# BASIC MATHEMATICS

## Learning outcomes of the course unit

Formative purposes:

Knowledge and understanding:

At the end of the course the student will have filled possible gaps and will have consolidated his knowledge of the programs of primary and secondary schools.

He will be able to best follow all the courses of the first year.

Moreover he will have learnt the first notions of Algebra and Mathematical analysis and tested himself on precise mathematical writing and easy proofs.

Applying knowledge:

At the end of the course the student should be able to resolve all the problems on basic mathematical knowledge such as operations, calculus of measurements, equations and inequalities in one variable, set theory, polynomials, trigonometry, equations and inequalities like irrational, exponential and logarithmic.

Besides he should be able to apply his theoretical knowledge to make use of propositions and mathematical induction, to analyse the graph of a function and to develop easy proofs.

Making judgments:

On getting through the exam the student should have acquired the logic ability necessary to deal with an easy problem and the skill to plan the solution.

At the same time he should have developed the precision in organising his work and the ability to check the credibility of the results.

Learning skills:

After getting through the exam, the student should have consolidated his basic mathematical knowledge to face, later, an autonomous analysis of possible applications during following courses.

## Prerequisites

Prerequisites:

None

## Course contents summary

Topics:

1. NUMBERS

2. EQUATIONS, INEQUALITIES, POLYNOMIALS

3. LOGIC OF PROPOSITIONS, SET THEORY

4. FUNCTIONS

5. ANALYTIC GEOMETRY, TRIGONOMETRY

6. EXPONENTIAL FUNCTIONS, LOGARITHMS

## Course contents

Topics:

1. NUMBERS

2. EQUATIONS, INEQUALITIES, POLYNOMIALS

3. LOGIC OF PROPOSITIONS, SET THEORY

4. FUNCTIONS

5. ANALYTIC GEOMETRY, TRIGONOMETRY

6. EXPONENTIAL FUNCTIONS, LOGARITHMS

## Recommended readings

Reference books:

E. Acerbi, G. Buttazzo: Matematica Preuniversitaria di Base. Pitagora Editrice, Bologna (2003).

Exercises with solution (available in TEACHING STUFF on ELLY)

Previous years' examinations with solution (available in TEACHING STUFF on ELLY)

## Teaching methods

Teaching methods:

The course is organised into a series of frontal lessons at the blackboard (1/2 of the course) and practical exercises (1/2 of the course). Each student individually has to do some exercises and the teacher will follow the progress using a series of revisions.

## Assessment methods and criteria

Method of testing learning:

The final test of the course consists of a written test which is weighted as follows:

(10%) Theoretical questions (knowledge)

(90%) Practical exercises (applying knowledge)

The theoretical questions concern logic of propositions, set theory, functions and mathematical induction.

The exam is passed with a final mark of minimum 18/30.

## Other informations

Other information:

This course(6CFU) is mandatory for all students in Mathematics.

A part of this course(3CFU) is mandatory for all students in Physics.

The course is concentrated in the first four weeks of the first semester, for 12 hours a week.

Attending to the course is strongly recommended.