# Course Details

#### Name:

**Matematica Discreta II / Discrete Mathematics II**

### Basic information

##### Credits:

*Bachelor Degree in Computer Science:* 6 Ects (a)

##### Degree(s):

Compulsory 1^{st} year Bachelor Degree in Computer Science curriculum General

##### 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 problem-solving 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

### 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 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.

### Teaching Methods

**Language**: Italian

Lectures and Exercices

### Assessment Methods and Criteria

Oral and written exam

### Textbooks

- Paola Favro e Andreana Zucco,
**Appunti di Geometria Analitica**. Quaderni Didattici del Dipartimento di Matematica-Università 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

### Online Teaching Resources

### Recent teaching material

This list contains only the latest published resources. Resources marked with an asterisk belong to other courses (indicated between brackets)

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### Course page updates

This course page is available (with possible updates) also for the following academic years:

*Course information last updated on: 14 febbraio 2014, 11:43*