### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
HECTOR CARLOS FREYTES (Tit.)
Period
Annual
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[30/46]  PRIMARY TEACHER EDUCATION [46/00 - Ord. 2011]  PERCORSO COMUNE 12 90

### Objectives

Knowledge and understanding
The main objective of the course is devoted to provide students with the key tools for dealing with different kind mathematical problems of various types (arithmetic, geometry, set theory, logic etc ...).

Making judgements
The student have to acquire an autonomous and critical reflection on the course’s issues.
Communication skills
At the end of the course, the student will be able to communicate information regarding to the basic mathematic topics.
Learning skills
Finally, the student must be able to find sources to update and deepen autonomously and constantly knowledges and professional competencies

### Prerequisites

Only basic notions on arithmetic and geometry are required

### Contents

The initial purpose of the course is to give the theoretical, conceptual and methodological fundamental issues in mathematic and logic. Application of the theoretical concept are considered.

Lesson 1) Natural language, formal language, sentences
Lesson 2) Logical conective, recursive grammar.
Lesson 3) Truth tables.
Lesson 5) Propositional arguments, valid argument forms.
Lesson 6) Inference rules
Lesson 7) Natural deduction
Lesson 8) Natural deduction with equivalence.
Lesson 9) Introduction to 1st order logic
Lesson 10) Axiomatic theories
Lesson 11) Naive set theory.
Lesson 12) Russel paradox, Zermelo axiom.
Lesson 13) Axiom of specification
Lesson 14) Inclusion, Union, Intersection, Complement.
Lesson 15) Cartesian products, power set.
Lesson 16) Binary Relations.
Lesson 17) Equivalence relations, partitions, quotiente set.
Lesson 18) Ordering.
Lesson 19) Functions, domain, co-domain, image.
Lesson 20) Injective, surjective and bijective functions.
Lesson 21) Plane Geometry
Lesson 23) Right triangles, Pitagora theorem
Lesson 24) Sine, Cosine, Tangent.
Lesson 25) Equation of a Straight Line
Lesson 26) Trigonometric functions
Lesson 27) Inverse Trigonometric functions
Lesson 28) Sinusoidal waves, frequence and period, maximum and efective values.
Lesson 29) Stationary sinusoidal Regime
Lesson 30) Sound waves

### Teaching Methods

Classroom lectures

### Verification of learning

Written test

The exam is expressed in thirtieths. In order to pass the exam that is with a minimum score of 18/30 the student must show a sufficient knowledge of all the addressed topics, with a proper use of the language. In order to achieve the maximum score of 30/30 cum laude, the student must show an excellent knowledge of all the dealt topics.

### Texts

1)Introduction to Logic, Irving Copi (Ed Pearson 2010)
2) Naive Set Theory, Paul halmos (Martino Publishing 2011)