MATHEMATICS: PREREQUISITES

The course is offered to the students who, as a consequence of the TOLC-E test, have received an additional learning requirement (OFA) in mathematics. In particular, the course is aimed at recovering the basic skills necessary to attend the courses of Mathematics - 1 and Mathematics - 2. In addition to the students with additional learning requirements, also the students who need to refresh their basic knowledge in mathematics are invited to attend.

1. Knowledge and understanding:
1.1. understanding the terminology and the methodology of mathematics;
1.2. understanding the properties of powers and logarithms;
1.3. recognizing the different types of function;
1.4. understanding the solution techniques for equations and inequalities.

2. Ability to apply knowledge and understanding:
2.1. understanding a textbook of mathematics;
2.2. formalizing mathematica statements and problems;
2.2. identifying the goal of a given problem;
2.3. making the necessary calculations to solve a given problem.

3. Judgement skill:
3.1. interpreting simple mathematical models;
3.2. analyzing problems formalized in mathematical terms.

No pre-requirement is necessary.

- Terms and forms of mathematical language: logical connectives; implication; quantifiers; definition; axiom; theorem.
- Natural and integer numbers. Rational and real numbers. Properties of powers. Logarithms and their properties. Algebraic expressions and polynomials. Percentages.
- Elements and sets. Subsets and operations between sets.
- Functions. Composite and inverse functions. Real functions of real variables: monotone; periodic; even; odd . Graph of a function. Transformations of function graphs. Linear, quadratic, exponential and logarithmic functions.
- Equations and inequalities: rational; irrational; with absolute value; exponential; logarithmic.
- Coordinate systems in the plane and in the space. Distance in the plane. Line, circumference, ellipse, hyperbole and parabola.

L.Battaia: Precorso di matematica, pdf format
L.Battaia: Corsi matematica OFA, pdf format
Castellani-Gozzi precorso, pdf format
These books can be downloaded from the moodle page of the course, where further indications are given on referral books and other material.

The written exam consists of 26 multiple choice questions. In particular, for each question there are 5 possible answers, of which only one is correct. For each correct answer one gets 1 point, for each wrong answer one gets -0.25 points, for each answer not given one gets 0 points. The exam is considered sufficient with a score equal to or greater than 8 points.

The course is articulated into:
a) classroom lectures;
b) classroom exercises;
c) individual study.
Students are strongly encouraged to actively attend classes, by reading the teaching material before the class and by performing exercises similar to those taken into account in the classroom after the class.
Online lectures are available in moodle.

Italian

The course is coordinated with that of Mathematics - 1 in order to optimize the recovery of the basic mathematical skills.

written