language;

understand the fundamental concepts of mathematical logic and should be aware of potential applications in computing.

demonstrate skill in mathematical reasoning, manipulation and calculation by synthesizing geometric concepts into algebraic, functional, and problemsolving activities;

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;

ability to read and understand other books/papers using notions learnt by the course and undertsnd their applications.
Prerequisites and Learning Activities
For LOGIC the student must have the basic mathematical notions and methods as acquired in the secondary Schools.
For GEOMETRY the student must know: 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
Oral and written exam
Textbooks
 Paola Favro e Andreana Zucco, Appunti di Geometria Analitica , Quaderni Didattici del Dipartimento di MatematicaUniversità di Torino. 2004. versione disponibile su internet, presente nel sito DISIM
 A. Asperti  A. Ciabattoni, Logica a Infromatica , McGraw Hill, . 1997. Versione disponibile su internet, presente sul sito DISIM
Notes
 This course consists of two Modules:
1) LOGIC
2) GEOMETRY
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: 14 febbraio 2014, 11:43