# BASIC MATHEMATICS

## Learning outcomes of the course unit

Formative purposes:

The aim of the course is to provide basic mathematical knowledge of the programmes of primary and secondary schools, necessary to follow all of the courses of the first year. During the formative activity the student can fill possible gaps or consolidate his knowledge.

At the end of the course the student is expected to be able:

Knowledge and understanding:

- to know the different sets of numbers and their properties

- to remember all the properties of equations, inequalities and systems

- to know function theory

- to know the basics of trigonometry

- to have understood the concepts of exponential and logarithm

- to know basic figures of analytical geometry and their equations

- to have understood logic of propositions and set theory

Applying knowledge and understanding:

- to order numbers, to factorize a polynomial

- to perform calculations with fractions, radicals, exponentials and logarithms

- to calculate sine, cosine and tangent of a known angle

- to solve equations, inequalities and systems of first and second degree, of degree larger than two, irrational, trigonometric, exponential and logarithmic

- to determine the domain, the range and the inverse image of a function whose graph is given; to prove that a function is injective, surjective, increasing or decreasing

- to draw the graph of an elementary function or of a piecewise defined function based on transformations of elementary functions

- to analyse and draw straight lines, parabolas, circumferences, ellipses, hyperbolas

- to analyse and to deny a proposition, to prove set’s properties

Making judgments:

- to be able to face an autonomous analysis of possible applications during the following courses

Communication skills:

- to have acquired the ability to work both autonomously and in groups

Learning skills:

- to be able to carry on with his scientific studies autonomously.

## Prerequisites

Prerequisites:

Mandatory prerequisites: elementary mathematics.

On the Elly platform 2020-21 in the CONOSCENZE PRELIMINARI section are available lectures and exercises on preliminary knowledge.

All further mathematical knowledge from primary and secondary schools is useful.

## Course contents summary

Topics:

1) EQUATIONS and INEQUALITIES

2) LOGIC OF PROPOSITIONS

3) FUNCTIONS

4) EXPONENTIAL FUNCTIONS, LOGARITHMS

5) ANALYTICAL GEOMETRY

6) FUNCTIONS (summing up)

7) In-depth analysis of LOGIC OF PROPOSITIONS, SET THEORY

8) TRIGONOMETRY

Degree course in Physics: 1 to 6.

## Course contents

Topics:

1) EQUATIONS and INEQUALITIES

2) LOGIC OF PROPOSITIONS

3) FUNCTIONS

4) EXPONENTIAL FUNCTIONS, LOGARITHMS

5) ANALYTICAL GEOMETRY

6) FUNCTIONS (summing up)

7) In-depth analysis of LOGIC OF PROPOSITIONS, SET THEORY

8) TRIGONOMETRY

Degree course in Physics: 1 to 6.

## Recommended readings

Reference books:

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

F.G. Alessio, C. de Fabritiis, C. Marcelli, P. Montecchiari: Matematica zero, Pearson Italia, Milano-Torino (2016).

Additional material (on the ELLY platform, https://elly2020.smfi.unipr.it/, MATEMATICA, primo anno, ELEMENTI DI MATEMATICA):

Lectures and exercises on preliminary knowledge.

Lectures 2017-18.

Exercises with solution.

Examinations with solution (from 2017-2018 to 2019-20).

## Teaching methods

Teaching methods:

Mathematics: 6 CFU, 56 hours of lectures and practices.

Physics: 3 CFU, 28 hours of lectures and practices.

The course takes place from the 14th of September to the 2nd of October 2020, with 22 hours the first week, 20 hours in the second one and 14 hours in the third one (for Physics 14, 8 and 6 hours).

The teaching activities will be performed online from Monday to Thursday on the Teams platform (guide http://selma.unipr.it/didattica-online/). Students will receive all instructions and will use the code and the link uploaded by the teacher on the Elly platform. Using Teams the students will be also able to meet and solve exercises together; moreover teachers will be available two afternoons per week to discuss lectured topics.

Every Friday will be devoted to 4 hours in the lecture-hall with the teacher for guided exercises during which the students, autonomously or in small groups, solve the proposed exercises with the supervision of the teacher.

During the course two formative tests (each 45 minutes long) are planned in order to point out gaps, evaluate the progress of the student’s learning and give a feedback to the students before the final test. The results of those tests will not affect the final test.

The first exam is fixed on the 5th of October.

At the beginning of the course all the material is uploaded on the Elly platform. Moreover, every week, worksheets of exercises regarding the topics of the week will be uploaded on the platform.

In order to download the teaching stuff, the on-line registration is needed.

The uploaded lectures are an integral part of the teaching material.

Non-attending students are advised to check the available teaching material and the information given by the teacher via the Elly platform.

## Assessment methods and criteria

Method of testing learning:

The final evaluation on the learning consists of a 3 hours long written test (2 hours for Physics); books, notes and electronic devices are not allowed.

The exam will take place in presence in the lecture-hall. If, due to the sanitary situation, the exams will need to be performed online, they will consist of a preliminary Quiz on the Elly platform, followed by the actual written test and by a mandatory oral exam. On the Elly platform will be available a template with all the instructions about the online exams.

The student must prove he/she has understood, and is able to apply, the basic concepts of every topic in the programme.

The written test is split into two parts: a theoretical test only for students of Mathematics and an applying knowledge test for all students in Mathematics and Physics.

The two tests are structured as follow:

1) theoretical test (1 hour) with questions on logic of propositions, set theory and function theory.

2) applying knowledge test (2 hours) made of exercises on the common programme to Mathematics and Physics.

The final mark is calculated on 32 points. The exam is passed with a final mark of minimum 18/30.

The results of the exam will be published on the Elly platform within two weeks from the written test.

The students can examine their written tests during the time specified by the teacher or by appointment.

## Other informations

Other information:

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

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

The course of Basic Mathematics is a prerequisite to Algebra and Mathematical Analysis 1. Attending to the course is mandatory (75%) for all students who have not passed their self-evaluation test or are relieved from it, for instance with the certificate of the final test of the CORDA Project with at least 50 points. For the full list of relieving conditions see the OFA (added formative obligations) in the Manifesto degli studi 2018-19 at the entry: ESONERO TEST VPI. Moreover for these students the course of Basic Mathematics is a prerequisite to all other exams in the degree course of Mathematics.

Attending to the course is strongly recommended to all students.