Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
STEFANO MONTALDO (Tit.)
Period
First Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2017]  PERCORSO COMUNE 8 64

### Objectives

KNOWLEDGE AND UNDERSTANDING

Know the language of set theory. Know and understand equivalence classes and quotient sets.
Know natural, integer, rational, real, and complex numbers. Know the rudiments of the number theory. Have a good knowledge of polynomials in one and more variables.

APPLYING KNOWLEDGE AND UNDERSTANDING

Ability to properly formulate mathematical statements and construct rigorous simple demonstrations. Know how to work with equivalence classes and quotient sets. Know how to use the properties of operations defined in numeric sets correctly. Know and know how to use the arithmetic of integers. Know how to manipulate polynomials in one and more variables.

MAKING JUDGEMENTS

Knowing how to recognize when a logical procedure is correct.

COMMUNICATION SKILLS

Learn how to use the modern language of algebra to properly communicate scientific results.

LEARNING SKILLS

Ability to learn how to solve independently complex exercises. Ability to be able to read and understand a text that uses the language of mathematics.

### Prerequisites

To follow the course you do not need specific knowledge of Mathematics, the notions learned in any school are more than enough. Nonetheless some students state that their preliminary knowledge is not enough. Actually, it is not the knowledge which is missing but a certain habit of mathematical reasoning. Many students come to the university with the idea that math is a great formulary from which one must find the formula that best suits the resolution of the proposed exercise. They remain baffled when they realize that during the Algebra 1 lessons there is no new formula to learn, exercise resolution consists in knowing how to use logic and intuition to check if a given statement is true or false. So the most important prerequisite is to have a healthy desire to understand why a procedure works and never assume anything for granted. With this attitude you usually get good results.

### Contents

Detailed plan:
https://www.unica.it/unica/protected/382494/0/def/ref/MAT228712/

### Teaching Methods

The tools used for the lectures will be the blackboard. For the student's preparation at home, the teacher has a web-site dedicated to students (https://www.unica.it/unica/page/it/stefanomontaldo) where they can find teacher notes, the lesson register, weekly exercises to be done at home and corrected in class during the exercises. Trying to solve at home the exercises is one of the most important steps for learning the math method. The student should not make the mistake of following the exercises without having tried the exercises (for several hours). The individual study, led by the teacher, plays a key role in the first year of Mathematics. Students are encouraged to discuss each other either to compare solutions found in exercises or to see if the topics taught in the lesson have been properly understood and assimilated. The course includes 32 frontal lectures of 2 hours each and 16 exercises of 2 hours each. The latter are assisted by an expert tutor.

### Verification of learning

The goal of the exam is to check the level of achievement of the above-mentioned training objectives.

Compatibly with the indications of the University on how to carry out the exams according to the evolution of the COVID-19 emergency, the exams could be held in the presence or online.

Examination consists of a written test and an oral exam.

The written test (3 hours) consists in a selection of 6 exercises similar to the homework assigned during the course. Each exercise is worth 5 points and the written test is deemed passed if the final score is not less than 18. In this test mainly occur: knowledge and understanding; knowledge and understanding applied; the ability to learn.

The oral exam (usually 40 minutes) consists of a discussion of at least three arguments. The student must demonstrate that they have understood and assimilated the arguments (knowledge and understanding, knowledge and understanding applied). In addition, students must demonstrate that they are able to explain the concepts and demonstrations learned during the course (Communication Skills). To this end it is necessary that the student, during the oral exam, write on the chalkboard and explain all the steps that it is following to reach the conclusion of an argument (independent judgment). It is advisable to answer exactly the questions without rambling and writing immediately all the necessary details (independent judgment, communication skills).

The final grade after the oral interview is assigned according to the following Docimological Table.

Insufficient: the student proves he did not understand many of the basic constructions of the discipline.

18-24: the student knows almost all the arguments submitted during the examination; demonstrates that has understood and assimilated the arguments sufficiently.

25-28: the student knows all the arguments submitted during the examination; demonstrates that has understood and assimilated well the arguments; the student uses mathematical language correctly.

29-30: the student knows very well all the arguments submitted during the examination; demonstrates that has understood and assimilated very well the arguments; the student uses mathematical language correctly; is able to explain the concepts learned.

30 e lode: the student knows perfectly all the arguments submitted during the examination; demonstrates that has understood and assimilated in depth all the topics; the student uses mathematical language correctly; is able to explain the concepts learned.

### Texts

Textbook

Notes of the teacher

Dikran Dikranjan, Maria Silvia Lucido, Aritmetica e algebra, Liguori editore

Other books
C. Casolo, Dispense del corso di ALGEBRA I, http://web.math.unifi.it/users/casolo/dispense/algebra1_11.pdf
L. Cerlienco, Numeri e poco altro, http://corsi.unica.it/matematica/files/2014/10/algebra1-1.pdf