MATHEMATICS

The course offers an additional learning requirement 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 and their properties;
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 mathematical 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.

The course is compulsory for students recommended by the School. No special prerequisites are required

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

Teacher's slides

For functions and basics of Trigonometry
David Lippman and Melonie Rasmussen (2020)
Precalculus - An Investigation of Functions
http://www.opentextbookstore.com/precalc/
sections indicated by the teacher.

For basics of algebra et al.
https://www.khanacademy.org/math/
sections indicated by the teacher.

Assessment methods:
- 10% for participation.
- 60% for on-going tests.
- 30% for the outgoing test.

The course is articulated into:
a) lectures dual mode;
b) exercises carried out during the lectures;
c) individual study.
Students are strongly encouraged to actively attend classes.
The exercises to be done partially individually, partially in groups. The correction will be immediate, when possible.

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